Beam bridge main girder static load deflection prediction method based on improved avoa-grnn network

Abstract

The application discloses a kind of beam bridge girder static load deflection prediction methods based on improved AVOA-GRNN network, comprising:1, establish vehicle bridge finite element model and add vehicle bridge uncertainty simulation bridge dynamic static load test, collect dynamic static load test data;2, the above data is selected using the characteristic of pearson linear correlation coefficient;3, using dynamic static load experimental data training GRNN neural network model, and construct the parameter of improved African vulture algorithm optimization GRNN, obtain the corresponding smooth factor when average absolute error is minimum;4, the dynamic load test data of prediction set is substituted into improved AVOA-GRNN network model and carries out static load deflection prediction.The application can use beam bridge girder dynamic load test data to predict corresponding static load deflection, so as to effectively solve the problems, such as high cost of predicting beam bridge static load test, great influence on traffic and easily causing damage to bridge structure.

Description

Technical Field

[0001] This invention belongs to the field of bridge health monitoring, specifically a method for predicting the static load deflection of the main girder of a beam bridge based on an improved AVOA-GRNN network. Background Technology

[0002] Bridge assessment is crucial for ensuring traffic safety, load-bearing capacity, extending service life, and rationally allocating economic resources. Load testing is considered one of the most effective methods for bridge condition assessment. For bridges assessed as Class IV and V, load testing is necessary to determine their load-bearing capacity. Load testing is divided into static load testing and dynamic load testing. Static load testing is the most direct and effective method for evaluating the strength, stiffness, and load-bearing capacity of a bridge, offering advantages such as realism, safety, reliability, accuracy, and adjustability. However, static load testing requires significant financial and human resources, disrupts traffic, and poses certain safety hazards, limiting its application. Dynamic load testing, on the other hand, is inexpensive and convenient, avoiding the shortcomings of static load testing. However, currently, effective assessment theories and methods are lacking, making dynamic load testing less reliable and accurate than static load testing in assessing bridge load-bearing capacity. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, this invention proposes a method for predicting the static load deflection of the main beam of a beam bridge based on an improved AVOA-GRNN network. This method aims to achieve high-precision prediction of the static load test results of bridges and effectively solve many problems such as high cost of predicting static load tests for beam bridges, significant impact on traffic, and easy damage to the bridge structure.

[0004] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0005] The present invention provides a method for predicting the static load deflection of the main girder of a beam bridge based on an improved AVOA-GRNN network, characterized by the following steps:

[0006] Step 1: Use finite element software to model the bridge and vehicle to obtain the vehicle-bridge finite element model, including: bridge finite element model and vehicle finite element model; among which, the vehicle finite element model is a four-degree-of-freedom half-vehicle model.

[0007] Step 2: Add uncertainties to the finite element model of the vehicle axle to simulate the real structure of the bridge and vehicle;

[0008] Step 2.1: Multiply the elastic modulus of each element in the bridge finite element model by its own random number to obtain the true elastic modulus of each element, which is used to simulate the material error of the bridge.

[0009] Step 2.2: Multiply the material unit weight of each element in the bridge finite element model by its own random number to obtain the true material unit weight of each element, which is used to simulate the quality error of the bridge;

[0010] Step 2.3: Set the stiffness Kv and damping Cv of the half-vehicle model to random values ​​within a certain range to simulate the uncertainty of the vehicle;

[0011] Step 3: Obtain dynamic and static load experimental data using the Newmark-β method:

[0012] During the simulated dynamic load test, the acceleration data X = (x1, x2, ... x) at the mid-span node of the bridge finite element model were obtained. i , ...x N ) T Where N is the total number of trials, x i x represents the acceleration number during the i-th test. i =(x i，1 x i，2 , ..., x i，j , ..., x i，M ), x i，j x represents the acceleration data of the i-th test. i The j-th feature data in the array, M is the number of features; T represents transpose;

[0013] During the simulated static load test, deflection data at the quarter-span position α, the three-quarter-span position β, and the mid-span node position γ of the bridge finite element model were acquired and standardized to obtain the standardized deflection data Y at the quarter-span position α. α =(y α，1 y α，2 , ...y α，i , ...y α，N ) T Deflection data Y at three-quarters position β after standardization β =(y β，1 y β，2 , ...y β，i , ...y β，N ) T Deflection data Y at the midpoint γ after standardization γ =(y γ，1 y γ，2 , ...y γ，i , ...y γ，N ) T , where y α，i y β，i y γ，i Let represent the deflection data at the quarter position α, the three-quarter position β, and the mid-span node position γ during the i-th test, respectively.

