Intelligent design method and system for triple friction pendulum support

Abstract

The application provides a triple friction pendulum support intelligent design method and system. First, the design variables of the triple friction pendulum support are determined, and then the following process is iteratively executed until convergence: inputting seismic data into a structure dynamics coding neural network model, calculating the dynamics response of the triple friction pendulum support by using the forward propagation mechanism of the model, extracting key performance indicators, constructing a three-level seismic resistance performance target system, and optimizing the key performance indicators and the design variables according to different fortification levels. In this process, based on the idea of physical coding neural network, the structure dynamics equation is coded into the network, so that the calculation process of the network has a clear physical meaning, ensuring the interpretability and physical consistency of the model, and improving the ability to effectively handle complex high-speed railway bridge seismic design problems, and realizing the optimization of key design variables under multi-objective performance constraints.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a smart design method and system for a triple friction pendulum support. Background Technology

[0002] In the field of high-speed railway bridge engineering, simply supported beam bridges have been widely used due to their technical and economic advantages. The seismic performance assessment and design optimization research of high-speed railway simply supported beam bridges is a core issue in current railway bridge seismic resistance. The rational application of seismic isolation and damping technologies can effectively improve the seismic performance of bridge structures. Through the rational design of seismic isolation and damping devices, performance-based seismic design of high-speed railway bridges can be achieved, and this technical approach has become an important development direction in engineering seismic resistance research. However, existing research still has shortcomings in the following aspects:

[0003] First, the definition of the seismic performance target of high-speed railway bridge structure is incomplete: the standard only specifies the performance status of the bridge structure and the upper and lower connecting components under the three design waterproof levels, and does not specify the seismic fortification target of the track structure; the traditional seismic isolation and reduction design method usually only designs for a single performance target and does not consider the safety of the track structure above the bridge.

[0004] Second, traditional data-driven neural networks have significant limitations in the design of seismic isolation bearings: traditional data-driven neural networks require large-scale labeled datasets for training to achieve parameter optimization and generalization capabilities. However, seismic isolation bearings need to be designed with limited computing resources, and the amount of effective training data available is insufficient. This makes it difficult for traditional neural networks to meet the data scale required for their training and to establish a reliable input-output mapping relationship through sufficient sample learning.

[0005] The third technical bottleneck of existing Physical Embedded Neural Networks (PENNs) is that existing research on PENNs lacks effective neural network adaptation and modification ideas for dealing with structural dynamics equations, which are second-order differential equations with strong nonlinear characteristics. There is also a lack of effective methods for systematically encoding them into neural network architectures. Summary of the Invention

[0006] This application proposes an intelligent design method and system for a triple friction pendulum support, which can solve one of the problems existing in the background technology.

[0007] To achieve the above objectives, this application adopts the following technical solution:

[0008] Firstly, a smart design method for a triple friction pendulum support is provided, including:

[0009] Determine the design variables for the triple friction pendulum support TFPB;

[0010] Furthermore, iterative execution until convergence: inputting seismic data into the SDENN (Structural Dynamics Encoding Neural Network) model; using the forward propagation mechanism of the SDENN model to calculate the dynamic response of the TFPB, and extracting key performance indicators from the dynamic response; using the key performance indicators to optimize the design variables. The calculation process of the SDENN model has a completely consistent mathematical form with the Euler method solution process of the structural dynamics equations, and the design variables correspond to the training parameters of the SDENN.

[0011] Based on the above technical solution, the design variables of TFPB are first determined, and then the following process is iteratively executed until convergence: Seismic ground motion data is input into the SDENN model, and the dynamic response of TFPB is calculated and key performance indicators are extracted using the model's forward propagation mechanism. A three-level seismic performance target system is constructed, and key performance indicators and design variables are optimized according to different design flood levels. In this process, based on the idea of ​​a physically encoded neural network, the structural dynamic equations are encoded into the network, giving the network's computation process clear physical meaning. This ensures the interpretability and physical consistency of the model, and improves the ability to effectively handle complex seismic design problems of high-speed railway bridges, achieving optimization of key design variables under multi-objective performance constraints.

[0012] In one possible design approach of the first aspect, the intelligent design method for the triple friction pendulum support further includes:

[0013] Count the number of components in TFPB;

[0014] The number of network parameters is determined by the number of components, and the network parameters are defined based on the design variables.

[0015] Stiffness matrix parameters W are constructed from network parameters k ;

[0016] And, by the stiffness matrix parameter W k Determine the first weight matrix W u and the second weight matrix W v As the training parameters.

[0017] In one possible design approach of the first aspect, the SDENN model includes a plurality of SDENN units connected in series. Each SDENN unit includes a displacement gate structure and a velocity gate structure. The displacement gate structure includes a first time step multiplication module and a first matrix addition module. The velocity gate structure includes a first matrix multiplication module, a second matrix multiplication module, a second matrix addition module, a second time step multiplication module, and a third matrix addition module. The velocity of the previous time step is used as the input to the first time step multiplication module. The displacement of the previous time step multiplied by the output of the first time step multiplication module is used as the input to the first matrix addition module. The output of the first matrix addition module and the first weight matrix are used as the input to the first matrix multiplication module. The inputs are: the velocity of the previous time step and the second weight matrix as inputs to the second matrix multiplication module; the outputs of the first matrix multiplication module, the second matrix multiplication module, and the ground motion data as inputs to the second matrix addition module; the output of the second matrix addition module as inputs to the second time step length multiplication module; the displacement of the previous time step and the output of the second time step length multiplication module as inputs to the third matrix addition module; the output of the first matrix addition module is the displacement of the current time step; and the output of the third matrix addition module is the velocity of the current time step. The preceding SDENN unit processes the displacement and velocity of the previous time step, and the subsequent SDENN unit processes the displacement and velocity of the current time step.

[0018] In one possible design approach of the first aspect, the first weighting matrix W is determined based on the fundamental equations of structural dynamics under seismic loading. u and the second weight matrix W v :

[0019] In the formula, m is the mass matrix, and α and β are the proportional coefficients defining Rayleigh damping.

