Research for Pedestrian Steel Bridge Design of Neural Network in Structural Model Updating

The application of the neural network method in health monitoring and structural system identification has received extensive attention. A reasonable neural network structure is very important for its performance. This paper takes the pedestrian bridge of the Xingfu intersection in Urumqi, China, as the research object and uses MIDAS/Civil to establish a finite element analysis model. Taking the natural vibration frequency obtained from the dynamic test of the actual bridge as the target, two kinds of neural networks are used to predict the structural material parameters. An appropriate bridge model correction method is selected by comparing the prediction results of the BP neural network and the GRNN. The test results show that the pedestrian bridge model based on MIDAS/Civil has a high accuracy, but it still does not meet the actual needs. The modified model based on the BP neural network is close to the actual measured results, and a more accurate finite element analysis model can be established by this method, which makes the modified model closer to the real stress state of the structure.


Introduction
e long-term health inspection of steel structure bridge is of great signi cance to its safety, and the current measures to ensure the long-term safety performance of the bridge mainly focus on the inspection and reinforcement. e health monitoring and prediction of bridges are based on nite element analysis. Firstly, the measuring points are arranged at each node of the bridge, and the measured data (concrete strength, de ection value, strain value, and loworder natural frequency of the bridge) are collected. en, the nite element model is established according to the existing design drawings and combined with external conditions. e state of the bridge is judged by the correlation analysis between the measured value and the calculated value. However, the measured results are often di erent from the calculated results of the bridge nite element model, and the degree of di erence often determines the evaluation results of the bridge. erefore, the establishment of a more accurate nite element model is the basis of structural analysis. Due to the discreteness degree of the nite element model, the setting of modeling parameters, some simpli ed assumptions are used in modeling, and the calculated values of the nite element model bring errors. In addition, the initial nite element model established strictly in accordance with the design drawings cannot actually re ect the mechanical behavior of the structure due to the in uence of material performance deviation, structural degradation or damage, and other factors [1]. erefore, it is necessary to modify the bridge nite element model according to the measured results of bridge detection to improve the accuracy and reliability of the bridge nite element model. e essence of nite element model modi cation is an approximation problem, and one or several indexes of the nite element model are in nitely close to the real value by modifying various parameters of the nite element model.
Using a neural network to modify the nite element model can not only reduce the calculation times but also make the predicted results tend to close the actual value [2]. is paper mainly adopts BP neural network and GRNN. BP neural network (backpropagation neural network) is a kind of multilayer feedforward neural network. e error between the actual output and the expected output of the system is reduced by changing the connection weights among neurons, and the weights and thresholds between the hidden layer and the output layer are adjusted forward and backward according to the gradient descent method. GRNN (general regression neural network) is a feedforward neural network model based on the nonlinear regression principle. GRNN is improved based on RBF and has a similar structure. e difference lies in the addition of a summation layer and the removal of the weight connection between the hidden layer and the output layer (the least-square superposition of the Gaussian weight). e core factor of the stability of a building structure is determined by its own material and structure. It is predicted by the neural network, which makes the model reference. Alkayem et al. [3][4][5][6][7] proposed that improving the accuracy of the intelligent algorithm for computing model correction is a direction worthy of study and summarized the model correction methods based on the neural network comprehensively. In 2004, Fei et al. [8][9][10] used RBF neural network to conduct a revision study on the aircraft model, and the results showed that the design parameter error was within 2%, and the modal frequency error was within 1%. In 2012, Wang et al. [11,12] applied a neural network to the finite element model modification of a reinforced concrete bridge and verified that the modified finite element model could reflect the physical state of the structure more truly and better reflect the real dynamic characteristics of the bridge structure. In 2017, Jia et al. [13,14] modeled the PC hollow beam that has been in service for more than 20 years and modified it by using a neural network intelligent algorithm. e physical state between the modified finite element model and the actual structure is very close. e elastic modulus of the steel strand is consistent with the experimental value, and all errors are controlled within 5%. In 2018, Bao et al. [15][16][17] used MIDAS to establish a bridge model and BP neural network to modify the model based on the deflection. e deflection error of the modified bridge finite element model was less than 10%, and a good correction effect was obtained.
Previous studies prove that neural network has a good effect on model modification, but few scholars apply a neural network to model modification of pedestrian steel bridge. In this paper, BP neural network and GRNN in radial basis neural network are used as the correction method. Urumqi Xingfu Road pedestrian bridge is taken as the model to be modified. Taking the characteristic quantity as the independent variable and the steel design parameters as the dependent variable, the neural network intelligent algorithm is used to approximate the nonlinear mapping relationship between the two [18]. en, the generalization property of the neural network is used to solve the target value of design parameters directly. rough the reliability comparison and error analysis of BP neural network and GRNN training test results, a model modification method suitable for the pedestrian bridge was found.