[0014] Step 4: Feature selection and data standardization;

[0015] Calculate the Pearson linear correlation coefficient between each feature data in X and the deflection data at the three locations. Sort the correlation coefficients in descending order by taking the absolute value of each coefficient. Then, based on the set number of features to select, M′, select the feature data corresponding to the first M′ correlation coefficients and standardize them to obtain the processed feature data, denoted as X′=(x′1,x′2,…x′). i ,…,x′ N ) T , where x′ i This represents the acceleration data after feature selection and data standardization in the i-th experiment; and x′ i =(x′) i，1 , x′ i，2 ,…,x′ i，j′ ,…,x′ i，M′ ), x′ i，j′ This represents the acceleration data x′ after feature selection and data standardization for the i-th experiment. i The j′-th feature data in;

[0016] Calculate the deflection data Y of column m and position j in X using equation (1). j The correlation coefficient rho(m,j):

[0017]

[0018] Among them, m∈[1, N]; j=α, β, γ; x m，i This represents the data in the m-th column and i-th row of X. y represents the mean of the data in the m-th column of X; j，i Y represents j The i-th row of data; This represents the mean value of the deflection data at the j-th position;

[0019] Step 5: Create a GRNN neural network model, including: an input layer, a pattern layer, a summation layer, and an output layer; use X′ as the input to the GRNN neural network model, and Y′ as the output. α Y β Y γ As the output of the GRNN neural network model, the GRNN neural network model is trained to obtain the trained static load deflection prediction model.

[0020] Step 6: Set the upper limit ub and lower limit lb of the smoothing factor, and optimize the smoothing factor σ using the improved African Vulture algorithm:

[0021] Step 6.1: Initialize the population and define the parameters, including: the size of the vulture population is Q, the maximum number of iterations is T, and the search space dimension of the vultures is 1;

[0022] Step 6.2: Initialize the t-th generation vulture population using the tent chaotic map. in, P represents the population of vultures in generation t. t The location of the qth vulture;

[0023] Step 6.3: Based on the mean absolute error between the true and predicted deflection values, calculate the fitness of each vulture in the t-th generation vulture population; then group the t-th generation vulture population according to the fitness of each vulture, placing the vultures with the best fitness in the first group, the vultures with the second best fitness in the second group, and the remaining vultures in the third group.

[0024] Step 6.4: Use equation (7) to obtain the location of the q-th vulture in the t-th generation vulture population after it has moved.

[0025]

[0026] In equation (7): This represents the location of the vulture with the best fitness in the t-th generation vulture population. Let L1 and L2 represent the position of the vulture with the second-best fitness in the vulture population of generation t. L1 and L2 are two parameters, where L1∈[0,1], L2∈[0,1], and L1+L2=1. This represents the fitness value of the q-th vulture in the t-th generation vulture population;

[0027] Step 6.5: Calculate the hunger level F of the vulture population in generation t using equation (8). t :

[0028]

[0029] In equation (8): z is a random number between [-1, 1], h is a random number between [-2, 2], k1 is a random number between [0, 1], and w is a fixed parameter;

[0030] Step 6.6: When |F t When |≥1, it indicates that the exploration phase is underway, and the position of the qth vulture in the (t+1)th generation vulture population is obtained using equation (9). Otherwise, proceed to the development phase in step 6.7;

[0031]

[0032] In equation (9): p1∈[0,1] is the set exploration parameter; Z represents the random position of the vulture, and is a random number between [0,2]; k p1 k2 and k3 are both random numbers between [0, 1];

[0033] Step 6.7: When |F t When |∈[0.5,1], the position of the qth vulture in the (t+1)th generation vulture population can be obtained using equation (10).

[0034]

[0035] In equation (10): p2∈[0,1] are the exploration parameters set. k4 and k5 are both random numbers in the range [0, 1].

[0036] When |F|∈[0, 0.5), the position of the nth vulture in the (t+1)th generation vulture population can be obtained using equation (11).

