A bridge bent-pier buckling-restrained diagonal-brace parameter optimization method, system and product

Abstract

The present application relates to a kind of bridge bent pier buckling restrained brace parameter optimization method, system and product.A kind of bridge bent pier buckling restrained brace parameter optimization method includes the following steps: S1, first by trained random forest-artificial neural network model prediction bridge seismic response;Again, μ φ 、V max And the objective function f of buckling restrained brace parameter is constructed;S2, by trained response surface model to f is solved.The present application adopts random forest-artificial neural network model prediction bridge seismic response, and according to seismic response, μ With the objective function f of buckling restrained brace parameter is constructed, subsequently by response surface model to f is solved, finally by Pareto optimal front the solution result of response surface model is optimized, so that the parameter of each position buckling restrained brace can be obtained, so that buckling restrained brace in bridge can realize optimal arrangement, improve rationality and economy.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge engineering, in particular to a bridge bent pier buckling restrained brace parameter optimization method, system and product. BACKGROUND

[0002] In China, especially in the western mountainous areas, it is common to set up beam bridges with double-column or multi-column bent high piers, which are usually 20-50 meters high to adapt to the terrain changes in mountainous areas. Meanwhile, concrete cross beams are set between the pier columns to enhance the lateral resistance of the bridge pier. A cross beam is generally set every 7 meters along the pier height, and multiple cross beams are set on the entire high pier to form a "multi-layer" structure. However, China is a country with frequent earthquakes, and the western mountainous areas are particularly prone to seismic activity. In recent years, the country has experienced several major earthquakes, causing severe damage to transportation infrastructure such as bridges, resulting in significant losses to the country and society. Beam bridges with bent high piers are critical nodes in the transportation network system in the western mountainous areas and may even be the only access to the earthquake zone. Therefore, their seismic performance is crucial and requires in-depth research and evaluation.

[0003] Setting buckling restrained braces between the pier columns of the bent pier can significantly improve the seismic performance of the bridge. The braces are generally set diagonally between the cross beams. Since the bent high pier is generally a multi-layer structure, it means that multiple sets of buckling restrained braces need to be set. How to reasonably select the design parameters of each layer of braces to achieve the optimal seismic response reduction and seismic performance improvement is a key problem for designers. In current research and engineering practice, the parameters of buckling restrained braces are mainly determined based on the designer's experience and specification formula calculation. Generally, uniform arrangement is used, i.e., the same design parameters are used for each layer of braces. This design method lacks certain rationality and economy and is difficult to achieve the optimal arrangement. On the other hand, if a parameter analysis method such as nonlinear time history analysis is used to determine the optimal multi-layer brace parameters, it involves a large number of parameter cases and nonlinear seismic response analysis, requiring a large amount of time to analyze and process data. SUMMARY

[0004] Therefore, it is necessary to provide a bridge bent pier buckling restrained brace parameter optimization method, system and product to solve the problem that existing braces are generally arranged uniformly and it is difficult to achieve the optimal arrangement.

[0005] In a first aspect, the present application provides a bridge bent pier buckling restrained brace parameter optimization method, which includes the following steps:

[0006] S1, first predict the seismic response of the bridge through the trained random forest-artificial neural network model; wherein the seismic response is represented by the maximum curvature ductility coefficient μ φand the maximum shear value V of the pier bottom max characterization is carried out;

[0007] reconstructing the mu φ , V max and the objective function f of the buckling-restrained brace parameters; wherein the buckling-restrained brace parameters include the cross-sectional area Si of the i th buckling-restrained brace;

[0008] The expression of f is:

[0009]

[0010] In the formula, f1 and f2 respectively represent two sub-functions of f; minimize represents minimization; n represents the number of buckling-restrained braces;

[0011] S2, solve f by using the trained response surface model, and obtain the minimized maximum curvature ductility coefficient minmu and the corresponding data pair of n, Si and seismic response φ and the minimized maximum shear value minV max ;

[0012] S3, the minmu φ and minV max are optimized by the Pareto optimal frontier, and the balanced maximum curvature ductility coefficient minmu φ ′ and the maximum shear value minV max ′ are obtained, wherein the formula of the trade-off optimization is:

[0013]

[0014] In the formula, J(n, Si) represents the overall performance of the bridge bent pier; ξ represents the balance coefficient, and ξ [0, 1]; represents the normalized minmu φ ; represents the normalized minV max ;

[0015] S4, the minmu φ ′ and minV max ′ are processed by using the trained response surface model, and the optimized Si is obtained according to the corresponding data pair of n, Si and seismic response.

