Introduction

As an important transportation infrastructure, bridges play a pivotal role in the development of transportation throughout the country. All transportation systems, whether railway, highway system or urban transportation network, rely heavily on the application of Bridges. With the vigorous development of bridge construction, construction safety accidents are gradually increasing.

Due to the characteristics of bridge construction such as long period, large scale and complex technology, the risk of artificial and natural factors contained in bridge construction is more and more obvious, construction safety accidents occur constantly, and bridge collapse accidents bring serious social and economic impact.

Based on the above-mentioned problems, it is imperative to analyze and classify the risk factors that affecting the bridge construction stage, and establish risk analysis indicators. According to the advantages of the random forest algorithm, which has accurate and robust risk assessment results, this research uses the random forest algorithm to evaluate the risk of bridge construction in order to reduce occupational accidents and provide reference decisions for the bridge construction personnel and the owner management affiliate, so as to prevent accidents in the future.

In developing countries, the number of bridge accidents is usually greater during construction than during operation, and improper construction is one of the most serious accidents resulting in death. Therefore, bridge construction risk identification analysis and assessment is the main topic of this study. The objective of this paper is to use random forest algorithm to evaluate the risk of bridge construction, and rank the importance of indexes, and define the indexes that have a greater influence on the risk, so as to prevent the accidents caused by man-made and natural disasters in the process of bridge construction.

Literature review

Bridge engineering is accompanied by all kinds of risk factors in the construction process, including the environment, personnel, technology, equipment, management and so on. These risk factors have great influence on the construction quality of bridge engineering. If these risk factors are found out in time or improperly handled, they will cause a wider range of personal injury accidents.

For the construction industry risk assessment and safety management, domestic and foreign scholars have carried out a lot of research. Fraczek1 analyzed the investigation results of the Structural Safety Committee of the American Society of Civil Engineers on the failure of concrete structures, and found that more than half of the problems occurred in the construction process, which ultimately led to the destruction of structures. Hadipriono2 collected the data of 147 bridge and building collapse and damage accidents in Europe and America in recent years, the study found that only a third of accidents were caused by external factors such as ship collisions, while the rest were due to structural design and construction problems. Therefore, it is important to establish a stable and efficient bridge construction risk assessment system. At present, many scholars use different methods to study the safety risk assessment of bridge construction. Abdollahzadeh et al. 3 applied the fault tree and event tree analysis (ETA) method to evaluate the risks in bridge construction, identified the main causes and determined the possible consequences of the risks. Yuan et al. 4 analyzed the network structure relationship between bridge construction risk factors and established a bridge construction safety risk assessment model based on the network analysis method and combined with the characteristics of bridge construction site operation. Zhu et al. 5 took the Pingtan Strait highway and Railway Bridge as the background, identified potential risks by analyzing the on-site construction conditions, and established a bridge construction safety risk assessment model by using WBS-RBS and fuzzy hierarchical synthesis. Pan et al. 6 proposed a fuzzy fault tree analysis method based on fuzzy set and possibility theory to evaluate the failure probability of bridge construction. However, although these studies consider the uncertainty of risk evaluation, they ignore the influence of expert subjective factors on index weight, which leads to the relatively optimal evaluation grade results. And the traditional mathematical statistical model is difficult to conduct in-depth data mining. As there are many risk factors in bridge construction, there are certain relationships among risk categories, and machine learning methods are good at accurately approximating arbitrary continuous functions, so some scholars have proposed various risk assessment methods based on machine learning. Ding et al. 7 identified the main risk factors in the bridge construction stage, constructed an evaluation index system, and established a bridge construction risk assessment model based on Monte Carlo method.

Gong8 proposed a construction risk assessment method for long-span cable-stayed Bridges based on neural network finite element Monte Carlo simulation. Elhag Taha and Wang et al. 9 studied the application of artificial neural network in bridge risk assessment, BP neural network model was used to simulate the risk classification and risk value of 506 maintained Bridges, and the average accuracy of risk value and risk classification reached 96%, and the comparison was made with multivariate analysis method. The results show that the neural network analysis method has higher precision. Li et al. 10 established a highway bridge construction safety risk assessment index system on the basis of relevant standards and norms, then weighted each risk index objectively by using cloud entropy weight method, carried out risk assessment by using cloud model theory, and directly determined the overall risk level of bridge construction and the level of risk index through cloud model images. Fu et al. 11 analyzed the risk evolution mechanism of large-scale bridge construction and established the risk factor structure system. Based on the theory of system dynamics, a causal loop diagram and a flow library diagram are constructed, and a large bridge construction project is taken as an example to assign actual values to each variable equation, and the construction risk level is simulated. The results show that the continuous investment of security funds can effectively reduce the overall risk level of the system. Miano et al. 12 discussed and investigated the multi-level approach proposed in the Italian guidelines for the management of complex existing bridge systems, focusing on operational methods for assessing the impact of structural defects on risk assessment. This work provides a useful tool to start with inspection results, assign defect levels to Bridges, and incorporate them into risk assessments.

