Optimal design method of seismic isolation parameters based on artificial neural network

Abstract

The present invention relates to the technical field of bridge seismic isolation and mitigation, and discloses an artificial neural network-based seismic isolation parameter optimization design method, comprising the following steps: determining all optimizable variables in a combined seismic isolation system and a high-precision feasible domain range of all optimizable variables; uniformly distributing and sampling multiple groups of sampling parameters for all optimizable variables within the corresponding high-precision feasible domain range; performing earthquake risk analysis based on all groups of sampling parameters of all optimizable variables and a numerical model of the combined seismic isolation system to obtain samples of a preset group of optimizable variables-system seismic risks; using a sample training model of the preset group of optimizable variables-system seismic risks to establish a seismic risk mapping model of all optimizable variables and the combined seismic isolation system; using the seismic risk mapping model as an objective function and combining it with a genetic algorithm for global optimization to search for a design parameter combination of all optimizable variables with the goal of minimizing seismic risks; and improving the safety and reliability of the combined seismic isolation system in earthquakes.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge seismic isolation and reduction, and in particular to a seismic isolation and reduction parameter optimization design method based on an artificial neural network. Background Art

[0002] In the field of high-speed rail bridge engineering, earthquake damage to high-speed rail bridges, and the resulting casualties and property losses, have always been a daunting challenge. As an effective earthquake mitigation measure, seismic isolation technology, by installing seismic isolation devices between high-speed rail bridges and their foundations, can significantly reduce the transfer of seismic energy to the upper structure, thereby ensuring the safety of high-speed rail bridges during earthquakes. It is also an effective measure to ensure the seismic safety of bridge-track structures in my country's high-speed rail network. In theory, a system with two or more seismic isolation devices that complement each other and work together, known as a combined seismic isolation system, can achieve significantly better shock absorption than a single device. Optimizing the design of seismic isolation parameters is crucial to fully realizing the effectiveness of seismic isolation technology. Reasonable parameter settings can improve the seismic resistance of high-speed rail bridges while balancing cost-effectiveness and achieving a balance between safety and economy. This not only helps protect people's lives and property, but also promotes the sustainable development of the high-speed rail bridge industry, with far-reaching implications for infrastructure construction and urban development in earthquake-prone areas.

[0003] At present, the conventional technologies used for seismic isolation parameter design are mainly based on empirical formulas, simplified theoretical models and numerical simulation methods. Although empirical formulas are simple and easy to use, they often lack comprehensive consideration of complex actual situations and have limited accuracy. Simplified theoretical models make many idealized assumptions about the structure and are difficult to accurately reflect the mechanical behavior of the real structure under earthquake action. Although numerical simulation methods can simulate structural responses in more detail, the computational cost is high and a large amount of manual intervention and trial and error are required during parameter adjustment and optimization, resulting in low efficiency. With the rapid development of computer technology and artificial intelligence, methods based on artificial neural networks have provided new ideas and approaches for the optimization design of seismic isolation parameters. Artificial neural networks have powerful nonlinear mapping and self-learning capabilities, and can effectively handle complex input-output relationships. They are expected to break through the limitations of traditional methods, achieve efficient and accurate optimization of seismic isolation parameters, and promote a wider and more scientific application of seismic isolation technology in the field of high-speed railway bridge engineering.

[0004] Therefore, the present invention proposes an optimization design method for seismic isolation parameters based on artificial neural network. Summary of the Invention

[0005] The present invention provides an optimization design method for seismic isolation parameters based on artificial neural networks. First, all optimizable variables in the combined shock absorption system and their high-precision feasible domain ranges are determined to ensure that the variable values ​​meet the actual engineering and high-precision design standards, and to indicate the correct direction for the optimization design. Then, the variables are evenly sampled in the feasible domain to obtain multiple groups of sampling parameters. The earthquake risk analysis is carried out in combination with the numerical model of the combined shock absorption system to obtain a representative preset group of optimizable variables-system earthquake risk samples, providing rich data for model training. These samples are then used to train the model and optimize the neural network structure to construct a mapping model that can accurately depict the complex nonlinear relationship between variables and earthquake risks. Finally, the model is used as the objective function, and the genetic algorithm is combined with global optimization to efficiently find the optimizable variable design parameter combination with the lowest earthquake risk as the goal in the complex variable space, thereby improving the safety and reliability of the combined shock absorption system in earthquakes, providing an accurate and efficient optimization solution for the design of shock absorption and isolation engineering, and helping to improve the seismic performance of engineering structures.

[0006] The present invention provides a method for optimizing the design of seismic isolation parameters based on an artificial neural network, comprising:

[0007] S1: Determine all optimizable variables in the combined shock absorption system and determine the high-precision feasible domain range of all optimizable variables;

[0008] S2: uniformly distribute sampling on all optimizable variables within the corresponding high-precision feasible region to obtain multiple groups of sampling parameters for all optimizable variables. Based on all groups of sampling parameters of all optimizable variables and the numerical model of the combined shock absorption system, earthquake risk analysis is performed to obtain samples of the preset group of optimizable variables-system earthquake risk;

[0009] S3: Using a preset set of optimizable variables-system earthquake risk sample training models, and optimizing the neural network structure, establish an earthquake risk mapping model for all optimizable variables and the combined shock absorption system;

[0010] S4: The earthquake risk mapping model is used as the objective function, and a genetic algorithm is used to perform global optimization to search for the design parameter combination of all optimizable variables with the goal of minimizing the earthquake risk.

[0011] Preferably, S1: determining all optimizable variables in the combined shock absorption system and determining the high-precision feasible domain range of all optimizable variables, including:

[0012] The friction coefficient, equivalent radius, damping clamp gap and yield force of the friction pendulum support in the combined damping system are all optimizable variables;

[0013] Establish a refined finite element model of the combined shock absorption system;

[0014] Set the seismic input under different parameter combinations of all optimizable variables, and calculate the displacement of the combined damping system, the acceleration of the track structure, and the internal force response of the bridge pier as the corresponding seismic output response;

[0015] Based on the safety threshold range of the seismic output response and the corresponding seismic output response under different parameter combinations of all optimizable variables, the high-precision feasible domain range of all optimizable variables is determined.

[0016] Preferably, based on the safety threshold range of the earthquake output response and the earthquake output response corresponding to different parameter combinations of all optimizable variables, the high-precision feasible region range of all optimizable variables is determined, including:

[0017] Among all parameter combinations of all optimizable variables, all parameter combinations whose corresponding earthquake output responses are within the corresponding safety threshold range are screened out as all feasible parameter combinations of all optimizable variables, and all parameter combinations whose corresponding earthquake output responses have at least one output response outside the corresponding safety threshold range are screened out as all infeasible parameter combinations of all optimizable variables;

[0018] Based on all feasible parameter combinations and all infeasible parameter combinations of all optimizable variables and a classification hyperplane method, a first feasible domain range of all optimizable variables is determined;

[0019] Determine a second feasible domain range of all optimizable variables based on the Mahalanobis distance between each feasible parameter combination of all optimizable variables and all infeasible parameter combinations;

[0020] Based on the first feasible domain range and the second feasible domain range of all optimizable variables, a high-precision feasible domain range of all optimizable variables is determined.