[0016] In the second aspect, the application further provides a bridge bent pier buckling-restrained brace parameter optimization system, which adopts the bridge bent pier buckling-restrained brace parameter optimization method of the first aspect. The bridge bent pier buckling-restrained brace parameter optimization system comprises a prediction module, an analysis module, a trade-off module and an optimization module.

[0017] The prediction module is used to predict the seismic response of bridges and construct μ. φ V max The objective function f is related to the buckling constraint brace parameters.

[0018] The analytical module is used to solve for f, and obtains the minimum maximum curvature ductility coefficient minμ based on the corresponding data of n, Si, and seismic response. φ and the minimized maximum shear force value minV max .

[0019] The trade-off module is used to weigh minμ φ and minV max By performing a trade-off optimization, the maximum curvature ductility coefficient minμ after equilibrium is obtained. φ ′ and maximum shear force value minV max ′.

[0020] The optimization module is used to optimize minμ φ ′ and minV max The process is performed, and the optimized Si is obtained based on the corresponding data of n, Si, and seismic response.

[0021] Thirdly, the present invention also proposes a software program product comprising program instructions that, when run on an electronic device, cause the electronic device to execute the steps of the method for optimizing the buckling constraint brace parameters of bridge piers in the first aspect.

[0022] The beneficial effects of this invention are as follows:

[0023] 1. This invention uses a random forest-artificial neural network model to predict the seismic response of bridges, and constructs an objective function f based on the seismic response and the buckling restraint brace parameters. Then, it solves f through a response surface model, and finally optimizes the solution results of the response surface model through Pareto optimal frontier, thereby obtaining the parameters of the buckling restraint braces at various locations. This enables the optimal arrangement of buckling restraint braces in bridges, improving rationality and economy.

[0024] 2. This invention employs a random forest-artificial neural network model and a response surface model to optimize the buckling constraint brace parameters. Compared to existing single learning algorithms, it exhibits better robustness and stability. Compared to nonlinear time history analysis, it requires less computation, significantly improving time efficiency.

[0025] 3. This invention retrains the response surface model using local optimal solutions, which not only reduces the number of samples but also improves the accuracy of model predictions.

[0026] 4、The present application can simultaneously consider the global optimal configuration of two contradictory optimization objectives in the buckling restrained brace parameter of the bridge bent pier by using the Pareto optimal frontier for trade-off. BRIEF DESCRIPTION OF DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only show some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor under the premise of the drawings.

[0028] Figure 1 The flow chart of the bridge bent pier buckling restrained brace parameter optimization method;

[0029] Figure 2 The training flow chart of the response surface model. DETAILED DESCRIPTION

[0030] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0031] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs. The terminology used in the description of the present application herein only for the purpose of describing specific embodiments and is not intended to limit the present application. The term "or / and" used herein includes any and all combinations of one or more related listed items.

[0032] Please refer to Figure 1 The present embodiment provides a bridge bent pier buckling restrained brace parameter optimization method, which comprises the following steps:

[0033] S1, first predict the seismic response of the bridge through the trained random forest-artificial neural network model; wherein the seismic response is characterized by the maximum curvature ductility coefficient μ φ and the maximum shear value V max of the pier bottom.

[0034] Then construct the target function f of μ φ , V max and the buckling restrained brace parameter; wherein the buckling restrained brace parameter comprises the cross-sectional area Si of the i-th buckling restrained brace.

[0035] In this step, the trained random forest-artificial neural network model is used to improve the model effect. The training process includes: first, select appropriate intensity indicators representing ground motion as input variable samples of the random forest-artificial neural network model. Then, considering the uncertainty of data from different sources, a large number of structure prototype numerical models are established by using Latin hypercube sampling method and other methods. A large number of structure prototype numerical models are randomly paired with the input excitation generated by the bridge parameters. Then, the engineering demand parameters are calculated by performing nonlinear time history analysis on the bridge-excitation pairs. The engineering demand parameters are used as the output variable samples of the random forest-artificial neural network model. Finally, the random forest-artificial neural network model is trained and parameterized by input variable samples and output variable samples, and the optimal configuration of the random forest-artificial neural network model is determined by k-fold cross-validation program. The trained random forest-artificial neural network model is applied to select the real seismic waves matched from the PEER database as the ground motion input of the random forest-artificial neural network model based on the selected bridge conditions, to obtain the seismic response of the bridge structure under potential seismic excitation.

