Bridge bent frame pier buckling constraint diagonal bracing parameter optimization method, system and product

Abstract

The invention relates to a method, a system and a product for optimizing buckling constraint diagonal bracing parameters of a bridge bent frame pier. The invention discloses a method for optimizing buckling restrained diagonal bracing parameters of a bridge bent frame pier. The method comprises the following steps: S1, predicting the seismic response of a bridge through a trained random forest-artificial neural network model; constructing a target function f of the mu phi, the Vmax and a buckling restrained brace parameter; and S2, f is solved through the trained response surface model. According to the method, a random forest-artificial neural network model is adopted to predict the seismic response of a bridge, an objective function f of buckling constraint diagonal bracing parameters is constructed according to the seismic response, then f is solved through a response surface model, and finally the solving result of the response surface model is optimized through a Pareto optimal leading edge, so that the seismic response of the bridge is predicted. Therefore, the parameters of the buckling restrained braces at all positions can be obtained, the buckling restrained braces in the bridge can be optimally arranged, and reasonability and economical efficiency are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge engineering, and particularly to a method, system and product for optimizing the parameters of buckling-restrained braces of bridge bent piers. Background Art

[0002] In China, especially in the mountainous areas of the west, beam bridges with double-column or multi-column bent high piers are quite common. Their characteristic is that the height is usually between 20 and 50 meters to meet the needs of terrain changes in mountainous areas. At the same time, concrete cross girders will be set between the pier columns to enhance the lateral anti-pushing stiffness of the piers. Generally, a cross beam is set every about 7 meters along the pier height, and multiple cross girders will be set on the entire high pier to form a "multi-layer" structural form. However, China is a country with frequent earthquakes, especially in the mountainous areas of the west where seismic activities are particularly frequent. In recent years, it has experienced many major earthquakes, and the serious seismic damage to transportation infrastructure such as bridges has caused huge losses to the country and society. The beam bridge with a bent high pier, as a key node of the transportation network system in the mountainous areas of the west and even possibly the only passage to the earthquake-stricken area, its seismic performance is crucial and in urgent need of in-depth research and evaluation.

[0003] Setting buckling-restrained braces between the pier columns of a bent pier can significantly improve the seismic performance of the bridge. The braces are generally obliquely arranged between the cross girders. Since the bent high pier is generally of a multi-layer structural form, this 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 best effect of reducing seismic response and improving seismic performance is a key problem facing designers. In current research and engineering practice, the setting of buckling-restrained brace parameters is mainly determined according to the experience of designers and calculation by specification formulas. Generally, it is through uniform arrangement, that is, the same design parameters are used for each layer of braces. This design method lacks a certain degree of rationality and economy and is difficult to obtain the optimal layout form. On the other hand, if a parameter analysis method such as the nonlinear time history analysis method is used to determine the optimal parameters of multi-layer braces, a large number of parameter conditions and nonlinear seismic response analyses need to be involved, and a large amount of time is required to analyze and process the data. Summary of the Invention

[0004] Based on this, in view of the problem that the existing braces are generally arranged uniformly and it is difficult to obtain the optimal layout form, it is necessary to provide a method, system and product for optimizing the parameters of buckling-restrained braces of bridge bent piers.

[0005] In the first aspect, the present invention proposes a method for optimizing the parameters of buckling-restrained braces of bridge bent piers, which includes the following steps:

[0006] S1. First, predict the seismic response of the bridge through a trained random forest-artificial neural network model; wherein, the seismic response is represented by the maximum curvature ductility coefficient μ of the pier cross-section φand the maximum shear force value V at the pier bottom max are characterized;

[0007] Then construct μ φ , V max and the objective function f of the buckling-restrained brace parameters; among them, 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 through the trained response surface model, and obtain the minimized maximum curvature ductility coefficient minμ φ and the minimized maximum shear force value minV max ;

[0012] S3. Perform trade-off optimization on minμ φ and minV max to obtain the balanced maximum curvature ductility coefficient minμ φ ′ and the maximum shear force value minV max ′, where the formula for 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 minμ φ ; represents the normalized minV max ;

[0015] S4. Process minμ φ ′ and minV max ′ through the trained response surface model, and obtain the optimized Si according to the corresponding data of n, Si and the seismic response.

[0016] In the second aspect, the present invention also proposes a system for optimizing the buckling-restrained brace parameters of a bridge bent pier, which adopts the method for optimizing the buckling-restrained brace parameters of a bridge bent pier in the first aspect. The system for optimizing the buckling-restrained brace parameters of a bridge bent pier includes: 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 the bridge and construct μ φ , V max and the objective function f of the parameters of the buckling-restrained brace.