However, little of these algorithms can effectively reveal the deeper potential causes of accidents and the internal logical relations among factors. The random forest algorithm constructs multiple decision trees through random resampling of sample points and random splitting of nodes, and obtains the final classification result through voting. In the calculation process, the weight of each index can be obtained, and has the advantages of fast convergence speed and high precision. Through a large number of theoretical and practical applications, many scholars have verified that RF method has lower generalization error and higher prediction accuracy than other methods, and is suitable for problems without prior knowledge, multi-variable nonlinear constraints and incomplete data 13. Sonobe 14 used random forest classifier (RF) to accurately classify crop types. Jahandideh et al. 15 improved the success rate of protein structure determination through random forest algorithm. Wang et al. 16 proposed an evaluation model based on RF to evaluate regional flood disaster risk, and achieved good prediction effect in Dongjiang River Basin with this risk assessment method. Fang et al. 17 conducted risk assessment of mountain flood disaster in Jiangxi Province based on random forest algorithm. Thapa et al. 18 used RF algorithm for feature selection and classification of different data sets, and the results showed that relevant variables selected by RF and classification based on RF had better performance than SVM and ANN.

Recently, Huang et al. 19 used machine learning to predict earthquake damage and empirical vulnerability curve to represent risk assessment results, creating a fast risk assessment program. The study’s findings can be used as a guide for selecting machine learning methods and their inputs to build rapid evaluation models for railway Bridges. Guo et al. 20 established a multi-parameter vulnerability model analysis framework for double-layer curved Bridges based on random forest algorithm and partial correlation graphs, and built an effective vector model in the analysis framework to predict the demand and bearing capacity of double-layer piers. The results show that the failure of the upper restrained system precedes the yield of the pier, and the failure risk of the upper beam is higher than that of the lower structure under all possible seismic excitation angles. Zhang et al. 21 proposed quantile random forest (QRF) based on Bayesian optimization as a data-driven probabilistic prediction method. A long-span cable-stayed bridge with a main span of 1088 m is used as the test platform to verify the effectiveness of the proposed method. For comparison purposes, other optimization algorithms used by QRF (grid search and random search) and response surface methods (RSM) are also implemented. The results show that QRF based on Bayesian optimization can provide a reliable probability estimate, which can quantify the uncertainty in the prediction.

In conclusion, random forest algorithm has been widely used in risk assessment and achieved good results, but there are few studies on bridge construction risk assessment. The risk factors of bridge construction are characterized by large data dimension and strong correlation among indicators. However, in the existing risk assessment stages of identification, analysis, estimation and evaluation, the assessment model in the estimation stage lacks a data processing method with strong applicability. Random forest algorithm is an integrated algorithm based on decision tree. It has the advantages of processing input samples with high dimensional features without dimensionality reduction, evaluating the importance of each feature in classification, and obtaining an unbiased estimation of internal generated errors in the generation process.

This paper demonstrates significant innovation and novelty in the field of bridge construction risk assessment. By comprehensively and systematically classifying human and environmental risk factors, and introducing the advanced machine learning technology of random forest algorithm for the first time, the objectivity, accuracy and robustness of risk assessment are improved. The algorithm not only completed the risk assessment, but also accurately ranked the importance of each indicator, successfully identified the key risk sources, and provided a scientific basis for the formulation of targeted prevention and control measures. The effectiveness and reliability of this method are proved by practical engineering verification, which brings a new idea and method for bridge construction safety management. In the model construction process, a large amount of data collected in the actual bridge construction project is used as a valuable training sample. Through in-depth data mining technology, the hidden correlation and rules among the data are revealed, and the utilization value of data resources is effectively improved. Compared with traditional risk assessment methods, this method significantly enhances the objectivity and accuracy of the assessment process and provides more solid data support for bridge construction management decisions. To verify the effectiveness of the proposed method, the research team selected a representative real bridge as a case and conducted a comprehensive risk assessment practice. The results show that the risk assessment results obtained by this method are highly consistent with the actual situation, which not only proves the applicability and superiority of the random forest algorithm in the risk assessment of bridge construction but also provides a reference example for the subsequent risk assessment of similar projects. The results of this study can guide bridge construction practice: bridge construction units can learn from this model to conduct detailed risk assessments at the early stage of a project, identify and deal with potential risks in advance, and ensure construction safety and progress. Optimize the risk management process: Through the risk assessment system integrated with the random forest algorithm, risk data can be processed automatically and intelligently, improving the efficiency of risk management and reducing human error. Promoting industry standardization: The methods and models of this study can provide references for the development of risk assessment standards in the bridge engineering industry, and promote the improvement of the risk management level of the entire industry. Deepening algorithm application: Future research can further explore the application of other advanced machine learning algorithms in bridge risk assessment, continuously optimize model performance, and improve the accuracy and breadth of risk assessment. Cross-___domain integration: The research results of bridge risk assessment are combined with other engineering fields, such as roads, tunnels, etc., to promote the overall progress in engineering technology. In conclusion, this study not only provides a novel and effective solution for bridge construction risk assessment but also points out the direction for the future development of bridge engineering risk management.

