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CN-122021298-A - Bridge random vibration analysis method based on mechanism enhanced physical information neural network

CN122021298ACN 122021298 ACN122021298 ACN 122021298ACN-122021298-A

Abstract

The invention belongs to the field of bridge structure anti-seismic design and safety evaluation, and relates to a bridge random vibration analysis method based on a mechanism enhanced physical information neural network, which comprises the steps of establishing a bridge structure motion equation configured with a nonlinear tuning inertial Rong Zuni device; the method comprises the steps of constructing a mechanism enhanced physical information neural network model comprising a three-head prediction module and a three-state gating mechanism, wherein the three-head prediction module decouples nonlinear restoring force prediction into three independent subtasks of acceleration, speed and symbols, the three-state gating mechanism divides time steps into a safety domain, a traversing domain and a singular point zero point domain according to the speed and the magnitude and adopts a differential supervision strategy, generating a sample based on a random near-fault earthquake motion model to train a network, and deeply fusing the trained mechanism enhanced physical information neural network with a direct probability integration method to efficiently and accurately calculate random vibration response and dynamic reliability of a bridge structure. The invention provides a high-efficiency and reliable analysis tool for the seismic safety assessment of the bridge structure.

Inventors

  • ZHOU ZHENG
  • YANG DIXIONG
  • Xiao Ningchang
  • LI HUI
  • CHEN GUOHAI

Assignees

  • 大连理工大学

Dates

Publication Date
20260512
Application Date
20260128

Claims (6)

