A large-span structure anti-seismic simulation method and system

Abstract

This invention relates to the field of computer simulation, specifically a method and system for simulating the seismic resistance of large-span structures. The method involves constructing a three-dimensional finite element baseline model of the structure, identifying and separating high-energy-consuming key components as physical test substructures based on the cumulative strain energy density distribution, generating non-uniform ground motion sequences using the spectral representation-orthogonal expansion method, and applying these sequences as equivalent loads to the numerical substructure. During the time-step cycle of the real-time hybrid test, the motion equations of the numerical substructure are solved by explicit integration to obtain the target interface displacement. A control law is constructed based on Lyapunov stability theory to adjust a multi-array system to track the target displacement. A pre-trained recurrent neural network time-delay compensation model is used to process the collected interface restoring force and actuator states online, feeding the compensated restoring force back to the next time-step solution of the numerical substructure in real time, thereby simulating the nonlinear dynamic response of the structure under complex ground motion.

Description

Technical Field

[0001] This application belongs to the field of computer simulation, and in particular relates to a method and system for simulating the seismic resistance of large-span structures. Background Technology

[0002] Due to their dynamic characteristics such as large span, high flexibility, dense frequency spectrum, and low damping ratio, long-span structures are extremely sensitive to seismic forces, and damage to them can cause enormous economic losses and social impacts. Traditional seismic research methods rely on scaled-down shaking table tests or pure numerical simulations. For long-span structures, large-scale scaled-down model tests are difficult to implement, while small-scale models face the dilemma of not being able to satisfy the similarity law of model materials and gravity. Pure numerical simulations, when dealing with strongly nonlinear behavior, suffer from insufficient computational accuracy due to the existence of restoring force models. Moreover, in terms of substructure division, existing methods are mostly based on engineering experience or geometric division, and the division results may be biased. For long-span structures, the spatial variability of seismic motion cannot be ignored, but existing tests are often simplified to uniform excitation, which cannot truly reflect the coherence and traveling wave effect of seismic waves during spatial propagation, leading to biases in structural response assessments. Furthermore, multi-array systems involve hydraulic servo control, which inherently exhibits dynamic response lag and nonlinear characteristics. The measured displacement of the physical substructure often lags behind the numerically calculated target displacement. Moreover, traditional time-delay compensation methods are typically based on linear assumptions, making it difficult to address the nonlinear time-varying characteristics of actuators during high-frequency motion. Therefore, there is an urgent need for a seismic simulation method for large-span structures that can comprehensively consider energy distribution, spatial seismic motion characteristics, and nonlinear time-delay compensation. Summary of the Invention

[0003] To address the problem that existing technologies fail to comprehensively consider energy distribution, spatial seismic motion characteristics, and nonlinear time delay compensation.

[0004] In the first aspect, the present invention proposes a seismic simulation method for large-span structures, comprising the following steps: A three-dimensional finite element benchmark model of a large-span structure is constructed, and the cumulative plastic strain energy density distribution of all nodes is calculated by dynamic time history test. Based on this, the benchmark model is divided into a physical test substructure containing high-energy-consuming key nonlinear components and a linear elastic numerical simulation substructure. A physical-numerical collaborative interaction interface that satisfies the conditions of force balance and displacement coordination is established. The non-uniform bedrock acceleration time histories at each shaking table site were generated using the spectral representation-orthogonal expansion method. After double integration and baseline correction, the reference seismic motion input sequence of the multi-array system was obtained, and the sequence was converted into the equivalent seismic load applied to the numerical simulation substructure. The motion equations of the numerical simulation substructure at the current time step are solved using an explicit integration algorithm to obtain the target displacement of the collaborative interaction interface; a control law is constructed, and the control parameters of the multi-array system are corrected online in real time based on the tracking error between the measured displacement and the target displacement. The target displacement is mapped into actuator stroke commands to drive the motion of the physical experiment substructure. The physical restoring force feedback signal and the current state of the actuator at the collaborative interaction interface are collected in real time. The physical restoring force feedback signal and the current state of the actuator are input into a pre-trained recurrent neural network time delay compensation model to predict the interface restoring force after eliminating the system response time delay. The compensated interface restoring force is fed back into the motion equation of the numerical simulation substructure to participate in the solution of the next time step until all time history conditions are loaded.

[0005] Optionally, the construction of a three-dimensional finite element benchmark model of a large-span structure involves performing dynamic time history calculations to determine the cumulative plastic strain energy density distribution at all nodes. Based on this, the benchmark model is divided into a physical experimental substructure containing high-energy-consuming key nonlinear components and a linearly elastic numerical simulation substructure, including: A typical seismic wave was selected to perform dynamic time history analysis on the finite element reference model. The stress tensor and plastic strain increment of each element node were extracted, the instantaneous plastic strain energy density of each node was calculated, and the cumulative plastic strain energy density was obtained by integrating along the time history. All nodes are sorted from largest to smallest according to their cumulative plastic strain energy density. The components corresponding to the node set with the highest ranking and the cumulative proportion reaching the preset total energy threshold are selected as key nonlinear components. The key nonlinear components are divided into physical test substructures, and the components corresponding to the remaining node sets are divided into numerical simulation substructures.

[0006] Optionally, the generation of non-uniform bedrock acceleration time histories at each shaking table site using the spectral representation-orthogonal expansion method includes: Establish the cross power spectral density matrix of ground motion at multiple array sites, and perform Cholesky decomposition on the matrix to obtain the lower triangular matrix; Using the elements of the lower triangular matrix as the modulus, combine them within the interval A series of cosine harmonic functions are constructed from randomly distributed phase angles within the uniformly distributed interior. The cosine harmonic functions at all frequency points are superimposed and summed to generate a spatially correlated stationary Gaussian process at each site. The stationary Gaussian process is then converted into a non-stationary bedrock acceleration time history by intensity envelope function modulation.