[0020] In one possible design approach of the first aspect, the number of network parameters is determined under linear or nonlinear conditions, the network parameters are defined, and the stiffness matrix parameters W are constructed. k .

[0021] In one possible design approach of the first aspect, the design variables are optimized using the key performance indicators, specifically by performing backpropagation design based on the calculation results of the loss function, and iteratively adjusting the design variables, wherein the loss function is defined by the key performance indicators.

[0022] In one possible design approach of the first aspect, the loss function L is:

[0023] In the formula, L j Let u be the loss function component of each component. j,t Let be the deformation values ​​of the j components at time t. Let x be the deformation limit of the j-th component. Relu is a linear rectified function, and the expression of the Relu function is Relu(x) = max(0,x).

[0024] In one possible design approach of the first aspect, the working process of the TFPB includes: a first stage corresponding to a frequent earthquake, a second stage corresponding to a design earthquake, and a third stage corresponding to a rare earthquake; the design variables include: the slip force F1, the stiffness K2 of the TFPB in the second stage, the maximum displacement limit d2 of the TFPB in the second stage, and the stiffness K3 of the TFPB in the third stage.

[0025] In one possible design approach for the first aspect, Here, is the parameter representing the stiffness of TFPB in SDENN, and n represents the number of TFPB supports. It is an implicit function of u, written in the following form:

[0026] F 1,j K 2,j d 2,j and K 3,j Let F be the design parameters for the j-th TFPB. Then, the training parameters for SDENN are F. 1,j K 2,j d 2,j and K 3,j (j=1,2,…,n) implements the mapping relationship between the parameters of TFPB and the parameters of SDENN.

[0027] Secondly, a triple friction pendulum support intelligent design system is provided, including:

[0028] Define the element used to determine the design variables of the triple friction pendulum support TFPB;

[0029] And, an iterative calculation unit, used for iterative execution until convergence: inputting seismic data into the SDENN (Structural Dynamics Encoding Neural Network) model, using the forward propagation mechanism of the SDENN model to calculate the dynamic response of TFPB, extracting key performance indicators from the dynamic response, and using the key performance indicators to optimize the design variables. The calculation process of the SDENN model has a completely consistent mathematical form with the Euler method solution process of the structural dynamics equations, and the design variables correspond to the training parameters of the SDENN. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a schematic diagram of the triple friction pendulum support provided in the embodiments of this application;

[0032] Figure 2 This is a schematic diagram of the triple friction pendulum support in different motion stages provided in the embodiments of this application. (a) is the state without oscillation, (b) is the internal pendulum vibration during a frequent earthquake, (c) is the external pendulum vibration during a designed earthquake, and (d) is all pendulum vibrations during a rare earthquake.

[0033] Figure 3 This is a force-displacement curve of the triple friction pendulum support provided in an embodiment of this application;

[0034] Figure 4 This is a schematic diagram of a 24-span, 32m high-speed railway simply supported beam bridge provided in an embodiment of this application;

[0035] Figure 5 This is a finite element model of a high-speed railway track-bridge system provided in the embodiments of this application;

[0036] Figure 6 This is a comparison chart of the average spectrum of the selected seismic wave and the standard design response spectrum provided in the embodiments of this application;

[0037] Figure 7 This is a schematic diagram of the SDENN unit provided in an embodiment of this application;

[0038] Figure 8 This is a diagram of the internal structure of the SDENN cell provided in an embodiment of this application;

[0039] Figure 9 The W provided in the embodiments of this application u A schematic diagram;

[0040] Figure 10 The W provided in the embodiments of this application v A schematic diagram;

[0041] Figure 11 This is a flowchart of the SDENN calculation provided in an embodiment of this application;

[0042] Figure 12 This is a schematic diagram of the 8-DOF model and its stiffness matrix provided in the embodiments of this application. Figure 12 (a) is a schematic diagram of an 8-DOF model. Figure 12 (b) is the stiffness matrix of the 8-DOF model;

[0043] Figure 13 This is a flowchart of the SDENN construction process provided in the embodiments of this application;

[0044] Figure 14 This is a schematic diagram of the TFPB intelligent design method based on SDENN provided in the embodiments of this application;

[0045] Figure 15 This is a schematic diagram illustrating the performance target loss function provided in the embodiments of this application;

[0046] Figure 16 This is a flowchart of the TFPB intelligent design based on SDENN provided in the embodiments of this application;

[0047] Figure 17 This is a track-bridge model of a 7-span high-speed railway simply supported beam bridge provided in the embodiments of this application. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0049] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0050] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0051] This embodiment provides a smart design method for a triple friction pendulum support based on a physical coding neural network, which mainly includes the following steps:

[0052] Constructing a three-level seismic performance target system for high-speed railway track-bridge systems:

[0053] like Figure 1As shown in the figure, the TFPB consists of three independent pendulum systems. The triple friction pendulum bearing is mainly composed of the following core components: upper plate, lower plate, upper sliding plate, lower sliding plate, and intermediate slider. Sliding materials, usually polytetrafluoroethylene (PTFE), are coated between the slider and the sliding plate, and between the sliding plate and the plate. Connection combination relationship: The upper plate is connected to the beam body through anchor bolts, and the lower plate is connected to the bridge pier through the bearing pad stone or embedded steel plate; The intermediate slider is located between the upper and lower plates and contacts the upper and lower plates through four independent curved sliding interfaces respectively.