[0021] Preferably, based on all feasible parameter combinations and all infeasible parameter combinations of all optimizable variables and a classification hyperplane method, a first feasible domain range of all optimizable variables is determined, including:

[0022] Based on all feasible parameter combinations and all infeasible parameter combinations of all optimizable variables and the classification hyperplane method, and introducing slack variables, the optimization problem is constructed:

[0023]

[0024] Where w=(w1,w2,…,w n ) T is the normal vector of the hyperplane, b is the bias term, ξ is the slack variable, ||w|| 2 is the square of the norm of w, is the objective function whose goal is to minimize half of the modulus of the hyperplane normal vector, C is the penalty coefficient, N v is the number of feasible parameter combinations, N u is the number of infeasible parameter combinations, ξ i is the slack variable of the i-th group of samples, y i is the label of the sample, y of the feasible parameter combination i =1, y of infeasible parameter combination i =-1, w T is the transposed matrix of w, X i is the i-th sample point in all parameter combinations of all optimizable variables;

[0025] The optimization problem is solved to obtain w and b. Based on the obtained w and b and the preset buffer coefficient, the first feasible region range of all optimizable variables is determined as:

[0026] w T X+b≥-∈

[0027] Where X=(x1,x2,…,x n ) T is an n-dimensional optimizable variable vector, and ∈ is the preset buffer coefficient.

[0028] Preferably, determining the second feasible domain range of all optimizable variables based on the Mahalanobis distance between each feasible parameter combination of all optimizable variables and all infeasible parameter combinations includes:

[0029] Determine the Mahalanobis distance between each feasible parameter combination and all infeasible parameter combinations of all optimizable variables;

[0030] All feasible parameter combinations whose Mahalanobis distance does not exceed the preset boundary threshold are regarded as all near-boundary feasible parameter combinations;

[0031] The second feasible region range of all optimizable variables is determined based on the convex hull algorithm and all near-boundary feasible parameter combinations.

[0032] Preferably, based on the first feasible domain range and the second feasible domain range of all optimizable variables, a high-precision feasible domain range of all optimizable variables is determined, including:

[0033] The intersection of the first feasible domain range and the second feasible domain range of all optimizable variables is regarded as the high-precision feasible domain range of all optimizable variables.

[0034] Preferably, S2: uniformly sampling all optimizable variables within the corresponding high-precision feasible domain to obtain multiple groups of sampling parameters for all optimizable variables, performing earthquake risk analysis based on all groups of sampling parameters of all optimizable variables and a numerical model of the combined shock absorption system to obtain a sample of the earthquake risk of a preset group of optimizable variables-system, including:

[0035] Using Latin hypercube sampling, all optimizable variables are sampled evenly within the corresponding high-precision feasible domain to obtain multiple sets of sampling parameters for all optimizable variables.

[0036] Conduct earthquake risk analysis based on each set of sampling parameters and the combined shock absorption system numerical model of all optimizable variables to obtain earthquake risk indicators for each set of sampling parameters;

[0037] Based on all group sampling parameters of all optimizable variables and the corresponding earthquake risk indicators, a sample of the preset group of optimizable variables-system earthquake risk is obtained.

[0038] Preferably, S3: using a sample training model of a preset set of optimizable variables-system earthquake risk, and optimizing the neural network structure, to establish an earthquake risk mapping model of all optimizable variables and the combined shock absorption system, including:

[0039] The artificial neural network model is trained using samples of a preset group of optimizable variables-system earthquake risks. The learning rate is dynamically adjusted, and an adaptive moment estimation optimizer is introduced. The number of hidden layer neurons is determined through cross-validation to optimize the neural network structure, and an earthquake risk mapping model of all optimizable variables and the combined shock absorption system is established.

[0040] Preferably, it also includes:

[0041] S5: Verify the effectiveness of the design parameter combination of all optimizable variables with the goal of minimizing earthquake risk through numerical simulation, and obtain the effectiveness verification value of the design parameter combination of all optimizable variables;

[0042] S6: Determine whether the validity verification value of the design parameter combination of all optimizable variables is lower than a preset threshold. If so, start the active learning mechanism and add a preset group of new optimizable variable-system earthquake risk samples to retrain the artificial neural network model until the validity of the new design parameter combination of all optimizable variables with the lowest earthquake risk as the goal determined based on the latest established earthquake risk mapping model of all optimizable variables and the combined shock absorption system is not lower than the threshold. Then, the newly obtained design parameter combination of all optimizable variables with the lowest earthquake risk as the goal is regarded as the optimal design parameter combination of all optimizable variables. Otherwise, the design parameter combination of all optimizable variables is regarded as the optimal design parameter combination of all optimizable variables.

[0043] Preferably, S5: verifying the validity of the design parameter combination of all optimizable variables with the goal of minimizing earthquake risk through numerical simulation, and obtaining the validity verification value of the design parameter combination of all optimizable variables, including:

[0044] Establish a verification model based on the refined finite element model of the combined vibration damping system and actual engineering constraints;

[0045] Set the earthquake motion input of the verification model and select the solution algorithm to obtain the key response output of the verification model;

[0046] Calculate the relative optimization effect value based on the key response output of the validation model;

[0047] Comparing the key response output of the verification model with the absolute threshold to obtain an absolute threshold verification result;

[0048] Compare the relative optimization effect value with the preset optimization effect threshold to obtain the relative optimization effect verification result;

[0049] The validity verification values ​​of the design parameter combinations of all optimizable variables are obtained based on the absolute threshold verification results and the relative optimization effect verification results.

[0050] The beneficial effects of the present invention compared to the prior art are as follows: first, all optimizable variables in the combined shock absorption system and their high-precision feasible domain ranges are determined to ensure that the variable values ​​meet the actual engineering and high-precision design standards, and to indicate the correct direction for the optimization design. Then, the variables are evenly sampled in the feasible domain to obtain multiple groups of sampling parameters, and the earthquake risk analysis is carried out in combination with the numerical model of the combined shock absorption system to obtain a representative preset group of optimizable variables-system earthquake risk samples, providing rich data for model training. These samples are then used to train the model and optimize the neural network structure to construct a mapping model that can accurately characterize the complex nonlinear relationship between variables and earthquake risks. Finally, the model is used as the objective function, combined with the genetic algorithm for global optimization, to efficiently find the optimizable variable design parameter combination with the lowest earthquake risk as the goal in the complex variable space, thereby improving the safety and reliability of the combined shock absorption system in earthquakes, providing a precise and efficient optimization solution for the design of seismic isolation engineering, and helping to improve the seismic performance of engineering structures.

[0051] Other features and advantages of the present invention will be described in the following description, and in part will become apparent from the description, or will be understood by practicing the present invention. The purpose and other advantages of the present invention can be achieved and obtained through the structures specifically pointed out in this application document.

[0052] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0054] Figure 1 This is a flow chart of a first method for optimizing seismic isolation parameters based on an artificial neural network in an embodiment of the present invention;

[0055] Figure 2 This is an execution logic diagram of a seismic isolation parameter optimization design method based on an artificial neural network in an embodiment of the present invention;

[0056] Figure 3 This is a flow chart of the second method for optimizing seismic isolation parameters based on artificial neural networks in an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0058] Example 1:

[0059] The present invention provides a method for optimizing the design of seismic isolation parameters based on artificial neural network. Figure 1 and Figure 2 ,include:

[0060] S1: Determine all optimizable variables in the combined shock absorption system and determine the high-precision feasible domain range of all optimizable variables;

[0061] S2: uniformly distribute sampling on all optimizable variables within the corresponding high-precision feasible region to obtain multiple groups of sampling parameters for all optimizable variables. Based on all groups of sampling parameters of all optimizable variables and the numerical model of the combined shock absorption system, earthquake risk analysis is performed to obtain samples of the preset group of optimizable variables-system earthquake risk;

[0062] S3: Using a preset set of optimizable variables-system earthquake risk sample training models, and optimizing the neural network structure, establish an earthquake risk mapping model for all optimizable variables and the combined shock absorption system;

[0063] S4: The earthquake risk mapping model is used as the objective function, and a genetic algorithm is used to perform global optimization to search for the design parameter combination of all optimizable variables with the goal of minimizing the earthquake risk.

[0064] In this example:

[0065] Combined damping systems consist of two or more damping devices that complement each other and work together. Compared to a single damping device, combined damping systems offer superior damping performance and are an effective measure for ensuring the seismic safety of bridge-track structures in my country's high-speed railway network. These systems include parameters such as the friction coefficient and equivalent radius of the friction pendulum bearings, the damping latch gap, and the yield strength. These parameters can be optimized to enhance the system's performance during earthquakes.

