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Review article, machine learning in structural design: an opinionated review.

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  • Department of Civil and Environmental Engineering, Imperial College London, London, United Kingdom

The prominence gained by Artificial Intelligence (AI) over all aspects of human activity today cannot be overstated. This technology is no newcomer to structural engineering, with logic-based AI systems used to carry out design explorations as early as the 1980s. Nevertheless, the advent of low-cost data collection and processing capabilities have granted new impetus and a degree of ubiquity to AI-based engineering solutions. This review paper ends by posing the question of how long will the human engineer be needed in structural design. However, the paper does not aim to answer this question, not least because all such predictions have a history of going wrong. Instead, the paper assumes throughout as valid the claim that the need for human engineers in conventional design practice has its days numbered. In order to build the case towards the final question, the paper starts with a general description of the currently available AI frameworks and their Machine Learning (ML) sub-classes. The paper then proceeds to review a selected number of studies on the application of AI in structural engineering design. A discussion of specific challenges and future needs is presented with emphasis on the much exalted roles of “engineering intuition” and “creativity”. Finally, the conclusion section of the paper compiles the findings and outlines the challenges and future research directions.

1 Introduction

We call structural design the process by which the number, distribution, shape and size of structural elements, and their connectivity is determined so that a given design objective is achieved while meeting a number of constraints of serviceability and resistance. The objective can be the minimization of material consumption but in practice, it is more likely to be related to cost minimization and to involve trade-offs between manufacturing, logistical and sometimes sustainability considerations. At the beginning of the structural design process, human engineers are usually provided with the overall geometry—through Building Information Models ( Jung and Joo, 2011 ), for example—and their task is to come up with specifications of the distribution of structural elements including their materials and sections. This process is carried out using a diverse collection of computational tools, from information modelling to structural analysis; sampling from catalogues involving hundreds of structural sections and with constant reference to thousands of pages of codes of practice. Consequently, as it stands today, structural design entails a significant and oftentimes tedious solution-searching process involving various complex and non-fully overlapping multi-dimensional domains, multiple constraints and large uncertainties, whereby arriving to a global optima would be a prohibitively time-consuming endeavour. Therefore, more often than not, the engineer’s search will be brief and they will settle for the first sub-optimal design that satisfies all the hard constraints. Unsurprisingly, a range of tools have been proposed to carry out the optimization of some of the better-posed problems involving a relatively low number of structural elements, e.g., ( Jewett and Carstensen, 2019 ; Amir and Shakour, 2018 ; Tsavdaridis et al., 2015 ); and more recently these tools have started to incorporate additional and more realistic complexities like dynamic actions ( Giraldo-Londoño and Paulino, 2021 ), manufacturing processes ( Zegard and Paulino, 2016 ; Carstensen, 2020 ), etc. However, the emphasis of this paper is not on the generation of targeted topology-optimized solutions for which excellent review articles can be found elsewhere, e.g., ( Thomas et al., 2021 ). Instead, this opinionated review concentrates on the exploration of large and complex integrated design spaces with the aid of artificial intelligence (AI) and, more specifically, the increasing role that Machine Learning (ML) algorithms are playing in this search.

Artificial Intelligence (AI) is the branch of science that is concerned with the re-creation of human cognitive functions by artificial means. Although this is most commonly attempted via digital computers, other media, notably biological systems ( Qian et al., 2011 ; Sarkar et al., 2021 ), have been and continue to be used with this purpose. This paper, however, focuses on the role of intelligent algorithms for digital computers; or more precisely, algorithms whose distinctive feature is their ability to learn. In this context, Machine Learning (ML) is a branch of AI whose central advantage is its potential to automatically detect patterns in data under uncertainty ( Murphy, 2012 ). This uncertainty arises inevitably from the limited size of the datasets employed but it also reflects errors in data collection (including measurement) as well as hard epistemic paucities.

One of the first approaches to replicate human cognition was to organize “knowledge” as a collection of mutually related facts. Once a database of facts was built, so the belief went, inference rules could be used to query it, revealing the interconnections and allowing questions, including those related to engineering design, to be answered. The use of this type of AI in structural design was discussed as early as 1978 by Fenves and Norabhoompipat (1978) and application examples appeared in the early 1980s. For example, Bennett et al. (1978) developed a program consisting of 170 production rules and 140 consultation parameters to assist the engineer in the application of Finite Element Analysis (FEA) to the design of building structures. Also, Maher and Fenves (1985) constructed an expert system for the preliminary design of high-rise framed buildings. They used weighing factors to compare different gravity and lateral resisting structural systems highlighting the “best” design according to the criterion of a linear evaluation function. Other researchers like Ishizuka et al. (1981) used rule-based systems to infer seismic damage on the basis of a database of earthquake accelerograms and visual inspection reports. However, it soon became apparent that hard rules can not replicate the human inferential process and that their contribution to design would be limited, not least because the world for which engineers design is brimming with uncertainty but also because exceptions to the rule are all too common. Logic-based AI was abandoned.

With the passage of time, probabilistic reasoning made its way into ML and message passing architectures, which model intelligence on the basis of human neural information passing ( Rumelhart et al., 1986 ), started to take the computational demands on storage and processing down to manageable levels. By the end of the 1980s, Bayesian Networks (BN) had become a practical scheme for ML ( Pearl, 1988 ). BN have proven useful in evaluating the reliability of structures and infrastructure systems with multiple components and multiple failure sequences ( Mahadevan et al., 2001 ). And Naive Bayes classifiers have been used to construct damage fragilities, e.g. ( Kiani et al., 2019 ), predict the strength of structural components, e.g. ( Mangalathu and Jeon, 2018 ), or estimate structural failure modes, e.g. ( Mangalathu et al., 2020 ).

Meanwhile, Artificial Neural Networks, or Neural Networks (NN) for short, started to be used in all branches of engineering design. One of the first studies to apply back-propagation NN—an approach initially devised by Rumelhart et al. (1986) —to structural engineering was conducted by Vanluchene and Sun (1990) . In their pioneering study, Vanluchene and Sun (1990) applied NN to the pattern recognition of a loaded beam, to the design of a simply supported reinforced concrete beam and to the structural analysis of a plate. NNs are abstractions of the functioning of the human brain that aim to replicate its ability to acquire knowledge through learning and storing in the form of interconnecting synaptic weights. In true fashion of the process originally hypothesised by Rumelhart et al. ( Figure 1 ) the network takes a set of features as inputs and applies complex feature fusion operations through a series of layers of neurons. The final layer outputs the end response either as a prediction or as a form of classification.

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FIGURE 1 . ( Rumelhart, 1994 ) Message Center near the end of processing when the semantics of the imput have been well defined.

NN models (and their deep learning variants) have become extremely popular nowadays driven by the media coverage of their superb feature recognition capabilities and the notorious increase in computational power together with the wide accessibility of tools and libraries. Accordingly, NN have been used in seismic response prediction, e.g., Morfidis and Kostinakis (2017) ; Lagaros and Fragiadakis (2007) , system identification, e.g., Sivandi-Pour et al. (2020) , damage localization, e.g., Bani-Hani et al. (1999) ; Gharehbaghi et al. (2021) and in structural control, e.g., ( Khalatbarisoltani et al., 2019 ; Suresh et al., 2010 ), among other structural engineering tasks. The literature on NN (and indeed ML) applications to structural engineering is vast. Sun et al. (2021) provide a comprehensive review of ML methods used to predict and asses structural performance and to identify structural conditions. Some of these can be used in support of structural design but do not directly deal with structural design per se , defined in the form presented earlier in this paper. In fact, issues related to ML and structural design, as defined above, are not particularly well covered in the literature despite the proven potential brought about by leveraging AI technologies and ML algorithms to improve the exploration of design alternatives beyond current human cognitive levels.

It follows from the previous discussion that existing design optimization methods concentrate on individual structural subassemblies and do not serve to automate the design of entire structures. By contrast, this paper will explore the use of ML algorithms to automate structural designs stricto sensu . To this end, this paper proceeds to review a selected number of studies on the application of ML in structural engineering design. A discussion of specific challenges and future needs is presented with emphasis on the much exalted roles of ‘engineering intuition’ and ‘creativity’. Finally, the conclusion section of the paper compiles the findings and outlines the challenges and future research directions. But first, the paper will provide a general introduction to AI and ML methods.

2 Background on AI and ML

As mentioned above, central to AI and ML algorithms is the ability to learn, potentially achieving the super-human ability of recognising patters in high-dimensional datasets that have remained impenetrable to the human mind. Figure 2 compares the way traditional and AI software operate. In a traditional piece of software, the coder writes a “comprehensive” set of rules that the program must follow. Therefore, it is the sole responsibility of the programmer to consider all possible scenarios and to hard-code into the algorithm all the appropriate responses to these scenarios. It should be possible, in principle, to arrive to the precise output by following the path through the code given a specific input. By contrast, in AI algorithms the rules are created by the algorithm itself and the coder only provides the scaffold (or architecture) and feeds data into it. The AI algorithm will analyse the data and fill this scaffold with its own through training. Once those rules are established, they can then be used in the traditional way to predict other outputs given an input. The fact that the coder is exempt from considering and including all potential scenarios makes AI particularly useful when dealing with large datasets or complex processes.

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FIGURE 2 . Traditional vs. AI algorithms.

The differences in construction and operation between traditional and AI software express themselves in a number of ways. Traditional code is naturally transparent and generally easy to predict while ML can be obscure and may produce unexpected results or include biases that are not always easy to detect. On the other hand, traditional algorithms will be limited to what the coder has predicted at first, while AI software is in principle easy to adapt without significant changes in the code. Traditional software demands the coder to capture carefully and accurately all the potential scenarios, while AI can handle complex problems more efficiently than humans, especially when they involve multiple dimensions or large datasets.