[0054] As Figure 2 shown, the working principle of the TFPB is as follows: From the perspective of mechanical properties, when the horizontal force F is less than the starting sliding force F1, the TFPB does not slide. The horizontal force F is a general variable, referring to the horizontal load or horizontal shear force acting on the TFPB. Under seismic action, this horizontal force mainly comes from the inertial force generated by the upper beam structure under the excitation of ground motion. The starting sliding force F1 is the first-stage critical starting sliding force of the entire TFPB, corresponding to the threshold for the first sliding interface to start sliding. At this time, its function is equivalent to that of an ordinary fixed bearing, and the sliding displacement d1 is approximately zero, which can meet the requirements of driving smoothness and stability under frequent earthquakes. By adjusting the parameters of the TFPB, the bearing can meet the horizontal force requirement of F1 < F < F2 under the design earthquake. F2 is the critical force for the triple friction pendulum bearing to enter the third stage from the second stage, that is, the threshold for the second sliding interface to start sliding (or the starting sliding force to enter the stiffness enhancement stage). At this time, the bearing stiffness is K2, playing a good seismic isolation and energy dissipation role. However, adding seismic isolation bearings will cause an increase in the displacement of the beam body, increasing the risk of collision. Therefore, the stiffness of the TFPB in the second stage cannot meet the stiffness requirements under rare earthquakes. At this time, when the bearing displacement d > d2, it will enter the stiffness enhancement stage. d2 is the maximum displacement limit of the triple friction pendulum bearing in the second stage, that is, the critical displacement point for the bearing to enter the third stage from the second stage. That is, when the horizontal force F > F2 under rare earthquake action, the bearing stiffness is increased to K3, and K3 is the stiffness of the triple friction pendulum bearing in the third stage. The above three stages refer to that under seismic action, the TFPB shows three different motion stages: The first stage: The horizontal force F is less than the starting sliding force F1, the bearing does not slide, and its function is equivalent to that of an ordinary fixed bearing, and the sliding displacement d1 is very small. At this time, it corresponds to frequent earthquakes; The second stage: The horizontal force is between F1 and F2, the bearing starts to slide, the stiffness is K2, and it plays a seismic isolation and energy dissipation role. At this time, it corresponds to the design earthquake; The third stage: The horizontal force is greater than F2, and the displacement exceeds the displacement limit d2 in the second stage. The bearing enters the stiffness enhancement stage, and the stiffness is increased to K3. At this time, it corresponds to rare earthquakes. Under seismic action, it shows three different motion stages, and its force-displacement relationship is as Figure 3 shown. Due to its multi-stage motion characteristics, designers can design the motion system under multi-level seismic actions according to the seismic performance objectives.

[0055] Based on the above analysis, the design of TFPB parameters needs to comprehensively consider the performance requirements of different seismic stages. The goal of this embodiment is to achieve intelligent optimization design of key TFPB parameters (F1, K2, d2, and K3) to meet the seismic performance objectives under different seismic loads.

[0056] A high-speed railway simply supported beam bridge with a standard span of 32 meters and four spans is selected as the research object, such as... Figure 4 As shown, the dynamic response of the bridge under different seismic loads is analyzed. The research objects include: abutments A0 and A5 located at both ends of the bridge; three piers, of which P1 and P3 are 8-meter-high piers and P2 is a 16-meter-high pier; and a 50-meter-long friction plate transition section on each side, used to connect the bridge and the roadbed structure. The beams are made of standard precast components, numbered B1, B2, B3 and B4 respectively, with each span of beam being 32.6 meters long, and a 0.1-meter expansion joint is set between adjacent beams. The cross-sectional dimensions of the beams and piers are determined according to "Tongqiao (2009) 2229-IV-Precast Post-Tensioned Prestressed Concrete Simply Supported Whole-Span Box Girder for Ballastless Track" and "Tongqiao (2021) 4301-IV-Circular-Ended Solid Pier for 350 km / h High-Speed ​​Railway".

[0057] This embodiment uses the OpenSees software, an open-system platform for earthquake engineering simulation, to establish a finite element model of a high-speed railway track-bridge. Figure 5 As shown.

[0058] For the seismic analysis of the track-bridge system of a simply supported beam high-speed railway, this embodiment, based on the relevant provisions of the "Code for Seismic Design of Railway Engineering" (GB50111-2006), determines the design response spectrum through parameters such as site category, fortification intensity, and characteristic period, and selects the corresponding seismic input accordingly. The engineering site conditions for the analysis example are: fortification intensity 8 degrees, Class II site, characteristic period zone 1, with peak ground acceleration (PGA) of 0.1g, 0.3g, and 0.57g for frequent earthquakes, design earthquakes, and rare earthquakes, respectively. Based on the code design response spectrum, 90 seismic records were selected from the Pacific Earthquake Engineering Research Center (PEER) database. The error between the average response spectrum of the selected seismic ground motions and the code design response spectrum is controlled within 20%, showing good consistency. Figure 6 As shown, 90 selected earthquakes were modulated to amplitudes of 0.1g, 0.3g, and 0.57g respectively and input into the high-speed railway track-bridge model as a uniform excitation of the foundation, and their dynamic response was calculated.

[0059] Based on seismic response analysis, a three-level seismic performance target system for high-speed railway track-bridge systems was derived:

[0060] For the first time, a three-level seismic performance target system for a high-speed railway simply supported beam bridge system was constructed, including the bridge structure (piers, beams, bearings) and the track structure (sliding layer, shear groove, CA mortar layer, shear reinforcement).

[0061] The system stipulates that under frequent earthquakes, the TFPB has not yet begun to slide, and its function is equivalent to that of an ordinary fixed support.

[0062] Under the design earthquake load, the TFPB begins to slide and plays a role in seismic isolation and damping. At this time, the piers are required to remain in an elastic state. Since the TFPB increases the displacement of the superstructure while reducing the displacement response of the piers, it is necessary to ensure that the supports do not fail under the design earthquake. Since the TFPB reduces the inconsistent displacement between beams, the displacement response of the shear tooth is reduced accordingly, allowing it to enter the plastic stage, but it is necessary to ensure that it does not fail.

[0063] Under rare earthquake conditions, the support displacement increases significantly, and the relative displacement between the beam and the pier increases, posing a risk of beam collapse. At this point, the TFPB should enter the stiffness enhancement stage to effectively control the relative displacement between the beam and the pier and prevent beam collapse. During this stage, the pier is allowed to enter a plastic state, but it must be ensured that it does not fail and that the nonlinear ductility ratio is less than 4.8 as specified in the code. At the same time, the displacement response of the shear tooth is increased compared to that under the design earthquake, but it is still necessary to ensure that it does not fail.