Project Overview
Xinjiang Urumqi Xingfu Road pedestrian steel bridge was built in 2002 and is located at the intersection of the Urumqi beltway and Xingfu Road in Urumqi, China, as shown in Figure 1. e main pedestrian bridge has a net height of 5 m and a span of 23.763 m and 25.762 m, respectively. e main girder adopts a uniform cross-section single-cell box girder structure, which is 1 m high and 4 m wide, and the thickness of the roof is 10 mm, the thickness of the bottom plate is 16 mm, the thickness of the web is 12 mm, and the box girder internal welding 10 mm thick stiffening ribs. e bridge is equipped with 4 escalators, which are welded with the main beam. e width of the staircase is 2.5 m, and the heightwidth ratio of the steps is 1 : 3. e ladder beams are all steel box girder structure, with a height of 280 mm and the plate thickness of 10 mm. e piers are made of hot-rolled seamless steel tubes, with a wall thickness of 16 mm and a diameter of 426 mm. e foundation is an expanded concrete foundation, the balustrade is a carbon stainless steel composite steel pipe, and the bridge deck pavement adopts a 15 mm thick rubber plate; Q235B killed steel is used for the pier column and main beam steel plate, and Q235C killed steel is used for other members. e main components are welded in the factory and then transported to the site for welding and assembly.

Initial Model Establishment.
According to the design drawing size of the pedestrian bridge, the finite element model of the pedestrian steel bridge is established by using MIDAS/Civil. Semirigid rubber bearings were set for the main beam, escalator beam, and column of the pedestrian bridge, and consolidation boundary conditions were  . e finite element model is shown in Figure 2.
e dynamic characteristics of the pedestrian bridge model were analyzed by using the subspace iteration method. e first 5-order natural vibration frequencies of the pedestrian bridge are calculated as shown in Table 1.
According to the study of Fan et al. [20,21], the walking frequency of human is 2∼4 Hz, and the first 2 vibration modes of the bridge need only be considered in model modification and dynamic test of the real bridge for the pedestrian bridge.

Self-Vibration Characteristics Test.
e test was conducted in the early morning in order to minimize the influence of external factors such as the stream of people and vehicles on the dynamic test results. JMC2-2091 acceleration-type vibration pickup and JMYD-1016 dynamic information acquisition instrument from Jinma High-tech Institute Changsha China were used. e acceleration-type vibration pickup is fixed at each measuring point to record the acceleration waveform when the pedestrian bridge vibrates. It is connected to the dynamic information acquisition instrument through the cable, and the acceleration signal is amplified, recorded, and analyzed. Finally, the acceleration signal is connected to a laptop computer and stored on a disk for spectrum analysis (Figure 3). 11 measuring points are selected in this dynamic test, and the layout is shown in Figure 4. Cylindrical semirigid rubber bearing is set on the top of the column, it is considered that no displacement occurs at this point, so no measuring point is set on the top of the column. e test was divided into two groups, and the first group was the measuring points 1-1 to 1-7 ( Figure 4). In order to connect the test data of the two groups, position 1-7 of the first group was kept unchanged as the position 2-7 of the second group. e test system is shown in Figure 5.
DASP software was used to analyze the measured data after the test [22,23]. DASP software shows that the firstorder vertical natural vibration frequency obtained from the dynamic test of the pedestrian bridge is 4.9804 Hz, and the second-order vertical natural vibration frequency is 5.9765 Hz. ere is some error between the test results and the finite element calculation results.
It can be seen from Table 2 that the maximum error of the initial model of the pedestrian bridge established by MIDAS/Civil is only 10% in strict accordance with the design drawings, which has high accuracy. e initial model error is small, the degradation of material properties causes the error, and the parameters of materials in the structure can be predicted using neural networks [24,25].