Broadly speaking, ML algorithms can be categorized in three main groups: supervised, unsupervised and reinforcement learning, depicted in Figure 3 . Supervised learning is probably the closest to human learning. A series of “examples” is used by the ML algorithm to build “knowledge” about a given task in a similar way to how humans build and use “past experience” ( Dietterich, 1996 ) like when small children are guided in their association of words to meanings. To this end, supervised models are given a set of features as input and labels as output. Then, the models attempt to find a set of rules to match a given set of features to the correct label guided by some measure of success. The process employs statistical methods for the learning operations and manual adjustments are usually not required. However, supervised ML relies on large amounts of correctly labelled input data, in quantities that can be significantly larger than those required by humans ( Kühl et al., 2020 ).

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FIGURE 3 . Categories of ML algorithms.

On the other hand, unsupervised learning can be applied to different data types. In this approach, labels are not required, just features. The model is given those features and its algorithm then groups them according to some unknown property. In general, unsupervised models try to do one of three things: either cluster the data provided, find an anomaly in it, or reduce the number of dimensions in which to express the dataset. Grouping works by clustering data points that share some features without knowing what labels or indeed what categories are present. In anomaly detection or pattern recognition, a defining set of features is found and the model classifies the data point as either part of the set or as an anomaly. This is very helpful in failure identification or structural characterization. Reinforcement learning builds on these ideas and sometimes uses the algorithms developed for supervised and unsupervised learning. It is used in situations where it is difficult to get perfectly correct labels. In such cases, the algorithm is provided with an input and a reward function that gives an indication of how well or bad the algorithm is doing. The algorithm then learns how to maximise the reward.

In general, the creation of a typical AI algorithm involves four main stages. It starts with the data preparation. This is a crucial stage that can take longer than the others. It involves the acquisition of data, its analysis and pre-processing. The quality and quantity of data are determinant for a good output of the model. The second stage is the design of the model, which is followed by the third stage of training and evaluation. It is not uncommon that at the end of this process, the coder realises that changes are required in the data or the model architecture, and the design should be re-adjusted. Once the model is considered well designed and trained it is ready to enter its final stage of deployment.

3 AI and the Design of Spatial Structures

Although shells, vaults and other spatial structures are already among the most efficient structural forms and have a notoriously complex structural response, they have been fertile ground for many structural design optimization explorations. This may be because shells can be discretised as meshes with known support locations which, despite requiring hundreds of variables, are usually single-layered and lend themselves more easily to parametrization than the reticulated multi-storey frames with a multitude of potential element locations, sizes and connection types used in buildings. However, even if a highly parametrized design space is used, its sheer size still makes it trackless to the human mind. Therefore, the basic capability of machine learning to discover and rebuild complicated underlying connections between input and output variables from a relatively big dataset ( Liu et al., 2020 ) can be of great use while designing spatial structures.

Mirra and Pugnale (2021) examined AI-generated design spaces built using Variational Autoencoder (VAE) models, and compared their outputs with those coming from a human-generated explicit definition of design variables. Two relatively simple but realistic cases were explored by Mirra and Pugnale involving triangular and square footprints. A dataset of 800 depth maps obtained from 3D models were used to train the VAE. Three objectives were set for the optimization, including: 1) the maximisation of the structural performance, quantified in terms of deformations obtained from Finite Element Analysis (FEA), 2) the maximisation of the height of the shell openings, and 3) the minimisation of the difference between the final and target footprints. They found that the AI-generated outputs had a greater diversity and responded better to the performance criteria in comparison with the solutions obtained from human-defined generative designs. Besides, AI solutions included structural configurations that would not have been possible to find within the human-defined design space. This hints to one of the main advantages of using AI in design: the possibility of exploring design options beyond those traditionally developed by human intelligence ( Mueller, 2014 ).

The exploration of diverse design options brought about by AI was also exploited by Maqdah et al. (2021) and Palmeri et al. (2021) while studying the provision of structurally-efficient regolith-based arch forms for extraterrestrial construction. They built unsupervised machine learning models (Convolutional Autoencoders, CAE) capable of detecting patterns and differentiating between arch geometries and their stress and deformation contours ( Figure 4 ). These models were then used to search for optimal sectional geometries considering the effects of extreme thermal changes and seismic action under low-gravity conditions. Various datasets, each one with over 500 thermal and static FEA analysis and a 60–40% training-validation split were constructed for this purpose. Although the optimal configurations found resembled those obtained by more traditional approaches ( McLean et al., 2021 ), the possibility of including a diversity of design actions (gravity, thermal, and seismic) and a substantial number of dimensions that are then reduced to a smaller latent space where a holistic search process can be used was featured as a clear contribution of AI. Moreover, Maqdah et al. (2021) and Palmeri et al. (2021) were able to elucidate some of the dependencies of the latent space (reduced) dimensions on geometric and structural parameters which can be helpful in making informed (partially explainable) searches. Alongside the CAE, regression models were used to allow the visualisation of the changes in the arch shape and stress fields when moving towards a certain direction in the design space.

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FIGURE 4 . Latent space representation of the data points coloured depending on the occupancy of the arches (a measure of the material usage) for the seismic design scenario. The latent space (A) is presented together with the plot of the mean occupancy of each cluster (B) and sample shapes from the best selected cluster (C) . Adapted from Palmeri et al. (2021) based on the CAE model of Maqdah et al. (2021) .

The works of Zheng et al. (2020) and Fuhrimann et al. (2018) have explored the use of ML in leveraging the fundamental relationship between force and form in shells. Zheng et al. (2020) trained a NN model to predict the relations between subdivision rules and structural and constructional performance metrics on the basis of graphic statics results. This surrogate use of ML models to enable a rapid exploration of design spaces constitutes one of many important attempts to improve the machine-human collaboration. Unfortunately, the parameters employed; notably for constructibility (i.e., number of faces with areas greater than a given threshold), may seem too simple proxies to capture the complexities of the manufacturing and construction challenges. On the other hand, Fuhrimann et al. (2018) also explored the potential of combining form-finding with ML in the form of Combinatorial Equilibrium Modelling and Self Organizing Maps. Central to these works is the need to grasp a complex space of solutions in order to both increase its diversity and to make it manageable to the designer.

The previously mentioned works have highlighted the basic capability of ML to discover and rebuild complicated underlying connections between input and output variables and to find relationships between structural shape and performance. Once those relationships are established, the corresponding optimization of the structural configuration is simplified ( Liu et al., 2020 ). However, to set an optimization process where the design parameters are chosen automatically by the machine (algorithm) without human intervention remains difficult. This is because these parameters must exist in a low-dimensional space that can be optimized while not sacrificing their representational capacity. An issue that was also observed while optimizing the design of materials ( Xue et al., 2020 ).

An alternative approach was followed by Danhaive and Mueller (2021) who tackled the design of a long span roof structure. For this purpose, they used variational auto encoders (VAE) to train low-dimensional (2D) models that are intuitive to explore by the human engineer. By conditioning the models on different performance indicators, the models can adapt their mappings. A new performance-driven sampling algorithm was proposed to generate databases that are biased towards design regions with high performing structures. The structural performance indicators employed in the case study are only mass dependent and are normalized so they are evenly distributed on the unit segment. A total of 36 design variables, mainly topological, were used in the design and dimensioning of the truss elements using the cross-section optimizer available in Karamba ( Preisinger and Heimrath, 2014 ). The salient feature of this approach is that it gives the human designer a greater control over performance trade-offs standing in the middle between optimization methods, on the one side, and undirected search algorithms, on the other.

The support provided by ML algorithms to the design of spatial structures are not conscripted to structural calculations but can include the quantification of traditionally less quantifiable metrics such as aesthetics. For example, Zheng (2019) developed a NN that could be used to quantitatively evaluate the personal taste of an architect. By using force diagrams of polyhedral geometries with unique and distinguishable forms and a clear data structure and asking the human architect to score the inputs, a NN was trained to learn their design preferences. The results, which may seem unsurprising at first sight, put in evidence the capability of ML to express what may be considered as inexplicit. In doing so, Zheng demonstrated not only that solutions with higher scores can be generated with a higher probability of satisfying any personal design taste, but what is more important, that ML can learn relationships that may be difficult to articulate in human parlance. It should be noted that, given the natural difficulties human designers face when asked to score many forms consistently to the same standard. In these cases, the scores were mapped into a grading scale, from A to D, which considers the number of times the forms have been selected. This explains the final selection presented in Figure 5 where a structure with an initial score of 0.729 is chosen on top of another with a score of 0.864. This is a compromised solution, but one that massively narrows down the variety of forms from which the designer has to choose. Thus, the door is open to integrate both mechanistic and quantifiable metrics with other kinds of design considerations and to apply this to a diversity of design tasks.

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FIGURE 5 . Selection of form-found structures considering user taste by Zheng (2019) .

4 AI Applied to the Design of Building Structures

The rationalization of the design process of building structures, within a structural optimization framework, has usually been separated into three components ( Havelia, 2016 ): 1) topology, which involves decisions on the number and connectivity of members, usually done without optimizing the connection itself; 2) shape, which involves decisions related to the location of elements and the layout of joints; and 3) sizing, which involves defining member cross sections. More often than not, these components are treated separately in the scientific literature, however, they are strongly interrelated and decisions involving one will greatly affect the others. Usually, the layout space is reduced by architectural considerations, but it will still encompass a large number of potential locations that are difficult to explore without any pre-determining guiding principle. Besides, early estimates of the building cost are usually based on weight, however, the majority of the total cost can sometimes be attributed to fabrication and erection which are not always directly proportional to weight ( Kang and Miranda, 2005 ) In addition, material costs depend not only on tonnage, but also on the type and size of cross sections utilized and erection costs are also highly contingent on geography and local market conditions Klanšek and Kravanja (2006) . These facts will automatically render impractical most topology optimization studies carried out to date.

