Dynamic response calculation method and system based on physical constraint and time step amplification

Abstract

The application discloses a dynamic response calculation method and system based on physical constraints and time step amplification, and the method comprises the following steps: defining a time step, obtaining load data based on a large time step; obtaining a large time step dynamic response result based on structural inherent parameters and the load data; predicting a residual error through a long short-term memory neural network based on the load data to obtain a predicted residual error result; and adding the large time step dynamic response result and the corresponding predicted residual error result to obtain a correction result. The system corresponds to the method. According to the application, the residual dynamic balance equation is embedded into a loss function as a physical constraint, the residual prediction accuracy is effectively improved, a decoupling architecture of residual prediction and independent numerical calculation is adopted, existing engineering software is compatible, and integration difficulty is reduced, only large time step load data is needed for training, data acquisition cost is reduced, and generalization ability is improved, the result accuracy is improved while the large time step calculation efficiency is ensured, and the quality of engineering structure dynamic response analysis is improved.

Description

Technical Field

[0001] This invention relates to the field of dynamic response technology for engineering structures, and in particular to a dynamic response calculation method and system based on physical constraints and time step amplification. Background Technology

[0002] Dynamic response analysis of engineering structures is a core method for evaluating the mechanical behavior of structures under dynamic loads in the fields of mechanical, civil, and aerospace engineering. Balancing accuracy and efficiency is crucial for its engineering applications. Traditional numerical integration methods rely on either large or small time step strategies for dynamic response analysis of engineering structures, but these methods suffer from the following problems: while large time steps reduce computational load, they also result in large truncation errors and difficulty in capturing high-frequency and transient responses; conversely, while small time steps offer high accuracy, they require tens of times the computational cost, creating an inherent contradiction between accuracy and efficiency.

[0003] Purely data-driven methods, such as RNNs and LSTMs, while reducing computation time, suffer from poor generalization, difficulty in adapting to complex loads, and a tendency to output non-physical results due to the lack of physical constraints. Fusion methods, such as physical-information neural networks, either suffer from poor adaptability due to deep coupling between numerical integration and the network, or their constraint design only applies to simple loads, making it difficult to achieve a balance between high precision, high efficiency, and high reliability. Therefore, there is an urgent need for a method that balances efficiency over large time steps, accuracy of physical constraints, and ease of engineering implementation.

[0004] Chinese invention patent application CN117113469A discloses an LSTM prediction method that integrates physical information. However, this invention patent application uses wind speed index to constrain its application range and fails to resolve the inherent contradiction between accuracy and efficiency.

[0005] In summary, there is an urgent need for a technical solution for dynamic response calculation that balances large time step efficiency, physical constraint accuracy, and ease of engineering implementation. Summary of the Invention

[0006] The main objective of this invention is to provide a dynamic response calculation method and system based on physical constraints and time step amplification, aiming to solve the technical problems in the existing structural dynamic response calculation methods that are difficult to balance calculation accuracy, efficiency and physical reliability, as well as the poor engineering adaptability or unreasonable physical constraint design of existing physical-driven and data-driven fusion methods.

[0007] To achieve the above objectives, this invention provides a dynamic response calculation method based on physical constraints and time step amplification, applicable to the dynamic response analysis of engineering structures, wherein the engineering structure includes at least a linear elastic engineering structure. The method includes:

[0008] Step 1: Define the time step. Set the interval before time step amplification as the small time step and the interval after amplification as the large time step. The small time step and the large time step are in a multiple relationship.