Factors Affecting Natural Vibration Frequency.
According to equations (1) and (2) for the approximate solution of the natural vibration frequency of the structure by the energy method given in the study of Ye et al. [26][27][28], the influencing factors of the natural vibration frequency of the structure can be determined.
where f is the frequency; ω is the circular frequency; E is the elastic modulus of material; I is the section moment of inertia; Y(x) is the sectional shape function; Y i is the amplitude of the particle m i ; m is the weight; l is the structural span.  Shock and Vibration e natural vibration frequency of the structure is related to the elastic modulus of the material, sectional structure, material density, and the structural form of the bridge according to (1) and (2). According to the size, shape, weight, and allowable deviation of hot-rolled steel plate and strip [29,30], a certain size deviation is allowed in the actual production process of components. e elastic modulus and density of components are the same, and the speci c range is shown in Table 3.

Sensitivity Analysis of In uencing Factors.
e sensitivity of candidate parameters should be identi ed rst, and insensitive factors should be eliminated when selecting correction parameters. Because the nonsensitive coe cient has no obvious correction result to the model during the correction, the correction has little signi cance. erefore, the model should be modi ed by modifying the sensitivity coe cient. Figure 6 shows that the elastic modulus and density of materials are the main factors a ecting the natural vibration frequency of structures. e sensitivity of the same parameter is not the same under di erent vibration modes. If only one mode is used as the correction target, the model modi cation will cause a certain deviation from the rest modes. erefore, di erent vibration modes of the model to be modi ed should be taken as the correction target at the same time. In the rst-and second-order cases, the elastic

Sample Selection.
A neural network algorithm mainly simulates the neural structure and working principle of biology to carry out mathematical modeling of the complex mapping relationship between input and output values [31]. Using a neural network to modify the computational model can not only avoid the iterative solution based on inverse problem model modi cation but also avoid the uncertainty and complexity of nonlinear optimization. e input layer, hidden layer, and output layer together constitute the basic structure of the neural network, and its working principle is shown in Figure 7.
It is the set of right samples that are needed to provide for network optimization when you are building a neural network. e optimization process is to compare the calculated output value with the input sample value and then adjust the weight and threshold value under the training of learning rules to make the model output close to the sample value [32][33][34]. Sample selection was carried out in combination with the modi ed parameters selected in Section 3.2 and the material performance interval in Table 3. 10 equal parts are divided according to the di erence between upper and lower limits of parameters; that is, each sample value increases the di erence by 10% compared with the last sample. is gives 11 values for each correction parameter; the 2 parameters of the model and 11 values of each parameter can be regarded as a common combination of all parameters of a test (112 times). Sample selection is shown in Table 4. e 121 training samples were divided into two parts, 111 training sets and 10 test sets, respectively. All samples were selected according to the principle of randomness in order to ensure the reliability of network training.

BP Neural Network.
As a basic multilayer forward neural network, BP neural network has one input layer and one output layer. ere are several hidden layers between the input and output layers, each adopts full connection mode, and the neurons of the same layer are independent [35,36]. e neurons of the hidden layer adopt the S-type function and linear transfer function in the output layer. A three-layer neural network with a hidden layer can approximate any

Input layer
Hidden layer  nonlinear function theoretically [37,38]. BP neural network correction adopts an error backpropagation algorithm, which takes the weight and threshold as the cause of the error and apportions the error to the weight and threshold of each neuron through backpropagation algorithm, as shown in Figure 8. ere are m neurons in the input layer, l neurons in the hidden layer, and n neurons in the output layer. e hidden layer adopts the S-type transfer function tansig, and   the output layer adopts the linear function purelin.
According to statistics, about 75% of neural networks are derived from BP neural network [39,40], and BP neural network is considered to be a relatively reliable neural network. BP neural network can be created by calling the new function in MATLAB neural network toolbox. e test results after training are shown in Table 5.