[0007] Optionally, obtaining the reference ground motion input sequence of the multi-array system after double integration and baseline correction includes: The trapezoidal integral formula is used to integrate the non-uniform bedrock acceleration time history point by point to obtain the velocity time history. The least squares method is used to fit the quadratic polynomial trend term in the velocity time history and then subtract it. The displacement time history is obtained by applying the trapezoidal integral formula to the detrended velocity time history again, and the cubic polynomial trend term in the displacement time history is fitted again by the least squares method and then subtracted to obtain the reference seismic motion displacement time sequence.

[0008] Optionally, the real-time acquisition of the physical restoring force feedback signal and the current state of the actuator from the collaborative interaction interface, and inputting the physical restoring force feedback signal and the current state of the actuator into a pre-trained recurrent neural network time-delay compensation model to predict the interface restoring force after eliminating the system response time delay, includes: A Long Short-Term Memory (LSTM) network is constructed as a time delay compensation model. The network includes an input layer, stacked hidden layers, and an output layer. The instruction displacement at the current time step, the measured displacement at the current time step, and the measured restoring force of the collaborative interaction interface at the current time step are combined to form a feature vector, which is then input into the input layer. The cell state is updated by using the gating unit of the hidden layer and the hidden state is output. The lag-free predicted interface resilience for the next time step is obtained by mapping through the fully connected output layer.

[0009] Optionally, the step of using an explicit integration algorithm to solve the motion equations of the numerically simulated substructure at the current time step to obtain the target displacement of the collaborative interaction interface includes: The central difference method is used to solve for the acceleration of the numerical substructure in the current time step by combining the acceleration and velocity calculated in the previous time step with the equivalent seismic load and the compensated interface restoring force input in the current time step. The velocity is updated half-step by using the acceleration of the current time step, and the displacement is updated full-step by combining the updated velocity, thereby solving for the numerical substructure interface target displacement of the next time step.

[0010] Optionally, the construction of the control law, which corrects the control parameters of the multi-array system in real time online based on the tracking error between the measured displacement and the target displacement, includes: The system tracking error is the difference between the measured displacement and the target displacement. A positive definite Lyapunov candidate function containing the squared term of the tracking error is constructed. Find the time derivative of the Lyapunov function and devise a feedforward control gain update law that keeps the derivative always negative. Within each control cycle, the correction amount of the control gain is calculated by substituting the current tracking error value into the update law, and the corrected control parameters are applied to the servo controller of the multi-array system.

[0011] In another aspect, the present invention also proposes a seismic simulation system for large-span structures, comprising the following modules: A module is established to construct a three-dimensional finite element benchmark model of a large-span structure, and to perform dynamic time history calculations to determine the cumulative plastic strain energy density distribution of all nodes. Based on this, the benchmark model is divided into a physical test substructure containing high-energy-consuming key nonlinear components and a linearly elastic numerical simulation substructure. A physical-numerical collaborative interaction interface that satisfies the conditions of force balance and displacement coordination is established. The conversion module is used to generate non-uniform bedrock acceleration time histories at each shaking table site using the spectral representation-orthogonal expansion method. After double integration and baseline correction, the reference seismic motion input sequence of the multi-array system is obtained, and the sequence is converted into an equivalent seismic load applied to the numerical simulation substructure. The driving module is used to solve the motion equation of the numerical simulation substructure at the current time step using an explicit integration algorithm to obtain the target displacement of the collaborative interaction interface; it constructs a control law to correct the control parameters of the multi-array system in real time online based on the tracking error between the measured displacement and the target displacement, and maps the target displacement into actuator stroke commands to drive the motion of the physical experiment substructure. The prediction module is used to collect the physical restoring force feedback signal and the current state of the actuator from the collaborative interaction interface in real time. The physical restoring force feedback signal and the current state of the actuator are input into the pre-trained recurrent neural network time delay compensation model to predict the interface restoring force after eliminating the system response time delay. The compensated interface restoring force is fed back into the motion equation of the numerical simulation substructure to participate in the solution of the next time step until all time history conditions are loaded.

[0012] Preferably, the construction of a three-dimensional finite element benchmark model for a large-span structure involves performing dynamic time-history calculations to determine the cumulative plastic strain energy density distribution across all nodes. Based on this, the benchmark model is divided into a physical experimental substructure containing high-energy-consuming key nonlinear components and a linearly elastic numerical simulation substructure, including: A typical seismic wave was selected to perform dynamic time history analysis on the finite element reference model. The stress tensor and plastic strain increment of each element node were extracted, the instantaneous plastic strain energy density of each node was calculated, and the cumulative plastic strain energy density was obtained by integrating along the time history. All nodes are sorted from largest to smallest according to their cumulative plastic strain energy density. The components corresponding to the node set with the highest ranking and the cumulative proportion reaching the preset total energy threshold are selected as key nonlinear components. The key nonlinear components are divided into physical test substructures, and the components corresponding to the remaining node sets are divided into numerical simulation substructures.