[0037]

[0038] In equation (11): λ1, λ2, θ1, θ2 represent parameters set in advance, and λ1, λ2∈(0,1), λ1+λ2=0, θ1, θ2∈(0,1), θ1+θ2=1; ξ and σ are two random numbers between [0, 1]; t ) 2 Let G(ξ, (σ) be the variance of the vulture population in generation t; t ) 2 ) has a mean of 0 and a standard deviation of (σ). t ) 2 The Gaussian function; levy(d) represents the flight operation, and d represents the search space dimension of the vulture;

[0039] Step 6.8: Determine if q = Q is true. If it is true, then the (t+1)th generation vulture population has been obtained. Otherwise, after assigning q+1 to q, return to step 6.4 and execute sequentially;

[0040] Step 6.9: Determine whether t+1≥T holds true. If it does, output the position of the vulture with the best fitness in the Tth generation vulture population and use it as the best smoothing factor. Otherwise, return to step 6.3 and execute sequentially.

[0041] Step 7: Substitute the optimal smoothness factor into the trained static load deflection prediction model to obtain the optimal static load deflection prediction model, which is used to predict static load deflection.

[0042] The characteristic of the method for predicting the static load deflection of the main girder of a beam bridge based on the improved AVOA-GRNN network in this invention is that step 5 includes:

[0043] Step 5.1: In the mode layer, X′ is calculated using equation (2) after passing through x′. i The resulting transfer function g i :

[0044]

[0045] In equation (2), σ is the smoothness factor; ||X′-x′ i || represents X′ and x′ i The exponential square of the Euclidean distance;

[0046] Step 5.2: The summation layer uses equation (3) to obtain the sum of transfer functions S. D :

[0047]

[0048] Using equation (4), we obtain the weighted sum S of position j. Nj :

[0049]

[0050] In equation (4), y j，i This represents the deflection data at the j-th position during the i-th test;

[0051] Step 5.3: The output layer uses equation (5) to calculate the predicted deflection value at the j-th position.

[0052]

[0053] Step 5.4: Construct a cross-entropy loss function based on the predicted and true values ​​of deflection at the j-th position, train the GRNN neural network model using gradient descent, and calculate the cross-entropy loss function to update the model parameters until the cross-entropy loss function converges, thereby obtaining the trained static load deflection prediction model.

[0054] Step 6.2 includes:

[0055] Step 6.2.1: Initialize t = 0, q = 1; generate a random number a0 ∈ [0, 1]. If a0 ∈ [0.2, 0.4, 0.6, 0.8], execute step 6.2.1; otherwise, execute step 6.2.2.

[0056] Step 6.2.2: Calculate the q-th chaotic coefficient a using equation (6). q If a qIf the ∈ [0, 0.25, 0.5, 0.75], then proceed to step 6.2.3; otherwise, proceed to step 6.2.4.

[0057]

[0058] In equation (6), u represents the parameter; tent represents the chaotic function;

[0059] Step 6.2.3: Place a q +ε is assigned to a q , where ε is a random number;

[0060] Step 6.2.4: Generate the location of the q-th vulture in the t-th generation vulture population. Each position represents a smoothing factor;

[0061] Step 6.2.5: Determine if n = Q holds true. If it does, then the vulture population of generation t is obtained. Otherwise, after assigning q+l to q, return to step 6.2.2 and execute sequentially.

[0062] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the static load deflection prediction method for the main girder of a beam bridge, and the processor is configured to execute the program stored in the memory.

[0063] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs the steps of the method for predicting the static load deflection of the main girder of a beam bridge.

[0064] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0065] 1. Compared with static load testing, this invention does not require huge amounts of funds and manpower, and has the advantages of high efficiency, short cycle and non-destructive nature. It overcomes the problems of high cost, large impact on traffic and easy damage to bridge structure caused by static load testing.

[0066] 2. Compared with dynamic load testing, by using dynamic load test results in conjunction with intelligent algorithms to achieve high-precision prediction of bridge static load test results, the prediction results can be used to more reliably and accurately assess the bridge's load-bearing capacity. This overcomes the lack of effective evaluation theories and methods in dynamic load testing, which makes it difficult to obtain bridge load-bearing capacity assessment results that are universally recognized by the engineering community, similar to those of static load testing.

[0067] 3. This invention only requires dynamic load test data from one measuring point to predict static load deflection data from multiple points, which improves prediction efficiency and reduces prediction cost.

[0068] 4. Since randomly generated initial samples have a high degree of randomness, it is not conducive to obtaining stable and diverse initial solutions. This invention uses the tent chaotic mapping to initialize the population in the African Vulture algorithm, which helps to get rid of local traps, improves the algorithm's global search capability, and thus can find the global optimal smoothness factor more quickly, and use it to build the optimal static load deflection prediction model.