Some studies have incorporated, albeit in a simplified manner, the design complexities outlined above. For example, Torii et al. (2016) developed an optimization algorithm that penalizes the number of members and joints in the structure in proportion to the number of connected elements. Unfortunately, this was only applied to trusses and no consideration was given to the fact that the connection type is determinant in their cost. Hassett and Putkey (2002) collected a comprehensive list of cost drivers and their values for the most common moment-resisting and pinned connections in the AISC catalogue. And Zhu et al. (2014) considered constructibility issues in the optimization of frames and demonstrated that some structures with a less efficient load path can improve constructibility and lead to overall lower costs. Zolfagharian and Irizarry (2017) used Principal Component Analysis, a clustering ML technique, to group constructibility factors into six major categories. To this end, they assembled a dataset, via industry interviews, on 79 different constructibility factors with given scores. As the design space increases exponentially with the number of structural elements, the number of structural typologies analysed, their connectivity and the constructibility considerations, most currently available optimization methods are rendered impractical for full-scale real implementation. Other proposals, like that of Havelia (2016) have used methods based on topology and sizing optimization within a multi-disciplinary architecture suitable for 2D steel framed buildings. Again, Havelia’s study showed that a heavier structure can be more economical than its lighter counterpart when connection and fabrication costs are taken into account. One drawback of this study is that serviceability constraints like maximum deflection or vibrations are not considered and therefore its applicability to real designs is hampered. On the other hand, high profile applications of structural optimization like the Chicago 800 West Fulton Market or Shezhen’s Financial Center do not aim to optimize the whole building economy or constructibility but are concerned with only a small proportion of its load carrying elements.

One of the first studies that departs from the above mentioned trend is that of Ranalli (2021) who proposed a new AI-based optimization module for the design of a flooring system with varying degrees of composite action. User-defined variables employed include the depth of the slab, the height of the steel deck, the properties of concrete, a range of possible cambers, the option to use shoring during construction, the degree of composite action, and the range of wide flange sections. The optimization framework iterates through each beam and girder, automatically determines its static scheme, computes the governing moment and deflection demands under the applied loads, and efficiently iterates through the set of available design options to find the most economical and feasible solution. Serviceability limits are considered and material and labour rates are assigned to arrive to an optimal solution through a scenario exploration. However, the gravity resisting columns are not considered, nor are issues related to their continuity and the rotational restraint (or flexibility) they provide to the floor. Nevertheless, the main strengths of Ranalli’s AI-driven optimization framework are its computational scalability and its readiness of applicability to new steel frame designs with minimal pre-processing efforts.

Another interesting work was performed by Chang and Cheng (2020) who re-formulate building frames as graphs ( Figure 6 )and use Graph NN (or GNN) trained on simulation results that can learn to suggest optimal beam and column cross-sections. This is one of the first attempts to use GNN in the realm of design optimization aided by differentiable approximators. The optimization objective employed by Chang and Cheng (2020) is simplistic, involving only mass minimization, but a variety of constraints is considered together with serviceability limits to produce optimal designs. The results are reported to be consistent with typical engineering designs and also comparable to outputs from Genetic Algorithm optimizations. The main limitations of this work are related to the absence of slab continuity effects and the treatment of the building skeleton as an input. However, the possibility of implementing a graph representation and generation algorithm in the initial phases of design to provide an end-do-end solution generating tool is worth exploring further.

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FIGURE 6 . An example building structure and its structural graph representation suitable for analysis by GNN, from Chang and Cheng (2020) .

Similarly, Ampanavos et al. (2021) developed a ML system for the automatic generation of building layouts aimed at helping architects present structurally feasible solutions during the early stages of the project. A peculiarity of the system is that it does not aim to estimate the full structure to start with, but uses an iterative approach where the neural network gradually extends the solution as necessary. In this way, the NN has better changes of identifying patterns on a small building area at each step. However, this approach is also prone to error accumulation for large structures, although this error is dependent on the size of the training dataset. Besides, the column positioning can be noisy. However, future combinations of this approach with element sizing tools and more sound structural considerations are likely to produce a scalable and helpful methodology.

In his thesis, Ranalli (2021) , mentioned above, also considered the problem of sizing lateral load resisting systems against strong loads typical of earthquakes. The author treated this problem in two iterative phases, the first of which searches for the most economical solution that meets strength, constructibility and ductility criteria. The second phase checks for lateral drift compliance and design load combinations. An energy based analysis is performed in case particular floors need to be adapted to comply with the drift limits. The strength of this study is that is able to combine commonly used analysis tools and relatively justified cost functions to provide a whole-encompassing approach to building design. It is also worth noting that a high variance of cost across different design scenarios was observed highlighting the important role of even small changes in the variables on the overall building cost.

The above mentioned studies are mainly devoted to steel framed solutions, where the domain is discrete since only a certain number of steel sections are available. This may simplify and reduce the design space and facilitate the consideration of constructibility functions. By contrast, designing concrete structures may introduce additional complications since a relatively broader design space is to be considered with added variations in member detailing. These issues were approached by Pizarro and Massone (2021) who aimed at supporting the design of reinforced concrete buildings by keeping track of previously accepted design solutions, in contrast with other topology optimization methods based on more heuristic approaches like those proposed by Zhang and Mueller (2017) , which do not have this feature.

Pizarro and Massone (2021) proposed a predictive model for the length and thickness of reinforced concrete building walls based on Deep NN trained with 165 Chilean residential projects. The walls were described in both geometrical and topological domains and three variations of the data, achieved by modifying the building plan angle and its scale, were considered. Highly accurate predictions of wall thickness and length were obtained and the authors recommend the method to provide the engineer with a preliminary but reliable wall plan. Although not holistic in its scope, this work stresses the potential of ML-based tools to enhance the engineer-architect interaction via the machine. Besides, although important in number, the database of 165 building designs employed puts in evidence the small-data nature of most structural engineering problems. In addition, the regressive model proposed by Pizarro and Massone (2021) does not incorporate contextual information and can lead to poor estimations of wall translation.

In a companion paper, Pizarro et al. (2021) improve upon their previous work and present Convolutional NN models that take the architectural data as input and can output the final engineering floor plan. To this end, two regressive models are used to predict the thickness, length, and translations of the wall. A second prediction of plan is obtained by using a model that generates a likely image of each wall. Both independently predicted plans are combined to lead to the final engineering design as shown in Figure 7 . This methodology was proven to be a feasible option to accelerate decisions regarding the building layout and can be adapted to incorporate estimations of building drift demands or force distributions.

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FIGURE 7 . Predicted plan obtained by Pizarro et al. (2021) .

Along the same vein as the above-mentioned studies, the work of Liao et al. (2021) uses generative adversarial networks (GAN), that have been previously used to generate building floor plans ( Chaillou, 2020 ), to perform structural designs of shear wall residential buildings. To this end, the authors use a semantic process to extract essential architectural and structural features from technical drawings of around 250 pairs of architectural-structural human designs. The outputs of the GAN model are evaluated in two case studies where their safety and economy are compared against designs carried out by competent human engineers. It is concluded that GAN-generated designs can improve significantly the speed at which new designs are generated without compromising the quality of building structures. Similarly, Lou et al. (2021) optimized the shear wall layout of high-rise buildings through a tabu search algorithm. Support vector machines (SVM) were used to construct surrogate models and speed-up the analysis time. Their objective was to minimize the structural weight with constraints on the period ratio and story drift. Through a series of case studies, the authors showed that the proposed approach works well. In this case, however, a meta-heuristic algorithm was used for the optimization part and the ML model was employed only to reduce the computational cost due to repetitive structural analyses.

5 The Grails of Creativity and Intuition

Modelling human intelligence on the perceived way we process and understand information has lead to remarkable tools that can augment the engineers’ design skills, allowing them to operate over large datasets and make ever more accurate predictions of response and performance. However, understanding and reasoning are not the only, or even the most frequent, ways engineers use to solve problems ( Graziano and Leone, 2019 ). Intuition, understood as “a form of recognition” ( Simon, 1995 ), or the ability to understand something almost instinctively without concious reasoning, plays an important role in engineering decisions. In fact, engineers, who may prefer to call it judgement, use intuition even when developing computer models such as when framing the design question the model is set to answer or deciding what to include and what to leave out of that question. Appeals to recognize the importance of intuition in engineering design have grown almost in parallel with the proliferation of computational tools in engineering ( Young, 2018 ).

Recent pioneering research has started to look at ways to integrate intuition into AI and ML with encouraging results in areas as diverse as chemical engineering ( Duros et al., 2019 ), automated planning ( Kim et al., 2017 ), and mathematics ( Davies et al., 2021 ). In all these cases, the authors propose schemes for the incorporation of a human experimenter as part of the solution-generation process. For example, Davies et al. (2021) approach is akin to a “test bed for intuition” where ML algorithms guide the experimenter by: 1) verifying the existence of a hypothesized mathematical pattern using supervised ML; and 2) if the pattern exists, by helping in understanding it using Attribution Techniques. Likewise, Duros et al. (2019) propose the integration of human and machine in the selection of potential chemical experiments within a single decision-making loop. In all these cases, by making human and machine work together, a significantly higher performance is achieved than either of them could achieve individually.

