1. Introduction
In globalization and urbanization, bridges, as crucial transportation facilities connecting cities, have consistently garnered significant attention regarding their construction quality and long-term performance. Particularly in China, recent years have witnessed massive infrastructure construction, driving rapid advancements in bridge engineering technology. However, the deflection phenomenon occurring during the construction phase of steel box girder bridges impacts the regular use of bridges and poses potential threats to public safety [
1]. Such incidents underscore the urgency and importance of assessing deflection risks during the construction phase of steel box girder bridges. Simultaneously, the stringent government regulation of infrastructure safety and the public’s heightened concern for structural safety [
2] provide vital policy and social contexts for this research. Against the backdrop of the digital economy and sustainable development, utilizing advanced technologies and methodologies for risk assessment [
3] to reduce unnecessary material usage, repeated construction, and lower carbon emission intensity represents a significant trend in current research [
4].
Numerous scholars globally have conducted in-depth research on the issue of deflection risks during the construction phase of steel box girder bridges. These studies encompass theoretical analysis, experimental validation, numerical simulations, and other aspects, aiming to enhance the accuracy and efficiency of risk assessment. For instance, Pan et al. [
5] employed the ABAQUS finite element software 6.1 to conduct a detailed stress analysis of steel box girder bridges during the construction phase, successfully predicting the occurrence areas of deflection, demonstrating the powerful capabilities of the finite element method in simulating complex structural behaviors. Cho et al. [
6], using ANSYS software 14.0, established a refined model of steel box girder bridges, evaluated deflection risks through simulation analysis of the construction phase, and proposed corresponding preventive measures.
In the context of the rise of the digital economy and the popularization of sustainable development, the combination of the genetic algorithm GA and BP provides a new idea for risk assessment of complex structures. BP is a multi-layer feed-forward neural network that adjusts the weights and biases to minimize the prediction error. GA simulates the process of biological evolution and searches for the optimal solution through selection, crossover, mutation, and other operations. GA-BP can be used for bridge safety assessment and health monitoring, dealing with multi-objective and multi-constraints, predicting structural state, and improving design efficiency and quality. Morab et al. [
7] applied genetic algorithms to the construction optimization of steel box girder bridges, effectively reducing deflection risks by optimizing construction sequences and material usage. Li [
8] utilized BP neural networks to predict deflection in steel box girder bridges, establishing a mapping relationship between deflection risks and construction parameters.
Of particular note, Wang et al. [
9] were the first to integrate finite element analysis with the MEC-BP algorithm for deflection risk assessment during the construction phase of steel box girder bridges. They provided training data through finite element simulations and optimized the risk assessment model using the GA-BP algorithm, achieving remarkable results. This research provides a valuable reference for combining finite element analysis with the GA-BP algorithm in deflection risk assessment during the construction phase of steel box girder bridges.
Mustafa [
10] employed Support Vector Machines (SVMs) for categorical prediction of deflection risks in reinforced concrete box girder bridges. This demonstrates SVMs’ risk assessment superiority compared to other machine learning algorithms. García-Segura [
11] adopted a multi-objective design based on artificial neural networks to optimize the construction process of box girder bridges, considering multiple objectives such as construction cost, safety, and corrosion initiation time. Despite using different algorithms and technologies, both studies reflect the significant role of neural networks or related machine learning technologies in risk assessment and construction optimization in bridge engineering.
Apart from the research above, other scholars have conducted beneficial explorations in deflection risk assessment during the construction phase of steel box girder bridges. Lee [
12] utilized Bayesian Networks for probabilistic reasoning on deflection risks during the construction phase of steel box girder bridges. By constructing dependency relationships among risk factors, they achieved a dynamic assessment of deflection risks, providing a more flexible and dynamic approach to risk assessment. Liu [
1,
13] conducted a sensitivity analysis on deflection risks during the construction phase of steel box girder bridges. By altering construction parameters and material properties, they assessed the influence of various factors on deflection risks, providing crucial insights for risk control and optimization. Finally, Khan et al. [
14] designed a sophisticated real-time monitoring system for collecting comprehensive data on stress, deformation, and other parameters during the entire construction process of box girder bridges. The authors evaluated deflection risks using advanced data analysis methodologies, thereby illustrating the promising potential of real-time monitoring technology in assessing risks during bridge construction.