[0069] 5. Compared with the traditional African vulture algorithm, this invention incorporates Gaussian mutation perturbation and weight time-varying mechanism in the later mining stage of the algorithm, which improves the algorithm's ability to jump out of local optima in the later stage and optimizes the smoothing factor more accurately, thereby improving the accuracy of deflection prediction. Attached Figure Description

[0070] Figure 1 This is a schematic diagram of the specific process of the method of the present invention;

[0071] Figure 2 This is a front view of the finite element model of the simply supported beam bridge and vehicle of the present invention;

[0072] Figure 3 This is a schematic diagram of the GRNN network structure of the present invention;

[0073] Figure 4 This is a flowchart of the improved AVOA algorithm of the present invention;

[0074] Figure 5 A comparison chart of predicted and actual static deflection values ​​at a quarter-node of a simply supported beam bridge;

[0075] Figure 6 A comparison chart of predicted and actual static load deflection at mid-span node of a simply supported beam bridge was invented.

[0076] Figure 7 A comparison chart showing the predicted and actual static load deflection values ​​at three-quarters nodes of a simply supported beam bridge. Detailed Implementation

[0077] In this embodiment, a method for predicting the static load deflection of the main girder of a beam bridge based on an improved AVOA-GRNN network is proposed. This method establishes the relationship between the bridge's dynamic response and its load-bearing capacity, and uses dynamic load test data to predict static load test data. The main steps include: 1. Establishing a vehicle-bridge finite element model and adding bridge and vehicle uncertainties to simulate dynamic and static load tests, collecting dynamic and static load test data; 2. Using the Pearson linear correlation coefficient to perform feature selection on the above data; 3. Training a GRNN neural network model using the dynamic and static load test data, and optimizing the GRNN parameters using an improved African vulture algorithm to obtain the smoothing factor corresponding to the minimum mean absolute error, thus constructing an improved AVOA-GRNN network model; 4. Substituting the dynamic load test data from the prediction set into the improved AVOA-GRNN network model to predict the static load deflection. Specifically, as... Figure 1 As shown, the method is performed according to the following steps:

[0078] Step 1: Model the bridge and vehicle using finite element software to obtain the vehicle-bridge finite element model, including: a bridge finite element model and a vehicle finite element model; the vehicle finite element model is a four-degree-of-freedom half-vehicle model; the bridge cross-section is rectangular, 30m long, 3m wide, and 2m high, with an elastic modulus of 32GPa and a density of 2400kg / m³. 3 A front view of the finite element model of the simply supported beam bridge and vehicles is shown below. Figure 2 As shown;

[0079] Step 2: Add uncertainties to the finite element model of the vehicle axle to simulate the real structure of the bridge and vehicle;

[0080] Step 2.1: Multiply the elastic modulus of each element in the bridge finite element model by its respective random number δ∈(0.7, 1.1) to obtain the true elastic modulus of each element, which is used to simulate the material error of the bridge;

[0081] Step 2.2: Multiply the unit weight of the material in each element of the bridge finite element model by its own random number ω∈(0.8,1) to obtain the true unit weight of the material in each element, which is used to simulate the quality error of the bridge.

[0082] Step 2.3: The stiffness K1 of the four-degree-of-freedom half-vehicle model is in the interval (2.0 × 10⁻⁶). 5 2.6×10 5 K2 is a random value within the interval (1.5 × 10). 5 2.0×10 5 Random values ​​within the interval (1.0 × 10⁻⁶). Damping C1 and C2 are random values ​​within the interval (1.0 × 10⁻⁶). 3 1.5×10 3 Random values ​​within ) are used to simulate the uncertainty of vehicle stiffness and damping;

[0083] Step 3: Obtain dynamic and static load experimental data using the Newmark-β method:

[0084] The vehicle weight was increased from 30 kN to 80 kN, with each increase being 1 kN; the vehicle speed was increased from 1 m / s to 5 m / s, with each increase being 1 m / s, resulting in 255 different combinations. The total number of test samples was 255. 10% of the total test samples were randomly selected as the test set, and the remainder were used as the training set.