[0036] The seismic response of the high pier of the bridge is related to its lateral stiffness, which is significantly affected by the cross-sectional area Si of the buckling-restrained brace (BRB). The seismic response can be represented by a damage metric indicator of the high pier, so the damage metric indicator of the high pier can be expressed as an objective function f related to n and Si, while ensuring the minimization of the pier damage:

[0037] minimize(DM)=f(n,Si).

[0038] In the formula, minimize represents minimization. n represents the number of buckling-restrained braces. The value of n is determined according to the actual situation before optimization, and n is a constant.

[0039] Further analysis shows that for high piers, the most widely used and most reliable damage metric indicator is the maximum curvature ductility factor μ φ In this embodiment, in addition to μ φ , the maximum shear value V max at the bottom of the high pier is also used to measure the damage metric indicator, that is, this embodiment finally considers two optimization objectives μ φ and V max . Therefore, the expression of f can be expanded as:

[0040]

[0041] Furthermore, after determining f, reasonable boundary conditions can be set according to actual conditions. Generally, the yield strength of BRB is greater than 500 kN and less than 3000 kN. Through conversion, the cross-sectional area of ​​BRB can be set to a range of 0.002 m². 2 ≤Si≤0.0128m 2 .

[0042] S2. Solve for f using the trained response surface model, and obtain the minimum maximum curvature ductility coefficient minμ based on n, Si, and the corresponding data of the seismic response. φ and the minimized maximum shear force value minV max .

[0043] Response surface methodology (RSM) is a mathematical and statistical method for establishing the relationship between input variables and output response. It approximates the input-output relationship of complex systems using polynomial functions, and can construct an approximate mathematical model of the system based on a finite number of sampling points. The basic idea of ​​RSM is to replace complex physical processes with simple mathematical forms, thereby significantly reducing computational costs. The advantages of RSM lie in its simplicity, high computational efficiency, ease of understanding and implementation, and ability to reflect the interactions between variables. In this embodiment, the input-output relationship of the RSM is the relationship between n and Si, representing the seismic response.

[0044] Training the response surface methodology is a key aspect of this step. The training methods for the response surface methodology are described below:

[0045] Please refer to Figure 2 The training method for response surface methodology includes the following steps:

[0046] S21. Obtain the input set for training the response surface model. Obtain the corresponding output set based on the input set.

[0047] The input set data includes the Si values ​​of each BRB. To improve training quality, the input set includes: uniformly distributed samples and boundary samples. The uniformly distributed samples are generated using a uniform design method. This method provides the most reasonable computational results with a limited number of samples because it maximizes the uniformity of spacing filling in the experimental domain. In other words, samples generated using the uniform design method are typically the most representative and uniformly distributed in the design space. Therefore, stable sampling quality can be achieved with a limited number of samples, thus greatly reducing the number of input sets required to generate a reasonable response surface model. Boundary samples are generated based on the defined boundaries of the input variables. Both uniformly distributed samples and boundary samples can be sampled using the BRB cross-sectional area range set in the above steps.

[0048] The data of the output set includes seismic responses. The seismic responses are calculated by the nonlinear time history analysis of the input set, selected ground motions compatible with the bridge parameters, and the like, and μ φ and V max are outputted to constitute the output set.

[0049] S22, the input set and the output set constitute a complete training sample. The training sample is divided into q subsets, and q-1 subsets are input into the response surface model RS0 in the initial state for training. The q subsets can be divided by a stratified sampling method, so that the q subsets are mutually exclusive subsets of the same size, and the consistency of the distribution of the training sample is maintained as much as possible.

[0050] S23, the training process is repeated L times to obtain the response surface model RS1 after preliminary training.

[0051] After obtaining RS1, a single subset remaining in S22 is used as a validation set, which uses root mean square error (RMSE), mean absolute percentage error (MAPE), and linear correlation factor (R) and other evaluation indexes to verify the performance of RS1. Specifically, RMSE reflects the deviation between the predicted value and the actual value, and is more sensitive to large errors. The smaller the value is, the more accurate the prediction is. The formula of RMSE is:

[0052]

[0053] In the formula, Predict represents the predicted value, True represents the actual value, and K is the total number of training samples in the subset.

[0054] MAPE is sensitive to errors and is suitable for problems where the target variable has a large difference in magnitude. The smaller the value is, the better the model fits the data. The formula of MAPE is:

[0055]

[0056] R is a statistical index for measuring the degree of linear correlation between two variables. Its value ranges from -1 to 1. Among them, 1 represents complete positive correlation, -1 represents complete negative correlation, and 0 represents no linear correlation. The formula of R is:

[0057]

[0058] In the formula, X k and Y k are one of the variables of the subset. represents the average value of X k . represents the average value of Y k .