[0013] Preferably, the generation of non-uniform bedrock acceleration time histories at each shaking table site using the spectral representation-orthogonal expansion method includes: Establish the cross power spectral density matrix of ground motion at multiple array sites, and perform Cholesky decomposition on the matrix to obtain the lower triangular matrix; Using the elements of the lower triangular matrix as the modulus, combine them within the interval A series of cosine harmonic functions are constructed from randomly distributed phase angles within the uniformly distributed interior. The cosine harmonic functions at all frequency points are superimposed and summed to generate a spatially correlated stationary Gaussian process at each site. The stationary Gaussian process is then converted into a non-stationary bedrock acceleration time history by intensity envelope function modulation.

[0014] Preferably, the step of obtaining the reference ground motion input sequence of the multi-array system after double integration and baseline correction includes: The trapezoidal integral formula is used to integrate the non-uniform bedrock acceleration time history point by point to obtain the velocity time history. The least squares method is used to fit the quadratic polynomial trend term in the velocity time history and then subtract it. The displacement time history is obtained by applying the trapezoidal integral formula to the detrended velocity time history again, and the cubic polynomial trend term in the displacement time history is fitted again by the least squares method and then subtracted to obtain the reference seismic motion displacement time sequence.

[0015] Preferably, the real-time acquisition of the physical restoring force feedback signal and the current state of the actuator from the collaborative interaction interface, and the input of the physical restoring force feedback signal and the current state of the actuator to a pre-trained recurrent neural network time delay compensation model to predict the interface restoring force after eliminating the system response time delay, includes: A Long Short-Term Memory (LSTM) network is constructed as a time delay compensation model. The network includes an input layer, stacked hidden layers, and an output layer. The instruction displacement at the current time step, the measured displacement at the current time step, and the measured restoring force of the collaborative interaction interface at the current time step are combined to form a feature vector, which is then input into the input layer. The cell state is updated by using the gating unit of the hidden layer and the hidden state is output. The lag-free predicted interface resilience for the next time step is obtained by mapping through the fully connected output layer.

[0016] Preferably, the step of using an explicit integration algorithm to solve the motion equations of the numerically simulated substructure at the current time step to obtain the target displacement of the collaborative interaction interface includes: The central difference method is used to solve for the acceleration of the numerical substructure in the current time step by combining the acceleration and velocity calculated in the previous time step with the equivalent seismic load and the compensated interface restoring force input in the current time step. The velocity is updated half-step by using the acceleration of the current time step, and the displacement is updated full-step by combining the updated velocity, thereby solving for the numerical substructure interface target displacement of the next time step.

[0017] Preferably, the construction of the control law, which corrects the control parameters of the multi-array system in real time online based on the tracking error between the measured displacement and the target displacement, includes: The system tracking error is the difference between the measured displacement and the target displacement. A positive definite Lyapunov candidate function containing the squared term of the tracking error is constructed. Find the time derivative of the Lyapunov function and devise a feedforward control gain update law that keeps the derivative always negative. Within each control cycle, the correction amount of the control gain is calculated by substituting the current tracking error value into the update law, and the corrected control parameters are applied to the servo controller of the multi-array system.

[0018] This invention defines the physical and numerical substructures by calculating the cumulative strain energy density distribution across all nodes, incorporating high-energy-consuming key components into physical experiments while ensuring the realism of the structural nonlinear damage evolution simulation. It utilizes the spectral representation-orthogonal expansion method to generate non-uniform bedrock acceleration time histories, fully reflecting the spatial correlation of seismic motions and improving the accuracy of response analysis for large-span structures under complex seismic fields. By combining Lyapunov stability theory with real-time correction of multi-array control parameters and employing a recurrent neural network model for time-delay compensation of interface restoring forces, it reduces actuator tracking errors and enhances the coordination of the physical-numerical interface. Attached Figure Description

[0019] Figure 1 A flowchart of the first embodiment; Figure 2 A schematic diagram illustrating the physical and numerical substructure division of a large-span structure; Figure 3 This is a schematic diagram of non-uniform bedrock excitation generation with multi-point spatial correlation. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0021] In the first embodiment, the present invention proposes a seismic simulation method for large-span structures, such as... Figure 1 As shown, it includes the following steps: S1. Construct a three-dimensional finite element benchmark model of a large-span structure, perform dynamic time history calculations to determine the cumulative plastic strain energy density distribution of all nodes, and divide the benchmark model into a physical test substructure containing high-energy-consuming key nonlinear components and a linearly elastic numerical simulation substructure. Establish a physical-numerical collaborative interaction interface that satisfies the conditions of force balance and displacement coordination. Specifically, a full-scale model of the large-span structure was established using general-purpose finite element analysis software. The geometric dimensions of beams, columns, cables, and other components, as well as the nonlinear constitutive relations of concrete and steel, were defined. A typical moderate or major earthquake acceleration record was input as excitation. Transient dynamics analysis was used for time history analysis, extracting stress and strain time history data for each element throughout the entire time history. The cumulative dissipated energy of each element was calculated by time integral of the product of stress and plastic strain increments, and the cumulative plastic strain energy density of all elements was calculated. An energy threshold was set, classifying elements and connection nodes with cumulative plastic strain energy densities exceeding the threshold as nonlinear regions, serving as physical test substructures. Elements with cumulative plastic strain energy densities below the threshold were classified as linear elastic regions, serving as numerical simulation substructures. Interface nodes were determined at the junction of the two substructures. In the numerical calculation software, coupling constraint equations were used to force the interface nodes to have the same displacement degrees of freedom on both sides of the numerical and physical substructures. Force balance detection points were set to ensure that the sum of the internal force vectors transmitted on both sides of the interface was zero. In the real-time hybrid experiment, the interface nodes in the numerical substructure model receive the measured displacement of the physical substructure as the boundary condition, and at the same time feed back the interface restoring force to the numerical substructure to achieve displacement coordination and force balance. Force balance detection points are set to ensure that the sum of the internal force vectors transmitted on both sides of the interface is zero.