[0018] The analysis module is used to solve f, and obtain the minimized maximum curvature ductility coefficient minμ φ and the minimized maximum shear force value minV max .

[0019] The trade-off module is used to perform trade-off optimization on minμ φ and minV max to obtain the balanced maximum curvature ductility coefficient minμ φ ′ and the maximum shear force value minV max ′.

[0020] The optimization module is used to process minμ φ ′ and minV max ′, and obtain the optimized Si according to the corresponding data pairs of n, Si and the seismic response.

[0021] In a third aspect, the present invention also proposes a software program product, which includes program instructions that, when running on an electronic device, cause the electronic device to execute the steps of the method for optimizing the parameters of the buckling-restrained brace of the bridge bent pier in the first aspect.

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

[0023] 1. The present invention uses a random forest-artificial neural network model to predict the seismic response of the bridge, constructs the objective function f of the parameters of the buckling-restrained brace according to the seismic response, then solves f through the response surface model, and finally optimizes the solution results of the response surface model through the Pareto optimal frontier, so as to obtain the parameters of the buckling-restrained brace at each position, so that the buckling-restrained braces in the bridge can achieve optimal layout, improving rationality and economy.

[0024] 2. The present invention uses a random forest-artificial neural network model and a response surface model to optimize the parameters of the buckling-restrained brace. Compared with the existing single learning algorithm, it has better robustness and stability. Compared with the nonlinear time history analysis, the required computational amount is less, and the time efficiency can be greatly improved.

[0025] 3. The present invention retrains the response surface model through the local optimal solution, which not only reduces the number of samples, but also improves the accuracy of model prediction.

[0026] 4. The present invention uses the Pareto optimal frontier for trade - off, and can simultaneously take into account the global optimal configuration of two conflicting optimization objectives in the parameters of the buckling - restrained brace. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0028] Figure 1 is a flowchart of the method for optimizing the parameters of the buckling - restrained brace of the bridge bent pier;

[0029] Figure 2 is a flowchart of the training of the response surface model. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

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

[0032] Please refer to Figure 1 , this embodiment provides a method for optimizing the parameters of the buckling - restrained brace of the bridge bent pier, which includes the following steps:

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

[0034] Then, construct the objective function f of μ φ , V max and the parameters of the buckling - restrained brace; among them, the parameters of the buckling - restrained brace include the cross - sectional area Si of the i - th buckling - restrained brace.

[0035] In this step, the random forest-artificial neural network model is trained and then used to improve the model performance. The training process includes: First, appropriate intensity indices representing ground motions are selected as the input variable samples of the random forest-artificial neural network model. Then, methods such as Latin hypercube sampling are adopted to consider the uncertainties of data from different sources, and a large number of numerical models of structural prototypes are established. A large number of numerical models of structural prototypes are randomly paired with the input excitations generated by bridge parameters. Subsequently, the engineering demand parameters are calculated through nonlinear time history analysis of the bridge-excitation pairs. These engineering demand parameters serve as the output variable samples of the random forest-artificial neural network model. Finally, the random forest-artificial neural network model is trained and tuned with the input variable samples and output variable samples, and the optimal configuration of the random forest-artificial neural network model is determined through k-fold cross-validation. Applying the trained random forest-artificial neural network model, based on the selected bridge conditions, real seismic waves matched from the PEER database are selected as the ground motion input of the random forest-artificial neural network model to obtain the seismic responses of the bridge structure under potential seismic excitations.

[0036] The seismic response of high piers of bridges is related to their lateral stiffness, and the lateral stiffness is significantly affected by the cross-sectional area Si of the buckling-restrained braces (hereinafter referred to as BRB in the following description). The seismic response can be characterized by the damage metric index of the high piers. Therefore, the damage metric index of the high piers can be expressed as an objective function f related to n and Si, while ensuring the minimization of pier damage:

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

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

[0039] Further analysis shows that for high piers, the most extensive and reliable damage metric index is the maximum curvature ductility coefficient μ of the pier cross-section φ . In this embodiment, in addition to μ φ , the maximum shear force value V at the bottom of the high pier max is also used to measure the damage metric index, that is, in this embodiment, two optimization objectives μ φ and V max are finally considered. Therefore, the expression of f can be expanded as follows:

[0040]

[0041] In addition, after determining f, reasonable boundary conditions can also be set according to actual conditions. Generally, the yield force of the BRB is greater than 500 KN and less than 3000 KN. Through conversion, the BRB cross-sectional area range can be set to 0.002 m 2 ≤Si≤0.0128 m 2 .