[0066] Optimizable variables refer to parameters within the combined damping system that can be adjusted and optimized. These include the friction coefficient and equivalent radius of the friction pendulum bearing, the gap between the damping clips, and the yield strength. Optimizing these variables effectively reduces the impact of earthquakes on the structure and improves the combined damping system's seismic resistance.

[0067] The high-precision feasible domain of all optimizable variables refers to the range of values ​​that can be taken by the optimizable variables while meeting actual engineering requirements and high-precision design standards. To determine this range, a refined finite element model of the combined damping system is first established. Different combinations of optimizable variable parameters are set and input into the seismic motion. The displacement of the combined damping system, the acceleration of the track structure, and the internal force response of the bridge piers are calculated as the seismic output responses. Based on the safety thresholds of these responses, feasible and infeasible parameter combinations of all optimizable variables are screened. The first feasible domain is determined using the classification hyperplane method. The second feasible domain is determined by calculating the Mahalanobis distance between each feasible parameter combination and all infeasible parameter combinations. Finally, the intersection of the two is taken to obtain the high-precision feasible domain. This range provides a reasonable interval for the values ​​of the optimizable variables, ensuring the feasibility and accuracy of the optimized design.

[0068] Multiple sets of sampled parameters for all optimizable variables: These sets of parameter values ​​are obtained by uniformly sampling across the high-precision feasible domain of all optimizable variables using Latin hypercube sampling. These sampled parameters fully cover the feasible domain and are representative. Subsequent earthquake risk analysis will be conducted based on these sampled parameters and the numerical model of the combined seismic mitigation system, providing a data foundation for establishing a relationship between optimizable variables and earthquake risk.

[0069] The numerical model of the combined seismic isolation system is a digital simulation model used to simulate the mechanical response of the combined seismic isolation system, such as displacement, track structure acceleration, and internal force response of bridge piers, under different combinations of optimizable variable parameters and earthquake inputs. This model is used to analyze seismic risk by combining multiple sets of sampled parameters for all optimizable variables, generating seismic risk indicators corresponding to different parameter combinations and, in turn, obtaining samples of the optimizable variable-system seismic risk.

[0070] Preset Group: A predefined number of samples or parameter combinations during implementation. For example, when obtaining samples for the variable that optimizes system earthquake risk, a "preset group" of samples is required to meet the data volume requirements for subsequent model training and other operations, ensuring the accuracy and reliability of the results.

[0071] Optimizable variable-system earthquake risk samples: Multiple sets of sampling parameters are obtained by uniformly sampling within the high-precision feasible domain of the optimizable variables. Seismic risk analysis is then conducted based on these sampling parameters and the numerical model of the combined seismic reduction system. The resulting sample set contains the sampling parameters of all optimizable variables and their corresponding earthquake risk indicators, which are used to train an artificial neural network model to establish a mapping between the optimizable variables and the earthquake risk of the combined seismic reduction system.

[0072] A seismic risk mapping model for all optimizable variables and the combined seismic absorption system was developed. This model was trained using a preset set of optimizable variable-system seismic risk samples. The neural network structure was optimized by dynamically adjusting the learning rate, introducing an adaptive moment estimation optimizer, and employing cross-validation to determine the number of hidden layer neurons. This model accurately depicts the complex, nonlinear relationship between all optimizable variables and the seismic risk of the combined seismic absorption system, providing a key basis for subsequently identifying the optimal design parameter combination.

[0073] Using the earthquake risk mapping model as the objective function, combined with a genetic algorithm, a global optimization search is conducted to identify the design parameter combination of all optimizable variables that minimizes earthquake risk. Using the established earthquake risk mapping model for all optimizable variables and the combined shock absorption system as the objective function, a genetic algorithm is used to simulate the selection, crossover, and mutation operations of biological evolution, conducting a global search within the complex space of all optimizable variables. Through continuous iterative optimization, the design parameter combination of all optimizable variables that minimizes the earthquake risk of the combined shock absorption system is found. This improves the safety and reliability of the combined shock absorption system during earthquakes and provides the optimal seismic isolation parameter design scheme for practical projects.

[0074] Example 2:

[0075] Based on Example 1, S1: Determine all optimizable variables in the combined vibration reduction system and determine the high-precision feasible domain range of all optimizable variables, including:

[0076] The friction coefficient, equivalent radius, damping clamp gap and yield force of the friction pendulum support in the combined damping system are all optimizable variables;

[0077] Establish a refined finite element model of the combined shock absorption system;

[0078] Set the seismic input under different parameter combinations of all optimizable variables, and calculate the displacement of the combined damping system, the acceleration of the track structure, and the internal force response of the bridge pier as the corresponding seismic output response;

[0079] Based on the safety threshold range of the seismic output response and the corresponding seismic output response under different parameter combinations of all optimizable variables, the high-precision feasible domain range of all optimizable variables is determined.

[0080] In this example:

[0081] The friction coefficient, equivalent radius, damping clip gap, and yield force of the friction pendulum bearing are all optimizable variables in the combined damping system. The friction coefficient of the friction pendulum bearing affects the friction between the bearing and the structure, changing the energy dissipation method; the equivalent radius determines the kinematic characteristics and mechanical properties of the friction pendulum bearing; the damping clip gap sets the range of relative motion between structural components, affecting the timing and degree of damping; and the yield force determines the critical force at which the damping clip begins to work. Optimizing these parameters can effectively adjust the damping performance of the combined damping system.

[0082] Establishing a refined finite element model of the combined damping system: This involves performing detailed numerical simulations of the combined damping system. Using the finite element method, the combined damping system is discretized into multiple finite elements, each assigned corresponding material properties, geometric characteristics, and connection relationships, accurately simulating the mechanical behavior of each component in the system and their interactions. This model can be used to set seismic inputs under different combinations of optimizable variable parameters and accurately calculate the system's response, providing a foundation for determining the feasible range of the optimizable variables and analyzing the damping effect.

[0083] Seismic inputs are set under different parameter combinations of all optimizable variables, and the displacements of the combined damping system, the accelerations of the track structure, and the internal force responses of the bridge piers are calculated. Based on a refined finite element model, various parameter combinations are set for optimizable variables such as the friction coefficient and equivalent radius of the friction pendulum bearing, the gap between the damping latches, and the yield force, while simultaneously inputting seismic motions simulating earthquakes. The model then calculates the displacements of the combined damping system under these different conditions to understand the overall positional changes of the structure; calculates the accelerations of the track structure to understand the dynamic response of the track section during an earthquake; and calculates the internal force responses of the bridge piers to clarify the forces acting on the piers. These calculation results can be used to evaluate the performance of the combined damping system under different parameters and earthquakes.

[0084] The displacement, track structure acceleration, and pier internal force responses of the combined damping system are the responses of the combined damping system to different combinations of preset optimizable variables and earthquake inputs. Displacement reflects the change in the spatial position of the system as a whole; excessive displacement may cause structural damage or affect its normal operation. Track structure acceleration reflects the intensity of vibration during an earthquake, affecting the stability and safety of track facilities. The pier internal force response indicates the forces, such as bending moment and shear force, to which the piers are subjected during an earthquake. Excessive internal forces may damage the piers. By analyzing these responses, the performance of the combined damping system and the effectiveness of different parameter combinations can be determined.

[0085] Safety threshold range for seismic output response: This is a pre-defined range of displacement, track structure acceleration, and pier internal force responses that ensures the safe and reliable operation of the combined damping system. If the calculated response of the combined damping system for a particular combination of optimizable variables and seismic input falls within this safety threshold range, the system performance corresponding to that parameter combination meets safety requirements and is considered a feasible parameter combination. Conversely, if at least one response falls outside the range, the parameter combination is considered infeasible. This range is an important basis for screening feasible parameter combinations for optimizable variables and determining their high-precision feasible domain.