[0022] In an optional embodiment, the construction of a three-dimensional finite element benchmark model of a large-span structure involves performing dynamic time-history calculations to determine the cumulative plastic strain energy density distribution at all nodes. Based on this, the benchmark model is divided into a physical experimental substructure containing high-energy-consuming key nonlinear components and a linearly elastic numerical simulation substructure, including: A typical seismic wave was selected to perform dynamic time history analysis on the finite element reference model. The stress tensor and plastic strain increment of each element node were extracted, the instantaneous plastic strain energy density of each node was calculated, and the cumulative plastic strain energy density was obtained by integrating along the time history. All nodes are sorted from largest to smallest according to their cumulative plastic strain energy density. The components corresponding to the node set with the highest ranking and the cumulative proportion reaching the preset total energy threshold are selected as key nonlinear components. The key nonlinear components are divided into physical test substructures, and the components corresponding to the remaining node sets are divided into numerical simulation substructures.

[0023] El Centro or Taft waves were selected as input excitations, and the peak ground acceleration was adjusted to the planned seismic level. A full-time nonlinear dynamic analysis was performed in the finite element software with an analysis step size of 0.01 s to 0.02 s. In the post-processing stage, the stress tensor of each element node i in the model was extracted at each time t. and plastic strain increment Using the formula Calculate the cumulative plastic strain energy density of the node over the entire earthquake duration T. .

[0024] The total cumulative plastic strain energy of all nodes in the statistical domain Set an energy percentage threshold. Preferably, 80%-90% is selected. All nodes are then... The values ​​are sorted in descending order, and the energy of each sorted node is accumulated until the total value is reached. At this point, considering the installation conditions of the shaking table, key local components with concentrated energy are identified, such as the seismic isolation bearings of large-span structures, the connection parts of key dampers, and the plastic hinge area at the tower-beam connection. These key local components are then used as substructures for physical testing, such as... Figure 2 As shown. The selection of physical substructures satisfies the principle of controllable boundaries, that is, the base is fixed to the shaking table surface, and the top or connecting part serves as the collaborative interaction interface. The remaining components are divided into numerical simulation substructures, which only participate in pure numerical calculations in the hybrid experiment.

[0025] S2. Establish a multi-point spatially correlated ground motion field, generate non-uniform bedrock acceleration time histories at each shaking table site using the spectral representation-orthogonal expansion method, obtain the reference ground motion input sequence of the multi-array system after double integration and baseline correction, and convert the sequence into an equivalent seismic load applied to the numerical simulation substructure. Specifically, based on the geological survey data of the engineering site, the target power spectral density function and spatial coherence function are determined. A spatial cross-spectral density matrix containing multiple shaking table sites is constructed. This matrix is ​​then subjected to Cholesky decomposition or orthogonal decomposition to obtain decoupled lower triangular matrices or eigenvalues ​​and eigenvectors. Using a set of uniformly distributed random phase angles within the interval, combined with the trigonometric series summation formula, a spatially correlated stationary Gaussian random process is synthesized at each site. The stationary process is then non-stationarized and modulated using an envelope function to obtain a non-uniform bedrock acceleration time history, such as… Figure 3As shown, the displacement time history is obtained by performing two numerical integrations on the acceleration time history in the time domain. The polynomial trend term in the displacement time history is fitted using the least squares method, and the trend term is subtracted to eliminate low-frequency drift, thus obtaining the reference displacement input sequence for each shaking table. According to the structural dynamics equation, the acceleration time history of each site is multiplied by the mass matrix of the numerical simulation substructure and negative, thereby calculating the equivalent nodal seismic force vector acting on each degree of freedom of the numerical substructure.

[0026] In an optional embodiment, generating the non-uniform bedrock acceleration time history at each shaking table site using the spectral representation-orthogonal expansion method includes: Establish the cross power spectral density matrix of ground motion at multiple array sites, and perform Cholesky decomposition on the matrix to obtain the lower triangular matrix; Using the elements of the lower triangular matrix as the modulus, combine them within the interval A series of cosine harmonic functions are constructed from randomly distributed phase angles within the uniformly distributed interior. The cosine harmonic functions at all frequency points are superimposed and summed to generate a spatially correlated stationary Gaussian process at each site. The stationary Gaussian process is then converted into a non-stationary bedrock acceleration time history by intensity envelope function modulation.

[0027] Determine the number of frequency discrete points N and the cutoff frequency. This causes the frequency increment For m shaking table sites, construct an m×m dimensional cross-power spectral density matrix. The self-power spectrum was modeled using the Clough-Penzien model, and the coherence function was modeled using the Harichandran-Vanmarcke model. The attenuation coefficient parameter α was set to 0.005 to 0.05. For each frequency point... The matrix below Performing Cholesky decomposition yields the lower triangular matrix. .

[0028] Using formula Generate stationary Gaussian processes at each site ,in The phase angle is random. To simulate the non-stationary characteristics of seismic motion, a three-segment intensity envelope function f(t) including the rising segment is selected. Stable phase and attenuation segment Modulating the stationary process, by The time history of non-uniform bedrock acceleration is calculated. This time history will be used as the input load for the numerical simulation substructure, driving the numerical model to generate a response, and then calculating the target displacement applied to the boundary of the physical substructure.