[0064] (II) Based on the idea of ​​physical coding neural networks, a structural dynamic coding neural network (SDENN) is proposed:

[0065] To address the limitations of traditional neural networks, a Structural Dynamics Encoded Neural Network (SDENN) is proposed based on the concept of a physically encoded neural network. SDENN directly encodes structural dynamics equations into its network architecture, ensuring that the model's computation process has explicit physical meaning. This effectively improves the network's generalization ability and reduces its dependence on large amounts of training data. The core idea of ​​SDENN is to embed structural dynamics equations into the neural network's computation process, enabling the network to directly reflect the physical characteristics of the structure and predict its dynamic response. This embodiment introduces the SDENN network structure, encodes the structural dynamics equations into the network structure, and embeds physical parameters such as the mass matrix, damping matrix, and stiffness matrix into the network structure. SDENN can directly reflect the physical characteristics of the structure, ensuring the model's interpretability and physical consistency. A detailed derivation of how to transform the structural dynamics equations into a form suitable for neural network computation is provided. The SDENN computation process is consistent with the iterative process of the Euler method, giving the network's computation process explicit physical meaning. SDENN lays the theoretical foundation for the subsequent design of TFPB.

[0066] 1. Network Architecture:

[0067] The proposed network structure SDENN unit encodes the structural dynamics equations, such as Figure 7 As shown, the network input is the ground motion, and the network output is the displacement response of each structure. Initial values ​​are assigned: both displacement and velocity are initially 0.

[0068] SDENN employs a simplified dual-gate structure to separately control the dynamic updates of displacement and velocity responses, defined as the displacement gate and velocity gate, respectively. Its structure is as follows: Figure 8 As shown.

[0069] Displacement gates are one of the core components of SDENN, such as... Figure 8 As shown in the upper left box, displacement gates are mainly used to implement temporal updates of displacement responses. The displacement gate input is the displacement response u from the previous moment. i-1 and velocity response v i-1 , using u i =u i-1 +v i-1 The recursive formula ×Δt, which has a clear physical meaning, is used to calculate the displacement response u at the current moment. i , where Δt represents the time step and i represents the i-th time step.

[0070] The structure of the speed gate is as follows Figure 8 The other box besides the displacement gate shows the velocity gate, which is used to update the velocity response. The velocity gate constructs a physically meaningful dynamic update process by combining the displacement response output by the displacement gate with three key pieces of information: the velocity response from the previous time step and the seismic excitation. The displacement response is then processed by the first weighting matrix W. u After mapping, it is compared with the second weight matrix W. v Mapped velocity response and seismic excitation Linear superposition, then with time step Δ Multiplying yields the speed increment, which is ultimately achieved through... An iterative formula is used to implement the timing update of the velocity response.

[0071] In summary, the SDENN model is a neural network model with specific physical meaning, and the network input is seismic motion. The output is the displacement response u of each structural component. i The overall structure is as follows Figure 8 As shown. The calculation formula for SDENN is as follows:

[0072] In the formula, W v and W u These are the relevant first weight matrix and second weight matrix, as shown in the following figures. Figure 9 and Figure 10As shown. The computation process (or formula) of SDENN has a completely consistent mathematical form with the Euler method solution process of the structural dynamics equations, where the network weight matrix W v and W u respectively correspond to m in the structural dynamics equation -1 c and m -1 k.

[0073] Based on knowledge of structural dynamics, the structural dynamics equations under seismic loading can be written as follows:

[0074] In the formula, m is the mass matrix, c is the damping matrix, and k is the stiffness matrix. This is the displacement response vector. Let k be the velocity response vector and u be the acceleration response vector. For a nonlinear system, k can be expressed as an implicit function of u:

[0075] Introducing intermediate variables The above structural dynamics equations can be transformed into the following system of first-order differential equations:

[0076] The implicit function described above, after being discretized over time, can be solved using the Euler method:

[0077] Therefore, each step of the SDENN calculation has a clear physical meaning, and the displacement gate realizes the update of the displacement response: u i =u i-1 +v i-1 ×Δt, the velocity gate is used to calculate the velocity response: The two work together to reproduce the numerical solution process of structural dynamics. Throughout the entire computational process, SDENN does not use any nonlinear activation functions; all operations are implemented in the network based on physical laws, ensuring the interpretability of the model and significantly improving the network's generalization ability by forcibly encoding known physical information.

[0078] 2. Network Input and Output:

[0079] The SDENN model proposed in this embodiment adopts an end-to-end deep learning architecture. Its network input is seismic motion time history data, and its output directly corresponds to the displacement response time history of each part of the structure. Figure 11 As shown, this model can realize the complete mapping process from seismic excitation to structural displacement response through iterative calculation of a single SDENN element.

[0080] 3. Network parameters:

[0081] Based on knowledge of structural dynamics, the structural dynamics equations under seismic loading can be written as follows:

[0082] In the formula, m is the mass matrix, c is the damping matrix, and k is the stiffness matrix. For nonlinear systems, k can be expressed as an implicit function of u.

[0083] Wv and Wu correspond to the structural dynamics equations and m, respectively. -1 c and m -1 k can be set as follows:

[0084] Then Wk is the parameter of SDENN corresponding to the overall stiffness matrix k of the structure. In this case, Wv, considering Rayleigh damping c = αm + βk, can be obtained from the following equation:

[0085] In the formula, α and β are the proportional coefficients that define Rayleigh damping.

[0086] Define W k,j W represents the stiffness of the j-th component. k,j Based on the coupling relationships between the structures, the overall stiffness matrix W of the structure is formed by combining them according to certain rules. k The stiffness W of each component k,j The overall stiffness matrix W is obtained. k Strictly following the classical theory of stiffness integration in structural mechanics, the stiffness W of each element is... k,j The components are assembled based on their topological connections, ultimately forming the system stiffness matrix W that reflects the overall structural mechanical properties. k The stiffness W of each component k,j The process of obtaining the overall stiffness matrix Wk reflects SDENN's encoding of the structure's geometric parameters, coupling relationships, and constraints.