[0086] Example 3:

[0087] On the basis of Example 2, based on the safety threshold range of the earthquake output response and the corresponding earthquake output response under different parameter combinations of all optimizable variables, the high-precision feasible region range of all optimizable variables is determined, including:

[0088] Among all parameter combinations of all optimizable variables, all parameter combinations whose corresponding earthquake output responses are within the corresponding safety threshold range are screened out as all feasible parameter combinations of all optimizable variables, and all parameter combinations whose corresponding earthquake output responses have at least one output response outside the corresponding safety threshold range are screened out as all infeasible parameter combinations of all optimizable variables;

[0089] Based on all feasible parameter combinations and all infeasible parameter combinations of all optimizable variables and a classification hyperplane method, a first feasible domain range of all optimizable variables is determined;

[0090] Determine a second feasible domain range of all optimizable variables based on the Mahalanobis distance between each feasible parameter combination of all optimizable variables and all infeasible parameter combinations;

[0091] Based on the first feasible domain range and the second feasible domain range of all optimizable variables, a high-precision feasible domain range of all optimizable variables is determined.

[0092] Example 3 has the following beneficial effects in determining the high-precision feasible domain range of all optimizable variables: by screening out parameter combinations whose corresponding seismic output responses are within the safety threshold range as feasible parameter combinations, and selecting parameter combinations whose responses are at least one outside the safety threshold range as infeasible parameter combinations, the feasibility of different parameter combinations is clearly distinguished, providing a clear data basis for the subsequent precise determination of the feasible domain range. This classification method is directly based on the relationship between the seismic output response and the safety threshold, closely combined with the safety requirements of actual projects, ensuring that the parameter combinations within the feasible domain can enable the structure to meet the safety standards under earthquake action. Using the classification hyperplane method, the first feasible domain range is determined based on feasible and infeasible parameter combinations. The classification hyperplane method can find a reasonable boundary in the parameter space, effectively distinguishing feasible from infeasible parameter combinations, preliminarily defining the feasible domain range from a macro perspective, providing a framework for subsequent further refinement, and also considering the overall distribution relationship between different parameter combinations. The second feasible domain range is determined using the Mahalanobis distance between each feasible parameter combination and the infeasible parameter combination. The Mahalanobis distance can take into account the covariance structure of the data, measure the degree of difference between each feasible parameter combination and the infeasible parameter combination, and further refine the feasible domain range from a microscopic level, so that the boundary of the feasible domain is more in line with the actual situation and more accurately reflects the feasibility of the parameter combination. The high-precision feasible domain range is determined by combining the first feasible domain range and the second feasible domain range, taking into account the analysis results at both the macro and micro levels, ensuring the rationality of the feasible domain range and improving its accuracy. This method of determining the high-precision feasible domain range can more accurately limit the values ​​of the optimizable variables, provide a more accurate value range for the subsequent optimization design of seismic isolation parameters, and help to more efficiently search for the optimal parameter combination while meeting the safety of the structure, improve the quality and effect of seismic isolation design, and ensure the safety and reliability of engineering structures in earthquakes.

[0093] Example 4:

[0094] On the basis of Example 3, based on all feasible parameter combinations and all infeasible parameter combinations of all optimizable variables and the classification hyperplane method, the first feasible domain range of all optimizable variables is determined, including:

[0095] Based on all feasible parameter combinations and all infeasible parameter combinations of all optimizable variables and the classification hyperplane method, and introducing slack variables, the optimization problem is constructed:

[0096]

[0097] Where w=(w1,w2,…,w n ) T is the normal vector of the hyperplane, b is the bias term, ξ is the slack variable, ||w|| 2is the square of the norm of w, is the objective function whose goal is to minimize half of the modulus of the hyperplane normal vector, C is the penalty coefficient, N v is the number of feasible parameter combinations, N u is the number of infeasible parameter combinations, ξ i is the slack variable of the i-th group of samples, y i is the label of the sample, y of the feasible parameter combination i =1, y of infeasible parameter combination i =-1, w T is the transposed matrix of w, X i is the i-th sample point among all parameter combinations of all optimizable variables, which may be a single infeasible parameter combination or a feasible parameter combination;

[0098] The optimization problem is solved to obtain w and b. Based on the obtained w and b and the preset buffer coefficient, the first feasible region range of all optimizable variables is determined as:

[0099] w T X+b≥-∈

[0100] Where X=(x1,x2,…,x n ) T is an n-dimensional optimizable variable vector, and ∈ is the preset buffer coefficient.

[0101] In this example:

[0102] The classification hyperplane method is used to find a hyperplane among all feasible and infeasible parameter combinations of all optimizable variables that separates the two types of data as accurately as possible. In multidimensional space, this hyperplane can be represented by the equation wTx+b=0 (where x is the vector of optimizable variables, ω is the normal vector of the hyperplane, and b is the bias term). By finding the optimal hyperplane, the boundary between the feasible and infeasible regions can be clearly defined, assisting in determining the first feasible region range for the optimizable variables.

[0103] The purpose of introducing slack variables is to deal with the linear inseparability that may exist in the data. In practical applications, due to the complexity of the data, it may not be possible to find a perfect hyperplane to completely separate the feasible and infeasible parameter combinations. i Some sample points are allowed to violate the classification rules (i.e., they are on the wrong side of the hyperplane), but such violations will be penalized in the objective function. This provides a certain degree of flexibility for the model, making the classification hyperplane method better adaptable to complex data distributions.

[0104] The bias term b adjusts the position of the hyperplane in the hyperplane equation wTx+b=0. The normal vector w determines the direction of the hyperplane, while the bias term b determines its specific position in space. By adjusting the bias term, the hyperplane can more accurately separate feasible and infeasible parameter combinations without changing its direction, thereby optimizing classification results.

[0105] The penalty coefficient C is a trade-off between the objective function's two goals: minimizing the norm of the hyperplane's normal vector (making the hyperplane more generalizable) and allowing samples to violate the classification rules (handling linear inseparability). A large C value means a heavier penalty for samples violating the classification rules. The model will try to avoid misclassification and tend to find a hyperplane that strictly separates the two classes of data, but this may lead to model overfitting. A small C value makes the model more tolerant of sample misclassification and prioritizes the generalization ability of the hyperplane, but this may result in poor classification results. Choosing the right penalty coefficient is crucial for accurately determining the feasible domain.

[0106] The slack variable ξ for each group of samples i Corresponding to each sample point, it indicates the degree to which the sample point violates the classification rule. There are corresponding slack variables for feasible parameter combination samples and infeasible parameter combination samples. If the sample point strictly meets the classification rule (the hyperplane is on the correct side), then ξ i =0; if the sample point violates the classification rule, ξ i The value of is greater than 0, and its size reflects the degree to which the sample deviates from the correct classification position. The slack variables of all samples participate in the calculation of the objective function together to achieve the optimization of the hyperplane.

[0107] The label y of the sample i Used to distinguish feasible parameter combination samples from infeasible parameter combination samples. When constructing an optimization problem, labels are used to determine the classification conditions that samples should meet. This condition and other parameters are used to determine the position and properties of the hyperplane, which in turn helps determine the feasible range of the optimizable variables.

[0108] The preset buffer coefficient ∈ is a parameter used to determine the first feasible region range of all optimizable variables. After obtaining the hyperplane w and b, through w T X + b ≥ - ∈ is used to determine the first feasible region. This provides an additional buffer zone on top of the hyperplane, making the determined feasible region more reasonable and secure. This avoids excluding some practical parameter combinations due to overly strict hyperplane divisions or data fluctuations, ensuring that the final feasible region better meets actual engineering needs.