GRNN.
GRNN, also known as a generalized neural network, is a feedforward neural network model based on the nonlinear regression principle. e structure of the GRNN is shown in Figure 9 [41,42]. e input layer of the GRNN only sends samples into the hidden layer, and the number of neurons in the hidden layer is the same as the number of samples in the training set [43,44]. In the hidden layer, the weight can be expressed by the Euclidean distance function IIdistII, and the radial basis function can be expressed by the Gaussian function. e output layer adopts linear output, and its weight function adopts normalized dot product weight function nprod. At last, the calculation network vector n 2 is provided to the line transfer function purlin to obtain the calculation result [45,46]. GRNN has the advantages of simple structure, simple training, and fast learning convergence.
GRNNs can be created by calling the MATLAB neural network toolbox newgrnn function. e test results after training are shown in Table 6.

Reliability Evaluation.
e test results of the two neural networks are all good through the preliminary judgment [47,48]. e relative error E i , relative error variance S 2 , and determination coe cient R 2 of test samples were selected to evaluate the reliability and error analysis of the two neural where Y i (i 1, 2, ···, n) is the predicted value of the sample i; Y i (i 1, 2, ···, n) is the theoretical value of the sample i; n is the total number of samples. e prediction of density and elastic modulus by the neural network is shown in Figure 10, where the abscissa is the sample ordinal number, and the ordinate is density and elastic modulus, respectively [51,52]. Figure 10 shows that the prediction curves of the two neural networks have a good coincidence with the real value curves. is indicates that the predicted value is very close to the real value, which proves that BP neural network and GRNN achieve good prediction results in density and elastic modulus. In terms of reliability, the R 2 values of the BP neural network in density and elastic modulus prediction are 0.99, and the GRNN is 0.92 and 0.97, respectively, which indicates the reliability of the BP neural network is better than GRNN in model modi cation [53,54].
Relative error and relative error value variance are calculated from (3) and (4), as shown in Figure 11.
As can be seen from Figure 11, in terms of model modi cation and prediction, BP neural network has better stability than GRNN, and the amplitude and incidence of mutation are also smaller. e reliability and error uctuation of the BP neural network in the model modi cation are better than that of the GRNN after comparison, which BP neural network model is better used to modify the pedestrian bridge. Using BP neural network, the predicted material density and elastic modulus are ρ 7.84 × 10 4 N/m 3 and E 2.15 × 10 11 Pa, respectively. e results are shown in Table 7.

Conclusion
In this paper, the dynamic characteristics of the pedestrian bridge in Urumqi China were tested to obtain the dynamic parameters of the bridge, and the neural network was used to  (1) e pedestrian bridge model established by MIDAS/ Civil has high accuracy, which is found by comparing the dynamic test results with the calculation results of the initial finite element model. e degraded material parameters can be simulated by the neural network, so that the simulation results can more truly reflect the actual stress state of the structure. (2) rough the calculation formula of natural vibration frequency, the factors affecting the natural vibration frequency of the structure are as follows: the dimensions, elastic modulus, and density of the material. e sensitivity analysis shows that the elastic modulus and material density have the greatest influence on the natural vibration frequency of the structure. e sensitivity of the same material is different in each order natural frequency.
(3) Based on reliability analysis and error analysis of calculation results of the BP neural network and GRNN, it can be seen that the two neural networks have a good effect on model modification, but the BP neural network has better reliability and smaller error fluctuation in model modification. BP neural network can be used to modify the structure model, and the modified model is closer to the real stress state of the structure.

Data Availability
e data used to support the findings of the study are included within the article.

Conflicts of Interest
e authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as potential conflicts of interest.