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

[0043] The response surface model is a mathematical and statistical method for establishing the relationship between input variables and output responses. It approximately describes the input-output relationship of a complex system through polynomial functions and can construct an approximate mathematical model of the system based on a limited number of sampling points. The basic idea of the response surface model is to use a simple mathematical form to replace a complex physical process, thereby greatly reducing the computational cost. The advantages of the response surface model are simple form, high computational efficiency, easy to understand and implement, and can reflect the interaction between variables. In this embodiment, the input-output relationship of the response surface model is the relationship between n, Si, and seismic response.

[0044] In this step, the training of the response surface model is one of the key points. The following introduces the training method of the response surface model

[0045] Please refer to Figure 2 , the training method of the response surface model includes the following steps

[0046] S21. Obtain the input set during the training of the response surface model. Obtain the corresponding output set according to the input set

[0047] The data in the input set includes Si of each BRB. To improve the training quality, the input set includes: uniformly distributed samples, boundary samples. The uniformly distributed samples are generated using the uniform design method. This method can provide the most reasonable calculation results under the condition of limited samples because it maximizes the uniformity of the spacing filling in the experimental domain. That is to say, the samples generated using the uniform design method are usually the most representative and evenly distributed in the design space. Therefore, stable sampling quality can be achieved under the condition of limited sample quantity, thereby greatly reducing the number of the input set required to generate a reasonable response surface model. The boundary samples are generated according to the defined boundaries of the input variables. At the same time, both the uniformly distributed samples and the boundary samples can be sampled through 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 through nonlinear time history analysis of the input set, the selected ground motions compatible with the bridge parameters, etc., and μ φ and V max used to characterize the seismic responses are taken as the output to form 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. Among them, the q subsets can be divided by the method of stratified sampling, 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. Repeat the training process L times to obtain the response surface model RS1 after preliminary training.

[0051] After obtaining RS1, use the remaining single subset in S22 as the validation set, and use evaluation indexes such as root mean square error (RMSE), mean absolute percentage error (MAPE) and linear correlation factor (R) to verify the performance of RS1. Specifically, RMSE reflects the deviation between the predicted value and the actual value and is more sensitive to larger errors. The smaller its value, the more accurate the prediction. 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 with large differences in the magnitudes of target variables. The smaller its value, the better the model fits the data. The formula of MAPE is:

[0055]

[0056] R is a statistical index used to measure the linear correlation degree between two variables. Its value range is between - 1 and 1. Among them, 1 represents a perfect positive correlation, - 1 represents a perfect negative correlation, and 0 represents no linear correlation. The formula of R is:

[0057]

[0058] In the formula, X k and Y k are respectively 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 through the RS1 trained in S23. The process includes: evenly dividing the definition space of the input set into m subspaces. In each subspace, input the input set into 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 it is necessary to satisfy m < n.

[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 training is completed to obtain the retrained response surface model RS2. Among them, z < m, and these z local optimal solutions should not have the same data as the previous training samples to avoid potential overfitting problems of RS2.

[0061] To ensure the stability and reliability of RS2, terminate the training iteration through two criteria:

[0062] (1) The best configuration of Si output by RS2 is the same as the best 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 criteria are met, it is considered that RS2 training is completed and has sufficient effectiveness. Otherwise, repeat the process of S24 until the two criteria are met to obtain the most effective RS2.

[0065] So far, the response surface model has been trained. Solve f through RS2 to obtain minμ φ and minV max .

[0066] S3. In the process of parameter optimization of BRB, the optimal BRB configuration is to ensure the simultaneous minimization of various objectives. However, since the two optimization objectives of μ φ and V max are contradictory: the smaller the BRB configuration of μ φ will result in a larger V max . To balance the two optimization objectives, trade - off optimization is performed on minμ φ and minV max through the Pareto optimal frontier to obtain the balanced maximum curvature ductility coefficient minμ φ ′ and the maximum shear force value minV max ′. Among them, the formula for balance optimization is:

[0067]

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

[0069] S4. Use the previously trained response surface model to process and analyze minμ φ ′ and minV max ′ again. Since n is a determined value, the optimized Si can be obtained by back-calculation based on the corresponding data of n, Si, and the seismic response.

[0070] In some other embodiments, there is also a parameter optimization system for the buckling-restrained braces of a bridge bent pier, which adopts the parameter optimization method for the buckling-restrained braces of a bridge bent pier as described above. The parameter optimization system for the buckling-restrained braces of a bridge bent pier includes: a prediction module, an analysis module, a trade-off module, and an optimization module.