[0009] Step 2: Based on the large time step, collect the load sequence of the target engineering structure under multiple sets of different dynamic loads to obtain load data;

[0010] Step 3: Based on the inherent parameters of the target engineering structure and the load data, obtain the large-time-step dynamic response results, including at least the large-time-step displacement response, large-time-step velocity response, and large-time-step acceleration response; wherein, the inherent parameters include at least mass, damping, and stiffness;

[0011] Step 4: Based on the load data, predict the residuals using a long short-term memory neural network embedded with structural dynamics laws to obtain the predicted residual results; wherein, the residual is the difference between the dynamic response results of the large time step and the dynamic response results of the small time step at the same moment, and includes at least the predicted values ​​corresponding to the displacement residual, velocity residual and acceleration residual;

[0012] Step 5: Add the large time step dynamic response result to its corresponding prediction residual result to obtain the corresponding displacement correction result, velocity correction result or acceleration correction result, which can be applied to the dynamic response analysis of engineering structures.

[0013] Preferably, the long short-term memory neural network is a residual long short-term memory neural network, and the loss function of the residual long short-term memory neural network incorporates the structural dynamics law.

[0014] Preferably, the structural dynamics law includes at least the residual dynamic equilibrium condition corresponding to the residual, which is expressed as a residual dynamic equilibrium equation, and the residual dynamic equilibrium equation is:

[0015]

[0016] in: For the quality of the engineering structure; Damping for engineering structures; For the stiffness of the engineering structure; In the first Time nodes Below, the displacement residuals of the displacement response at small time steps and the displacement response at large time steps; In the first Time nodes Below, the velocity residual between the small time step velocity response and the large time step velocity response; In the first Time nodes Below, the acceleration residuals between the small-time-step acceleration response and the large-time-step acceleration response; To discretize the continuous time and use it for dynamic response calculation Each time point.

[0017] Preferably, the acquisition of the training dataset for the residual long short-term memory neural network includes:

[0018] Using finite element analysis software, based on the inherent parameters of the target engineering structure, the large-time-step dynamic response results and the small-time-step dynamic response results under various dynamic loads are calculated respectively, and the residuals are then calculated as training labels; wherein, the inherent parameters include at least mass, damping and stiffness.

[0019] Preferably, the total loss function of the residual long short-term memory neural network is:

[0020]

[0021] in: This is the total loss function; For data loss function; For physical loss function; and This represents the weight of the corresponding item.

[0022] Preferably, the data loss function is as follows:

[0023]

[0024] in, For prediction type Predicted values ​​of residuals, prediction type Including displacement prediction, velocity prediction, and acceleration prediction. For prediction type The true value of the residual between the large-time-step dynamic response result and the small-time-step dynamic response result.

[0025] Preferably, the physical loss function is as follows:

[0026]

[0027] Where: formula This indicates that the physical loss function is used when the prediction type is the displacement prediction. This is the predicted value of the displacement residual. This represents the true value of the velocity residual. The true value of the acceleration residual; Equation This indicates the physical loss function when the prediction type is the velocity prediction. This represents the true value of the displacement residual. The predicted value of the velocity residual; Equation This indicates that the prediction type is the physical loss function used for acceleration prediction. The predicted value is the acceleration residual; and the physical loss function corresponds to the prediction type in the data loss function.

[0028] Preferably, the correction result in step five is based on Add them together; where, For prediction type The following are the results of the large time step dynamic response. For prediction type The predicted residual results are as follows. For prediction type The following are the corrected results.

[0029] Preferably, the calculation method for obtaining the large time step dynamic response result in step three includes at least a numerical integration algorithm, which includes at least the Newmark-β numerical integration algorithm, and the initial conditions for obtaining the large time step response sequence are that the initial displacement, initial velocity, and initial acceleration are all 0.

[0030] To achieve the above objectives, the present invention also provides a dynamic response calculation system based on physical constraints and time step amplification, applied to the dynamic response calculation method based on physical constraints and time step amplification as described above. The system includes:

[0031] The time step definition module is used to define time steps, setting the interval before time step amplification as a small time step and the interval after amplification as a large time step, wherein the small time step and the large time step are in a multiple relationship.

[0032] The data acquisition module is used to collect load sequences of the target engineering structure under multiple sets of different dynamic loads based on the large time step, and obtain load data.