[0087] For a linear elastic model, the parameter W represents the stiffness of each component. k,1 W k,2 ,……,W k,n These are the training parameters. In the 2D case, considering the shear, tension, compression, and torsion of the component, the number of network parameters n can be obtained from the following formula:

[0088] In the formula, m represents the number of components in the model.

[0089] For nonlinear models, W k,jIt is an implicit function of u, and can be written in the following form:

[0090] θ j These are the parameters of the function f. At this point, the training parameters of the network are the parameters θ of each component. j In the 2D case, considering the shear, tension, compression, and torsion of the component, the number of network parameters n is:

[0091] In the formula, m is the number of model components, and n V ,n F and n M The number of parameters in the functions that determine the shear stiffness, axial stiffness, and bending stiffness of the component, respectively.

[0092] by Figure 12 (a) Taking the 8-DOF model as an example, the training parameters of the network are explained. Only the lateral displacement at each node is considered; k1, k2, ..., k8 represent the lateral stiffness of each node. According to structural mechanics, the stiffness matrix k of this structure is composed of k1, k2, ..., k8 according to certain rules, such as... Figure 12 As shown in (b).

[0093] The training parameters of the SDENN model with this structure are W. k,1 W k,2 ,……,W k,8 According to the formation rules of the stiffness matrix k, the corresponding W k for:

[0094] Network training parameters W k,j The initial value can be random, or the possible stiffness value can be estimated based on the characteristics of the component itself. During the training process of the network, the stiffness value is adjusted by adjusting W... k,j With continuous optimization, W in ideal circumstances k The value of will eventually be consistent with k.

[0095] 4. Construction process of neural network encoding structural dynamics equations:

[0096] The SDENN construction process is as follows: Figure 13 As shown, the first step is to determine the physical structure and count the number of components, clarify the topology of the target physical system, and accurately count the number of its discretized components, denoted as m. Accurate component counting is a fundamental prerequisite for subsequent network parameterization modeling. The number of network parameters is determined; in the linear case, n = 3m. For the nonlinear case, the network parameters are determined based on the constitutive relations and hysteresis curves of each component. The network parameters are defined; in the linear case, the network parameter is defined as W.k,j (j=1,2,⋯,n). In the nonlinear case, the network parameters are defined as θ. j (j=1,2,⋯,n). Construct the stiffness matrix parameter W. In the linear case, it is directly derived from W. k,j Assemble W k In the nonlinear case, based on the constitutive relations and hysteresis curves of each component, a function is used... From θ j Determine W k,j And then integrate to obtain W k Construct the first weight matrix W. u Second weight matrix W v Using the obtained stiffness matrix parameters W k Through formula W u =m −1 W k and W v =m −1 (αm+βW k Construct W respectively u and W v , where α and β are correlation coefficients. SDENN is formed, and W... u and W v The matrix is ​​embedded into the SDENN computational framework to complete the construction of the structural dynamics equivalent network.

[0097] (III) A TFPB intelligent design method based on SDENN is proposed:

[0098] 1. Intelligent design method for triple friction pendulum support:

[0099] The triple friction pendulum support in this embodiment requires design parameters F1, K2, d2, and K3. The TFPB intelligent design method based on SDENN is as follows: Figure 14 As shown, Here, is the parameter representing the stiffness of TFPB in SDENN, and n represents the number of TFPB supports. It is an implicit function of u, and can be written in the following form:

[0100] F 1,j K 2,j d 2,j and K 3,j Let F be the design parameters for the j-th TFPB. Then, the training parameters for SDENN are F. 1,j K 2,j d 2,j and K 3,j(j=1,2,…,n). The loss function represents the structural design objective, the network training parameters are TFPB parameters, and the structural design is completed based on the backpropagation process using the neural network training process.

[0101] in accordance with Figure 14 Input ground motion layer: The figure shows a set of ground motion time history curves, which are the ground motion acceleration time history data input into the SDENN network. The subscripts 1, 2, ..., n represent different time steps.

[0102] SDENN layer: This is the unfolded SDENN recurrent neural network. Each "SDENN" block represents a SDENN unit, corresponding to the calculation of one time step. The internal state (displacement and velocity) of the previous SDENN unit is passed to the next unit, forming a loop, thereby simulating the entire dynamic response process of the structure under continuous earthquake action.

[0103] Output displacement response layer: Each SDENN element outputs a result, labeled as u1, u2, u3, u4, u5, u6, u7, u8, u9, u1, u9, u1, u1, u9, u1, u1, u1, u2, u1, u1, u2, u1, u2, u3, u1 ... n This is the time history of the structural displacement response output by the network, u i Corresponding to t i At any given moment, the displacement of the structure after an input seismic motion.

[0104] After outputting the displacement, the displacement response u is obtained from the output. i Extract the maximum value u from the entire time history. max Then, this maximum displacement is fed into the "performance target encoding loss function" module and compared with the preset "performance target".

[0105] Backpropagation: Calculate the performance target loss function according to the formula, perform backpropagation design based on the calculation result of the loss function, iteratively adjust the TFPB design variables until the loss value converges to 0, at which point the design process stops.

[0106] The performance objective is encoded as a loss function, and the network is trained accordingly. Ideally, the parameters F of the trained network will be... 1,j K 2,j d 2,j and K 3,j (j=1,2,…,n) are the TFPB parameters that satisfy the seismic performance objectives.

[0107] 2. Performance target loss function:

[0108] The deformation values ​​of each component are used as control indicators for seismic performance targets. Each seismic performance target can be uniformly encoded into the network's loss function L using the following formula:

[0109] In the formula, L j Let u be the loss function component of each component. j,t Let be the deformation values ​​of the j components at time t. Let x be the deformation limit of the j-th component. ReLU is a linear rectifier function. The expression of the ReLU function is ReLU(x) = max(0,x). The function of the ReLU function is to change values ​​less than 0 to 0.