This research falls within the interdisciplinary field of civil engineering and computer science, focusing on risk assessment in structural engineering. By integrating field monitoring, the finite element method, sensitivity analysis, artificial neural networks, and other methods, this study delves into the impacts of structural parameters, environmental parameters, foundation settlement, and other factors on the deflection of steel box girder bridges. Firstly, a finite element model is established and validated to simulate and accurately predict mechanical behaviors during construction. Secondly, sensitivity analysis is conducted to identify sources of deflection risks, yielding key risk factors. Finally, a neural network model is established and trained to alleviate the computational burden of finite element analysis and improve risk assessment efficiency. Hopefully, this research can provide a more scientific, accurate, and efficient technical solution for construction monitoring and risk assessment of steel box girder bridges, offering robust support for improving construction quality and safety and ensuring long-term stable operation of bridges.
3. Neural Network Modeling
3.1. BP Neural Network Algorithm Based on Genetic Algorithm
The BP neural network model is a multi-layer feedforward network trained using the BP algorithm. According to the Universal Approximation Theorem proposed by Robert Hecht-Nielsen, a three-layer BP neural network can adequately approximate arbitrarily complex nonlinear relationships, demonstrating high self-learning and adaptive capabilities [
22]. An artificial neural network (ANN) is a biomimetic mathematical model that possesses learning abilities akin to the human brain and the capacity to judge based on learned information, enabling the processing of data and information [
23]. The BP neural network is one of the most widely applied neural network models, characterized by forward signal transmission and error backpropagation. It employs the steepest descent method and utilizes genetic algorithms to iteratively adjust the network weights according to the training objective function, thereby identifying the optimal initial network weights. Through backpropagation, the network weights are continuously adjusted to minimize the sum of squared errors. Initially, the safety assessment indicators of bridges are classified, and characteristic indicators are extracted as input information fed into a three-layer network comprising an input layer, a hidden layer (or layers, depending on user requirements, with more than one hidden layer constituting a deep learning architecture), and an output layer for training. Once trained, the network becomes a stable pattern evaluator capable of outputting assessment results [
24,
25].
The BP neural network can be regarded as a nonlinear function, with the network input and output values serving as this function’s independent and dependent variables, respectively. When the number of nodes in the input layer is n, and the number of nodes in the output layer is 1, the BP neural network expresses a functional mapping relationship from n independent variables to one dependent variable. The classic BP neural network consists of three parts: an input layer, a hidden layer (or layers, depending on user requirements), and an output layer. The specific structure used in this study is illustrated in
Figure 12.
In selecting a method for under-deflection risk prediction of highway interchanges, the traditional BP neural network is used for prediction rather than popular methods such as ASAPSO-CNN, DCNN, or CNN-BiGRU. First, the BP neural network, as a classical and widely used neural network model, possesses robust nonlinear mapping ability and good generalization performance. It efficiently learns and models the input–output relationship of complex systems, which is crucial for predicting the under-deflection risk of interchanges. In contrast, despite its effectiveness in steel bridge damage identification [
26], the design intention and advantages of ASAPSO-CNN are more focused on domain-specific damage identification. It may only partially apply to the generalized prediction scenarios of the under-deflection risk of interchange bridges. Furthermore, DCNN has significant applications in recovering missing measurement data in structural health monitoring [
27]. However, in predicting the under-deflection risk of interchanges, we are more concerned with utilizing the existing data to predict future risk scenarios rather than recovering the missing data. Consequently, although DCNN is excellent in addressing missing data, it may not be the best choice for predicting under-deflection risk. Moreover, CNN-BiGRU combines the advantages of CNN and BiGRU to handle time-series data efficiently and has achieved significant results in reconstructing the accelerated response of structures subjected to extrusion at ambient temperature [
28]. However, predicting the under-deflection risk of interchange bridges requires processing time series data and considering the combined effects of multiple factors (e.g., bridge structure, material properties, traffic loads). Hence, although CNN-BiGRU performs well in handling time-series data, it may not comprehensively capture and predict all the influencing factors of under-deflection risk. In contrast, although popular methods perform well in some areas, they may not fully apply to the prediction scenarios of under-deflection risk of interchanges.