[0085] During the simulated dynamic load test, the acceleration data X = (x1, x2, ... x) at the mid-span node of the bridge finite element model were obtained. i , ...x N ) T Where N = 229 is the number of samples in the prediction set, x i x represents the acceleration number during the i-th test. i =(x i，1 x i，2 , ..., x i，j , ..., x i，M ), x i，j x represents the acceleration data of the i-th test. i The j-th feature data in the array, M = 1000 is the number of features; T represents transpose;

[0086] During the simulated static load test, deflection data at the quarter-span position α, the three-quarter-span position β, and the mid-span node position γ of the bridge finite element model were acquired and standardized to obtain the standardized deflection data Y at the quarter-span position α. α =(y α，1 y α，2 , ...y α，i , ...y α，N ) T Deflection data Y at three-quarters position β after standardization β =(y β，1 y β，2 , ...y β，i , ...y β，N ) T Deflection data Y at the midpoint γ after standardization γ =(y γ，1 y γ，2 , ...y γ，i , ...y γ，N ) T , where y α，i y β，i y γ，i Let represent the deflection data at the quarter position α, the three-quarter position β, and the mid-span node position γ during the i-th test, respectively.

[0087] Step 4: Feature selection and data standardization;

[0088] Calculate the Pearson linear correlation coefficient between each feature data in X and the deflection data at the three locations. Sort the correlation coefficients in descending order after taking the absolute value of each coefficient. Set the number of features selected, M′ = 50. Select the feature data corresponding to the first 50 correlation coefficients and standardize them to obtain the processed feature data, denoted as X′ = (x′1, x′2, ... x′). i ,…,x′ N ) T , where x′ i This represents the acceleration data after feature selection and data standardization in the i-th experiment; and x′ i =(x′) i，1 , x′ i，2 ,…,x′ i，j′ ,…,x′ i，M′ ), x′ i，j′ The acceleration data x′ represents the feature selection and data standardization of the i-th test. i The j′-th feature data in;

[0089] Calculate the deflection data Y of column m and position j in X using equation (1). j The correlation coefficient rho(m,j) in the equation is:

[0090]

[0091] Among them, m∈[1, N]; j=α, β, γ; x m，i This represents the data in the m-th column and i-th row of X. y represents the mean of the data in the m-th column of X; j，i Y represents j The i-th row of data; The mean of the deflection data at the j-th position.

[0092] Step 5: Create a GRNN neural network model, including: an input layer, a pattern layer, a summation layer, and an output layer; use X′ as the input to the GRNN neural network model, and Y′ as the output. α Y β Y γ As the output of the GRNN neural network model, and used to train the GRNN neural network model, a trained static load deflection prediction model is obtained; the schematic diagram of the GRNN network structure is shown below. Figure 3 As shown;

[0093] Step 5.1: In the mode layer, X′ is calculated using equation (2) after passing through x′. i The resulting transfer function g i :

[0094]

[0095] In equation (2), σ is the smoothness factor; ||X′-x′ i || represents X′ and x′ i The exponential square of the Euclidean distance.

[0096] Step 5.2: The summation layer uses equation (3) to obtain the transfer function g. i Arithmetic summation S D Using equation (4), the weighted sum S of position j is obtained. Nj In equation (4), y j，i This represents the deflection data at position j during the i-th test;

[0097]

[0098]

[0099] Step 5.3: The output layer uses equation (5) to calculate the predicted deflection value at position j.

[0100]

[0101] Step 5.4: Construct a cross-entropy loss function based on the predicted and true values ​​of deflection at the j-th position, train the GRNN neural network model using gradient descent, and calculate the cross-entropy loss function to update the model parameters until the cross-entropy loss function converges, thereby obtaining the trained static load deflection prediction model.

[0102] Step 6: Set the upper limit of the smoothing factor ub = 30 and the lower limit lb = 0.01, and optimize the smoothing factor σ using the improved African Vulture algorithm; the flowchart of the improved AVOA algorithm is shown below. Figure 4 As shown.

[0103] Step 6.1: Initialize the population and define the parameters, including: the size of the vulture population is Q = 50, the maximum number of iterations is T = 10, and the search space dimension of the vultures is 1;

[0104] Step 6.2: Initialize the vulture population using the tent chaos map:

[0105] Step 6.2.1: Initialize, t = 0, q = 1; generate a random number a0 ∈ [0, 1]. If a0 ∈ [0.2, 0.4, 0.6, 0.8], execute step 6.2.1; otherwise, execute step 6.2.2.

[0106] Step 6.2.2: Calculate the q-th chaotic coefficient a using equation (6). q If a qIf the ∈ [0, 0.25, 0.5, 0.75], then proceed to step 6.2.3; otherwise, proceed to step 6.2.4.

[0107]

[0108] In equation (6), u represents a parameter; in this embodiment, u = 0.5 is set; and tent represents a chaotic function.