[0109] Example 5:

[0110] On the basis of Example 3, a second feasible domain range of all optimizable variables is determined based on the Mahalanobis distance between each feasible parameter combination of all optimizable variables and all infeasible parameter combinations, including:

[0111] Determine the Mahalanobis distance between each feasible parameter combination and all infeasible parameter combinations of all optimizable variables;

[0112] All feasible parameter combinations whose Mahalanobis distance does not exceed the preset boundary threshold are regarded as all near-boundary feasible parameter combinations;

[0113] The second feasible region range of all optimizable variables is determined based on the convex hull algorithm and all near-boundary feasible parameter combinations.

[0114] The Mahalanobis distance is a distance metric that accounts for the covariance structure of the data and measures the similarity or difference between each feasible parameter combination and all infeasible parameter combinations. For each feasible parameter combination of the optimizable variables, calculating the Mahalanobis distance between it and all infeasible parameter combinations provides a more comprehensive and accurate reflection of the distance between that feasible parameter combination and the infeasible region.

[0115] Assuming there are n optimizable variables, a feasible parameter combination can be viewed as a point x in n-dimensional space. i , the infeasible parameter combination is the point set {y j}(j=1,2,…,m). First calculate the mean vector of the infeasible parameter combination point set And the covariance matrix Σ. Then the feasible parameter combination x i The Mahalanobis distance dM(x i ) is calculated as:

[0116]

[0117] By calculating the Mahalanobis distance between each feasible parameter combination and the infeasible parameter combination, we can understand the degree of deviation of each feasible parameter combination relative to the infeasible region, providing a basis for subsequent screening of feasible parameter combinations near the boundary.

[0118] The preset boundary threshold is a pre-set value used to determine whether a feasible parameter combination is close to the boundary of the feasible domain. After obtaining the Mahalanobis distance between each feasible parameter combination of all optimizable variables and all infeasible parameter combinations, the Mahalanobis distance is compared with the preset boundary threshold. If the Mahalanobis distance of a feasible parameter combination does not exceed the preset boundary threshold, then the feasible parameter combination is considered to be close to the boundary of the feasible domain, that is, it is regarded as a near-boundary feasible parameter combination. The setting of the preset boundary threshold needs to comprehensively consider factors such as actual engineering needs, data characteristics, and accuracy requirements for the feasible domain range. It plays a key role in screening near-boundary feasible parameter combinations in the process of determining the second feasible domain range.

[0119] The convex hull algorithm is an algorithm for finding the smallest convex polygon (convex polyhedron in multidimensional space) that contains a given set of points. In this embodiment, all near-boundary feasible parameter combinations whose Mahalanobis distance does not exceed a preset boundary threshold are input into the convex hull algorithm as a point set.

[0120] The convex hull algorithm processes these near-boundary feasible parameter combinations to construct a convex polygon (or convex polyhedron). The area contained in this convex polygon (or convex polyhedron) is the second feasible domain range of all optimizable variables. The convex hull algorithm is used because it ensures that the determined area contains all near-boundary feasible parameter combinations and has a minimal boundary, making the determined second feasible domain range both accurate and compact, providing an important component for ultimately determining the high-precision feasible domain range. The second feasible domain range determined in this way can reflect the feasible value range of the optimizable variables from another perspective. Combined with the first feasible domain range, the high-precision feasible domain range of the optimizable variables can be more accurately determined.

[0121] Example 6:

[0122] On the basis of Example 3, based on the first feasible domain range and the second feasible domain range of all optimizable variables, the high-precision feasible domain range of all optimizable variables is determined, including:

[0123] The intersection of the first feasible domain range and the second feasible domain range of all optimizable variables is regarded as the high-precision feasible domain range of all optimizable variables.

[0124] Example 6 further refines the method of determining the high-precision feasible domain range of the optimizable variables, and determines the high-precision feasible domain range by taking the intersection of the first feasible domain range and the second feasible domain range. This method can effectively integrate the advantages of the feasible domains determined by two different methods. The first feasible domain is based on the classification hyperplane method, which divides the feasible and infeasible areas in the parameter space from a macro level, providing a relatively broad but overall guiding range framework; the second feasible domain is determined based on the Mahalanobis distance, which more accurately measures the difference between each feasible parameter combination and the infeasible parameter combination from a micro level, so that the feasible domain boundary is more in line with the actual situation. Taking the intersection of the two, on the one hand, can ensure that the high-precision feasible domain range conforms to the overall distribution logic of the parameter combination at a macro level, ensure that the determined range is reasonable and practical as a whole, and avoid the situation where the local optimum may appear only from a micro perspective but the overall irrationality; on the other hand, the accuracy of the micro level is used to further refine the macro range, remove the unreasonable boundaries that may exist in the macro range, improve the accuracy of the feasible domain range, and make the determined high-precision feasible domain range both comprehensive and accurate. This high-precision feasible domain provides a more accurate and reliable range of variable values ​​for subsequent optimization of seismic isolation parameters. Optimizing within this range allows for more efficient search for parameter combinations that meet structural safety requirements and offer superior performance. This helps improve the quality and efficiency of seismic isolation design, ensuring the stability and safety of engineering structures during earthquakes, minimizing damage to structures, and reducing potential economic losses and casualties.

[0125] Example 7:

[0126] Based on Example 1, S2: uniformly distribute sampling is performed on all optimizable variables within the corresponding high-precision feasible domain to obtain multiple groups of sampling parameters for all optimizable variables, and earthquake risk analysis is performed based on all groups of sampling parameters of all optimizable variables and the numerical model of the combined shock absorption system to obtain a sample of the earthquake risk of a preset group of optimizable variables-system, including:

[0127] Using Latin hypercube sampling, all optimizable variables are sampled evenly within the corresponding high-precision feasible domain to obtain multiple sets of sampling parameters for all optimizable variables.

[0128] Conduct earthquake risk analysis based on each set of sampling parameters and the combined shock absorption system numerical model of all optimizable variables to obtain earthquake risk indicators for each set of sampling parameters;

[0129] Based on all group sampling parameters of all optimizable variables and the corresponding earthquake risk indicators, a sample of the preset group of optimizable variables-system earthquake risk is obtained.

[0130] In this example:

[0131] Latin hypercube sampling is a stratified sampling technique that ensures that samples are evenly distributed within the value range of each variable during the sampling process, and is also highly representative in multidimensional space. In this embodiment, since the high-precision feasible domain range of all optimizable variables has been determined, this sampling method is used to perform sampling operations on each optimizable variable (such as the friction coefficient of the friction pendulum support, the equivalent radius, the gap between the shock-absorbing latch and the yield force, etc.) within this established value range. In this way, multiple sets of sampling parameters can be obtained. These parameter combinations not only fully cover the feasible domain, but also avoid excessive concentration of samples in certain areas, ensuring the diversity and representativeness of the samples, and providing a rich and representative data basis for subsequent earthquake risk analysis based on these sampling parameters.

[0132] After obtaining multiple sets of sampling parameters for all optimizable variables, each set of sampling parameters is input into the numerical model of the combined shock absorption system. This numerical model can simulate the mechanical response of the combined shock absorption system when subjected to earthquakes under different parameter settings. Through calculation and analysis of the model, a quantitative indicator reflecting the degree of earthquake risk faced by the combined shock absorption system under this set of sampling parameters is obtained, that is, the earthquake risk index for each set of sampling parameters. These indicators may include but are not limited to the degree of structural damage, the probability of displacement exceeding the limit, the stress level of key parts, etc. The selection of specific indicators depends on the actual analysis needs and engineering concerns. This analysis method based on numerical models can more accurately evaluate the risk status of the combined shock absorption system in earthquakes under different parameter combinations.