[0029] In an optional embodiment, obtaining the reference seismic motion input sequence of the multi-array system after double integration and baseline correction processing includes: The trapezoidal integral formula is used to integrate the non-uniform bedrock acceleration time history point by point to obtain the velocity time history. The least squares method is used to fit the quadratic polynomial trend term in the velocity time history and then subtract it. The displacement time history is obtained by applying the trapezoidal integral formula to the detrended velocity time history again, and the cubic polynomial trend term in the displacement time history is fitted again by the least squares method and then subtracted to obtain the reference seismic motion displacement time sequence.

[0030] In the signal processing stage, the sampling time interval is set. Integrating the acceleration a(t) yields the initial velocity v(t), and a quadratic polynomial trend model is established. Solve for the coefficients and calculate using the least squares method. .right Integrating, we obtain the initial displacement u(t) and construct a cubic polynomial trend model. Calculate the baseline correction displacement time history .

[0031] Since seismic waves are applied to the numerical substructure, the resulting non-uniform bedrock acceleration time history will be used as the input load for the numerical model, for example, as the foundation acceleration excitation applied to the support points of the numerical substructure; while the displacement sequence obtained after integral correction... The driving force for the physical substructure will be: if the physical substructure includes a ground support, the corrected displacement will be used as the basic excitation component of the shaking table, and superimposed with the interface relative displacement command calculated by the numerical substructure to synthesize the total target displacement driving the shaking table.

[0032] S3. The motion equation of the numerical simulation substructure at the current time step is solved by an explicit integral algorithm to obtain the target displacement of the collaborative interaction interface. The control law is constructed based on Lyapunov stability theory. The control parameters of the multi-array system are corrected online in real time according to the tracking error between the measured displacement and the target displacement. The target displacement is mapped into actuator stroke command by inverse kinematics solution to drive the motion of the physical experiment substructure. The central difference method or operator splitting method is adopted as an explicit integration strategy. Using the displacement, velocity, and acceleration of the previous time step, combined with the equivalent seismic load of the current step and the restoring force fed back from the previous step, the motion equation of the current time step is solved. The displacement components of the interface nodes are extracted as the loading target of the physical substructure. The tracking error is defined as the difference between the target displacement and the measured displacement of the actuator. A positive definite Lyapunov function containing the square term of the tracking error is constructed. The function is differentiated and the derivative is set to be less than zero to derive the update law of the control gain. According to the update law, the proportional, integral, and derivative gain parameters of the PID controller are adjusted in each control cycle. Then, according to the geometric parameters and coordinate transformation matrix of the shaking table system, the six-degree-of-freedom target displacement of the interface node in the Cartesian coordinate system is solved into the extension and retraction length command of each hydraulic actuator. The command is sent to the actuator through the servo valve to drive the physical specimen to deform.

[0033] In an optional embodiment, the step of using an explicit integration algorithm to solve the motion equations of the numerically simulated substructure at the current time step to obtain the target displacement of the collaborative interaction interface includes: The central difference method is used to solve for the acceleration of the numerical substructure in the current time step by combining the acceleration and velocity calculated in the previous time step with the equivalent seismic load and the compensated interface restoring force input in the current time step. The velocity is updated half-step by using the acceleration of the current time step, and the displacement is updated full-step by combining the updated velocity, thereby solving for the numerical substructure interface target displacement of the next time step.

[0034] The integration algorithm uses the central difference method, and the time integration step size must be ensured. Less than the critical step size , Let be the minimum natural period of the structure. At each time step i, the dynamic equilibrium equation is: .in, The equivalent nodal loads are calculated based on the earthquake acceleration time history generated above. , It includes the internal elastic force of the numerical component and the physical substructure interface restoring force predicted and fed back by the LSTM network.

[0035] Calculate the acceleration Then, using the half-step formula Update speed, then use the formula Calculate the displacement at the next moment. The displacement... This refers to the target position that the top of the physical substructure should reach in the next moment. The control system will drive the vibration table to make the physical substructure follow the target displacement.

[0036] In an optional embodiment, the step of constructing a control law based on Lyapunov stability theory and correcting the control parameters of the multi-array system in real time online according to the tracking error between the measured displacement and the target displacement includes: The system tracking error is the difference between the measured displacement and the target displacement. A positive definite Lyapunov candidate function containing the squared term of the tracking error is constructed. Find the time derivative of the Lyapunov function and devise a feedforward control gain update law that keeps the derivative always negative. Within each control cycle, the correction amount of the control gain is calculated by substituting the current tracking error value into the update law, and the corrected control parameters are applied to the servo controller of the multi-array system.

[0037] The tracking error of the j-th array is defined as... Constructing Lyapunov functions ,in For feedforward control gain The estimation error, The gain coefficient is preferably between 0.1 and 10.0.

[0038] The derived update law is In the digital controller of a multi-array system, errors are read in real time. Combined with target speed Calculate the gain correction amount and adjust the feedforward gain. The corrected control law outputs drive signals, which are then distributed to each hydraulic actuator after coordinate transformation. This method can compensate for the decrease in shaking table tracking performance caused by drastic changes in the stiffness of the physical substructure, ensuring that the table accurately reproduces the interface displacement response calculated by the numerical substructure.

[0039] S4. Real-time acquisition of physical restoring force feedback signals and actuator current states from the collaborative interaction interface. Inputting the physical restoring force feedback signals and actuator current states into a pre-trained recurrent neural network time delay compensation model to predict the interface restoring force after eliminating system response time delay. Feeding the compensated interface restoring force back into the motion equations of the numerical simulation substructure to participate in the solution of the next time step until all time history conditions are loaded.