[0110] The above formula is explained as follows: For example... Figure 15 As shown, the deformation response of the component at some moments exceeds the limit specified by the seismic performance target (the part marked by the box in the figure), where |u t / u lim |-1 in u t >u lim When |u is greater than 0, the opposite is true. t / u lim |-1 in u t lim When it is less than 0. After the ReLU function, only u... t >u lim WhenRelu(|u t / u lim |-1) is greater than 0, in u t lim WhenRelu(|u t / u lim The value of |-1) is 0. Therefore, ∑Relu(|u t / u lim -1) represents the portion of the component's deformation response that exceeds the limit specified by the seismic performance target. During network training, reducing the loss function means reducing the portion of the seismic response that exceeds the limit specified by the seismic performance target. When the loss function drops to 0, it means that the deformation response of all components does not exceed the limit, and the resulting F... 1,j K 2,k d 2,j and K 3,j (j=1,2,…,n) are the TFPB parameters that satisfy the seismic performance objectives.

[0111] 3. Intelligent Design Process of Triple Friction Pendulum Support

[0112] The TFPB intelligent design flow based on SDENN is as follows: Figure 16 ​​As shown. In the model building phase, the primary task is to clarify the specific parameters of the design object, including structural type and material properties, and clearly define performance objectives, thereby building the SDENN framework. In the parameter initialization step, the design variables of the TFPB (F1, K2, d2, and K3) are determined, and the weight parameters of SDENN are initialized, and a performance objective loss function is constructed. After inputting seismic ground motion data, the forward propagation mechanism of SDENN is used to calculate the dynamic response of the TFPB and extract key performance indicators. The performance objective loss function is calculated according to the formula, and backpropagation design is performed based on the calculation results of the loss function, iteratively adjusting the TFPB design variables until the loss value converges to 0, at which point the design process stops. Finally, the optimized TFPB design scheme is output, and its compliance with the predetermined performance objectives is verified using a finite element model.

[0113] (iv) The method of this embodiment will be further explained below with reference to an example:

[0114] by Figure 17 Taking the OpenSees model of a 7-span high-speed railway simply supported beam bridge as an example, the proposed seismic isolation bearing design method is verified. Using a 7-span high-speed railway simply supported beam bridge as the research object, the TFPB intelligent design method based on SDENN is adopted to design the key TFPB design parameters (F1, K2, d2, and K3) to ensure that the bridge meets the specified performance targets.

[0115] After SDENN is trained, the network parameters are extracted to obtain the design parameters of TFPB. The parameters are rounded as shown in Table 1.

[0116] Table 1 Design Results of TFPB

[0117] The designed TFPB bearing was applied to a 7-span high-speed railway track-bridge model for seismic response analysis. Using the 90 ground motions described earlier, the analysis examined whether the structure could meet the performance objectives outlined above, validating the design method described in the previous section. The analysis results show that:

[0118] (1) Piers: The peak displacement response of the 8m pier under different seismic motions was extracted. Under frequent earthquakes and design earthquakes, the peak seismic response of the pier was less than 12mm, indicating that the 8m pier was in an elastic state. Under rare earthquakes, the peak response of the pier was less than 55mm, indicating that the pier entered plasticity but did not fail, thus meeting the expected performance target. The peak displacement response of the 16m pier under different seismic motions was also extracted and analyzed. Under frequent earthquakes and design earthquakes, the peak seismic response of the pier was less than 39mm, indicating that the 16m pier was in an elastic state. Under rare earthquakes, the peak response of the pier was less than 166mm, indicating that the pier entered plasticity but did not fail, thus meeting the expected performance target. The nonlinear displacement ratio (μu) of the 8m and 16m piers was calculated. The nonlinear displacement ratio of both types of piers was less than the limit, thus meeting the expected performance target.

[0119] (2) Beams: The spacing between adjacent beams of this bridge is 100mm. 90 seismic motions were extracted. The relative displacement peak of adjacent beams under seismic action was less than 100mm. This indicates that adjacent beams will not collide under seismic action, achieving the expected performance target.

[0120] (3) Shear tooth groove: The peak displacement response of 90 seismic shear tooth grooves was extracted and analyzed. Under frequent earthquakes, the peak seismic response of the shear tooth groove was less than 1.9 mm and was in an elastic state. Under rare earthquakes and design earthquakes, the peak response of the shear tooth groove was less than 11.76 mm. At this time, the shear tooth groove entered the plastic state but was not damaged, thus meeting the expected performance target.

[0121] (4) Support: The peak displacement response of 90 seismic shear grooves was extracted and analyzed. Under rare earthquakes and design earthquakes, the peak seismic response of the support is less than 50 mm, and the support has not failed. Under rare earthquakes, the peak response of the support is greater than 50 mm, and the support may fail. However, according to the above, the support failure can be allowed at this time. As long as the beam does not fall, the index can be met.

[0122] (5) CA mortar layer, shear reinforcement, and fasteners: Based on the previous analysis, due to the seismic isolation mechanism formed by the sliding layer and shear groove, the CA mortar layer, shear reinforcement, and fasteners will remain elastic under seismic loading. This section extracts the peak displacement response values ​​of 90 seismic shear grooves to verify the above conclusion. Under rare earthquakes, the peak displacement of the CA mortar layer under different seismic motions is less than 0.4 mm, indicating an elastic state; the peak displacement of the shear reinforcement under different seismic motions is less than 0.6 mm, indicating an elastic state; and the peak displacement of the fasteners under different seismic motions is less than 2 mm, indicating an elastic state.

[0123] In summary, the TFPB design method based on SDENN has completed the design of the support, and the design results have achieved the predetermined performance goals.