Statistics of bridge collapse accidents in China

Bridge engineering accidents date back to the early nineteenth century, the Nuremberg Saar Bridge in Germany collapsed in its second year, killing 50 people. In 1940, ta-Coma Narrows, an American suspension bridge built just four months ago, was destroyed by force eight winds. In 1980, a serious ship collision occurred in Tampa Bay, Florida, causing the collapse of the bridge and direct economic loss of tens of millions of dollars.

Until 2019, a number of Bridges at home and abroad collapsed or were damaged due to various reasons. This paper makes a statistical analysis of the time, place, casualties and causes of bridge collapse accidents in the world in recent five years (2014–2019) as shown in Table 1. As can be seen from Table 1, in the past 5 years, there were 28 bridge accidents in the world and 20 serious bridge accidents occurred in China, including 13 in the construction stage and 7 in the operation stage. Other countries, including Sweden and Italy, had nine bridge collapses, including four during construction and five during operation.

Table 1 List of bridge accidents worldwide during 2014 and 2019.
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Figure 1 shows the statistical results of accident classification according to the bridge construction period. In China, the number of accidents in construction period is larger than that in operation period, while in foreign countries, the number of accidents in construction period is smaller than that in operation period. The main reason is that China is still in the stage of infrastructure construction, while developed countries have completed the infrastructure construction. In short, the occurrence of these bridge accidents makes people realize that it is urgent and important to accurately evaluate the potential risks during bridge construction and operation.

Fig. 1
figure 1

Classified statistics of bridge collapse accidents.

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According to the investigation statistics and analysis of bridge accidents, we find that there are possibilities of dangerous accidents in different stages of bridge life cycle, such as construction, use and demolition. Small probability events and different risk factors may cause serious losses and consequences. The causes of bridge risk accidents mainly come down to two aspects: One is the reasons outside the bridge structure system, that is, natural factors (hydrology, geology, meteorology), human factors (design, construction, operation and management, vehicle overload, vehicle-ship collision); Second, the risk factors in the bridge structure system, such as design errors, construction factors, operation period maintenance caused by structural defects and insufficient or declining bearing capacity.

Bridges are faced with various risks from planning and design, construction, operation and final demolition. Identification and analysis of risks according to different sources of risks is conducive to more accurate identification and evaluation of project risks by decision makers, and is also helpful to formulate and implement effective preventive and early warning measures to avoid or reduce unnecessary losses. According to the above statistics, in China, bridge collapse caused by bridge construction accounted for the largest proportion, accounting for 41 percent, indicating the importance of construction to ensure bridge safety.

There are many factors that affect the safety of bridge construction. At present, risk analysis is generally recognized from five aspects: personnel, materials, equipment, theory and environment. According to the form of bridge structure, combined with the content of bridge construction management and the construction characteristics of different construction stages, the risk of the whole process of bridge construction is divided into units, and different risk factors are classified into each unit. It is difficult to consider each bridge structure and its various risks due to many factors such as different types of bridge structures, different technologies of construction units and different surrounding environments. Therefore, taking the relatively large beam bridge as the research object, a useful data set or data creation database is established by selecting appropriate main risk indicators to provide data basis for the establishment of the analysis model.

Random forest algorithm and its risk assessment process

Random forest algorithm

RandomForests (RF) algorithm 26 is a classifier group composed of multiple decisiontrees (DT). All decision trees are generated randomly to form RF, and there is no association between trees in the forest. Bootstrap method was used to randomly select several samples from the original sample set, and build decision trees on these samples respectively, and then form the combinatorial classifier. The specific algorithm process is shown in Fig. 2.