  1. 1. The bridge random vibration analysis method based on the mechanism enhanced physical information neural network is characterized by comprising the following steps of: step (1) establishing a bridge structure finite element model configured with a nonlinear tuned inertial damping device (NTID), and deducing a bridge structure motion equation containing the NTID based on the finite element model; step (2) constructing a mechanism enhanced physical information neural network model ME-PINN based on a bridge structure motion equation containing NTID; The ME-PINN comprises a TCN-LSTM characteristic extraction module, a three-head prediction module, a physical assembly module, a single convolution layer module SCL and a loss function module containing a tri-state gating mechanism; The forward propagation path sequentially passes through a TCN module to extract multi-scale time sequence characteristics, an LSTM module to capture long-term time sequence dependency, a three-head prediction module to decouple NTID nonlinear restoring force prediction into three independent subtasks of acceleration prediction, speed prediction and symbol prediction, a physical assembly module to assemble a complete restoring force time course according to NTID constitutive relation, and an SCL module to calculate a bridge global state vector through discrete convolution operation; The reverse propagation path realizes network parameter optimization through a loss function module comprising a tri-state gating mechanism, wherein the loss function module consists of basic physical loss and symbol loss, the tri-state gating mechanism divides time steps into three physical areas of a security domain, a crossing domain and a singular point zero point domain according to the speed and adopts a differential supervision strategy; Step (3) generating a seismic oscillation sample based on a random near-fault seismic oscillation model to train the ME-PINN model; generating a sliding impact type and forward direction type pulse earthquake motion sample by adopting a spectrum matching random near-fault earthquake motion model; Dividing the generated earthquake motion samples according to the dividing proportion of the training set and the verification set; Training an ME-PINN model by adopting an Adam optimizer, and judging the convergence condition of the model through training loss and verifying a loss curve; After training is completed, verifying model prediction accuracy by adopting actually recorded near-fault earthquake motion and spectrum matching earthquake motion samples; And (4) after the step (3) is completed, combining a direct probability integration method with the trained ME-PINN model, and calculating the random seismic response and the dynamic reliability result of the bridge structure.
  2. 2. The bridge random vibration analysis method based on the mechanism enhanced physical information neural network according to claim 1, wherein the step (1) is specifically as follows: The method comprises the steps of obtaining a mass matrix M, a rigidity matrix K and a damping matrix C of a bridge structure to establish an SCL module of an ME-PINN model, establishing a bridge structure model configured with a nonlinear tuned inertial damper NTID by adopting a finite element method, and correspondingly establishing a motion equation of the bridge structure configured with the NTID under the random near-fault earthquake action based on the finite element model, wherein the motion equation is expressed as follows: (1) wherein M, C, K respectively represent a mass matrix, a damping matrix and a rigidity matrix of the bridge structure without NTID, U (t), 、 Respectively representing displacement, speed and acceleration vectors of the bridge structure; Representing random seismic excitation, wherein θ is a random vector that characterizes near-fault seismic randomness; And A unit influence vector representing the NTID application position and the seismic excitation application position, respectively, u NTID , 、 The relative displacement, the speed and the acceleration among NTID connection nodes are respectively; A state vector representing the NTID, Representing the nonlinear restoring force provided by the NTID device; 、 、 Respectively representing the inertia coefficient, the viscous friction coefficient and the coulomb friction force amplitude, k represents the rigidity of the spring in the NTID device, c represents the linear damping coefficient of the NTID, and sign (&) is a sign function.
  3. 3. The bridge random vibration analysis method based on the mechanism enhanced physical information neural network according to claim 1, wherein the forward propagation path in the step (2) sequentially comprises the following five functional modules connected in series according to the signal flow direction: The TCN feature extraction module is used as a first-stage module and receives an earthquake excitation time interval as input, is formed by sequentially cascading three time sequence blocks, wherein each time sequence block internally comprises two convolution layers, a ReLU activation layer, a Dropout regularization layer and residual connection, the expansion factors of the three time sequence blocks are sequentially increased to be 1, 2 and 4, the number of filters is sequentially increased to be 64, 128 and 196, and the convolution kernel size is 3; The LSTM feature coding module is used as a second-stage module and is formed by longitudinally stacking three layers of LSTM networks, wherein the first layer of LSTM receives the TCN output features, the hidden state of the TCN output features is transmitted to the second layer of LSTM, the hidden state of the second layer of LSTM is transmitted to the third layer of LSTM, and the output of the third layer of LSTM is used as a coded time sequence feature representation; the three-head prediction module is used as a third-stage module for receiving the coding features output by the LSTM feature coding module, and comprises three parallel fully-connected neural network branches, wherein the three parallel fully-connected neural network branches are respectively as follows: The acceleration pre-measuring head comprises two full-connection layers, wherein the middle layer is activated by ReLU, the output layer is activated linearly, and the relative acceleration a pred (t) of NTID is predicted; the speed predicting head comprises two full-connection layers, wherein the middle layer is activated by ReLU, the output layer is activated linearly, and the relative speed v pred (t) of NTID is predicted; The symbol pre-measuring head comprises two full-connection layers, wherein