[0124] This embodiment proposes an intelligent design method for a triple friction pendulum support based on a physical coding neural network. The main innovations are as follows:

[0125] (1) Combining the mechanical properties of triple friction pendulum seismic isolation bearing (TFPB), a three-level seismic performance target system for high-speed railway track-bridge system was constructed for the first time: a three-level seismic performance target system for high-speed railway simply supported beam bridge system including bridge structure (pier, beam, bearing) and track structure (sliding layer, shear tooth groove, CA mortar layer, shear reinforcement) was constructed.

[0126] The system stipulates that under frequent earthquakes, the TFPB has not yet begun to slide, and its function is equivalent to that of an ordinary fixed support.

[0127] Under the design earthquake load, the TFPB begins to slide and plays a role in seismic isolation and damping. At this time, the piers are required to remain in an elastic state. Since the TFPB increases the displacement of the superstructure while reducing the displacement response of the piers, it is necessary to ensure that the supports do not fail under the design earthquake. Since the TFPB reduces the inconsistent displacement between beams, the displacement response of the shear tooth is reduced accordingly, allowing it to enter the plastic stage, but it is necessary to ensure that it does not fail.

[0128] Under rare earthquake conditions, the support displacement increases significantly, and the relative displacement between the beam and the pier increases, posing a risk of beam collapse. At this point, the TFPB should enter the stiffness enhancement stage to effectively control the relative displacement between the beam and the pier and prevent beam collapse. During this stage, the pier is allowed to enter a plastic state, but it must be ensured that it does not fail and that the nonlinear ductility ratio is less than 4.8 as specified in the code. At the same time, the displacement response of the shear tooth is increased compared to that under the design earthquake, but it is still necessary to ensure that it does not fail.

[0129] Unconventional reason: While the current "Code for Seismic Design of Railway Engineering" (GB50111-2006) clearly defines the seismic performance targets for the main structure of bridges, it does not specify requirements for the seismic fortification of track structures. This embodiment is the first to incorporate track structures into a quantitative performance target system, and based on the graded energy dissipation characteristics of TFPB, it realizes graded performance targets for the entire track-bridge system under three-level seismic loading.

[0130] (2) Based on the idea of ​​physical coding neural network, a structural dynamic coding neural network (SDENN) is proposed: the network architecture encodes the structural dynamic equation into the network, ensuring that the network's calculation process has a clear physical meaning and avoiding the limitations of traditional black box models such as long short-term memory network LSTM; SDENN embeds physical parameters such as mass matrix, damping matrix and stiffness matrix into the network, so that the network can directly reflect the physical characteristics of the structure, ensuring the interpretability and physical consistency of the model.

[0131] Unconventional reason: Traditional neural networks, such as LSTM and Gated Recurrent Units (GRUs), lack physical interpretability when dealing with structural dynamics problems, requiring a large amount of training data to ensure the model's generalization ability. SDENN can directly reflect the physical characteristics of the structure, ensuring the model's interpretability and physical consistency. This not only significantly improves the network's generalization ability but also reduces its dependence on large amounts of training data.

[0132] (3) A TFPB intelligent design method based on SDENN is proposed: by utilizing the threshold screening characteristic of the ReLU function, the excess value of the component deformation response is used as the network training objective, driving the SDENN parameters to iterate in the direction of satisfying multi-level performance constraints. This method can effectively handle the complex seismic design problem of high-speed railway bridges, especially the parameter optimization under multi-objective performance constraints.

[0133] Unconventional reason: Due to its segmented motion characteristics, the TFPB can achieve graded seismic isolation and control of bridge piers, beams, and track structures under multi-level seismic action. However, traditional design methods struggle to efficiently determine the parameters of the TFPB that meet performance objectives.

[0134] This application also provides an intelligent design system for a triple friction pendulum support based on a physical coding neural network, including:

[0135] Define the element used to determine the design variables of the triple friction pendulum support TFPB;

[0136] And, an iterative calculation unit, used for iterative execution until convergence: inputting seismic ground motion data into the SDENN model, using the forward propagation mechanism of the SDENN model to calculate the dynamic response of TFPB, extracting key performance indicators from the dynamic response, and using the key performance indicators to optimize the design variables. The calculation process of the SDENN model has a completely consistent mathematical form with the Euler method solution process of the structural dynamics equations, and the design variables correspond to the training parameters of the SDENN.

[0137] This application also provides an electronic device, including: a processor, and a memory coupled to the processor, the memory being used to store a computer program; the processor being used to execute the computer program stored in the memory, so that the electronic device performs the method as described in any of the above embodiments.

[0138] Electronic devices can be computing devices such as desktop computers, laptops, handheld computers, and cloud servers. These electronic devices may include, but are not limited to, processors and memory.

[0139] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the electronic device, connecting various parts of the device via various interfaces and lines.

[0140] The memory can be used to store the computer program, and the processor implements various functions of the electronic device by running or executing the computer program stored in the memory and calling the data stored in the memory.

[0141] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system, applications required for at least one function, etc.; the data storage area may store data created based on the use of the mobile phone, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0142] This application also provides a storage medium, which is a computer-readable storage medium. The computer program is stored in the computer-readable storage medium, and when executed by a processor, the computer program can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0143] This application also provides a computer program product, including: a computer program or instructions that, when the computer program or instructions are run on a computer, cause the computer to perform any of the above possible implementation methods.

[0144] The above description is the preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications are also considered to be within the scope of protection of this application.