[0040] Specifically, high-precision force and displacement sensors are installed at the connection points of the collaborative interaction interface. The current interface reaction force and actuator displacement values ​​are read in real time at a kilohertz sampling frequency. A recurrent neural network containing long short-term memory units or gated recurrent units is constructed. Historical data from sinusoidal scanning or random wave loading experiments are used for offline pre-training of the network, enabling the recurrent neural network to learn the time lag between the system's input displacement and output reaction force. In real-time experiments, the measured displacement and measured reaction force from the current and several past time steps form a feature vector, which is input into the network. The network output instantly predicts the ideal restoring force value for the next time step without time lag. This predicted restoring force value is directly substituted into the numerical simulation substructure motion equations as the corrected physical substructure feedback force. Combined with an explicit integration algorithm, the structural response for the next time step is calculated. This process is repeated until the entire seismic wave input sequence has been loaded.

[0041] Optionally, the equation of motion is a dynamic equilibrium equation, and a specific expression is as follows: Where: M is the mass matrix of the numerical simulation substructure or the mass matrix of the entire system; C is the damping matrix of the numerical simulation substructure; It is a numerical simulation substructure of linear elasticity; , , These are the displacement, velocity, and acceleration vectors of the collaborative interaction interface, respectively. It is the interface restoring force vector after time delay compensation by recurrent neural network, that is, the compensated interface restoring force; It is the equivalent seismic load vector applied to the numerical simulation substructure.

[0042] In an optional embodiment, the real-time acquisition of the physical restoring force feedback signal and the current state of the actuator from the collaborative interaction interface, and the input of the physical restoring force feedback signal and the current state of the actuator to a pre-trained recurrent neural network time-delay compensation model to predict the interface restoring force after eliminating the system response time delay, includes: A Long Short-Term Memory (LSTM) network is constructed as a time delay compensation model. The network includes an input layer, stacked hidden layers, and an output layer. The instruction displacement at the current time step, the measured displacement at the current time step, and the measured restoring force of the collaborative interaction interface at the current time step are combined to form a feature vector, which is then input into the input layer. The cell state is updated by using the gating unit of the hidden layer and the hidden state is output. The lag-free predicted interface resilience for the next time step is obtained by mapping through the fully connected output layer.

[0043] The recurrent neural network time delay compensation model is preferably based on a long short-term memory network architecture, consisting of an input layer, hidden layers, and an output layer. The input layer accepts feature vectors with a dimension of 3. The feature vector includes commanded displacement, measured displacement, and measured restoring force. Hidden layers are configured with a 2-3 layer stacked structure, each containing 64-128 neurons. The sliding window length for the time series is set to 20-50 time steps. The training set consists of vibration table response data covering a frequency range of 0.1Hz to 5Hz and an amplitude range of 1mm to 50mm. Offline training is performed using mean squared error as the loss function. The model input consists of the normalized commanded displacement, measured displacement, and measured restoring force of the collaborative interaction interface at the current time step. The model output is the un-normalized predicted interface restoring force for the next time step without time delay. In real-time experiments, the network updates cell states through the collaborative work of forget gates, input gates, and output gates, predicting the elapsed time delay before explicitly integrating to solve for the next step. True recovery value after The predicted force value will serve as the restoring force for the next time step, participating in the solution of the dynamic equations of the numerical substructure for the next time step, thereby offsetting the negative damping effect caused by the actuator response lag and ensuring the stability of the real-time hybrid experiment.

[0044] To more fully illustrate the present invention, the implementation process of the present invention will be described below in conjunction with a specific function call process: A three-dimensional finite element model of the large-span structure was built using OpenSeesPy, defining nodes and elements using `opensees.node` and `opensees.element`. To identify nonlinear regions, dynamic time-history calculations were performed, defining seismic waves using `opensees.timeSeries` and executing dynamic analysis using `opensees.system('ProfileSPD')` and `opensees.analyze`. After calculation, nodal stress and strain data were extracted, and the cumulative plastic strain energy density was calculated using NumPy. Based on the calculation results, high-energy-consuming elements were identified as physical test substructures in the code logic through index filtering, while the remaining parts were retained as numerical substructures. Constraints were applied at the boundaries using the `opensees.equalDOF` or `opensees.fix` commands to establish a collaborative interactive interface that satisfies displacement compatibility.

[0045] Based on the spectral representation-orthogonal expansion method, random phases are generated using `numpy.random.normal`, and the bedrock acceleration time histories at each shaking table are synthesized using `numpy.fft.fft` and `numpy.fft.ifft`. Further, `scipy.integrate.cumulative_trapezoid` is called to perform a double integral on the acceleration to obtain the displacement, and `scipy.signal.detrend` is used to eliminate baseline drift caused by the integration, generating a reference ground motion input sequence. According to the principles of the large mass method or stiffness method, the processed ground motion data is transformed into load terms on the right-hand side of the numerical substructure equations, ready for loading in the next step.

[0046] In the main loop of the hybrid experiment, an explicit integration algorithm is set up, and the solver is configured by calling `opensees.integrator('CentralDifference')` and `opensees.algorithm('Linear')`. At each time step, `opensees.analyze(1,dt)` is executed to solve the numerical substructure and obtain the target displacement of the boundary nodes. The program sends the target displacement to the control system via `socket.send`. The control system calculates the control law based on Lyapunov theory and performs inverse kinematics calculation to drive the shaking table. Real-time communication via Ethernet or reflected memory ensures synchronization between the numerical model and the physical equipment.