In the structural engineering field, a relatively similar approach has been attempted by Danhaive and Mueller (2021) . In their work, briefly described in the previous section, Danhaive and Mueller allow the design engineer access to a family of 2D latent spaces that can be adapted by changing the user-defined performance condition. This feature encourages designers to investigate different trade-offs between performance and other design features and opens the door for a more integrated machine-designer collaboration that does not aim to replace intuition with deterministic and quantitative rules but instead to incorporate it within the design process. However, to make the latent space intuitive and apt for human exploration, Danhaive and Mueller have to limit it to two dimensions. This highlights a defining feature of human intuition: that it emerges from the natural inability of the human mind to process scenarios with multiple variables ( Halford et al., 2005 ). It is when faced with high uncertainties and multiple unknowns that the engineer resorts to intuition to be able to define a direction of exploration without getting boggled by the details. One would expect that the growing ability of AI to identify complex patterns in high-dimensional spaces will supersede the advantages of rules of thumb and educated guesses in determining high level features of the design process. Until then, the integration of human and machine intelligence offers a promising alternative. In addition, intuition’s deciding role during the initial design stages fades down as the design is gradually informed by mechanics and structural analyses. Nevertheless, intuition remains as one of the last strongholds of traditional structural engineering practice as it adapts and responds to the challenges of digitalization. The other being creativity.

Creativity is usually defined as the generation of novel and useful ideas ( Jung et al., 2013 ). This immediately invokes the existence of a judge, a person to whom the idea, or in our case the design, would appear novel or useful. It is perhaps this subjective strength of the term the reason for its recent prominence in the discussions around the training of the next generation of structural engineers ( Ibell, 2015 ) where it is usually pitted against the more quantifiable (and declining) numerical skills. However, this subjectivity is not amorphous or ethereal since creativity does not emerge in the vacuum but is rather tied to socially contextualized phenomena ( Kaufman and Sternberg, 2010 ). As such it will appear that creativity can be taught and learnt, if by humans also by machines. In this regard, the examples presented in previous sections have highlighted the possibility of incorporating measures of taste in ML tools and algorithms have been shown to enhance the diversity of the solutions found. In this context, it has been argued that novelty constitutes a critical issue to address with computational approaches, e.g., ( Amabile, 2020 ). This is due to the fact that training of ML models usually relies on minimizing a loss expectation function and therefore the model is encouraged to perform well in the most common elements of already established knowledge.

A number of approaches could be taken to improve the “creativity” of ML algorithms ( Boden, 1998 ), namely: 1) by producing novel designs from the combination of familiar solutions, 2) by discovering new paths in conceptual spaces, and 3) by disrupting the design space with solutions that were not previously considered. Consequently, it would seem that there are yet many routes to encourage artificial creativity. These aspects are in fact being developed within (and are probably more suited to) reinforcement learning approaches. Similarly, efforts to incorporate heuristic thinking into AI have been trialled in other branches of design ( Nanda and Koder, 2010 ) and it may be beneficial to explore those in structural engineering also. At the end of the day, heuristics (intuition) is already routinely used by engineers to reduce the search space of potentially feasible designs, e.g., ( Maqdah et al., 2021 ; Palmeri et al., 2021 ; Danhaive and Mueller, 2021 ). A perceived hurdle, however, comes form the fact that much of the progress of ML and AI has come from the formalization of mathematical and logical approaches aiming at well defined problems with clear goals. To answer this, may be the distinction between: 1) algorithms that search the entire decision space, and 2) those that perform bounded searches to provide satisfactory solutions ( Simon, 2019 ) can be helpful here. Ultimately, much to the regret of the new breed of curriculum transformation proposers, computer programs constitute a body of empirical phenomena to which the student of design can address himself and which he can seek to understand. There is no question, since these programs exist, of the design process hiding behind the cloak of “judgment” or “experience” ( Simon, 2019 ). To which we may add:“ or creativity”.

None of the above mentioned explorations to embed artificial intuition or to enhance artificial creativity in machine intelligence has yet been fully explored in structural engineering design. This constitutes an area of great research potential. Since much of the ML research has been based on mimicking the theories of human cognition it is entirely possible that the restrictions of human creativity and intuition are in turn limiting machine intelligence. This calls for a re-evaluation of the human-machine creative partnership. New investigations that take at face value the human-machine duo, like it has been done in other creative industries ( Nika and Bresson, 2021 ), are likely to benefit the realm of structural design with fresh and surprising views. So it seems that in the short term we may be seeing more design cooperation between human and machine where the role of ML, however, is not circumscribed to repetitive tasks but can assist in the creative work itself.

6 Conclusion

It has been suggested ( Gero, 1994 ) that there are three views that can be taken about artificial intelligence in design: 1) AI as a framework in which to explore ideas about design; 2) AI as provider of a schema to model human design; and 3) AI as a means to allow the development of tools for human designers. This review paper has concerned itself with a strong version of the third view, by highlighting the path not only towards the development and proliferation of ML tools but also towards the automation of entire parts of the design process. In fact, a multitude of ML tools have been proposed aimed at different individual tasks along the design chain (like predicting the strength or condition of a given element, or the optimization of a section or connection). Design, however, is more complex than any of these individual tasks and ML methods aimed at it are more scarce.

It has been shown that ML tools have now started to appear that allow engineers to access complex multi-dimensional spaces beyond the ability of human intelligence alone. It was argued that the defining characteristic of ML to identify complex patterns and use those to predict or propose new engineering design solutions will form the basis for the automatization of increasingly large portions of the design endeavour. Importantly, these ML-enabled explorations can include not only hard mechanistic constraints but also metrics of taste and intuition. Indeed, although currently still producing timid results, the learning capacity of ML algorithms can be used to incorporate aesthetic and creative criteria that is sometimes difficult to articulate but which nevertheless the machine can learn. In addition, this learning can feed not only from engineering precedents at large but from the “best” precedents we currently have.

Another advantage of ML algorithms applied to design is found in the increased diversity of outputs produced. ML algorithms have been shown to increase the design diversity by recombining the features that characterise individual designs producing solutions beyond those which would have been imagined by human engineers. This recombination is usually neglected in engineering designs due to the large demands of data and time associated with it. However, with the use of data augmentation tools and computer simulation, it is expected that this hurdle will be solved sooner rather than later.

Nonetheless, the data requirements of ML algorithms will continue to be a limiting factor, particularly in the structural engineering field. If the ML-enabled design automation is to be attained, larger datasets of real-world designs should be made freely available. Most of the ML algorithms reviewed herein have used training datasets in the order of the hundreds. This is “small data” science and requires specific data augmentation techniques that the focus on “big data” is currently concealing. Data acquisition and curation is indeed the single most important step in the development of ML models. Robust, complete and reliable data sources should be produced and shared. Echoing current public demands in the sustainability and industrial ecology quarters of the design enterprise (in terms of environmental impact, LCA, etc.) ( D’Amico et al., 2019 ) the field of structural ML design also needs all its stakeholders to contribute their design databases. Only then, truly optimal and “out of the box” ML-enabled design solutions can be realistically proposed paving the way towards more resilient, economical and sustainable new structures.

All in all, we should continue to guard against the well known dangers lurking around ML implementation. To this end, issues of interpretability and overfitting should continue to be raised and efforts made to increase model explainability (by conducting and reporting sensitivity tests and marginal effects studies for example), increase data sources, improve noise filtering processes and carefully select the ML models (to reduce overfitting) should carry on. Finally, it has been said that ML tremendous success so far has been achieved by showing that some cognitive processes thought to be complex and difficult are, in fact, not so. This, taken together with the acceptance that routine design is broadly defined as that activity that occurs when all the necessary knowledge is available ( Gero, 1994 ); should prepare us well to be less surprised when the next generation of ML tools hits the structural design enterprise with the automation of large portions of the design process. Hence the question of how long until, not if, the human engineer is superseded in structural design.

Author Contributions

CM-C contributed to conception and design of the study, it organisation, wrote the paper, read and revised it.

Conflict of Interest

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s Note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Keywords: artificial intelligence, machine learning, structural design, structural engineering, design space

Citation: Málaga-Chuquitaype C (2022) Machine Learning in Structural Design: An Opinionated Review. Front. Built Environ. 8:815717. doi: 10.3389/fbuil.2022.815717

Received: 15 November 2021; Accepted: 13 January 2022; Published: 09 February 2022.

Reviewed by:

Copyright © 2022 Málaga-Chuquitaype. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Christian Málaga-Chuquitaype , [email protected]

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1.1: Introduction to Structural Analysis

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Introduction to Structural Analysis

1.1 Structural Analysis Defined

A structure, as it relates to civil engineering, is a system of interconnected members used to support external loads. Structural analysis is the prediction of the response of structures to specified arbitrary external loads. During the preliminary structural design stage, a structure’s potential external load is estimated, and the size of the structure’s interconnected members are determined based on the estimated loads. Structural analysis establishes the relationship between a structural member’s expected external load and the structure’s corresponding developed internal stresses and displacements that occur within the member when in service. This is necessary to ensure that the structural members satisfy the safety and the serviceability requirements of the local building code and specifications of the area where the structure is located.

1.2 Types of Structures and Structural Members

There are several types of civil engineering structures, including buildings, bridges, towers, arches, and cables. Members or components that make up a structure can have different forms or shapes depending on their functional requirements. Structural members can be classified as beams, columns and tension structures, frames, and trusses. The features of these forms will be briefly discussed in this section.