3.2. Principles of Genetic Algorithms
GA is a heuristic optimization algorithm that can conduct a comprehensive global search across the entire search space, thereby circumventing the trap of local optimal solutions. Structural damage identification problems frequently exhibit complex search landscapes and nonlinear behaviors, characteristics that GA can efficiently address. GA is robust to initial population and parameter settings, has strong adaptability and stability, and can sustain optimal performance across diverse environments and conditions [
29]. GA does not depend on the gradient information of the objective function and can optimize noncontinuous, non-differentiable, or high-dimensional objective functions. When subjected to temperature variations, the dynamic parameters of the structure will alter, and GA can accommodate these changes through dynamic adjustments to the population’s iterative update process. Consequently, GA is selected for parameter optimization due to its advantages above.
GA-BP is to use a genetic algorithm to optimize the initial weights and thresholds of BP neural networks so that the optimized BP neural networks can better predict the function output. The process of GA optimization of the BP neural network can be divided into the following steps:
1. Population initialization. The individual coding method is real number coding. Each individual is one real number string, which consists of 4 parts: input layer and hidden layer connection weights, hidden layer threshold, hidden layer and output layer connection weights, and output layer threshold. Individuals contain all the weights and thresholds of the neural network, thus constituting a neural network with a defined structure, weights, and thresholds.
2. Determine the fitness function. The initial weights and thresholds of the BP neural network are obtained according to the individual, and the BP neural network is trained with the sample data and the sum of the absolute values of the errors between the predicted outputs and the actual values, e, is taken as the individual fitness F. The BP neural network is trained with the sample data.
where n is the number of network output nodes; y
i is the desired output of the ith node of the BP neural network; o
i is the predicted output of the ith node; and k is the constant factor.
Selection operations. Genetic algorithm selection operation has roulette method, tournament method, and so on. In this paper, we choose the roulette method, i.e., the selection strategy based on the proportion of fitness, and the selection probability of each individual is
.
where F
i is the fitness value of individual i. Since larger fitness is better, the inverse of the fitness value is taken before individual selection; n is the number of individuals in the population.
Crossover operation. Since the individuals are coded in real numbers, the crossover operation method is used in real number crossover, and the crossover operation for the first chromosome, and the first chromosome, in place, is shown in Equation (4).
Mutation operation. The first gene of the first individual is selected for mutation, and the mutation operation is described in Equations (5) and (6).
where A
max and A
min are the upper and lower bounds of gene A
ij, r
2 is a random number, g is the number of current iterations, G
max is the maximum number of evolutions, and r is the random number between [0, 1].
Calculate the fitness value F.
Determine whether the iteration of the algorithm is finished or not, if the fitness value is not satisfied, return to (3) and repeat.
The GA-BP is a process that encompasses three primary stages: determination of the BP neural network structure, optimization via genetic algorithms, and BP neural network prediction [
30]. Initially, the structure of the BP neural network is established based on the data samples, with the weights and thresholds of the network being initialized. Subsequently, the genetic algorithm encodes all individuals within the population, where the fitness value of each individual is computed using a fitness function. Ultimately, the optimal individual with the highest fitness value is obtained through genetic operators, representing the optimal initial weights and thresholds for the network. Finally, utilizing these optimal weights and thresholds, the network undergoes training to produce prediction results. The algorithmic workflow [
31] is illustrated in
Figure 13.