[0133] The earthquake risk index for each set of sampling parameters is a numerical value that quantitatively assesses the degree of earthquake risk faced by the combined shock absorption system under a specific combination of sampling parameters. It comprehensively reflects the combined shock absorption system's ability to resist earthquake effects and the possible damage that may occur under the corresponding parameter settings. For example, if the stress in the key parts of the structure calculated under a certain set of sampling parameters is close to the ultimate strength of the material, then the earthquake risk index corresponding to this set of sampling parameters may be high, which means that under this parameter combination, the combined shock absorption system is more likely to be damaged in an earthquake. These indicators provide an objective basis for comparing the advantages and disadvantages of different sampling parameter combinations, which will help to subsequently screen out more optimal parameter combinations to reduce the earthquake risk of the combined shock absorption system.

[0134] The sampling parameters for all optimizable variables obtained through Latin hypercube sampling, along with the seismic risk indicators obtained for each set of sampling parameters through seismic risk analysis, are integrated. These sampling parameters are then paired with the corresponding seismic risk indicators according to a predefined number of samples (i.e., predefined groups), forming a sample set of optimizable variables and system seismic risk. These samples contain rich information, demonstrating the relationship between different combinations of optimizable variable values ​​and the seismic risk of the combined damping system. These samples provide crucial data support for the subsequent development of a seismic risk mapping model for all optimizable variables and the combined damping system. By studying and analyzing these samples, the model is able to capture the complex nonlinear relationship between optimizable variables and seismic risk.

[0135] Example 8:

[0136] On the basis of Example 1, S3: using a sample training model of a preset set of optimizable variables and system earthquake risk, and optimizing the neural network structure, an earthquake risk mapping model of all optimizable variables and the combined shock absorption system is established, including:

[0137] The artificial neural network model is trained using samples of a preset group of optimizable variables-system earthquake risks. The learning rate is dynamically adjusted, and an adaptive moment estimation optimizer is introduced. The number of hidden layer neurons is determined through cross-validation to optimize the neural network structure, and an earthquake risk mapping model of all optimizable variables and the combined shock absorption system is established.

[0138] In this embodiment, the artificial neural network model is trained using a preset set of samples of optimizable variables and system earthquake risk in order to allow the model to learn the complex relationship between the optimizable variables and earthquake risk. The specific process is as follows:

[0139] Dynamically adjust the learning rate: The learning rate determines the step size of parameter updates during model training. In the early stages of training, a larger learning rate allows the model to converge quickly to a rough solution space, but may skip the optimal solution. Later in training, a smaller learning rate helps the model fine-tune near the optimal solution, improving model accuracy. Dynamically adjust the learning rate to automatically change the learning rate based on training progress. For example, gradually reducing the learning rate as the number of training rounds increases can ensure training speed while improving model accuracy.

[0140] Introducing the Adaptive Moment Estimation Optimizer: The Adaptive Moment Estimation (Adam) optimizer is a commonly used optimization algorithm. It combines the advantages of the momentum method and the RMSProp algorithm, and can adaptively adjust the learning rate of each parameter. When training artificial neural network models, the Adam optimizer dynamically adjusts the learning rate of each parameter by calculating the first-order moment estimate (i.e., mean) and second-order moment estimate (i.e., uncentered variance) of the gradient. This enables the model to update parameters more efficiently during training, accelerating convergence while also avoiding problems such as excessively large learning rates leading to model non-convergence or excessively small learning rates leading to prolonged training times.

[0141] Determine the number of hidden layer neurons through cross-validation to optimize the neural network structure: The number of hidden layer neurons has an important impact on the performance of artificial neural networks. If the number of neurons is too small, the model may not be able to learn the complex patterns in the data; if the number of neurons is too large, it may lead to overfitting, and the model performs well on the training data, but has poor generalization ability on new data. Cross-validation is a method for evaluating model performance. It divides the samples of a preset set of optimizable variables - system earthquake risk - into multiple subsets, using a part of the subset as the training set each time and the rest as the validation set. By trying different numbers of hidden layer neurons and training and validating on different subsets, the performance indicators of the model on the validation set (such as mean square error, accuracy, etc.) are observed. The number of hidden layer neurons that optimizes the performance of the validation set is selected to optimize the neural network structure.

[0142] Establish a seismic risk mapping model between all optimizable variables and the combined seismic absorption system: Following the aforementioned steps, the artificial neural network model is trained using a preset set of optimizable variable-system seismic risk samples, combined with a dynamically adjusted learning rate, an adaptive moment estimation optimizer, and an optimal number of hidden layer neurons determined through cross-validation. Once trained, the model establishes a mapping relationship between all optimizable variables and the seismic risk of the combined seismic absorption system. Specifically, given a set of optimizable variable values ​​as input, the model outputs the corresponding predicted seismic risk value for the combined seismic absorption system. This mapping model provides the foundation for subsequently identifying the optimal design parameter combination for the optimizable variables that minimizes seismic risk.

[0143] Example 9:

[0144] Based on Example 1, Figure 3 , also includes:

[0145] S5: Verify the effectiveness of the design parameter combination of all optimizable variables with the goal of minimizing earthquake risk through numerical simulation, and obtain the effectiveness verification value of the design parameter combination of all optimizable variables;

[0146] S6: Determine whether the validity verification value of the design parameter combination of all optimizable variables is lower than a preset threshold. If so, start the active learning mechanism and add a preset group of new optimizable variable-system earthquake risk samples to retrain the artificial neural network model until the validity of the new design parameter combination of all optimizable variables with the lowest earthquake risk as the goal determined based on the latest established earthquake risk mapping model of all optimizable variables and the combined shock absorption system is not lower than the threshold. Then, the newly obtained design parameter combination of all optimizable variables with the lowest earthquake risk as the goal is regarded as the optimal design parameter combination of all optimizable variables. Otherwise, the design parameter combination of all optimizable variables is regarded as the optimal design parameter combination of all optimizable variables.

[0147] In this example:

[0148] The effectiveness verification value of the design parameter combination for all optimizable variables is a quantitative value used to measure the actual effectiveness of the design parameter combination of all optimizable variables determined with the goal of minimizing seismic risk. It is obtained through a series of verification steps based on numerical simulation: first, a verification model is established based on the refined finite element model of the combined seismic absorption system and actual engineering constraints. Then, the seismic input is set for the verification model and an appropriate solution algorithm is selected to obtain the key response output of the verification model. Based on these key response outputs, the relative optimization effect value is calculated. At the same time, the key response output is compared with the absolute threshold to obtain the absolute threshold verification result. The relative optimization effect value is compared with the preset optimization effect threshold to obtain the relative optimization effect verification result. Finally, based on these two verification results, the effectiveness verification value is comprehensively derived. This value can intuitively reflect the performance of the design parameter combination in actual application and determine whether it meets the engineering requirements.

[0149] The preset threshold is a pre-set standard value used for comparison with the validation values ​​of all design parameter combinations for optimizable variables. If the validation value falls below the preset threshold, it indicates that the current optimizable design parameter combination, determined to minimize earthquake risk, may not meet the actual project requirements for seismic reduction or other related performance, and further optimization is required. The setting of the preset threshold requires comprehensive consideration of multiple factors, including actual project needs, safety standards, and cost. It is a key factor in determining whether to initiate the active learning mechanism.

[0150] When the validity verification value of the design parameter combination of all optimizable variables is lower than a preset threshold, the active learning mechanism is started. The active learning mechanism aims to improve the model by obtaining more valuable data. In this embodiment, a preset group of new optimizable variable-system earthquake risk samples will be added. These new samples are usually selected from parameter space areas that have not been fully explored or areas with great potential for improving model performance. After collecting the new samples, they are merged with the original samples and then the artificial neural network model is retrained. During the retraining process, the model will further adjust its own parameters based on the new sample data to optimize the mapping relationship between the optimizable variables and the earthquake risk. It is expected that through multiple such cycles, the validity of the design parameter combination of all optimizable variables determined based on the latest established mapping model with the lowest earthquake risk as the goal will reach or exceed the preset threshold, thereby obtaining a better design parameter combination and improving the safety and reliability of the combined shock absorption system in earthquakes.