1.2.1 Beams

Beams are structural members whose longitudinal dimensions are appreciably greater than their lateral dimensions. For example, the length of the beam, as shown in Figure 1.1 , is significantly greater than its breadth and depth. The cross section of a beam can be rectangular, circular, or triangular, or it can be of what are referred to as standard sections, such as channels, tees, angles, and I-sections. Beams are always loaded in the longitudinal direction.

fig1-1.jpg

1.2.2 Columns and Tension Structures

Columns are vertical structural members that are subjected to axial compression, as shown in figure 1.2a . They are also referred to as struts or stanchions. Columns can be circular, square, or rectangular in their cross sections, and they can also be of standard sections. In some engineering applications, where a single-member strength may not be adequate to sustain a given load, built-up columns are used. A built-up column is composed of two or more standard sections, as shown in Figure 1.2b . Tension structures are similar to columns, with the exception that they are subjected to axial tension.

fig1-2.jpg

1.2.3 Frames

Frames are structures composed of vertical and horizontal members, as shown in Figure 1.3a . The vertical members are called columns, and the horizontal members are called beams. Frames are classified as sway or non-sway. A sway frame allows a lateral or sideward movement, while a non-sway frame does not allow movement in the horizontal direction. The lateral movement of the sway frames are accounted for in their analysis. Frames can also be classified as rigid or flexible. The joints of a rigid frame are fixed, whereas those of a flexible frame are moveable, as shown in Figure 1.3b .

fig1-3.jpg

1.2.4 Trusses

Trusses are structural frameworks composed of straight members connected at the joints, as shown in Figure 1.4 . In the analysis of trusses, loads are applied at the joints, and members are assumed to be connected at the joints using frictionless pins.

fig1-4.jpg

1.3 Fundamental Concepts and Principles of Structural Analysis

1.3.1 Equilibrium Conditions

Civil engineering structures are designed to be at rest when acted upon by external forces. A structure at rest must satisfy the equilibrium conditions, which require that the resultant force and the resultant moment acting on a structure be equal to zero. The equilibrium conditions of a structure can be expressed mathematically as follows:

eq1-1.jpg

1.3.2 Compatibility of Displacement

The compatibility of displacement concept implies that when a structure deforms, members of the structure that are connected at a point remain connected at that point without void or hole. In other words, two parts of a structure are said to be compatible in displacements if the parts remain fitted together when the structure deforms due to the applied load. Compatibility of displacement is a powerful concept used in the analysis of indeterminate structures with unknown redundant forces in excess of the three equations of equilibrium. For an illustration of the concept, consider the propped cantilever beam shown in Figure 1.5a . There are four unknown reactions in the beam: the reactive moment, a vertical and horizontal reaction at the fixed end, and another vertical reaction at the prop at point B . To determine the unknown reactions in the beam, one more equation must be added to the three equations of equilibrium. The additional equation can be obtained as follows, considering the compatibility of the structure:

eq1-2.jpg

1.3.3 Principle of Superposition

The principle of superposition is another very important principle used in structural analysis. The principle states that the load effects caused by two or more loadings in a linearly elastic structure are equal to the sum of the load effects caused by the individual loading. For an illustration, consider the cantilever beam carrying two concentrated loads P 1 , and P 2 , in Figure 1.6a . Figures 1.6b and 1.6c are the responses of the structure in terms of the displacement at the free end of the beam when acted upon by the individual loads. By the principle of superposition, the displacement at the free end of the beam is the algebraic sum of the displacements caused by the individual loads. This can is written as follows:

eq1-3.jpg

In this equation, ∆ B is the displacement at B ; ∆ BP 1 and ∆ BP 2 are the displacements at B caused by the loads P 1 and P 2 , respectively.

fig1-6.jpg

1.3.4 Work-Energy Principle

The work-energy principle is a very powerful tool in structural analysis. Work is defined as the product of the force and the distance traveled by the force, while energy is defined as the ability to do work. Work can be transformed into various energy, including kinetic energy, potential energy, and strain energy. In the case of a structural system, based on the law of conservation of energy, work done W is equal to the strain energy U stored when deforming the system. This is expressed mathematically as follows:

eq1-4.jpg

The total work done is represented as follows:

eq1-6.jpg

Thus, the strain energy is written as follows:

eq1-7.jpg

1.3.5 Virtual Work Principle

The virtual work principle is another powerful and useful analytical tool in structural analysis. It was developed in 1717 by Johann Bernoulli. Virtual work is defined as the work done by a virtual or imaginary force acting on a deformable body through a real distance, or the work done by a real force acting on a rigid body through a virtual or fictitious displacement. To formulate this principle in the case of virtual displacements through a rigid body, consider a propped cantilever beam subjected to a concentrated load P at a distance x from the fixed end, as shown in Figure 1.8a . Suppose the beam undergoes an elementary virtual displacement δu at the propped end, as shown in Figure 1.8b . The total virtual work performed is expressed as follows:

eq1-9.jpg

Since the beam is in equilibrium, δW = 0 (by the definition of the principle of virtual work of a body).

The principle of virtual work of a rigid body states that if a rigid body is in equilibrium, the total virtual work performed by all the external forces acting on the body is zero for any virtual displacement.

fig1-8.jpg

1.3.6 Structural Idealization

Structural idealization is a process in which an actual structure and the loads acting on it are replaced by simpler models for the purpose of analysis. Civil engineering structures and their loads are most often complex and thus require rigorous analysis. To make analysis less cumbersome, structures are represented in simplified forms. The choice of an appropriate simplified model is a very important aspect of the analysis process, since the predictive response of such idealization must be the same as that of the actual structure. Figure 1.9a shows a simply supported wide-flange beam structure and its load. The plan of the same beam is shown in Figure 1.9b , and the idealization of the beam is shown in Figure 1.9c . In the idealized form, the beam is represented as a line along the beam’s neutral axis, and the load acting on the beam is shown as a point or concentrated load because the load occupies an area that is significantly less than the total area of the structure’s surface in the plane of its application. Figures 1.10a and 1.10b depict a frame and its idealization, respectively. In the idealized form, the two columns and the beam of the frame are represented by lines passing through their respective neutral axes. Figures 1.11a and 1.11b show a truss and its idealization. Members of the truss are represented by lines passing through their respective neutral axes, and the connection of members at the joints are assumed to be by frictionless pins.

fig1-9.jpg

1.3.7 Method of Sections

The method of sections is useful when determining the internal forces in structural members that are in equilibrium. The method involves passing an imaginary section through the structural member so that it divides the structure into two parts. Member forces are determined by considering the equilibrium of either part. For a beam in equilibrium that is subjected to transverse loading, as shown in Figure 1.12 , the internal forces include an axial or normal force, N , shear force, V , and bending moments, M .

fig1-12.jpg

1.3.8 Free-Body Diagram

A free-body diagram is a diagram showing all the forces and moments acting on the whole or a portion of a structure. A free-body diagram must also be in equilibrium with the actual structure. The free-body diagram of the entire beam shown in Figure 1.13a is depicted in Figure 1.13b . If the free-body diagram of a segment of the beam is desired, the segment will be isolated from the entire beam using the method of sections. Then, all the external forces on the segment and the internal forces from the adjoining part of the structure will be applied to the isolated part.

fig1-13.jpg

1.4 Units of Measurement

The two most commonly used systems in science and technology are the International System of Units (SI Units) and the United States Customary System (USCS).

1.4.1 International System of Units

In the SI units, the arbitrarily defined base units include meter (m) for length, kilogram (kg) for mass, and second (s) for time The unit of force, newton (N), is derived from Newton’s second law. One newton is the force required to give a kilogram of mass an acceleration of 1 m/s 2 . The magnitude, in newton, of the weight of a body of mass m is written as follows:

W (N) = m (kg) × g (m/s 2 )

g = 9.81 m/s 2

1.4.2 United States Customary System

In the United States Customary System, the base units include foot (ft) for length, second (s) for time, and pound (lb) for force. The slug for mass is a derived unit. One slug is the mass accelerated at 1 ft/s 2 by a force of 1 lb. The mass of a body, in slug, is determined as follows:

f0018-01.jpg

The two systems of units are summarized in Table 1.1 below.

Table 1.1. Comparison of unit measurement systems.

tab1-1.jpg

Table 1.2. Unit conversion.

tab1-2.jpg

1.4.3 SI Prefixes

Prefixes are used in the International System of Units when numerical quantities are quite large or small. Some of these prefixes are presented in Table 1.3 .

Table 1.3. SI prefixes.

tab1-3.jpg

Chapter Summary

Introduction to structural analysis: Structural analysis is defined as the prediction of structures’ behavior when subjected to specified arbitrary external loads.

Types of structures : Structural members can be classified as beams, columns and tension structures, frames, and trusses.

f0020-01.jpg

Fundamental concepts of structural analysis: The fundamental concept and principles of structural analysis discussed in the chapter include equilibrium conditions, compatibility of displacement, principle of superposition, work-energy principle, virtual work principle, structural idealization, method of sections, and free-body diagram.

Structural Analysis of the Evolution Mechanism of Online Public Opinion and its Development Stages Based on Machine Learning and Social Network Analysis

  • Research Article
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  • Published: 09 June 2023
  • Volume 16 , article number  99 , ( 2023 )

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  • Zixuan Liu 1 , 2 &
  • Xianwen Wu   ORCID: orcid.org/0000-0003-2258-3078 2  

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Internet public opinion is a complex and changeable system, and its trend development is characterized by explosive, evolutionary uncertainty, concealment and interactivity due to the participation of the vast number of Internet users. Today, with the rapid development of network information technology, public opinion has an increasing influence on the stable development of society. Computational intelligence is the frontier field of artificial intelligence development, and computational intelligence is used to mine and analyze public opinion text information and study the evolution of online public opinion. This paper uses the Changchun Changsheng Vaccine Incident as an example, and the netizens’ degree of attention to emergency-related keyword searches in the Baidu Index as a descriptive variable for the development of network public opinion. After applying the optimal segmentation algorithm, the development of public opinion is divided into phases. On this basis, a social network analysis is adopted to analyze the spatial and topological structure of each phase of network public opinion, using data from the Sina Weibo platform. Based on optimal segmentation, the development of network public opinion of the Changchun Changsheng Vaccine Incident can be divided into four phases, namely latent, spreading, control, and stable; each phase has different spatial and topological characteristics. Corresponding policy suggestions on network public opinion governance are put forward for each phase.