Fig. 2
figure 2

Random forest algorithm flow.

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Suppose the combinatorial classifier of the random forest is \({\text{h}}_{1} \left( {\text{X}} \right),h_{2} \left( {\text{X}} \right), \ldots ,{\text{h}}_{{\text{k}}} \left( {\text{X}} \right)\}\), where K represents the number of decision trees in the random forest, \(h\left( X \right)\) represents the output result generated by a single classifier for input vector X, the training set of each classifier is randomly sampled from the original data set (X,Y) subject to random distribution. Y is the corresponding classification result of the training set. The Margin Function is defined as follows:

$${\text{mg}}\left( {{\text{X}},{\text{Y}}} \right) = {\text{a}}v_{k} I\left( {h_{k} \left( X \right) = Y} \right) - max{\text{a}}v_{k} I\left( {h_{k} \left( X \right) = j} \right) \left( {j \ne Y} \right)$$
(1)

k is the training times of classifier; I() is an indicator function, it measures to what extent the number of correct classification is greater than the number of wrong classification. \({\text{av}}_{{\text{k}}}\) is the average value of the interval function. The smaller the interval function is, the lower the confidence level of model classification is. Generalization error is used to reflect the quality of the model, which can show the prediction level of the model by data other than the training set. The generalization error of the classifier set is defined as:

$$PE^{*} = P_{X,Y} (mg\left( {X,Y} \right) < 0)$$
(2)

Estimation of random forest generalization error:\({\text{ PE}}^{*} \le \overline{\rho }\left( {1 - {\text{S}}^{2} } \right)/{\text{S}}^{2}\), \({\overline{\rho }}\) is the correlation between the classifier set \(\{ {\text{h}}\left( {{\text{x}},\theta } \right):\theta \euro \Theta\)},θ is the random variable of a single decision tree subject to independent and identically distributed. The greater the correlation between trees in the forest, the worse the classification performance of random forest.

In the bootstrapping process, the generation of each decision tree requires self-sampling, and 1/3 of the data is not selected, this part of the data is called out-of-bag data(OOB). These data are not used to train the model, so they can be used for model validation. Random forest algorithm does not need cross-validation or separate test set to obtain unbiased estimation of test set error.

Feature evaluation and feature selection

The idea of feature importance assessment with random forest is to see how much contribution each feature makes to each tree in the random forest, then take an average, and finally compare the contribution of each feature. Contribution is usually measured by Gini Index or OOB error rate.

In this study, Gini significance score and mean decrease accuracy (MDA) of random forest were used as evaluation indexes for feature selection. Among them, variable importance measures are represented by VIM, assuming m features X1, X2, X3,…, Xm, Now calculating the Gini index score of each feature Xj, that is, the average change of the Gini feature in all RF decision trees. The Gini importance score VIM was obtained according to the Gini index variation before and after the decision tree branch of the random forest. The calculation formula of Gini index is:

$${\text{Gini}}\left( {\text{P}} \right) = \mathop \sum \limits_{k = 1}^{K} P_{k} \left( {1 - P_{k} } \right) = 1 - \mathop \sum \limits_{k = 1}^{K} P_{k}^{2}$$
(3)

k represents the number of categories of feature samples, and \(P_{k}\) represents the proportion of category k in all nodes. The importance of feature \(X_{j}\) in node M is the Gini index change before and after node M branches.

$$VIM_{jm}^{{\left( {Gini} \right)}} = GI_{m} - GI_{l} - GI_{r}$$
(4)

\({\text{G}}I_{l}\) and \({\text{G}}I_{r}\) represent the Gini index of the two new nodes after the branch. The importance of feature \(X_{j}\) on the i-th tree is:

$${\text{VIM}}_{{{\text{ij}}}}^{{\left( {{\text{Gini}}} \right)}} = \mathop \sum \limits_{m \in M} VIM_{jm}^{{\left( {Gini} \right)}}$$
(5)

Given a total of n trees, the sum of the importance of the feature \(X_{j}\) is:

$$VIM_{j}^{{\left( {Gini} \right)}} = \mathop \sum \limits_{i = 1}^{n} VIM_{ij}^{{\left( {Gini} \right)}}$$
(6)

After normalization, Gini importance score \(VIM_{j}\) is:

$$VIM_{j} = \frac{{VIM_{j} }}{{\mathop \sum \nolimits_{i = 1}^{c} VIM_{i} }}$$
(7)