[0047] During physical loading, the physical restoring force and state feedback of the actuator are acquired in real time via the API of the data acquisition system, such as NI-DAQmx, or via socket.recv. The acquired sequence data is input into a pre-trained model, and model.forward(input_tensor) or model(input_tensor) is used directly to predict the restoring force after time lag elimination, where model is an instance of torch.nn.RNN or torch.nn.LSTM. The predicted restoring force value is used as an external force and applied to the boundary nodes of the numerical substructure by calling opensees.pattern('Plain') and opensees.load to complete the force balance correction for this step, and then the loop proceeds to the next time step.

[0048] In a second embodiment, the present invention also provides a seismic simulation system for large-span structures, comprising the following modules: A module is established to construct a three-dimensional finite element benchmark model of a large-span structure, and to perform dynamic time history calculations to determine the cumulative plastic strain energy density distribution of all nodes. Based on this, the benchmark model is divided into a physical test substructure containing high-energy-consuming key nonlinear components and a linearly elastic numerical simulation substructure. A physical-numerical collaborative interaction interface that satisfies the conditions of force balance and displacement coordination is established. The conversion module is used to generate non-uniform bedrock acceleration time histories at each shaking table site using the spectral representation-orthogonal expansion method. After double integration and baseline correction, the reference seismic motion input sequence of the multi-array system is obtained, and the sequence is converted into an equivalent seismic load applied to the numerical simulation substructure. The driving module is used to solve the motion equation of the numerical simulation substructure at the current time step using an explicit integration algorithm to obtain the target displacement of the collaborative interaction interface; it constructs a control law to correct the control parameters of the multi-array system in real time online based on the tracking error between the measured displacement and the target displacement, and maps the target displacement into actuator stroke commands to drive the motion of the physical experiment substructure. The prediction module is used to collect the physical restoring force feedback signal and the current state of the actuator from the collaborative interaction interface in real time. The physical restoring force feedback signal and the current state of the actuator are input into the pre-trained recurrent neural network time delay compensation model to predict the interface restoring force after eliminating the system response time delay. The compensated interface restoring force is fed back into the motion equation of the numerical simulation substructure to participate in the solution of the next time step until all time history conditions are loaded.

[0049] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The various embodiments can be combined as needed, and the same or similar parts can be referred to each other.

[0050] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A seismic simulation method for large-span structures, characterized in that, Includes the following steps: A three-dimensional finite element benchmark model of a large-span structure is constructed, and the cumulative plastic strain energy density distribution of all nodes is calculated by dynamic time history test. Based on this, the benchmark model is divided into a physical test substructure containing high-energy-consuming key nonlinear components and a linear elastic numerical simulation substructure. A physical-numerical collaborative interaction interface that satisfies the conditions of force balance and displacement coordination is established. The non-uniform bedrock acceleration time histories at each shaking table site were generated using the spectral representation-orthogonal expansion method. After double integration and baseline correction, the reference seismic motion input sequence of the multi-array system was obtained, and the sequence was converted into the equivalent seismic load applied to the numerical simulation substructure. The motion equations of the numerical simulation substructure at the current time step are solved using an explicit integration algorithm to obtain the target displacement of the collaborative interaction interface; a control law is constructed, and the control parameters of the multi-array system are corrected online in real time based on the tracking error between the measured displacement and the target displacement. The target displacement is mapped into actuator stroke commands to drive the motion of the physical experiment substructure. The physical restoring force feedback signal and the current state of the actuator of the collaborative interaction interface are collected in real time. The physical restoring force feedback signal and the current state of the actuator are input into the pre-trained recurrent neural network time delay compensation model to predict the interface restoring force after eliminating the system response time delay. The compensated interface restoring force is fed back into the motion equations of the numerical simulation substructure to participate in the solution of the next time step until all time history conditions have been loaded.

2. The method according to claim 1, characterized in that, The three-dimensional finite element benchmark model of the large-span structure is constructed, and dynamic time history calculations are performed to determine the cumulative plastic strain energy density distribution of all nodes. Based on this, the benchmark model is divided into a physical test substructure containing high-energy-consuming key nonlinear components and a linearly elastic numerical simulation substructure, including: A typical seismic wave was selected to perform dynamic time history analysis on the finite element reference model. The stress tensor and plastic strain increment of each element node were extracted, the instantaneous plastic strain energy density of each node was calculated, and the cumulative plastic strain energy density was obtained by integrating along the time history. All nodes are sorted from largest to smallest according to their cumulative plastic strain energy density. The components corresponding to the node set with the highest ranking and the cumulative proportion reaching the preset total energy threshold are selected as key nonlinear components. The key nonlinear components are divided into physical test substructures, and the components corresponding to the remaining node sets are divided into numerical simulation substructures.

3. The method according to claim 1, characterized in that, The generation of non-uniform bedrock acceleration time histories at each shaking table site using the spectral representation-orthogonal expansion method includes: Establish the cross power spectral density matrix of ground motion at multiple array sites, and perform Cholesky decomposition on the matrix to obtain the lower triangular matrix; Using the elements of the lower triangular matrix as the modulus, combine them within the interval A series of cosine harmonic functions are constructed from randomly distributed phase angles within the uniformly distributed interior. The cosine harmonic functions at all frequency points are superimposed and summed to generate a spatially correlated stationary Gaussian process at each site. The stationary Gaussian process is then converted into a non-stationary bedrock acceleration time history by intensity envelope function modulation.