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1 Introduction

China is in a critical period of economic and social transformation in which many contradictions and risks that require citizens to adjust to a changing dynamic among different social groups lead to frequent public emergencies. Some government agencies have inadequate governance, regulations, control, and communication to manage emergencies effectively, while others ignore or counteract the interests of individuals engaged in event information dissemination. This has led netizens to promote the dissemination of network public opinion of emergencies. Only by actively guiding the public and quickly quelling emergencies can social peace and stability be maintained. General Secretary Xi Jinping made it clear at the National Network Security Information Work Conference that network governance capabilities should be improved. His objective is to form a comprehensive network governance pattern featuring government-led management, media cooperation, supervision, and netizen self-discipline. Therefore, it is necessary to: (1) identify the developing mechanisms of network public opinions related to emergencies;, (2) identify the network topology of network public opinion at different phases; (3) conduct a spatial analysis on each phase of the network public opinion development; and (4) put forward phased optimization suggestions for governance to ensure that the proposed countermeasures can guide the development of network public opinion rationally, scientifically, and efficiently.

2 Literature review

In China, a significant part of current academic research focuses on the propagation law of public opinion and on effectively guiding its healthy development. Public opinion presents itself in various states with different characteristics. It also develops and changes; the time development of network public opinion of unconventional emergencies is the directional change in netizens’ attention to such emergencies (using search engines) over time. The development scale is based on the progressive stages of different life cycles. In this study, we focus on issues that caused widespread public concern in 2018, using the Changchun Changsheng Vaccine Incident as a case study. First, we used the optimal segmentation algorithm to identify the different stages of the development of an event. Next, we conducted a social network analysis to examine the characteristics of the network structure of the event at different propagation stages and to uncover the qualitative propagation law of the public opinion event at each life cycle stage.

Network public opinion refers to the sum of various attitudes, opinions, and emotions expressed by the public, in response to public events, and disseminated through the Internet within a certain time and space [ 1 ]. As such, network public opinion is also a reflection of social conditions and public opinion. Network public opinion of emergencies refers to the views and opinions expressed by netizens on emergencies, as disseminated through Internet platforms [ 2 ]. The development of network public opinion of emergencies is a dynamic process involving three types of actors; namely the government, the network media, and netizens [ 3 ]. Emergencies are reflected in and perceived through public opinion, and while netizens are producers of public opinion, the network media are an important force in the promotion and development of public opinion. Equally, in China, the government is a body tasked with regulating and guiding public opinion. Thus, the government needs to grasp the patterns and characteristics of the development of public opinion to play a decisive guiding role [ 4 ]. The public’s need to explore the truth about an event and the overall desire to maintain social justice are the driving mechanisms for the spread and diffusion of the network public opinion about that event. The development of public opinion has thus become more complex and uncertain, with new opportunities for disseminating information and opinions; this has attracted widespread attention in academia [ 5 ].

Many scholars in China have used case studies to test a hypothesis by analyzing a specific situation. This paper uses a particular event as a case study and analyzes it to uncover the development process of network public opinion of emergencies, with an eye to informing the development of best practices for managing these processes [ 6 ]. Using the social network analysis method, Kang et al. (2014) conducted an empirical analysis on the speed and scope of the spread of network public opinion following the “11.16” school bus accident, thus providing a strategic solution to guide network public opinion in the wake of this emergency [ 7 ]. Zhu and Wang (2019) examined the case of “Child Abuse Incidents in RYB Kindergartens” and concluded that early warning systems for social emotions, control of information pollution, and disclosure of event handling information are critical to the management of network public opinion [ 8 ]. Cao and Li (2019) used the “Yabuli Incident” as an example and revealed that social network public opinion is jointly influenced by public opinion events, media, netizens, multiple subjects of the government, and related factors, and that the government can improve its ability to guide and control public opinion events [ 9 ].

Scholars have researched the subject elements and development stages in the evolution of online public opinion on emergencies, mostly revealing the shape or law of the evolution of online public opinion from two dimensions: process and subject. Current research has different ways to divide the stages of social network opinion evolution, including the three-stage theory with the division of latent → proliferation → fading [ 10 ]. The four-stage theory that divides latent → sudden → spread → end [ 11 ]; The five-stage theory of latency → emergence → acceleration → maturity → decline as a division [ 12 ]; The six-stage theory of latent period → growth period → spread period → outbreak period → decline period → death period is the way to divide [ 13 ]. There are also the "four points and four stages" [ 14 ] and the multi-stage theory [ 15 ], which are based on the communication characteristics of emergencies. At different stages of the evolution of social network public opinion, its propagation elements, element characteristics, and element association relations all present differences. Although scholars have not yet reached a consensus on the stage division of public opinion evolution, the development of online public opinion is generally considered to have a certain life cycle, following the vein extension rule of conception, spurt, proliferation, and decay.

As a comprehensive set of theoretical concepts and analytical methods, the social network analysis method provides new insights into the mechanisms at work. It allows for both individual-level and system-level analyses, which gives the method the potential to explain changes in structural relationships and their results [ 16 ]. The formation and development of public opinion cannot be separated from the communicative relationships among citizens; therefore, the social network analysis method has a specific reference value for public opinion research [ 17 ].

Al Omoush (2017) conducted empirical research based on public opinion data on unexpected events and classified events according to the time, region, and emotional attitudes of relevant subjects, thereby analyzing the depth of network public opinion dissemination [ 18 ]. Tokakis et al. (2019) analyzed the scope and effect of opinion leaders’ influence in emergencies to evaluate their comprehensive influence on network public opinion [ 19 ]. After reconstructing the route of online public opinion dissemination, Zeng and Zhu (2019) conducted a quantitative analysis on the topological structures of public opinion dissemination, such as the small-world effect, power-law distribution, and community structure [ 20 ]. Kang et al. (2014) used the case of the “4.20” Ya’an earthquake to analyze the network structure of public opinion and identify the key nodes in its dissemination during emergencies [ 21 ]. Wang et al. (2018) analyzed the information dissemination characteristics and social network attributes of network public opinion [ 22 ]. Wang and Sun (2017) used a social network analysis to measure and analyze the structure of the “Wei Zexi Incident” public opinion dissemination network [ 23 ]. Finally, Zhao and Wang (2018) used the case of the flood disaster in Daxian Village to excavate and identify key nodes in public opinion dissemination and to explain their internal structural features and development rules [ 24 ].

This paper considers the combination of time and space of network public opinions in emergencies as the starting point, uses the netizens' attention of the Baidu index as the real data for quantitative analysis in the time stage, and uses the optimal segmentation algorithm to divide the continuous data of time into four evolution stages according to the evolution law of data, so as to find the evolution characteristics of the time of network public opinions. Following this, the social network analysis method is used to analyze the spatial evolution of network public opinion in each stage. Thus, its temporal and spatial evolution rules provide a new research method for the spatial and temporal transmission evolution rules of other emergency network public opinions, which is more conducive to monitoring the evolution of irregular emergency network public opinions, and to reducing the secondary harm risk of irregular emergency.

3 R esearch Hypotheses

The spatial structure of networks circulating event information comprises the mutual relations between primary and secondary disseminating, or receiving, subjects. Different subjects have different modes of interaction, thus forming different network topologies. When the subjects are closely connected, their number is large, and the interconnection among the nodes is relatively complex; the nodes will connect to form a complex social network group. However, network public opinion of emergencies is itself a complex social network with multiple hierarchical structures that exist due to the connection of multiple subjects engaged in the interactive development, generation, dissemination, and reception of relevant information. In the process of collecting and disseminating information on emergencies, individuals involved in a network continuously send and receive information to promote its broader circulation, thus forming a large “group social network.” The network media’s rapid development have gradually made it a platform for the communication of social ideology, culture, and public opinion. There are many uncertain factors in the process of transmitting and circulating information on emergencies, and network media influence the way nodes are connected through various kinds of information. Therefore, our first research hypothesis is as follows: As the promoter of the development of network public opinion of emergencies, the network media play a key role in shaping the network structure.

During a critical period of social transformation and conflict in China, the active degree of network public opinion has been on the rise. Netizens have concentrated their attention on the process of occurrence, development, and dissemination of public emergency information, and the explosive spread of relevant event information has led to the openness, popularity, and instability of online public opinion of emergencies. Meanwhile, media platforms have also become venues to spread negative information about an emergency, and this negative content generates public rumors that can cause widespread panic. Once an emergency is consistent with the anti-social sentiment of Internet users, it is easy for a public opinion crisis to emerge and endanger social stability. In the communication process of online public opinion of emergencies, the government, online media, and netizens are the three most important subjects. The interactions among these three have an impact on the popularity, pace of spread, and development of an online public opinion of emergencies; it is thus meaningful to study the role of government in the development process. Therefore, our second research hypothesis is that in the development phase of network public opinion of emergencies, the government’s role is to guide public opinion continuously.

4 R esearch Methods and Model Construction

4.1 optimal segmentation theory.

The temporal development of public opinion of emergencies and data on social conditions and public opinion is a continuous process. By using continuous data on netizen attention to emergency-related search terms in the Baidu index, the development of network public opinion may be divided into orderly progressive phases. Scholars in natural sciences, including geology, hydrology, and information systems, have made advances in research in orderly progressive phases [ 25 ]. Optimal segmentation theory and optimal segmentation algorithm can effectively solve the problem of time series segmentation, as the data used in this study demonstrated through continuous clustering characteristics. Optimal segmentation algorithm comprises the following steps: (1) The sums of squared deviations of the measured data are used as the diameter of ordered clustering (segmentation) so as not to break the time series; (2) the sums of squared deviations of various types are obtained by traversing the segmentation; and (3) these are compared to select the minimum value, thus obtaining the ordered progressive phases.