[0059] S24, first obtain the local optimal solution by the RS1 trained in S23, the process includes: the definition space of the input set is evenly divided into m subspaces. In each subspace, the input set is input to the RS1 for processing to obtain m local optimal solutions corresponding to the m subspaces. Among them, the number of subspaces can be divided according to the boundary conditions of Si, and m < n should be met.

[0060] Then use the local optimal solution to enhance the effectiveness of RS1, and obtain the global optimal design configuration. The process includes: randomly select z from the m local optimal solutions and add them to the training samples to retrain RS1 until RS1 is trained to obtain the retrained response surface model RS2. Among them, z < m, and the z local optimal solutions should not have the same data as the previous training samples, in order to avoid the potential overfitting problem of RS2.

[0061] To ensure the stability and reliability of RS2, two standards are used to terminate the training iteration:

[0062] (1) The optimal configuration of Si output by RS2 is consistent with the optimal configuration of Si output by RS1.

[0063] (2) Under the same data, the error between the corresponding seismic demand predicted by RS2 and the corresponding seismic demand calculated by the finite element model in the time history analysis is within the set range.

[0064] If the two standards are met, it is considered that RS2 is trained and has sufficient effectiveness. Otherwise, repeat the process of S24 until the two standards are met to obtain the most effective RS2.

[0065] At this point, the response surface model has been trained, and RS2 is used to solve f to obtain minμ φ and minV max .

[0066] S3, in the parameter optimization process of BRB, the optimal BRB configuration is to minimize various objectives at the same time, but since the two optimization objectives μ φ and V max are contradictory: the smaller the BRB configuration μ φ , the larger the V max . In order to balance the two optimization objectives, the minμ φ and minV max are optimized by the Pareto optimal front to obtain the balanced maximum curvature ductility coefficient minμ φ ' and the maximum shear value minV max '. Among them, the formula for balanced optimization is:

[0067]

[0068] wherein J(n, Si) represents the overall performance of the bridge bent pier, wherein different values of J(n, Si) can be used to estimate the overall performance of the bridge bent pier with different ξ. ξ represents the balance coefficient, and ξ ∈ [0, 1]. represents the normalized minμ φ . represents the normalized minV max . The normalized normalization mode thereof can be determined according to actual conditions. After balance optimization, minμ and minV are restored to obtain corresponding minμ φ ' and minV max '.

[0069] S4, the previously trained response surface model is used again to process and analyze minμ φ ' and minV max '. Since n is a determined value, according to n, Si and the corresponding data of the seismic response, the inverse calculation can obtain the optimized Si.

[0070] In some other embodiments, another bridge bent pier buckling restrained brace parameter optimization system is provided, which adopts the bridge bent pier buckling restrained brace parameter optimization method as described above. The bridge bent pier buckling restrained brace parameter optimization system comprises a prediction module, an analysis module, a trade-off module and an optimization module.

[0071] The prediction module is configured to predict the seismic response of the bridge and construct μ φ , V max and the objective function f of the buckling restrained brace parameters. The analysis module is configured to solve f, and obtain the minimum maximum curvature ductility coefficient minμ φ and the minimum maximum shear value minV max according to n, Si and the corresponding data of the seismic response. The trade-off module is configured to trade-off and optimize minμ φ and minV max to obtain the balanced maximum curvature ductility coefficient minμ φ ' and the maximum shear value minV max '. The optimization module is configured to process minμ φ ' and minV max ', and obtain the optimized Si according to n, Si and the corresponding data of the seismic response.

[0072] In some other embodiments, a software program product is also provided, which comprises program instructions, and when the program instructions are executed on an electronic device, the electronic device is caused to perform the steps of the bridge bent pier buckling restrained brace parameter optimization method as described above.

[0073] The technical features of the above-described embodiments can be combined in any manner. For the sake of brevity, not all possible combinations of the technical features are described, but it is understood that the scope of the present specification includes all possible combinations.