4. The method according to claim 2, characterized in that, The process of obtaining the reference ground motion input sequence for the multi-array system after double integration and baseline correction includes: The trapezoidal integral formula is used to integrate the non-uniform bedrock acceleration time history point by point to obtain the velocity time history. The least squares method is used to fit the quadratic polynomial trend term in the velocity time history and then subtract it. The displacement time history is obtained by applying the trapezoidal integral formula to the detrended velocity time history again, and the cubic polynomial trend term in the displacement time history is fitted again by the least squares method and then subtracted to obtain the reference seismic motion displacement time sequence.

5. The method according to claim 1, characterized in that, The real-time acquisition of the physical restoring force feedback signal and the current state of the actuator from the collaborative interaction interface, and inputting the physical restoring force feedback signal and the current state of the actuator into a pre-trained recurrent neural network time delay compensation model to predict the interface restoring force after eliminating the system response time delay, includes: A Long Short-Term Memory (LSTM) network is constructed as a time delay compensation model. The network includes an input layer, stacked hidden layers, and an output layer. The instruction displacement at the current time step, the measured displacement at the current time step, and the measured restoring force of the collaborative interaction interface at the current time step are combined to form a feature vector, which is then input into the input layer. The cell state is updated by using the gating unit of the hidden layer and the hidden state is output. The lag-free predicted interface resilience for the next time step is obtained by mapping through the fully connected output layer.

6. The method according to claim 1, characterized in that, The step of using an explicit integration algorithm to solve the motion equations of the numerically simulated substructure at the current time step to obtain the target displacement of the collaborative interaction interface includes: The central difference method is used to solve for the acceleration of the numerical substructure in the current time step by combining the acceleration and velocity calculated in the previous time step with the equivalent seismic load and the compensated interface restoring force input in the current time step. The velocity is updated half-step by using the acceleration of the current time step, and the displacement is updated full-step by combining the updated velocity, thereby solving for the numerical substructure interface target displacement of the next time step.

7. The method according to claim 5, characterized in that, The constructed control law, based on the tracking error between the measured displacement and the target displacement, corrects the control parameters of the multi-array system in real time online, including: The system tracking error is the difference between the measured displacement and the target displacement. A positive definite Lyapunov candidate function containing the squared term of the tracking error is constructed. Find the time derivative of the Lyapunov function and devise a feedforward control gain update law that keeps the derivative always negative. Within each control cycle, the correction amount of the control gain is calculated by substituting the current tracking error value into the update law, and the corrected control parameters are applied to the servo controller of the multi-array system.

8. A seismic simulation system for large-span structures, characterized in that, Includes the following modules: A module is established to construct a three-dimensional finite element benchmark model of a large-span structure, and to perform dynamic time history calculations to determine the cumulative plastic strain energy density distribution of all nodes. Based on this, the benchmark model is divided into a physical test substructure containing high-energy-consuming key nonlinear components and a linearly elastic numerical simulation substructure. A physical-numerical collaborative interaction interface that satisfies the conditions of force balance and displacement coordination is established. The conversion module is used to generate non-uniform bedrock acceleration time histories at each shaking table site using the spectral representation-orthogonal expansion method. After double integration and baseline correction, the reference seismic motion input sequence of the multi-array system is obtained, and the sequence is converted into an equivalent seismic load applied to the numerical simulation substructure. The driving module is used to solve the motion equation of the numerical simulation substructure at the current time step using an explicit integration algorithm to obtain the target displacement of the collaborative interaction interface; it constructs a control law to correct the control parameters of the multi-array system in real time online based on the tracking error between the measured displacement and the target displacement, and maps the target displacement into actuator stroke commands to drive the motion of the physical experiment substructure. The prediction module is used to collect the physical restoring force feedback signal and the current state of the actuator of the collaborative interaction interface in real time, and input the physical restoring force feedback signal and the current state of the actuator into the pre-trained recurrent neural network time delay compensation model to predict the interface restoring force after eliminating the system response time delay. The compensated interface restoring force is fed back into the motion equations of the numerical simulation substructure to participate in the solution of the next time step until all time history conditions have been loaded.

9. The system according to claim 8, characterized in that, The three-dimensional finite element benchmark model of the large-span structure is constructed, and dynamic time history calculations are performed to determine the cumulative plastic strain energy density distribution of all nodes. Based on this, the benchmark model is divided into a physical test substructure containing high-energy-consuming key nonlinear components and a linearly elastic numerical simulation substructure, including: A typical seismic wave was selected to perform dynamic time history analysis on the finite element reference model. The stress tensor and plastic strain increment of each element node were extracted, the instantaneous plastic strain energy density of each node was calculated, and the cumulative plastic strain energy density was obtained by integrating along the time history. All nodes are sorted from largest to smallest according to their cumulative plastic strain energy density. The components corresponding to the node set with the highest ranking and the cumulative proportion reaching the preset total energy threshold are selected as key nonlinear components. The key nonlinear components are divided into physical test substructures, and the components corresponding to the remaining node sets are divided into numerical simulation substructures.

10. The system according to claim 8, characterized in that, The generation of non-uniform bedrock acceleration time histories at each shaking table site using the spectral representation-orthogonal expansion method includes: Establish the cross power spectral density matrix of ground motion at multiple array sites, and perform Cholesky decomposition on the matrix to obtain the lower triangular matrix; Using the elements of the lower triangular matrix as the modulus, combine them within the interval A series of cosine harmonic functions are constructed from randomly distributed phase angles within the uniformly distributed interior. The cosine harmonic functions at all frequency points are superimposed and summed to generate a spatially correlated stationary Gaussian process at each site. The stationary Gaussian process is then converted into a non-stationary bedrock acceleration time history by intensity envelope function modulation.

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