[0109] Step 6.2.3: Place a q +ε is assigned to a q , where ε is a random number;

[0110] Step 6.2.4: Generate the location of the q-th vulture in the t-th generation vulture population. Each position represents a smoothing factor;

[0111] Step 6.2.5: Determine if n = Q holds true. If it does, then the vulture population of generation t is obtained. Subsequent iterations do not require re-initialization; otherwise, assign q+1 to q and return to step 6.2.2 for sequential execution.

[0112] Step 6.3: Based on the mean absolute error between the true and predicted deflection values, calculate the fitness of each vulture in the t-th generation vulture population; then group the t-th generation vulture population according to the fitness of each vulture, placing the vultures with the best fitness in the first group, the vultures with the second best fitness in the second group, and the remaining vultures in the third group.

[0113] Step 6.4: Use equation (7) to obtain the location of the q-th vulture in the t-th generation vulture population after it has moved.

[0114]

[0115] In equation (7): This represents the location of the vulture with the best fitness in the t-th generation vulture population. Let L1 and L2 represent the position of the vulture with the second-best fitness in the vulture population of generation t. L1 and L2 are two parameters, where L1∈[0,1], L2∈[0,1], and L1+L2=1. This represents the fitness value of the q-th vulture in the y-th generation vulture population;

[0116] Step 6.5: Calculate the hunger level F of the vulture population in generation t using equation (8). t :

[0117]

[0118] In equation (8): z is a random number between [-1, 1], h is a random number between [-2, 2], k1 is a random number between [0, 1], and w is set to 2.5;

[0119] Step 6.6: When |F t When |≥1, it indicates that the exploration phase is underway, and the position of the qth vulture in the (t+1)th generation vulture population is obtained using equation (9). Otherwise, proceed to the development phase in step 6.7;

[0120]

[0121] In equation (9): p1∈[0,1] is the set exploration parameter; Z represents the random position of the vulture, which is a random number between [0,2]; k p1 k2 and k3 are both random numbers between [0, 1];

[0122] Step 6.7: When |F t When |∈[0.5,1], the position of the qth vulture in the (t+1)th generation vulture population can be obtained using equation (10).

[0123]

[0124] In equation (10): p2∈[0,1] are the exploration parameters set. k4 and k5 are both random numbers in the range [0, 1].

[0125] When |F|∈[0, 0.5), the position of the nth vulture in the (t+1)th generation vulture population can be obtained using equation (11).

[0126]

[0127] In equation (11): λ1, λ2, θ1, θ2 represent parameters set in advance. In this embodiment, λ1 = -0.3, λ2 = 0.3, θ1 = 0.6, θ2 = 0.4; ξ and σ are two random numbers between [0, 1]; t ) 2 Let G(ξ, (σ) be the variance of the vulture population in generation t; t ) 2 ) has a mean of 0 and a standard deviation of (σ). t ) 2 The Gaussian function; levy(d) represents the flight operation, where d indicates that the vulture's search space dimension is 1;

[0128] Step 6.8: Determine if q = Q is true. If it is true, then the (t+1)th generation vulture population has been obtained. Otherwise, after assigning q+1 to q, return to step 6.4 and execute sequentially;

[0129] Step 6.9: Determine whether t+1≥T holds true. If it does, output the position of the vulture with the best fitness in the Tth generation vulture population and use it as the best smoothing factor. Otherwise, return to step 6.3 and execute sequentially.

[0130] Step 7: Substitute the optimal smoothing factor into the trained static load deflection prediction model to obtain the optimal static load deflection prediction model, which is used to predict the static load deflection of the test set. The test set has 26 samples. Table 1 shows the average relative error between the predicted and actual values ​​of the test set.

[0131] Table 1

[0132] one-quarter 1.6474 Crossing the Middle 1.1503 Three-quarters 1.5306

[0133] As shown in Table 1, the average absolute error of the static load deflection prediction at the three locations is less than 2%, indicating accurate prediction results. A comparison of the predicted and actual static load deflection values ​​at the quarter-span node, mid-span node, and three-quarter-span node of a simply supported beam bridge is shown in the figure below. Figure 5 , Figure 6 , Figure 7 As shown.