Claims

1. A smart design method for a triple friction pendulum support, characterized in that, include: Determine the design variables for the triple friction pendulum support TFPB; as well as, Iterative execution until convergence: input seismic data into the SDENN structural dynamics encoding neural network model; The forward propagation mechanism of the SDENN model is used to calculate the dynamic response of TFPB and extract key performance indicators from the dynamic response. The design variables are then optimized using the key performance indicators. The calculation process of the SDENN model has a completely consistent mathematical form with the Euler method solution process of the structural dynamics equations. The design variables correspond to the training parameters of the SDENN. The intelligent design method for the triple friction pendulum support also includes: Count the number of components in TFPB; The number of network parameters is determined by the number of components, and the network parameters are defined based on the design variables. Stiffness matrix parameters W are constructed from network parameters k ;as well as, From the stiffness matrix parameter W k Determine the first weight matrix W u and the second weight matrix W v As the training parameters; The SDENN model comprises several SDENN units connected in series. Each SDENN unit includes a displacement gate structure and a velocity gate structure. The displacement gate structure includes a first time step multiplication module and a first matrix addition module. The velocity gate structure includes a first matrix multiplication module, a second matrix multiplication module, a second matrix addition module, a second time step multiplication module, and a third matrix addition module. The velocity of the previous time step is used as the input to the first time step multiplication module. The displacement of the previous time step and the output of the first time step multiplication module are used as the input to the first matrix addition module. The output of the first matrix addition module and the first weight matrix are used as the input to the first matrix multiplication module. The velocity and the second weight matrix are used as inputs to the second matrix multiplication module. The outputs of the first matrix multiplication module, the second matrix multiplication module, and the ground motion data are used as inputs to the second matrix addition module. The output of the second matrix addition module is used as input to the second time step multiplication module. The displacement of the previous time step and the output of the second time step multiplication module are used as inputs to the third matrix addition module. The output of the first matrix addition module is the displacement of the current time step. The output of the third matrix addition module is the velocity of the current time step. The preceding SDENN unit processes the displacement and velocity of the previous time step, and the subsequent SDENN unit processes the displacement and velocity of the current time step. Based on the fundamental equations of structural dynamics under seismic loading, the first weight matrix W is determined. u and the second weight matrix W v : In the formula, m is the mass matrix, and α and β are the proportionality coefficients that define Rayleigh damping; The optimization of the design variables using the key performance indicators specifically involves: performing backpropagation design based on the calculation results of the loss function, and iteratively adjusting the design variables, wherein the loss function is defined by the key performance indicators; The loss function L is: In the formula, L j Let u be the loss function component of each component. j,t Let be the deformation values ​​of component j at time t. Let x be the deformation limit of the j-th component. Relu is a linear rectified function, and the expression of the Relu function is Relu(x) = max(0,x).

2. The intelligent design method for a triple friction pendulum support as described in claim 1, characterized in that, Determine the number of network parameters, define the network parameters, and construct the stiffness matrix parameters W under linear or nonlinear conditions. k .

3. The intelligent design method for a triple friction pendulum support as described in claim 1, characterized in that, The working process of the TFPB includes: a first stage corresponding to a frequent earthquake, a second stage corresponding to a design earthquake, and a third stage corresponding to a rare earthquake; the design variables include: the slip force F1, the stiffness K2 of the TFPB in the second stage, the maximum displacement limit d2 of the TFPB in the second stage, and the stiffness K3 of the TFPB in the third stage.

4. The intelligent design method for a triple friction pendulum support as described in claim 3, characterized in that, Here, is the parameter representing the stiffness of TFPB in SDENN, and n represents the number of TFPB supports. It is an implicit function of u, written in the following form: F 1,j K 2,j d 2,j and K 3,j Let F be the design parameters for the j-th TFPB. Then, the training parameters for SDENN are F. 1,j K 2,j d 2,j and K 3,j (j=1,2,…,n) implements the mapping relationship between the parameters of TFPB and the parameters of SDENN.

5. A triple friction pendulum support intelligent design system, characterized in that, include: Define the element used to determine the design variables of the triple friction pendulum support TFPB; as well as, An iterative calculation unit is used to iteratively execute until convergence: inputting seismic data into the SDENN (Structural Dynamics Encoding Neural Network) model, using the forward propagation mechanism of the SDENN model, calculating the dynamic response of the TFPB, extracting key performance indicators from the dynamic response, and using the key performance indicators to optimize the design variables. The calculation process of the SDENN model has a completely consistent mathematical form with the Euler method solution process of the structural dynamics equations, and the design variables correspond to the training parameters of the SDENN. The system is also used for: Count the number of components in the TFPB; determine the number of network parameters based on the number of components, define the network parameters according to the design variables; construct the stiffness matrix parameter W from the network parameters. k ;as well as The stiffness matrix parameter W k Determine the first weight matrix W u and the second weight matrix W v As the training parameters; The SDENN model comprises several SDENN units connected in series. Each SDENN unit includes a displacement gate structure and a velocity gate structure. The displacement gate structure includes a first time step multiplication module and a first matrix addition module. The velocity gate structure includes a first matrix multiplication module, a second matrix multiplication module, a second matrix addition module, a second time step multiplication module, and a third matrix addition module. The velocity of the previous time step is used as the input to the first time step multiplication module. The displacement of the previous time step and the output of the first time step multiplication module are used as the input to the first matrix addition module. The output of the first matrix addition module and the first weight matrix are used as the input to the first matrix multiplication module. The velocity and the second weight matrix are used as inputs to the second matrix multiplication module. The outputs of the first matrix multiplication module, the second matrix multiplication module, and the ground motion data are used as inputs to the second matrix addition module. The output of the second matrix addition module is used as input to the second time step multiplication module. The displacement of the previous time step and the output of the second time step multiplication module are used as inputs to the third matrix addition module. The output of the first matrix addition module is the displacement of the current time step. The output of the third matrix addition module is the velocity of the current time step. The preceding SDENN unit processes the displacement and velocity of the previous time step, and the subsequent SDENN unit processes the displacement and velocity of the current time step. Based on the fundamental equations of structural dynamics under seismic loading, the first weight matrix W is determined. u and the second weight matrix W v : In the formula, m is the mass matrix, and α and β are the proportionality coefficients that define Rayleigh damping; The optimization of the design variables using the key performance indicators specifically involves: performing backpropagation design based on the calculation results of the loss function, and iteratively adjusting the design variables, wherein the loss function is defined by the key performance indicators; The loss function L is: In the formula, L j Let u be the loss function component of each component. j,t Let be the deformation values ​​of component j at time t. Let x be the deformation limit of the j-th component. Relu is a linear rectified function, and the expression of the Relu function is Relu(x) = max(0,x).

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