[0074] The above-described embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be pointed out that, for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are all within the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A bridge bent pier buckling restrained brace parameter optimization method, characterized in that, It comprises the following steps: S1, first predict the seismic response of the bridge by the trained random forest-artificial neural network model; wherein the seismic response is characterized by the maximum curvature ductility coefficient μ φ of the pier body section max and the maximum shear value V of the pier bottom reconstructing μ φ , V max a target function f of the buckling-restrained brace parameters; wherein the buckling-restrained brace parameters comprise a cross-sectional area Si of the ith buckling-restrained brace; The expression of f is: In the formula, f1 and f2 respectively represent two sub-functions of f; minimize represents minimization; n represents the number of buckling restrained braces; S2, solve f by the trained response surface model, get the minimum maximum curvature ductility coefficient minμ according to n, Si and the corresponding data pair of seismic response φ and the minimum maximum shear value minV max ; S3, minμ is optimized by Pareto optimal frontier φ and minV max , to get balanced maximum curvature ductility coefficient minμ φ ′ and maximum shear value minV max ′, wherein the formula of trade-off optimization is: In the formula, J(n, Si) represents the overall performance of the bridge bent pier; ξ represents a balance coefficient, and ξ ∈ [0, 1]; represents normalized minψ φ ; represents normalized minV max ; S4, processing minμ φ and minV max to obtain the optimized Si according to the corresponding data of n, Si and seismic response.

2. The method of claim 1, wherein the bridge bent column buckling restrained brace parameter optimization method is characterized by, In S1, the real seismic waves matched from the PEER database are used as the seismic input of the random forest-artificial neural network model to obtain the seismic response of the bridge.

3. The method of claim 1, wherein the bridge bent column buckling restrained brace parameter optimization method is characterized by, In S1, boundary conditions are set for Si: 0.002 m 2 ≤ Si ≤ 0.0128 m 2 .

4. The method of claim 1, wherein the bridge bent column buckling restrained brace parameter optimization method is characterized by, In S2, the training method of the response surface model comprises the following steps: In S21, the input set during the training of the response surface model is obtained. According to the input set, the corresponding output set is obtained. In S22, the input set and the output set constitute a complete training sample. In S23, the training sample is divided into q subsets, and q-1 subsets are input into the response surface model RS0 in the initial state for training. In S23, the training process is repeated L times to obtain the response surface model RS1 after preliminary training. In S24, the definition space of the input set is divided into m subspaces. In the m subspaces, the input set is input into RS1 for processing to obtain m local optimal solutions corresponding to the m subspaces. Z local optimal solutions are selected and added to the training sample to retrain RS1 until RS1 is trained to obtain the retrained response surface model RS2; wherein z < m; RS2 is the trained response surface model.

5. The method of claim 4, wherein the bridge bent column buckling restrained brace parameter optimization method is characterized by, In S21, the input set includes: uniformly distributed samples generated by using the uniform design method, and boundary samples generated by inputting the boundary of the variable. The input set is calculated by nonlinear time history analysis to obtain the seismic response; the seismic response is used as the output set.

6. The method of claim 4, wherein the buckling-restrained brace parameters of the bridge bent column are optimized by, In S22, the remaining one subset is used as the validation set of RS1. The evaluation indexes of the validation set include: root mean square error, mean absolute percentage error, and linear correlation factor.

7. The method for optimizing the buckling-restrained brace parameters of bridge piers according to claim 4, characterized in that, In S24, the retraining completion standard satisfies two conditions; the two conditions are: (1) the optimal configuration of Si output by RS2 is consistent with the optimal configuration of Si output by RS1; (2) under the same data, the error between the corresponding seismic demand predicted by RS2 and the corresponding seismic demand calculated by the finite element model is within a set range.

8. The method of claim 1, wherein the bridge bent column buckling restrained brace parameter optimization method is characterized by, In S1, the value of n is determined before optimization, and n is a constant.

9. A bridge bent column buckling restrained brace parameter optimization system, characterized by, The bridge bent column buckling restrained brace parameter optimization system comprises: a prediction module for predicting the seismic response of the bridge and constructing μ φ , V max and the target function f of the buckling-restrained brace parameters; a resolution module for solving f, obtaining a minimized maximum curvature ductility coefficient minμ from the corresponding data pairs of n, Si and seismic response φ and a minimized maximum shear value minV max ; a balancing module for balancing and optimizing minμ φ and minV max to obtain balanced maximum curvature ductility coefficient minμ φ ′ and maximum shear value minV max ′; an optimization module for processing minμ φ and minV max to derive an optimized Si from the corresponding data pairs of n, Si and seismic response.

10. A software program product characterized in that The software program product comprises program instructions which, when executed on an electronic device, cause the electronic device to perform the steps of the bridge bent column buckling restrained brace parameter optimization method according to any one of claims 1 to 8. The software program product comprises program instructions which, when executed on an electronic device, cause the electronic device to perform the steps of the bridge bent column buckling restrained brace parameter optimization method according to any one of claims 1 to 8.

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