4.2 Social Network Analysis Method

Yousefi-Nooraie et al. (2012) describes the social network analysis method as an analysis of the relationship between behavioral subjects. By capturing the interaction and interplay among a group of people, one can ascertain the behavioral patterns in a given environment and uncover the socio-spatial structure reflected in these relationships. The social network analysis method usually adopts matrices to present data and charts to present the network structure. “Centrality” is one of social network analysis’ foci. Subsequently, factors indicating the positions netizens and other subjects occupy within the social network structure, whether they are in the central position, and what kind of power they have, all demonstrate the influence of individuals in the network structure. By using social network analysis, we can analyze the phased overall morphology of the network structure and identify the subjects that may occupy important positions, or have greater influence, at any given phase [ 26 , 27 ].

In today’s complex Internet environment, information about emergencies is a special type of information in a disseminating situation, and the network space structure based on event information mainly consists of information management subjects, transmission routes, transmission subjects, and inter-subject relationships. In the process of information generation and transmission, the constant sending and receiving of messages lead to an intensive sharing of information that results, in a sociological sense, in a “group social network.” In existing research on the development of online public opinions on emergencies, group research is generally transformed into research on specific subjects, and the context and nature of the crisis is typically central in the discussion.

4.3 Construction of Optimal Segmentation Model

Data on the development phases of network public opinion of emergencies are defined as X = (X 1 ,X 2 ,X 3 ,…X j ), where X j represents the specific value of searches by netizens obtained on the j-th day of the development process. The specific calculation process for the phased development of network public opinion of emergencies is as follows. [ 28 ]

4.3.1 Data Normalization

The continuous data Xj in matrix X is normalized by Formula 2 to obtain Yj, the normalized matrix of which is Y = (Y 1 ,Y 2 ,Y 3 ,…Y n ).

4.3.2 Calculation of the Variation Matrix

Assuming that the normalized matrix distribution within a certain period [a, b] is [Y a ,Y a+1 ,Y a+2 ,…Y b ], the differential value of network public opinion development in this period is expressed as follows:

When the matrix Y is divided into k segments, a variation matrix D = (D 1 ,D 2 ,D 3 ,…D k ) can be obtained and the following can be calculated: \(D_{i} = \left[ {d_{a \, b} } \right], \, i = 1,2, \cdots ,k\)

4.3.3 Division of the Optimal Segmentation Points

If P(n, k) represents that n consecutive search engine attention values in the matrix Y are divided into k segments and k = 2, then the optimal segmentation points can be obtained by the objective function shown in Eq.  3 .

When k  = 3, the optimal segmentation points can be obtained by the objective function shown in Eq.  4 .

Through such continuous iterations, the objective function formula that confirms the division of network public opinion into k segments can be obtained as follows:

Finally, the inverse method is used to solve Eq.  6 ; that is, the optimal segmentation points for division into k-1 phases can be obtained.

4.3.4 Determination of the Optimal Number of Phases

As the optimal segmentation method does not calculate the exact number of segments, the ratio method is required to determine the optimal k value:

According to the operation rules, the larger the value represented by a, the better the effect of dividing it into k + 1 segment rather than k segments. In addition, when the value of a is infinitely close to 1, this indicates that there is no need for an iterative inversion.

4.3.5 Validation of the Segmentation Result

To determine the most suitable number of segments, we must ensure that the segmentation result conforms to the rules of an F-test. The mathematical formula for calculating the F-test value is as follows:

According to the operation rules, when the F-test value is higher than the given significance level, the validation has passed. This suggests that the effect of dividing the temporal development of network public opinion into k segments is relatively significant and that the obtained k -1 optimal segmentation points are effective segmentation points.

5 Empirical Results and Discussion

Figure  1 shows that the Changchun Changsheng Vaccine Incident began to attract public attention in July 2018. As netizens have unlimited scope for emotional expression and demands, both they and the media paid attention to the political/public discussion. During this unexpected event, netizens experienced a crisis of trust in the government, and this inevitably became the focus of public opinion.

figure 1

On Changchun Changsheng vaccine incident

During the Changchun Changsheng Vaccine Incident, it was evident that social media intensified the process of accumulating and generating public opinion, and latent discussions resulted in an outbreak of public opinion online in a short time.

On July 15, 2018, the state drug administration (now the National Medical Product Administration) issued a notice regarding the company’s vaccine fraud. On July 19 and 20, Changsheng Bio-Technology Co., Ltd. and the Shenzhen Stock Exchange reacted to the development. On July 21, 2018, “Beast Lord,” a former Southern Weekend journalist, published “The king of vaccines” on his official public WeChat (a social media application) account. It quickly drew the attention of a circle of netizens and an online platform, which led to the rapid dissemination of the event from its incubation. Different types of “self-published media,” more commonly known as “self-media,” which is created by the general public to release and disseminate their own news and information, condemned the vaccine company’s fraudulent behavior.

After just 6 days, netizens gradually moved from being concerned about the event to expressing distrust in vaccine safety in general, as well as distrust in regulators. When a large amount of information floods the Internet, public opinion intensifies. Netizens became concerned for their own security, and their distrust of authorities also had a sustained effect on public opinion.

When emergencies occur, such as the Changchun Changsheng Vaccine Incident, the platforms which network media are most likely to turn to for gathering information are Baidu and Weibo. These platforms are thus an important medium for communication and discussion. Figure  1 illustrates the number of hits on a Baidu search using search terms related to the “Changchun Changsheng vaccine” between July 16, 2018, and August 13, 2018, demonstrating the trend of netizens’ concern about the event over time.

6 Results of Data Processing and Analysis

This study used “Changchun Changsheng Vaccine Incident” as a keyword to search the Baidu index. It also used continuous data on netizens’ attention to this incident over the course of 29 days, from July 16, 2018 to August 13, 2018, as the real-world data on temporal development phases of network public opinion of this incident ( X  = [0, 5280, 3832, 3179, 5949, 10,362, 148,189, 213,230, 131,408, 66,003, 32,676, 20,935, 16,962, 12,986, 14,541, 11,706, 7102, 6199, 5928, 4310, 3599, 5470, 6508, 7132, 5138, 4156, 2729, 2373, 3089]). MATLAB7.0 software was used to normalize the above data ( Z  = [0.0138, 0.0069, 0.0038, 0.0170, 0.0379, 0.6915, 1.0000, 0.6120, 0.3018, 0.1437, 0.0880, 0.0692, 0.0503, 0.0577, 0.0443, 0.0224, 0.0181, 0.0169, 0.0092, 0.0058, 0.0147, 0.0196, 0.0226, 0.0131, 0.0085, 0.0017, 0, 0.0034]). The variation matrix D of X was calculated using Eq.  3 , from which the minimum variation value of network public opinion development under k segments could be determined (as illustrated in Table 1 and Fig.  1 ).

As the development of network public opinion may be divided into different phases, the optimal segment number of the index is determined by Eq.  7 . Through our calculations, we found that a34 = 0.8364 > a23 = 0.722 and that the larger the optimal segment value of the index, the better. Therefore, the minimum variation values when k  = 4 and k  = 3 were substituted into Eq.  4 , thus deriving the F-values of 0.4563 and 0.2576, respectively, which are less than the test value of 3.049 when the significance level is 0.05. However, when k  = 4, the F -value is closer to 3.049. Thus, through repeated iterations and significance level tests, the development of the network public opinion of the “Changchun Changsheng Vaccine Incident” was divided into four phases: latent, spreading, control, and stable (as illustrated in Fig.  2 ). From here, it can be seen that the evolution of online public opinion of sensational events is basically consistent with the "four-stage" evolution mechanism: first, under the stimulation of key events, online public opinion bursts into the open stage; second, with further development of the situation, netizens and the media pay attention; third, the degree of public opinion escalates and emotional infection helps intensify public opinion of the Internet that then enters the dissemination stage; and fourth, with the intervention of the government and other governance entities, or the public’s "emotional slack," the public opinion curve has an inflection point and the mood of Internet public opinion is tense. When the situation eased, the influence of the event began to decline, attention gradually cooled, and online public opinion entered the stage of control. However, based on the event’s cessation or the appearance of other public opinion events, people no longer pay attention to the original one, network public opinion evolves to a stable stage and then gradually disappears, and the public opinion information ecosystem reaches an equilibrium state. Of course, because public opinion has a memory function, once a similar incident occurs again, the dispelled online public opinion will be retrieved and enter a new round of online public opinion evolution cycle.

figure 2

Analysis of the development phases of network public opinion of the Changchun Changsheng Vaccine Incident

6.1 Analysis of the Spatial Structure of Network Public Opinion in the Latent Phase of Development

Weibo is a mainstream social media platform in China and an effective tool for think tanks to use social media to develop knowledge services, disseminate knowledge, and guide public opinion. Given its longevity and influence, Sina.com—one of the “four major portals in China”—was used as the research platform for this study. Using the search function provided by the Sina Weibo platform, we searched using “Changchun Changsheng Vaccine Incident” as the keyword. A total of 50 individuals who disseminated the event through Sina Weibo and achieved the highest numbers of reposts were selected. Following this, 5 of these 50 were selected randomly as initial information distribution nodes, and another 5 individuals who reposted or commented on posts about this incident from these 5 sources were randomly selected as secondary information distribution nodes. For this incident, we established a 75*75 dissemination matrix model and analyzed the spatial dissemination effect among the 75 nodes.

Latent phase (July 16, 2018, to July 21, 2018)

In the latent phase, the emergency incident had just occurred, and only public advocacy groups and members of the public with vested interests in the incident paid attention to the emergency information. As evident from the spatial structure diagram in Fig.  3 , the main dissemination groups that promoted the development of public opinion in this phase were the official media or opinion leaders who had relevant information about the Changchun Changsheng Vaccine Incident.

figure 3

Spatial structure diagram of the latent phase of network public opinion of the Changchun Changsheng Vaccine Incident

A dual-core network spatial structure formed during the latent phase. It had two different factions: one centered on “Headline News” and one on “Interface.” “Headline News” established direct connection channels with “Beijing News” and “Kaidi Network,” while “Interface” established direct information exchange channels with “CCTV Finance” and “National Business Daily.” The nodes within these two factions were interconnected, thus improving the speed of information exchange between them. However, the factions had no relationship with each other. Therefore, while the information flow within the factions was smooth, the flow between the factions was more difficult. This demonstrates that in the latent phase of the development of network public opinion of emergencies, each faction is isolated from the other, making it difficult to carry out quick and effective information dissemination.