The mean accuracy decline (MDA) was assessed against the out-of-bag sample (OOB) of the random forest. During the construction of each tree in the random forest, the training samples are randomly extracted and replaced. The training samples that are not drawn are called out-of-pocket samples. Let xj (j = 1,2,…, n) is the permutation feature, where n is the number of remaining features. For each decision tree f in the random forest, the corresponding OOB data is used to calculate its out-of-pocket data error, which is denoted as errOOBf. The out-of-pocket data error after the replacement feature xj plus noise interference is denoted as errOOBf*. The MDA score of \(X_{j}\) was:

$${\text{VI}}\left( {X_{j} } \right) = \frac{1}{ntree}\mathop \sum \limits_{f} \left( {errOOB_{f} - errOOB_{f}^{*} } \right)$$
(8)

The decision tree of random forest is ntree represents the number, and the characteristics of random forest decision tree and its replacement determine the accuracy of the model. By comparing the performance of a feature before and after it is replaced by a random value, the weight and importance of the feature can be inferred. Therefore, MDA scores directly measure the impact of each feature on model accuracy. In addition, on the basis of calculating the importance of features, the steps of feature selection are as follows: (1) calculate the importance of each feature and rank it in descending order; (2) determine the proportion to be removed, remove the corresponding proportion of features according to the importance of features, and get a new feature set; (3) repeat the above process with the new feature set until the remaining M features (m is the value set in advance); (4) according to the out-of-bag error rate corresponding to each feature set obtained in the above code, select the feature set with the lowest out-of-bag error rate.

Model evaluation index

The correctness of the model can only be accurately verified by using the appropriate evaluation indicators, in the random forest model, goodness of fitting \(R^{2}\) and mean square error MSE are two appropriate evaluation indexes. Goodness of fit \(R^{2}\) is used to test the fitting degree of regression model to sample data, ranging from 0 to 1. The larger the value is, the higher the fitting degree is. The mean square error (MSE) is used to show the dispersion degree of samples and is the sum of the absolute difference between the predicted value of the estimator and the actual observed value. The closer the mean square error (MSE) is to 0, the better. However, the MSE is also affected by the predicted value, the expressions of the two evaluation indicators are as follows:

$${\text{MSE}} = \frac{1}{N}\mathop \sum \limits_{i = 1}^{N} \left( {f_{i} - y_{i} } \right)^{2}$$
(9)

\(R^{2}\) is defined as follows:

$$R^{2} = 1 - \frac{u}{v}$$
(10)
$$u = \mathop \sum \limits_{i = 1}^{N} \left( {y_{i} - f_{i} } \right)^{2}$$
(11)
$$v = \mathop \sum \limits_{i = 1}^{N} \left( {y_{i} - \hat{y}} \right)^{2}$$
(12)

where u is the sum of residual squares (MSE * N), v is the total sum of squares, N is the number of samples, and i is each data sample, \(f_{i}\) is the predicted value of the model, \(y_{i}\) is the actual value label of sample point i, and \(\hat{y}\) is the average value of the real value label.

Conception of bridge construction risk assessment

Based on random forest algorithm, combined with the actual situation of bridge construction, the risk assessment model using random forest is constructed. The construction risk assessment model is mainly divided into two modules: modeling process and use prediction.

Firstly, the risk factors of bridge construction are identified and analyzed, and the relevant characteristic parameters are extracted, and formed the data set \({\text{D}} = \left\{ {\left( {x_{1} ,y_{1} } \right),\left( {x_{2} ,y_{2} } \right), \ldots ,\left( {x_{m} ,y_{m} } \right)} \right\}\); Then, the importance degree of index is calculated and sorted by random forest algorithm. Select several feature variables that have great influence on the algorithm, update the data set, and then train the algorithm. The network model is tested with project-specific data and compared with actual risk values. By adjusting the parameters, an evaluation model with high accuracy was obtained. Finally, the quality risk factor data of the project to be evaluated are input into the random forest model, and the risk assessment objective is obtained. The specific algorithm design process is shown in Fig. 3.

Fig. 3
figure 3

RF method of bridge construction risk assessment.

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Risk assessment of bridge construction based on random forest algorithm

Bridge construction risk assessment index system

The primary work of bridge construction risk assessment is to establish the evaluation index system. Due to the different risks of bridge construction, the consequences are different in severity. In risk identification, neither all risk factors can be included into the risk analysis system, nor can some serious risk loss factors be omitted, and otherwise it will affect the decision results.