[0151] Example 10:

[0152] Based on Example 9, S5: verifying the validity of the design parameter combination of all optimizable variables with the goal of minimizing earthquake risk through numerical simulation, and obtaining the validity verification value of the design parameter combination of all optimizable variables, including:

[0153] Establish a verification model based on the refined finite element model of the combined vibration damping system and actual engineering constraints;

[0154] Set the earthquake motion input of the verification model and select the solution algorithm to obtain the key response output of the verification model;

[0155] Calculate the relative optimization effect value based on the key response output of the validation model;

[0156] Comparing the key response output of the verification model with the absolute threshold to obtain an absolute threshold verification result;

[0157] Compare the relative optimization effect value with the preset optimization effect threshold to obtain the relative optimization effect verification result;

[0158] The validity verification values ​​of the design parameter combinations of all optimizable variables are obtained based on the absolute threshold verification results and the relative optimization effect verification results.

[0159] In this example:

[0160] Based on the refined finite element model of the combined damping system and actual engineering constraints, a verification model was established:

[0161] First, the refined finite element model of the combined damping system simulates the system with high precision. It discretizes the system into numerous finite elements, accurately describing the mechanical properties, connections, and interactions of each component. Actual engineering constraints encompass various limiting factors found in actual projects, such as material performance limitations, structural size requirements, and construction process conditions.

[0162] Building a validation model based on these two factors involves incorporating practical engineering constraints into the refined finite element model. For example, the elastic modulus and yield strength of the modeled materials are limited based on the mechanical properties of the available materials; and the range of structural dimensions is set based on actual site conditions and high-speed rail bridge specifications. This approach creates a validation model that better reflects the actual engineering situation, enabling subsequent accurate evaluation of the effectiveness of design parameter combinations for optimizable variables.

[0163] Setting the seismic input for the validation model applies vibration excitation to the model that simulates a real earthquake. The seismic input must be selected or generated based on the actual seismic characteristics of the project area (such as seismic wave type, peak acceleration, and spectral characteristics) to ensure that it accurately reflects the impact of potential earthquakes in the area on the combined seismic isolation system.

[0164] Selecting a solution algorithm involves choosing an appropriate numerical method to verify the model's mechanical response to earthquake input. Different solutions are suitable for different types of mechanical problems. For example, explicit solutions are suitable for solving high-speed dynamics problems, while implicit solutions may be more advantageous for complex contact and static problems. Choosing the right solution algorithm can improve computational efficiency and result accuracy.

[0165] By applying seismic input and performing calculations using the selected solution algorithm, key response outputs for the validation model can be obtained. These key response outputs may include displacements, accelerations, and internal forces of the combined damping system. They reflect the actual mechanical response of the combined damping system under a specific design parameter combination and earthquake action, and are an important basis for evaluating the effectiveness of the design parameter combination.

[0166] The relative optimization effect value is used to measure the degree of optimization of the current design parameter combination of the optimizable variables compared to a baseline. First, a baseline must be determined. This benchmark can be the response of the combined damping system before parameter optimization, or the response of a standard design generally recognized in the industry.

[0167] Then, by comparing the key response outputs of the validation model (such as displacement, acceleration, internal force, etc.) with the corresponding responses under the baseline condition, a specific calculation formula is used to determine the relative optimization effect value. For example, if the key response output is displacement, the calculation formula might be: Relative Optimization Effect Value = (Baseline Displacement - Displacement under the Current Design Parameter Combination) / Baseline Displacement × 100%. The larger this value, the more significant the optimization effect of the current design parameter combination on the combined vibration reduction system.

[0168] The absolute threshold is a pre-set, fixed value used to determine whether the critical response output of the validation model meets absolute safety standards. It is determined based on multiple factors, including engineering safety regulations, structural design standards, and actual operational requirements. For example, for the displacement response of a combined damping system, the absolute threshold might be set based on the maximum allowable displacement without structural damage or impacting normal operation. For internal force responses, the absolute threshold might be the ultimate internal force that the material can withstand. Comparing the critical response output with the absolute threshold evaluates the feasibility of the design parameter combination for the optimizable variables from an absolute safety perspective.

[0169] The key response outputs of the verification model (such as displacement, acceleration, internal force, etc.) obtained through calculation are compared with the pre-set absolute thresholds.

[0170] If the key response output is within the absolute threshold, it indicates that the combined seismic isolation system's response to an earthquake meets basic safety requirements under the current design parameter combination of the optimizable variables, and the absolute threshold verification result is a pass. Conversely, if the key response output exceeds the absolute threshold, it indicates that the design parameter combination may cause the combined seismic isolation system to be unsafe during an earthquake, and the absolute threshold verification result is a fail. The absolute threshold verification result is an important step in determining the effectiveness of the design parameter combination and directly reflects whether the design parameter combination can ensure the basic safety of the structure in an earthquake.

[0171] The preset optimization effect threshold is a pre-set standard used to measure whether the relative optimization effect value has reached the ideal optimization level. It comprehensively considers factors such as project cost, technical feasibility, and the expected improvement in vibration reduction performance. For example, if improving the vibration reduction performance of a combined vibration reduction system requires a significant increase in cost or the use of complex technology, and a high preset optimization effect threshold may make it difficult to achieve in actual engineering, the preset optimization effect threshold needs to be adjusted appropriately based on the actual situation. This threshold provides a standard for judging whether the current design parameter combination of the optimizable variables meets the engineering requirements in terms of optimization effect.

[0172] The relative optimization effect value calculated based on the key response output of the verification model is compared with the preset optimization effect threshold.

[0173] If the relative optimization effect value is greater than or equal to the preset optimization effect threshold, it indicates that the design parameter combination of the current optimizable variables has achieved the expected requirements in terms of optimizing the shock absorption effect, and the relative optimization effect verification result is passed. If the relative optimization effect value is less than the preset optimization effect threshold, it indicates that the optimization effect of the design parameter combination has not reached the expected level, and the relative optimization effect verification result is failed. The relative optimization effect verification result further evaluates the effectiveness of the design parameter combination from the perspective of optimization degree, and together with the absolute threshold verification result, provides a comprehensive basis for determining the effectiveness of the design parameter combination.

[0174] The validity verification value is determined by combining the absolute threshold verification results and the relative optimization effect verification results. The validity verification value is a quantitative indicator that comprehensively evaluates whether the design parameter combination of the optimizable variables is effective.

[0175] One possible method for determining this is to assign a high validity verification value if both the absolute threshold verification result and the relative optimization effect verification result pass, indicating that the design parameter combination performs well in terms of both safety and optimization effect. If the absolute threshold verification result passes but the relative optimization effect verification result fails, the validity verification value may be relatively low, indicating that while basic safety requirements are met, the optimization effect needs to be improved. If the absolute threshold verification result fails, regardless of the relative optimization effect verification result, the validity verification value will be very low or even zero, indicating that the design parameter combination cannot guarantee the safety of the structure in an earthquake and is seriously insufficient in validity. Through this comprehensive evaluation method, the validity verification value obtained can comprehensively and accurately reflect the effectiveness of the design parameter combination of the optimizable variables in actual engineering projects.

[0176] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the present invention and its equivalents, the present invention is intended to include these modifications and variations.

Claims

1. The method for optimizing the seismic isolation parameters based on artificial neural network is characterized by: include: S1: Determine all optimizable variables in the combined shock absorption system and determine the high-precision feasible domain range of all optimizable variables; S2: uniformly distribute sampling on all optimizable variables within the corresponding high-precision feasible region to obtain multiple groups of sampling parameters for all optimizable variables. Based on all groups of sampling parameters of all optimizable variables and the numerical model of the combined shock absorption system, earthquake risk analysis is performed to obtain samples of the preset group of optimizable variables-system earthquake risk; S3: Using a preset set of optimizable variables-system earthquake risk sample training models, and optimizing the neural network structure, establish an earthquake risk mapping model for all optimizable variables and the combined shock absorption system; S4: The earthquake risk mapping model is used as the objective function, and a genetic algorithm is used to perform global optimization to search for the design parameter combination of all optimizable variables with the goal of minimizing the earthquake risk.