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

[0072] In some other embodiments, a software program product is also proposed. The software program product includes program instructions that, when running on an electronic device, cause the electronic device to execute the steps of the parameter optimization method for the buckling-restrained braces of a bridge bent pier as described above.

[0073] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as falling within the scope described in this specification.

[0074] The above-described embodiments only express several implementation manners of the present invention, and the description thereof is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention patent shall be subject to the appended claims.

Claims

1. A method for optimizing the parameters of buckling-restrained braces of a bridge bent pier, characterized in that It includes the following steps: S1. First, predict the seismic response of the bridge through the trained random forest-artificial neural network model; among them, the seismic response is characterized by the maximum curvature ductility coefficient μ of the pier cross-section φ and the maximum shear force value V at the pier bottom max for characterization; Reconstruct μ φ , V max and the objective function f of the parameters of the buckling-restrained brace; among them, the parameters of the buckling-restrained brace include the cross-sectional area Si of the i-th 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 restraint braces; S2. Solve for f using the trained response surface model, and obtain the minimized 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 ; S3. Through the Pareto optimal frontier, balance minμ φ and minV max to obtain the balanced maximum curvature ductility coefficient minμ φ ' and the maximum shear force value minV max ', where the formula for the balance optimization is: 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 minψ φ ; represents the normalized minV max ; S4. Process minμ φ ′ and minV max ′ through the trained response surface model, and obtain the optimized Si based on the corresponding data of n, Si, and seismic response.

2. The method for optimizing the parameters of the buckling-restrained diagonal bracing of a bridge bent pier according to claim 1, wherein In S1, the real seismic waves matched from the PEER database are used as the ground motion input of the random forest-artificial neural network model to obtain the seismic response of the bridge.

3. The method for optimizing the parameters of the buckling-restrained diagonal bracing of a bridge bent pier according to claim 1, wherein, In S1, set the boundary condition for Si: 0.002m 2 ≤ Si ≤ 0.0128m 2 .

4. The method for optimizing the parameters of the buckling-restrained diagonal braces of a bridge bent pier according to claim 1, wherein In S2, the training method of the response surface model includes the following steps: S21. Obtain the input set during the training of the response surface model; Obtain the corresponding output set according to the input set; S22. The input set and the output set constitute a complete training sample; Divide the training sample into q subsets, and input q - 1 subsets into the response surface model RS0 in the initial state for training; S23. Repeat the training process L times to obtain the preliminarily trained response surface model RS1; S24. Divide the definition space of the input set into m subspaces; In the m subspaces, input the input set into RS1 for processing respectively to obtain m local optimal solutions corresponding to the m subspaces; Select z local optimal solutions and add them to the training sample to retrain RS1 until RS1 is trained to completion to obtain the retrained response surface model RS2; where z < m; RS2 is the trained response surface model.

5. The method for optimizing the parameters of the buckling-restrained diagonal braces of the bridge bent pier according to claim 4, wherein In S21, the input set includes: uniformly distributed samples generated using the uniform design method, and boundary samples generated through the boundaries of the input variables; Calculate the seismic response of the input set through nonlinear time history analysis; the seismic response is used as the output set.

6. The method for optimizing the parameters of the buckling-restrained diagonal bracing of a bridge bent pier according to claim 4, wherein 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 parameters of the buckling-restrained diagonal bracing of the bridge bent pier according to claim 4, wherein In S24, the criteria for the completion of retraining satisfy two conditions; the two conditions are: (1) The optimal configuration of Si output by RS2 is the same as 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 the set range.

8. The method for optimizing the parameters of the buckling-restrained diagonal braces of a bridge bent pier according to claim 1, characterized in that In S1, the value of n is determined before optimization, and n is a fixed value.

9. A buckling-restrained brace parameter optimization system for a bridge bent pier, characterized in that, It adopts the buckling restraint brace parameter optimization method for the bridge bent pier as described in any one of claims 1 to 8; the buckling restraint brace parameter optimization system for the bridge bent pier includes: A prediction module, which is used to predict the seismic response of a bridge and construct μ φ , V max and the objective function f of the parameters of the buckling-restrained brace; An analysis module, which is used to solve for f, and obtain the minimized 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 ; A weighing module, which is used to weigh and optimize minμ φ and minV max to obtain the balanced maximum curvature ductility coefficient minμ φ ' and the maximum shear force value minV max '; Optimization module, which is used to process minμ φ ′ and minV max ′, and obtain the optimized Si according to the corresponding data of n, Si and seismic response.

10. A software program product, characterized in that, This software program product includes program instructions, which, when running on an electronic device, cause the electronic device to execute the steps of the buckling restraint brace parameter optimization method for the bridge bent pier as described in any one of claims 1 to 8.

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