3.3. Training and Test Samples
Given the thousands of computational costs in subsequent risk analyses, this paper establishes a finite element surrogate model based on the GA-BP algorithm to simplify calculations. To train the risk assessment model for the bridge neural network established above, MATLAB R2023a’s Neural Network Toolbox is selected [
32]. The key risk factors during the construction phase of the B ramp of the Fuxing Interchange Bridge (structural self-weight and temperature difference between the top and bottom plates) and the vertical displacement of the main girder calculated using Midas Civil 2023 are used as training data. As demonstrated in Chapter 2, the mid-span deflection in the first span is the most severe. Thus, the deflection results of the first span are selected as the output of the neural network’s deflection results. The confidence interval for structural self-weight is [0.95, 1.05], with a step size of 0.01, resulting in 11 gradient values; the confidence interval for temperature difference is [
5,
30], with a step size of 1, yielding 26 gradient values. A total of 286 combinations are generated by freely combining these two risk factors, which are then substituted into the finite element model to calculate the corresponding deflections, resulting in 286 deflection data points. The modified combinations are inputs, and the corresponding deflection values are used as outputs to train the artificial neural network. Ninety percent of the data samples are selected as the training set for the neural network, while the remaining ten percent are used as the test set.
In the context of neural network training, utilizing 90% of the dataset ensures that the model is exposed to a vast amount of information, thereby facilitating the discovery of underlying patterns and relationships within the data. The remaining 10%, designated as the test set, provides an adequate and manageable sample size for validating model performance while mitigating the risks of overfitting or underfitting. However, in scenarios where the dataset is relatively small, adopting a split ratio such as 80–20% or even lower could potentially compromise the training process, as the reduced training set may not be sufficient for the model to learn from the data thoroughly, adversely affecting its performance. Furthermore, in cases of uneven data distribution, such splits may inadvertently introduce discrepancies between the training and test sets, ultimately impacting the accuracy of model evaluation.
Prior to utilizing the input–output data for neural network training, normalization of the data is often performed to prevent the magnitude of parameters from influencing the final learning outcome of the network. The normalization formula is as follows:
where
is the any value in the training data for a risk factor;
is the maximum value in training data for a risk factor;
is the minimum value in the training data for a risk factor;
is the input values in the training data for a particular risk factor.
3.4. Constructing a GA-BP Neural Network Model
The GA-BP model established in this study comprises an input layer with two nodes corresponding to the structural self-weight and the temperature difference between the top and bottom decks and an output layer with one node representing the vertical displacement of the main girder. The hidden layer, serving as the core component of the neural network, is responsible for processing the input data and extracting its features, thereby playing a pivotal role in the learning and modeling processes of the neural network. However, there is currently a lack of reliable research to determine the number of neurons in the hidden layer accurately. A neural network with too few neurons in the hidden layer may lack predictive capability, whereas an excessive number of neurons may lead to an increase in training time. In theory, increasing the number of hidden layers can improve the fitting ability of a neural network, which may improve the prediction accuracy. This is especially true when the problem involves multiple interacting variables. However, increasing the number of hidden layers also poses a risk of overfitting. Overfitting is when a model performs well on training data but poorly on unseen test data.
where m is the number of hidden layer neurons; n is the number of output layer neurons; l is the number of input layer neurons;
is the constant from 1 to 10.
In this study, the fitness function in the genetic algorithm is selected as the error function in the BP algorithm to optimize the initial weights and thresholds of the BP neural network using the genetic algorithm.
where
is the number of training samples;
is the neural network prediction data for the jth sample;
is the output data for the jth sample.
This study integrates empirical formulas with neural network training experiments, determining an optimal number of hidden layer neurons as 8. Consequently, the structure of the BP neural network is established as a 2-8-1 configuration, comprising an input layer with two input features, eight hidden layers, and one output layer. BP neural networks have three training functions: the Levenberg–Marquardt function, the Bayesian regularization function, and the scaled conjugate gradient function. The Levenberg–Marquardt function was selected in this research due to its fast training speed and ability to rapidly iterate the training process until satisfactory error results are obtained.
It also explores measures to reduce data complexity to improve accuracy. Before neural network training, the interference of redundant features on model performance is reduced by characterizing the dataset and selecting features that significantly impact the target variable for training. This approach not only reduces the complexity of the data but also improves the generalization ability of the model [
33,
34]. In the data preprocessing stage, we standardized the dataset by unifying the feature values of different magnitudes to the same magnitude, thus eliminating the impact of magnitude differences between features on model training.