Based on the existing research results 27,28,29,30, combined with the actual characteristics of bridge engineering construction, this paper establishes the bridge engineering construction safety risk evaluation index system according to 4M1E31, as shown in Table 2.

Table 2 Safety risk assessment index system of bridge construction.
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In order to maintain the consistency of the evaluation results of prediction data standard, on the classification of tectonic attribute set, according to “highway bridge and tunnel engineering construction safety risk assessment guide” 32, combined with the engineering practice, the scope of the project risk assessment is divided into five, namely rather low, low, medium, high risk, super, as shown in Table 3.

Table 3 Evaluation table of project risk grade.
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Determination of sample data of bridge construction risk factors

According to the bridge construction risk assessment index system established in this paper, relevant data of 10 Bridges are collected and normalized, as shown in Table 4. The 10 bridge risk level is low risk, low risk, moderate risk and high risk, by calculated their evaluation value is (0.171, 0.265, 0.279, 0.201, 0.171, 0.281, 0.316, 0.308, 0.312, 0.613). The risk assessment levels of these 10 Bridges are based on the actual data in the construction process, the bridge construction risk assessment index system carefully constructed in this paper is quantitatively analyzed, and after normalization processing, the random forest algorithm is used to train and test a large number of data. The algorithm automatically identifies key risk factors and assigns a corresponding value to each bridge based on the combined impact of these factors to determine its risk level (low risk, medium risk or high risk). This process embodies the scientificity and accuracy of data-driven and statistical methods in bridge construction risk assessment, and ensures the objectivity and reliability of assessment results.These data are used as the training and testing sample space of random forest algorithm.

Table 4 Risk index data of bridge construction.
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The transformation of data sources into risk assessment index system is a systematic process, which includes data collection, data preprocessing to remove noise and standardize formats, feature selection by random forest algorithm, identification of the most influential factors for risk assessment, and finally construction of a multi-dimensional and comprehensive risk assessment index system. This process ensures the scientificity and accuracy of the evaluation system, and provides a solid foundation for the subsequent model building and risk assessment.

Establish RF risk assessment model and validation

Based on the basic principle and construction method of data modeling mentioned above, the corresponding risk assessment system of bridge construction risk is established. The feature quantities in Table 4 are used to construct the input sample space for the training of random forest algorithm. Since the sample data is relatively small, in order to make the results more reliable, the whole data set is randomly divided into training set and test set by 8:2, so the training set and test set are different each time.

The prediction accuracy of the model was judged by the mean square error (MSE) and goodness of fit \(R^{2}\). Goodness of fit \(R^{2}\) is used to test the fitting degree of regression model and sample data, ranging from 0 to 1. The larger the value is, the higher the fitting degree is. The mean square error (MSE) is used to show the dispersion degree of samples, and the closer MSE is to 0, the better. In this experiment, the optimal training model was obtained after many times of training and constant adjustment of parameters. The \(R^{2}\) of this model is 0.8935, MSE is 0.0015, and the accuracy of the model is good, which verifies the reliability and accuracy of the model and can be used to evaluate the risk of bridge construction.

Index importance analysis

In order to improve the training speed and effect, the indicators need to be improved. Rank the importance of attributes according to the real situation of the samples to be tested. These redundant information have an adverse effect on the establishment of RF model, so it is necessary to carry out feature screening, that is, to retain the factors with higher importance. The principle of Variable Importance Measures (VIM) with RF is to calculate the contribution of each feature to each tree in the random forest, and then compare the contribution of each factor. The importance ranking of each risk factor index was obtained through model training, as shown in Fig. 4.

Fig. 4
figure 4

Importance score of random forest variables.

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As can be seen from Fig. 4, in the bridge construction risk assessment index system established in this paper, the communication and coordination of the project participants, the maximum span of a single hole of the bridge, the number of system changes, the matching degree of equipment, the experience of technical personnel, and the traffic flow are the most important factors that constitute the risk of bridge construction, which is basically consistent with the bridge construction theory.

At the same time, it is also found that the mechanical failure rate, safety education, building materials, basic wind pressure and other indicators, index importance decreased significantly. In order to further explore the action rules of each feature, the top 14 variables were selected as input variables to reconstruct the random forest model and the prediction accuracy and \(R^{2}\) were shown in Table 5. It can be seen that the performance of the model is improved after removing the index of low-impact factors. Considering the efficiency and difficulty of actual evaluation, several important indexes can be selected to predict the risk degree of bridge construction.