a middle layer is activated by a ReLU, an output layer is restrained in a [ -1,1] interval by a tanh activation function, and a friction force direction s pred (t) is predicted; The three prediction heads simultaneously receive the same input characteristics and independently output three prediction values in parallel; The physical assembly module is used as a fourth-stage module and receives three outputs of the three-head prediction module, and the module assembles the predicted values of acceleration, speed and sign into a complete nonlinear restoring force time interval F pred (t) according to NTID constitutive relation F pred (t) = b·a pred (t) + c v ·v pred (t) + f 0 ·s pred (t), wherein b is an inertial coefficient, c v is a viscous friction coefficient, and F 0 is a coulomb friction amplitude; The SCL module is used as a fifth-stage module for receiving the restoring force time F pred (t) and the original seismic excitation a g (t) output by the physical assembly module, and firstly combining the two modules into a global excitation vector Discrete convolution calculations are then performed over a single layer convolution network, the formula of which can be expressed as: (2) Wherein V i is the bridge global state vector of the ith time step, F j is the global excitation vector, the time step subscript range of the time step is j epsilon { i-m+1, i-m+2, & gt, i-1}, A k,1 is the k-th order influence coefficient matrix, k=1, 2, & gt, m, m is the truncated term number of the influence coefficient matrix, and the calculation formula for the influence coefficient matrix A k,1 is as follows: (3) (4) Wherein 0 and I respectively represent zero matrix and identity matrix, parameters beta and gamma are time integral parameters of Newmark-beta method, parameter deltat represents time step of earthquake, Q 1 、Q 2 , T is intermediate calculation matrix, H, S 1 、S 2 , W is state space conversion auxiliary matrix, a x , x=0, 1,2, and 5 is auxiliary calculation coefficient of influence coefficient matrix, influence coefficient matrix a k,1 calculated by formula (4) is kept fixed in model training process, global state vector V i of bridge is finally calculated based on formula (2), wherein V i = [ solution ] , T Represents the displacement of the bridge key node at time t i Sum speed of Response based on the obtained speed response Corresponding calculation is carried out according to a forward differential formula to obtain acceleration response The method comprises the following steps: (5)。
  4. 4. The method for analyzing random vibration of a bridge based on a mechanism enhanced physical information neural network according to claim 1, wherein in the counter propagation path in step (2): The loss function module consists of two parts, namely basic physical loss and symbol loss, wherein the basic physical loss comprises acceleration loss L a and speed loss L v , the basic physical loss is respectively used for supervising the output precision of an acceleration pre-measuring head and a speed pre-measuring head, and the calculation formulas are respectively as follows: (6) (7) wherein t i is the i-th time, N is the total time step, And Acceleration and speed values calculated by SCL module respectively, and three-state gating mechanism based on speed according to speed symbol prediction Dividing time steps into three physical areas and adopting a differential supervision strategy, wherein the security area is M/s, direct supervisor symbol prediction, crossing the outer periphery of the domain M/s, using acceleration symbol as symbol prediction guided by physical information, singular point zero point domain as M/s, adopting soft constraint to allow a certain prediction tolerance, wherein symbol losses corresponding to the three regions are respectively as follows: (8) (9) (10) The method comprises the steps of obtaining a total loss function, wherein L s,safe 、 L s,cross 、 L s,zero is the symbol loss of a safety domain, a crossover domain and a singular point zero point domain respectively, v 0 = 10 -2 M/s is a normalization parameter, v soft = 10 -3 M/s is a soft constraint tolerance parameter, M safe 、M cross 、M zero is the binary masks of the safety domain, the crossover domain and the singular point zero point domain respectively, the total symbol loss is L s = L s,safe + L s,cross + L s,zero , and finally, the total loss function realizes the optimization of the whole model through weighted aggregation: (11) wherein ω a 、ω v 、ω s is the weight coefficient of the acceleration loss, the velocity loss and the sign loss, respectively.
  5. 5. The bridge random vibration analysis method based on the mechanism enhanced physical information neural network according to claim 1, wherein the step (4) is specifically as follows: Based on the ME-PINN model trained in the step (3), the model is integrated into a direct probability integration method DPIM framework as an efficient proxy model to replace a finite element time-course analysis method, so that the efficient calculation of random vibration response and dynamic reliability is realized, and for the random vibration response of a bridge structure configured with a nonlinear tuning inertial Rong Zuni device under the random near-fault earthquake action, the calculation formula of a probability density function p Y (y, t) is as follows: (12) Wherein y represents bridge seismic response, N tol is the number of representative points required by the DPIM method, theta q is the q-th representative point, P q is the probability of assignment of the corresponding representative points, g (theta q , t) is a physical mapping function, and sigma (t) is a smoothing parameter; Based on the direct probability integration method, the calculation formulas of the time-varying mean E [ Y (t) ] and the standard deviation Std [ Y (t) ] of the random vibration response can be expressed as follows: (13) (14) the power reliability R (t) is expressed as: (15) Wherein Y thd is the failure threshold value, For extreme response, H is the Heaviside function.
  6. 6. The method for analyzing the random vibration of the bridge based on the mechanism enhanced physical information neural network according to claim 5, wherein the optimal representative point number N tol is adaptively determined by adopting an iterative sequence sampling strategy, wherein the strategy firstly generates a candidate representative point pool based on a GF-difference point selection method, then iteratively increases representative points and calculates extremum response, and the method is terminated when the relative error of continuous 5 iterations is less than 5 multiplied by 10 -5 .