6.2 Analysis of the Spatial Structure of Network Public Opinion in the Spreading Phase of Development

Spreading phase (July 22, 2018, to July 24, 2018)

In this phase, network public opinion demonstrated a pulsed rapid growth trend. Most netizens learned about the Changchun Changsheng Vaccine Incident and expressed their personal opinions through Internet platforms, which accelerated the widening and deepening of public opinion dissemination. At this time, netizens who participated in the information dissemination were mainly motivated by exogenous attractions such as curiosity and related interest, and by endogenous impetuses such as power and achievement. After 9 days of development, the spatial structure of the network public opinion of the Changchun Changsheng Vaccine Incident finally formed 18 factions (Fig.  4 ). Among them, “Headline News” belonged to 16 factions, “People’s Daily” belonged to 24 factions, and “Shanghai Huangpu” belonged to seven factions simultaneously.

figure 4

Spatial structure diagram of the spreading phase of network public opinion of the Changchun Changsheng Vaccine Incident

Although there were many factions, the continuous connection and overlap among these made them closely linked. The overlapping nodes not only ensured full communication of information within the factions, but also information flow between them, and this contributed to further improvement of network cohesion. In addition, “Sina Finance,” “People’s Daily,” “Headline News,” and “CCTV News” formed the most prominent factions in the public opinion dissemination network of the spreading phase. “CCTV News” and “People’s Daily” had the strongest dissemination power, followed by “CCTV Finance” and “CCTV News.”

Moreover, judging from the attributes of these four nodes, they were all derived from “the field of official public opinion.” This demonstrates that, in the spreading phase, the media (“People’s Daily” and “CCTV News”) and opinion leaders played the most important roles in the dissemination and circulation of information. These four nodes were adjacent to each other and closely linked. They could exchange and coordinate information within their factions first, reach consensus, and then spread out through their respective fan groups, thereby forming a larger information circle. This was significant for the government’s efforts to guide the development of network public opinion. This proves Hypothesis 1: the network media, in its role as promoter of the development of online public opinion in emergencies, continue to play a key role in shaping the network structure.

6.3 Analysis of the Spatial Structure of Network Public Opinion in the Control Phase of Development

Control phase (July 25, 2018, to August 11, 2018)

In this phase, network public opinion demonstrated a “pulsed” decreasing trend. As illustrated in Fig.  5 , the number of nodes and connections in the central position were significantly lower in the control phase than in the previous one. At this time, opinion leaders and the official (government) media were the main groups to comment on the event. Relevant information on the Changchun Changsheng Vaccine Incident was published in posts by relevant personnel, and their dissemination activities pushed network public opinion into the stable phase. In the control phase, opinion leaders continuously released real-time information on the emergency incident, repeating a process of government explanation (official news release), netizens' questions regarding it, government reinterpretation (official news release), further questioning, and so on.

figure 5

Spatial structure diagram of the control phase of network public opinion of the Changchun Changsheng Vaccine Incident

Netizens’ emotions gradually intensified as their understanding of this emergency incident deepened and faded when their attention gradually decreased. At this time, the speed of information dissemination through the network media slowed down and remained in a declining state. This proves Hypothesis 2: in the development stage of online public opinion of emergencies, the government plays a continuous guiding role.

6.4 Analysis of the Spatial Structure of Network Public Opinion in the Stable Phase of Development

Stable phase (Since August 12, 2018)

From Fig.  6 , we see that the temporal development of network public opinion presented a “power law attenuation” distribution. With the guidance of the government and the decline in netizens’ own dissemination interests, the spatial structure of network public opinion of the emergency eventually evolved into a single-core structure with “People’s Daily” as the center. At this time, most of the remaining nodes comprised communications media, which continued to attend to and disseminate public opinion when other netizens had withdrawn from communication.

figure 6

Spatial structure diagram of the stable phase of network public opinion of the Changchun Changsheng Vaccine Incident

7 C onclusions

Netizens are the main participants in Internet activities, as well as the main producers and disseminators of network public opinion. Due to different personal backgrounds, educational levels, and professional orientations, netizens have different views on online events and public emergency incidents according to their subjective values. Initially, some netizens may not openly express their opinions. However, as the public incident continues to progress, netizens will begin to repost and comment together with others, according to their own interests. Through the mutual reposts and comments among numerous netizens, massive and scattered information is continuously gathered and superimposed according to different perspectives and preferences. Gradually, this process forms the network public opinion of the incident or event. Netizens, the media, and the government continually interact, even while expressing their attitudes and opinions in their respective factions, throughout the continuous accumulation and superposition of network public opinion. Together, these three subjects push network public opinion to its peak.

The development of network public opinion is affected by event information at different points in time and spaces, as evident in different peak fluctuations. If an incident violates public morality and reaches the most remote demographic, discussions about it will become more intense, making it difficult to reduce them in a short time, though this would depend on whether they are closely related to public life. However, if there are no developments to hold the attention of netizens in the short term, their attention to the event will gradually decrease over time, the public mood will tend to stabilize, and the network public opinion will gradually enter a relaxed phase until the next major event occurs. If the relevant authorities do not handle such emergencies effectively, the force of the reaction through network public opinion will be even stronger. If relevant authorities respond promptly and positively, they can, to a certain extent, actively guide public opinion, thereby promoting its healthy development. As government authorities continue to intervene in the handling of incidents, the public will pay less attention to emergencies. When new public events occur, these will divert the attention of netizens away from earlier events, and network public opinion will gradually enter a decelerated phase. In this phase, the emotions generated by different ideological groups among netizens slowly subside.

7.1 Policy Recommendations

(1) In the latent phase of network public opinion of public emergencies, the speed of information disclosure by government departments should be increased, and effective emergency measures should be taken. In this phase, only a few netizens have information about public emergencies, and only some will participate in the discussions. As netizens pay little attention to emergencies, and enthusiasm for disseminating information is very low at this point, netizens’ opinions do not form a large-scale storm of public opinion dissemination. There is, therefore, a window of opportunity for information disclosure by government departments, and their efforts to deal with public emergencies determine the speed and dissemination enthusiasm of network public opinion. The failure of government departments to take prompt and effective measures following a public emergency is a fundamental reason for the continuous development, intensification, and spread of network public opinion.

(2) Guidance of public opinion in the network media should be strengthened during the spreading phase of public emergencies. The network media should establish a standard to pursue their own values, report event information fairly and truthfully, report real-time information about public emergencies to the public, and supervise government departments as they manage public emergencies. However, the network media should also exert their particular function as a “second supervisor;” they should attempt to understand government departments’ plans and decisions to manage emergencies by strengthening interaction with them, and they should convey the departments’ emergency response measures to the public promptly so that the public can access accurate and practical information. This enables the government to guide the trend of network public opinion in the right direction. Relevant theories about network public opinion are indispensable for guiding it during public emergencies. Only by scientifically applying the theories of “gatekeeper” and agenda-setting in network public opinion can the government cooperate with mainstream media, release accurate and detailed information, satisfy the public’s right to know, actively guide network public opinion, reduce public losses, and maintain social stability. The “gatekeeper” theory has played an important role in managing public emergencies, for example, by facilitating on-site interventions, encouraging the rolling release of news, enabling timely response to public questions, and eliciting positive responses to adverse reports. Therefore, the government should ensure the accuracy of information to avoid misunderstanding and misinformation among the public. Important data, facts, figures, and locations should be reviewed and verified continuously to issue authoritative and reliable information openly, transparently, and truthfully, and to guide the public’s online behavior promptly and effectively.

The keen attention of the public makes it easy for public information on emergencies to become the focus of network public opinion. Everyone wants to be the first to report. During the spreading phase, the government should take the initiative to release information and build a benign and harmonious public opinion environment.

(3) In the face of public emergencies, the government’s first response must be to disclose clear and correct information, because public panic can be caused by the lack of information or credulous reliance on gossip and online rumors due to insufficient information sources. Building an honest government is the most important step that it can take to effectively control and guide the development of network public opinion. Therefore, it is necessary to establish laws and regulations related to the government’s disclosure of information about public emergencies; specify the government’s responsibility to disclose such information; establish a system for the government to exchange information with online media, netizens, and other social groups; revise and adjust government information dissemination in real-time.

(4) Netizens, as one of the three main groups of actors that influence the development of network public opinion, have the right to speak freely and maximize their own interests in all the phases of network public opinion of public emergencies. However, the state’s power to maintain public safety and order must correspond to the individual rights of netizens. In response to public crises, netizens should take the initiative and actively assume corresponding social responsibilities.

Netizens’ obligations and rights are inseparable. In essence, by undertaking corresponding obligations, netizens are protecting their own legitimate rights (such as the right to unimpaired life, health, and property). Moreover, as individuals embedded in social relationships, netizens who ignore the interests of others or cause damage to the legitimate interests of others when dealing with public crises will undoubtedly be punished and restrained at the social morals level. Netizens’ active participation in public crises is an important supplement to government measures, and it can significantly reduce or even eliminate the limitations of such measures. The network public opinion propagation of public health events like new crown pneumonia is characterized by significant time change particularity, spatial distribution diversity, and periodicity of evolution process.

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Liu, Z., Wu, X. Structural Analysis of the Evolution Mechanism of Online Public Opinion and its Development Stages Based on Machine Learning and Social Network Analysis. Int J Comput Intell Syst 16 , 99 (2023). https://doi.org/10.1007/s44196-023-00277-8

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