Claims

1. A method for predicting the static load deflection of the main girder of a beam bridge based on an improved AVOA-GRNN network, characterized in that, The steps include the following: Step 1: Use finite element software to model the bridge and vehicle to obtain the vehicle-bridge finite element model, including: bridge finite element model and vehicle finite element model; among which, the vehicle finite element model is a four-degree-of-freedom half-vehicle model. Step 2: Add uncertainties to the finite element model of the vehicle axle to simulate the real structure of the bridge and vehicle; Step 2.1: Multiply the elastic modulus of each element in the bridge finite element model by its own random number to obtain the true elastic modulus of each element, which is used to simulate the material error of the bridge. Step 2.2: Multiply the material unit weight of each element in the bridge finite element model by its own random number to obtain the true material unit weight of each element, which is used to simulate the quality error of the bridge; Step 2.3: Set the stiffness Kv and damping Cv of the half-vehicle model to random values ​​within a certain range to simulate the uncertainty of the vehicle; Step 3: Obtain dynamic and static load experimental data using the Newmark-β method: During the simulated dynamic load test, the acceleration data X = (x1, x2, ..., x) at the mid-span node of the bridge finite element model were obtained. i ,···x N ) T Where N is the total number of trials, x i x represents the acceleration number during the i-th test. i =(x i,1 ,x i,2 ,…,x i,j ,…,x i,M ), x i,j x represents the acceleration data of the i-th test. i The j-th feature data in the array, M is the number of features; T represents transpose; During the simulated static load test, deflection data at the quarter-span position α, the three-quarter-span position β, and the mid-span node position γ of the bridge finite element model were acquired and standardized to obtain the standardized deflection data Y at the quarter-span position α. α =(y α,1 ,y α,2 ,···y α,i ,···y α,N ) T Deflection data Y at three-quarters position β after standardization β =(y β,1 ,y β,2 ,···y β,i ,···y β,N ) T Deflection data Y at the midpoint γ after standardization γ =(y γ,1 ,y γ,2 ,···y γ,i ,···y γ,N ) T , where y α,i y β,i y γ,i Let represent the deflection data at the quarter position α, the three-quarter position β, and the mid-span node position γ during the i-th test, respectively. Step 4: Feature selection and data standardization; Calculate the Pearson linear correlation coefficient between each feature data in X and the deflection data at the three locations. Sort the correlation coefficients in descending order by taking the absolute value of each coefficient. Then, based on the set number of features to select, M′, select the feature data corresponding to the first M′ correlation coefficients and standardize them to obtain the processed feature data, denoted as X′=(x′1,x′2,…x′). i ,…,x′ N ) T , where x′ i This represents the acceleration data after feature selection and data standardization in the i-th experiment; and x′ i =(x′) i,1 ,x′ i,2 ,…,x′ i,j′ ,…,x′ i,M′ ), x′ i,j′ This represents the acceleration data x′ after feature selection and data standardization for the i-th experiment. i The j′-th feature data in; Calculate the deflection data Y of column m and position j in X using equation (1). j The correlation coefficient rho(m,j): Among them, m∈[1,N]; j=α, β, γ; x m,i This represents the data in the m-th column and i-th row of X. y represents the mean of the data in the m-th column of X; j,i Y represents j The i-th row of data; This represents the mean value of the deflection data at the j-th position; Step 5: Create a GRNN neural network model, including: an input layer, a pattern layer, a summation layer, and an output layer; use X′ as the input to the GRNN neural network model, and Y′ as the output. α Y β Y γ As the output of the GRNN neural network model, the GRNN neural network model is trained to obtain the trained static load deflection prediction model. Step 6: Set the upper limit ub and lower limit lb of the smoothing factor, and optimize the smoothing factor σ using the improved African Vulture algorithm: Step 6.1: Initialize the population and define the parameters, including: the size of the vulture population is Q, the maximum number of iterations is T, and the search space dimension of the vultures is 1; Step 6.2: Initialize the t-th generation vulture population using the tent chaotic map. in, P represents the population of vultures in generation t. t The location of the qth vulture; Step 6.3: Based on the mean absolute error between the true and predicted deflection values, calculate the fitness of each vulture in the t-th generation vulture population; then group the t-th generation vulture population according to the fitness of each vulture, placing the vultures with the best fitness in the first group, the vultures with the second best fitness in the second group, and the remaining vultures in the third group. Step 6.4: Use equation (7) to obtain the location of the q-th vulture in the t-th generation vulture population after it has moved. In equation (7): This represents the location of the vulture with the best fitness in the t-th generation vulture population. Let L1 and L2 represent the position of the vulture with the second-best fitness in the vulture population of generation t. L1 and L2 are two parameters, where L1∈[0,1], L2∈[0,1], and L1+L2=1. This represents the fitness value of the q-th vulture in the t-th generation vulture population; Step 6.5: Calculate the hunger level F of the vulture population in generation t using equation (8). t : In equation (8): z is a random number between [-1, 1], h is a random number between [-2, 2], k1 is a random number between [0, 1], and w is a fixed parameter; Step 6.6: When |F t When |≥1, it indicates that the exploration phase is underway, and the position of the qth vulture in the (t+1)th generation vulture population is obtained using equation (9). Otherwise, proceed to the development phase in step 6.7; In equation (9): p1∈[0,1] is the set exploration parameter; Z represents the random position of the vulture, and is a random number between [0,2]; k p1 k2 and k3 are both random numbers between [0,1]; Step 6.7: When |F t When |∈[0.5,1], the position of the qth vulture in the (t+1)th generation vulture population can be obtained using equation (10). In equation (10): p2∈[0,1] are the exploration parameters set. k4 and k5 are both random numbers in the range [0,1]. When |F|∈[0,0.5), the position of the nth vulture in the (t+1)th generation vulture population can be obtained using equation (11). In equation (11): λ1, λ2, θ1, θ2 represent parameters set in advance, and λ1, λ2∈(0,1), λ1+λ2=0, θ1, θ2∈(0,1), θ1+θ2=1; ξ and σ are two random numbers between [0,1]; t ) 2 Let G(ξ,(σ) be the variance of the vulture population in generation t; t ) 2 ) has a mean of 0 and a standard deviation of (σ). t ) 2 The Gaussian function; levy(d) represents the flight operation, and d represents the search space dimension of the vulture; Step 6.8: Determine if q = Q is true. If it is true, then the (t+1)th generation vulture population has been obtained. Otherwise, after assigning q+1 to q, return to step 6.4 and execute sequentially; Step 6.9: Determine whether t+1≥T holds true. If it does, output the position of the vulture with the best fitness in the vulture population of generation T, and use it as the best smoothing factor. Otherwise, return to step 6.3 and execute sequentially. Step 7: Substitute the optimal smoothness factor into the trained static load deflection prediction model to obtain the optimal static load deflection prediction model, which is used to predict static load deflection.