Table 5 Comparison of prediction errors of different numbers of indicators.
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It can be seen that the mechanical failure rate, equipment renewal, safety education, earthquake grade, basic wind pressure and other indicators have little influence on the final assessment results of overall risk. Because in the actual construction, the use of machinery, earthquake grade, safety education and basic wind pressure are usually fully demonstrated and considered in the process of bridge site selection and construction, so these factors have a relatively small impact on the probability of bridge accidents.

The technical level of the engineering personnel, the communication and coordination of the project participants, the number of changes in the bridge structural system, geological conditions and equipment matching degree and other more than a dozen indicators have an important impact on the risk judgment results. Of course, if different index systems are used, there are certain differences in the importance ranking of risk factors, because different regions and their environments, the risk factors of bridge construction have certain differences. Therefore, in the process of using the method in this paper, it is necessary to select, adjust and evaluate the bridge according to the actual situation of the specific project.

Case analysis and discussion

Typical case analysis and application

The pedestrian bridge in Xiamen city, China, it is a steel–concrete composite continuous beam and suspension cable composite bridge. The span arrangement is 20*5 (steel–concrete composite continuous beam segment) + 70.5 m (suspension cable segment), the deck width is 4.4 m, and the bridge section is in the form of thin-walled flat steel box girder. As the footbridge is located in the center of the city, the surrounding environment of the footbridge is complicated. The concrete scene of the bridge is shown in Fig. 5.

Fig. 5
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Pedestrian bridge of a combination system in Siming District, Xiamen City.

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According to the construction data and site investigation, the above analyzed risk index data affecting bridge construction safety are normalized, and the index data are as follows: (0.510, 0.356, 0.300, 0.498, 0.521, 0.560, 0.300, 0.479, 0.397, 0.360, 0.647, 0.153, 0.682, 0.600, 0.800, 0.600, 0.416, 0.428, 0.497, 0.511, 0.680, 0.623, 0.699, 0.463, 0.700, 0.525), at the same time, important indicators were selected based on the importance of the above indicators. Fourteen important indicators were selected and the data of these 14 indicators were input into the random forest algorithm, and the predicted value was 0.412.

As can be seen from Table 3, the risk assessment result of the urban complex pedestrian bridge project based on the method in this paper is medium risk, which is consistent with the risk assessment result of the bridge in literature 33, which further verifies the correctness of the method proposed in this paper. Now, the pedestrian bridge has been successfully completed and put into use. In the actual construction process, there has been no risk accident of casualties. The construction process is relatively smooth, and the project is completed according to the expected effect.

In exploring the risk assessment process of this unique steel–concrete continuous beam-suspension pedestrian bridge in Xiamen, China, the stochastic forest algorithm based risk assessment model adopted in this study has the advantage of being able to process complex and variable input data and effectively identify key factors affecting the bridge's construction safety. This method is not only applicable to steel–concrete composite Bridges, but also can be extended to other types of bridge structures, such as prestressed concrete Bridges, arch Bridges, cable-stayed Bridges, etc., providing strong support for the risk assessment of various bridge projects. The model ensures the comprehensiveness and flexibility of the evaluation system by selecting 14 important indexes covering construction environment, technical conditions, material properties, and other dimensions. This design makes the model applicable to bridge construction projects in different regions and under different climatic conditions and provides a reference frame for the risk assessment of bridge engineering. The ability of the random forest algorithm to deal with nonlinear relationships and interactions enables the model to dynamically adjust the risk assessment results based on constantly updated data during the construction process. This is of great significance for dealing with unforeseen factors, design changes or external environment changes that may occur in bridge construction, and ensures the timeliness and accuracy of risk assessment.

In addition to risk assessment, the model can also provide scientific basis for decision-making in the process of bridge construction. By identifying high-risk areas and key links, project managers can take targeted preventive measures or optimize construction plans, thereby effectively reducing construction safety risks and improving project quality and efficiency. This study provides a new idea for the standardization of bridge engineering safety management by verifying the effectiveness of random forest algorithm in bridge risk assessment. With the continuous accumulation and improvement of similar studies, it is expected to form a unified bridge risk assessment standard system to promote the standardized development of the industry. Combined with modern information technology such as the Internet of Things and big data, the risk assessment model is embedded into the intelligent system of bridge construction management to realize real-time monitoring and risk early warning of the construction process. This will greatly enhance the intelligent level of bridge construction and contribute to the construction of a safe, efficient, and green modern transportation system. Through scientific and objective risk assessment results, showing the public the security measures and risk control capabilities in the process of bridge construction will help enhance public confidence in the safety of Bridges and promote social harmony and stability. In summary, this study not only provides a strong guarantee for the successful construction of the pedestrian bridge in Xiamen but also demonstrates the wide applicability and far-reaching impact of the risk assessment model based on the random forest algorithm in the field of bridge engineering.