Description

Bridge random vibration analysis method based on mechanism enhanced physical information neural network Technical Field The invention belongs to the field of seismic design and safety evaluation of bridge structures, and relates to a bridge random vibration analysis method based on a mechanism enhanced physical information neural network. Background As a key component of modern traffic infrastructure, the seismic safety of bridges is directly related to the reliable operation of traffic lifeline systems. Particularly in near fault areas, the earthquake motion presents remarkable random characteristics and impulse effects, and forms a serious threat to the safety of bridge structures. The traditional deterministic earthquake response analysis method is based on calculation of single or limited number of earthquake motion records, cannot fully reflect the influence of the randomness of earthquake motion (especially near fault earthquake motion) on bridge response, and is difficult to realize accurate evaluation of bridge earthquake resistance and scientific quantification of safety risks. Therefore, performing random vibration analysis to comprehensively evaluate the seismic performance of the bridge under the random near-fault earthquake motion has become an urgent need. The existing bridge structure random vibration analysis method mainly comprises a Monte Carlo method (Monte Carlo Simulation, MCS), a Quasi Monte Carlo method (Quasi-Monte Carlo Simulation, QMCS) and the like. The method is faced with the common problem of low calculation efficiency when carrying out bridge random vibration analysis, namely, to accurately obtain probability distribution characteristics of structural response, repeated nonlinear time-course analysis is usually carried out on hundreds to tens of thousands of seismic samples, each analysis needs iterative solution to a dynamics equation in a plurality of time steps, and the calculation cost is extremely high. This severely restricts the application of the existing random vibration analysis method in bridge engineering. Aiming at the problem of low calculation efficiency of the existing random vibration analysis method, a fast-developed deep learning technology in recent years provides a new solution for efficient prediction of structural seismic response. Wherein physical information neural networks (Physics-Informed Neural Networks, PINN) have achieved some success in predicting the seismic response of linear or smooth nonlinear structures by embedding physical constraints in the architecture or loss function of the neural network. However, the existing PINN method faces technical difficulties for bridge structures equipped with strong nonlinear shock absorbing devices such as nonlinear tuned inertial damping devices (NTID) containing coulomb friction, etc. In particular, the strong nonlinearity and discontinuity of the sign function in coulomb friction makes it difficult for the neural network to accurately learn and predict its mechanical behavior. While there have been approaches to approximating a sign function with a smooth function to achieve scalability, this approach introduces significant prediction errors. Therefore, how to construct a high-efficiency PINN model capable of accurately capturing strong nonlinearity such as coulomb friction and strong discontinuous mechanical characteristics and combining the model with a random vibration analysis theory to realize high-efficiency and accurate random seismic response and dynamic reliability calculation of a bridge structure under random near-fault seismic excitation is a key technical problem to be solved in the current bridge seismic field. Disclosure of Invention In order to solve the problems, the invention provides a bridge random vibration analysis method based on a mechanism enhanced physical information neural network, which is suitable for random dynamics analysis of a bridge structure provided with a nonlinear tuned inertial damping device (NTID) under the random near-fault earthquake vibration excitation effect. The invention is a fusion framework of a mechanism enhanced physical information neural network (ME-PINN) and a direct probability integration method, thereby realizing efficient and accurate random vibration analysis of a bridge structure provided with a strong nonlinear damping device. The method mainly comprises the steps of establishing a motion equation of a bridge structure with NTID, constructing an ME-PINN model comprising a three-head prediction module, a three-state gating mechanism and other modules, generating a sample training ME-PINN model based on a random near-fault earthquake motion model, and accurately and efficiently calculating random vibration response and dynamic reliability of the structure by combining a trained ME-PINN model through a direct probability integration method. The ME-PINN effectively solves the inherent defect of the traditional PINN in the process of treating the