2. The method for predicting the static load deflection of the main girder of a beam bridge based on the improved AVOA-GRNN network according to claim 1, characterized in that, Step 5 includes: Step 5.1: In the mode layer, X′ is calculated using equation (2) after passing through x′. i The resulting transfer function g i : In equation (2), σ is the smoothness factor; ||X′-x′ i || represents X′ and x′ i The exponential square of the Euclidean distance; Step 5.2: The summation layer uses equation (3) to obtain the sum of transfer functions S. D : Using equation (4), the weighted sum S of position j is obtained. Nj : In equation (4), y j,i This represents the deflection data at the j-th position during the i-th test; Step 5.3: The output layer uses equation (5) to calculate the predicted deflection value at the j-th position. Step 5.4: Construct a cross-entropy loss function based on the predicted and true values ​​of deflection at the j-th position, train the GRNN neural network model using gradient descent, and calculate the cross-entropy loss function to update the model parameters until the cross-entropy loss function converges, thereby obtaining the trained static load deflection prediction model.

3. The method for predicting the static load deflection of the main girder of a beam bridge based on the improved AVOA-GRNN network according to claim 2, characterized in that, Step 6.2 includes: Step 6.2.1: Initialize t = 0, q = 1; generate a random number a0 ∈ [0, 1]. If a0 ∈ [0.2, 0.4, 0.6, 0.8], execute step 6.2.1; otherwise, execute step 6.2.

2. Step 6.2.2: Calculate the q-th chaotic coefficient a using equation (6). q If a q If the ∈[0,0.25,0.5,0.75], then proceed to step 6.2.3; otherwise, proceed to step 6.2.

4. In equation (6), u represents the parameter; tent represents the chaotic function; Step 6.2.3: Place a q +ε is assigned to a q , where ε is a random number; Step 6.2.4: Generate the location of the q-th vulture in the t-th generation vulture population. Each position represents a smoothing factor; Step 6.2.5: Determine if n = Q holds true. If it does, then the vulture population of generation t is obtained. Otherwise, assign q+1 to q and return to step 6.2.2 for sequential execution.

4. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store programs that support the processor in executing the static load deflection prediction method for the main girder of a beam bridge according to any one of claims 1-3, and the processor is configured to execute the programs stored in the memory.

5. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is run by the processor, it executes the steps of the method for predicting the static load deflection of the main girder of a beam bridge as described in any one of claims 1-3.

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