However, hidden dangers in the process of bridge construction also threaten the service life and safe operation of pedestrian bridge. The average time for engineers to complete a single project with machinery is long, which reflects the low proficiency of construction technicians in the operation and use of engineering machinery. If the construction personnel of the use of engineering machinery proficiency is not enough, it will lead to improper operation in the process of construction and the threat to the construction personnel.

Therefore, for the complex composite system of pedestrian bridge, in order to ensure smooth construction, the owner, the construction affiliate, the design affiliate and the supervision affiliate form a liaison mechanism, carry out project construction status analysis, characteristics analysis, identification and control analysis, and put forward risk control, risk retention, risk transfer and other control strategies, so as to reduce the bridge construction risk level thus ensure the quality and benefit of bridge engineering and guarantee the normal operation of bridge engineering.

Discussions

There are a lot of uncertainties in the risk assessment during bridge constructions, which are mainly reflected in the diversity of accidents, the uncertainty of the spatial and temporal distribution of parameters, the accuracy and completeness of information and data collection, as well as the rationality and completeness of the processing of assumptions, simplification and boundary conditions. In this paper, we propose a risk assessment method based on random forest, a complex pedestrian bridge is taken as an example for evaluation and verification.

Example analysis shows that the index system of bridge construction risk assessment established in this paper, in the process of bridge construction, the top 5 key factors affecting the safety of bridge construction are the technical level of engineering personnel, the communication and coordination of project participants, the change times of bridge structural system, geological conditions and equipment matching degree. At the same time, it can be seen that since the random forest can score the importance of each variable, after selecting risk factors through the random forest algorithm, the risk assessment model obtained by training is higher in terms of \({R}^{2}\), RMSE and other indicators than those without the random forest algorithm for feature selection. Therefore, it is necessary to analyze and select the importance of indicators to improve the training speed and accuracy.

In addition, risk is the combination of accident possibility and accident consequence severity, and is nonlinear. After determining the main effective causes of the risk, corresponding risk response measures should be taken to reduce or transfer the risk. There are some risks in the preliminary design risk assessment of the complex footbridge in this paper,and it was completed successfully through risk transfer. At the same time, the definition of risk level still needs the continuous development of the bridge construction risk assessment work, and the practice of testing and modification, to enrich and improve the risk assessment system.

Conclusion and future development

In this paper, a new exploration is made on the establishment method of bridge risk assessment index system. The random forest algorithm is combined with the bridge construction safety risk assessment system, and a relatively accurate method for the establishment of risk assessment model is given, which solves the modeling problem of determining the weight of risk index by using the existing engineering data. Taking the risk assessment of the construction process of urban complex footbridge as an example, the risk level of the construction of the bridge is quickly obtained, which is basically consistent with the actual risk level of the bridge. This method can be well applied to the data processing of risk analysis.

This paper analyzes and classifies the artificial and environmental risk factors that affect the bridge construction stage, and establishes 26 risk factors in 5 categories according to the characteristics of bridge construction and the actual situation of the project. At the same time, the random forest algorithm, SVR, Bagging, and regressor were used for comparative analysis and research in the early stage of the test to analyze the error results of different prediction models, and the results show that the random forest algorithm has obvious advantages compared with other methods. Based on the advantages of the random forest algorithm and the characteristics of bridge construction risk, the random forest algorithm is used to evaluate the bridge construction risk, and the importance of the index is sorted, and the index that has a greater impact on the risk is identified.

The random forest algorithm is used to evaluate the risk of bridge construction. It is found that the model established by random forest method can accurately evaluate the risk probability of bridge with fewer parameters, which greatly improves the calculation efficiency, reduces the difficulty of sample collection, is more convenient to use, and the model has good generalization ability. This method provides a new idea for further study of bridge construction safety risk assessment in the future.

At the same time, we can use the powerful function of data mining technology to process the existing bridge construction safety risk assessment information, establish a data warehouse, use data mining tools to find the association rules, and conduct classification, cluster analysis, so as to further evaluate its development trend, to provide managers with reliable risk management basis.

It can be predicted that with the rapid development of artificial intelligence technology and the high integration of artificial intelligence algorithm and bridge construction, it is bound to provide effective solutions for risk assessment in all stages of bridge construction, even operation and maintenance.