5. Discussion
This study discusses the deflection risk of steel box girder bridges under the influence of temperature difference between the top and bottom slabs and the self-weight of the structure and quantitatively analyzes and predicts the degree of deflection. It was found that the GA-BP neural network model prediction can simulate the nonlinear relationship between structural response and risk factors well. These findings help to provide a scientific basis for risk management, construction optimization, and safety assurance of future bridge projects, as well as to improve the overall quality and safety of bridges.
The GA-BP method improves the sustainability of bridge construction by minimizing waste, reducing carbon emissions, and optimizing resource use. It achieves the goal of sustainable development by preventing unnecessary material use and duplication of construction. GA-BP incorporates finite element analysis for greater accuracy and adaptability than traditional methods and has potential in other engineering fields. The limitation of this study is the focus on ±5% variation in self-weight during construction, which, while representing common load fluctuations, may require a more extensive range (e.g., ±10% or more) for specialized or complex bridges to assess performance under extreme conditions. Due to limited training data, the GA-BP model may be limited in its generalization ability, which may reduce prediction accuracy. The model may also exhibit instability with new data. Improvements that can be made in future research include increasing the range values of the influencing factors, expanding the dataset, augmenting the data, tuning the model, and introducing new algorithms. Real-time monitoring, exploring additional risk factors, and applying it to large projects and life cycle assessments.
6. Conclusions
Assessing structural safety risks during bridge construction is a pivotal concern within bridge engineering. This study, exemplified by the Fuxing Interchange Bridge, employs methodologies such as FEM, regression analysis, GA, and artificial neural networks to quantitatively evaluate the risk of steel box girder deflection during construction through sensitivity analysis of risk factors. Furthermore, BP and GA-BP neural network models are established to predict the degree of steel box girder deflection influenced by various factors. Overall, the GA-BP neural network model exhibits more stable predictions and minor relative errors than the BP neural network model, effectively simulating the nonlinear relationship between structural responses and risk factors. Specific conclusions are drawn as follows:
(1). The temperature difference between the top and bottom plates is the primary factor influencing steel box girder deflection. A maximum increase in deflection of 10.3 mm occurs when this temperature difference reaches 30 °C. In comparison, a 1.55 mm increase in deflection is observed when the structural self-weight is 1.05 times its average value. The maximum deflection of the main girder exhibits the highest sensitivity to structural temperature, followed by structural self-weight and bearing settlement. Consequently, temperature differences between the top and bottom plates and structural self-weight are selected as key risk factors affecting structural safety during the construction of the interchange bridge.
(2). By measuring the deflection changes after temperature variations in the weather, measurement points A1 on the top plate and A2 on the bottom plate of the tested cross-section, and comparing them with numerically simulated deflection values, a substantial consistency is observed, validating the accuracy of the finite element model. As the temperature difference between the top and bottom plates increases, the numerically simulated deflection values also increase significantly, indicating that predicting the deflection of the unfinished girder sections can aid in assessing structural safety.
(3). To identify risk sources impacting structural responses, a finite element model is utilized to compute a certain number of structural responses. The risk factors and corresponding structural responses are then output as training samples to train both BP and GA neural network models separately. The GA-BP neural network model yields more stable predictions and minor relative errors than the BP neural network model, effectively simulating the nonlinear relationship between structural responses and risk factors.
(4). The findings of this study offer valuable insights into the construction control of steel box girder bridges. Potential structural issues can be promptly identified by predicting potential deflection scenarios, and necessary measures can be taken to ensure structural safety. However, due to time and resource constraints, this study did not comprehensively cover all possible construction risk factors, potentially limiting the assessment results in specific scenarios. Therefore, future research should further refine the assessment model, enhance the objectivity and accuracy of parameters, and consider various construction risk factors as comprehensively as possible to provide more precise and comprehensive structural safety risk assessment methodologies.