2. The method for optimizing seismic isolation parameters based on artificial neural network according to claim 1, characterized in that: S1: Determine all optimizable variables in the combined shock absorption system and determine the high-precision feasible domain range of all optimizable variables, including: The friction coefficient, equivalent radius, damping clamp gap and yield force of the friction pendulum support in the combined damping system are all optimizable variables; Establish a refined finite element model of the combined shock absorption system; Set the seismic input under different parameter combinations of all optimizable variables, and calculate the displacement of the combined damping system, the acceleration of the track structure, and the internal force response of the bridge pier as the corresponding seismic output response; Based on the safety threshold range of the seismic output response and the corresponding seismic output response under different parameter combinations of all optimizable variables, the high-precision feasible domain range of all optimizable variables is determined.

3. The method for optimizing seismic isolation parameters based on artificial neural network according to claim 2, characterized in that: Based on the safety threshold range of the seismic output response and the corresponding seismic output response under different parameter combinations of all optimizable variables, the high-precision feasible region range of all optimizable variables is determined, including: Among all parameter combinations of all optimizable variables, all parameter combinations whose corresponding earthquake output responses are within the corresponding safety threshold range are screened out as all feasible parameter combinations of all optimizable variables, and all parameter combinations whose corresponding earthquake output responses have at least one output response outside the corresponding safety threshold range are screened out as all infeasible parameter combinations of all optimizable variables; Based on all feasible parameter combinations and all infeasible parameter combinations of all optimizable variables and a classification hyperplane method, a first feasible domain range of all optimizable variables is determined; Determine a second feasible domain range of all optimizable variables based on the Mahalanobis distance between each feasible parameter combination of all optimizable variables and all infeasible parameter combinations; Based on the first feasible domain range and the second feasible domain range of all optimizable variables, a high-precision feasible domain range of all optimizable variables is determined.

4. The method for optimizing seismic isolation parameters based on artificial neural network according to claim 3 is characterized in that: Based on all feasible parameter combinations and all infeasible parameter combinations of all optimizable variables and the classification hyperplane method, the first feasible domain range of all optimizable variables is determined, including: Based on all feasible parameter combinations and all infeasible parameter combinations of all optimizable variables and the classification hyperplane method, and introducing slack variables, the optimization problem is constructed: Where w=(w1,w2,…,w n ) T is the normal vector of the hyperplane, b is the bias term, ξ is the slack variable, ||w|| 2 is the square of the norm of w, is the objective function whose goal is to minimize half of the modulus of the hyperplane normal vector, C is the penalty coefficient, N v is the number of feasible parameter combinations, N u is the number of infeasible parameter combinations, ξ i is the slack variable of the i-th group of samples, y i is the label of the sample, y of the feasible parameter combination i =1, y of infeasible parameter combination i =-1, w T is the transposed matrix of w, X i is the i-th sample point in all parameter combinations of all optimizable variables; The optimization problem is solved to obtain w and b. Based on the obtained w and b and the preset buffer coefficient, the first feasible region range of all optimizable variables is determined as: w T X+b≥-∈ Where X=(x1,x2,…,x n ) T is an n-dimensional optimizable variable vector, and ∈ is the preset buffer coefficient.

5. The method for optimizing seismic isolation parameters based on artificial neural network according to claim 3 is characterized in that: The second feasible domain range of all optimizable variables is determined based on the Mahalanobis distance between each feasible parameter combination of all optimizable variables and all infeasible parameter combinations, including: Determine the Mahalanobis distance between each feasible parameter combination and all infeasible parameter combinations of all optimizable variables; All feasible parameter combinations whose Mahalanobis distance does not exceed the preset boundary threshold are regarded as all near-boundary feasible parameter combinations; The second feasible region range of all optimizable variables is determined based on the convex hull algorithm and all near-boundary feasible parameter combinations.

6. The method for optimizing seismic isolation parameters based on artificial neural network according to claim 3 is characterized in that: Based on the first feasible domain range and the second feasible domain range of all optimizable variables, the high-precision feasible domain range of all optimizable variables is determined, including: The intersection of the first feasible domain range and the second feasible domain range of all optimizable variables is regarded as the high-precision feasible domain range of all optimizable variables.

7. The method for optimizing seismic isolation parameters based on artificial neural network according to claim 1, characterized in that: S2: Perform uniformly distributed sampling of all optimizable variables within the corresponding high-precision feasible domain to obtain multiple groups of sampling parameters for all optimizable variables. Perform earthquake risk analysis based on all groups of sampling parameters of all optimizable variables and the numerical model of the combined shock absorption system to obtain a sample of the preset group of optimizable variables-system earthquake risk, including: Using Latin hypercube sampling, all optimizable variables are sampled evenly within the corresponding high-precision feasible domain to obtain multiple sets of sampling parameters for all optimizable variables. Conduct earthquake risk analysis based on each set of sampling parameters and the combined shock absorption system numerical model of all optimizable variables to obtain earthquake risk indicators for each set of sampling parameters; Based on all group sampling parameters of all optimizable variables and the corresponding earthquake risk indicators, a sample of the preset group of optimizable variables-system earthquake risk is obtained.

8. The method for optimizing seismic isolation parameters based on artificial neural network according to claim 1, characterized in that: S3: Utilize the sample training model of the preset set of optimizable variables and system earthquake risk, optimize the neural network structure, and establish an earthquake risk mapping model of all optimizable variables and the combined shock absorption system, including: The artificial neural network model is trained using samples of a preset group of optimizable variables-system earthquake risks. The learning rate is dynamically adjusted, and an adaptive moment estimation optimizer is introduced. The number of hidden layer neurons is determined through cross-validation to optimize the neural network structure, and an earthquake risk mapping model of all optimizable variables and the combined shock absorption system is established.

9. The method for optimizing seismic isolation parameters based on artificial neural network according to claim 1, characterized in that: Also includes: S5: Verify the effectiveness of the design parameter combination of all optimizable variables with the goal of minimizing earthquake risk through numerical simulation, and obtain the effectiveness verification value of the design parameter combination of all optimizable variables; S6: Determine whether the validity verification value of the design parameter combination of all optimizable variables is lower than a preset threshold. If so, start the active learning mechanism and add a preset group of new optimizable variable-system earthquake risk samples to retrain the artificial neural network model until the validity of the new design parameter combination of all optimizable variables with the lowest earthquake risk as the goal determined based on the latest established earthquake risk mapping model of all optimizable variables and the combined shock absorption system is not lower than the threshold. Then, the newly obtained design parameter combination of all optimizable variables with the lowest earthquake risk as the goal is regarded as the optimal design parameter combination of all optimizable variables. Otherwise, the design parameter combination of all optimizable variables is regarded as the optimal design parameter combination of all optimizable variables.

10. The method for optimizing seismic isolation parameters based on artificial neural network according to claim 9, characterized in that: S5: Verify the effectiveness of the design parameter combinations of all optimizable variables with the goal of minimizing earthquake risk through numerical simulation, and obtain the effectiveness verification values ​​of the design parameter combinations of all optimizable variables, including: Establish a verification model based on the refined finite element model of the combined vibration damping system and actual engineering constraints; Set the earthquake motion input of the verification model and select the solution algorithm to obtain the key response output of the verification model; Calculate the relative optimization effect value based on the key response output of the validation model; Comparing the key response output of the verification model with the absolute threshold to obtain an absolute threshold verification result; Compare the relative optimization effect value with the preset optimization effect threshold to obtain the relative optimization effect verification result; The validity verification values ​​of the design parameter combinations of all optimizable variables are obtained based on the absolute threshold verification results and the relative optimization effect verification results.

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