[0033] The numerical integration module is used to obtain the large-time-step dynamic response results based on the inherent parameters of the target engineering structure and the load data, including at least the large-time-step displacement response, the large-time-step velocity response, and the large-time-step acceleration response; wherein the inherent parameters include at least mass, damping, and stiffness.

[0034] The residual prediction module is used to predict residuals based on the load data by using a long short-term memory neural network embedded with structural dynamic laws, and to obtain the predicted residual results; wherein, the residual is the difference between the dynamic response results of the large time step and the dynamic response results of the small time step at the same moment, and includes at least the predicted values ​​corresponding to the displacement residual, velocity residual and acceleration residual;

[0035] The response correction module is used to add the large time step dynamic response result to its corresponding prediction residual result to obtain the corresponding displacement correction result, velocity correction result or acceleration correction result, which can be applied to the dynamic response analysis of engineering structures.

[0036] Beneficial effects: This application solves the technical problems of structural dynamic response calculation methods struggling to balance computational accuracy, efficiency, and physical reliability, as well as the poor engineering adaptability or unreasonable physical constraint design of existing fusion methods of physical-driven and data-driven approaches. By embedding the residual dynamic equilibrium equation as a dedicated physical constraint into the loss function, the correction results possess both data fitting and physical regularity, effectively improving the accuracy of residual prediction. It adopts a decoupled architecture of residual prediction and independent numerical calculation, ensuring compatibility with existing engineering software and reducing integration difficulty. Training with only large time-step load data is required, reducing data acquisition costs and improving generalization ability. While ensuring computational efficiency over large time steps, the accuracy of the results approaches the level of small time steps, resolving the inherent contradiction of traditional methods struggling to balance accuracy and efficiency, and improving the quality of dynamic response analysis of engineering structures. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 A flowchart illustrating the dynamic response calculation method based on physical constraints and time step amplification provided in an embodiment of the present invention;

[0039] Figure 2 The network scheme based on residual long short-term memory neural network (RES-LSTM) provided in the embodiments of the present invention;

[0040] Figure 3 A flowchart illustrating the architecture of dynamic response calculation based on physical constraints and time step amplification provided in an embodiment of the present invention;

[0041] Figure 4 A structural block diagram of a dynamic response calculation system based on physical constraints and time step amplification provided in an embodiment of the present invention;

[0042] Figure 5 The simplified single-degree-of-freedom structural model and its parameters corresponding to the single-story shear-type building provided in Embodiment 1 of the present invention;

[0043] Figure 6 The comparison results of the index parameters provided in Embodiment 1 of the present invention;

[0044] Figure 7 A comparison diagram of displacement responses calculated using a large time step and a small time step respectively using the traditional numerical integration algorithm (Newmark-β numerical integration algorithm) provided in Embodiment 1 of the present invention;

[0045] Figure 8 A comparison diagram of the dynamic response calculation method based on physical constraints and time step amplification provided in Embodiment 1 of the present invention and the displacement response calculated by the traditional numerical integration algorithm using a small time step.

[0046] Figure 9 The simplified three-story shear-type building structure model and its parameters provided in Embodiment 2 of the present invention are as follows:

[0047] Figure 10 The comparison results of the index parameters provided in Embodiment 2 of the present invention;

[0048] Figure 11 The image shows a comparison of the displacement responses calculated using a traditional numerical integration algorithm (Newmark-β numerical integration algorithm) with large and small time steps, respectively, according to Embodiment 2 of the present invention.

[0049] Figure 12 This is a comparison diagram of the dynamic response calculation method based on physical constraints and time step amplification provided in Embodiment 2 of the present invention and the displacement response calculated by the traditional numerical integration algorithm using a small time step.

[0050] The implementation, functional features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0051] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0052] Structural dynamic response analysis is a core method for evaluating the mechanical behavior of structures under dynamic loads, playing an irreplaceable role in fields such as mechanical engineering, civil engineering, and aerospace. For example, the seismic performance assessment of high-rise buildings, the launch vibration analysis of spacecraft, and the operational stability testing of mechanical equipment all require accurate dynamic response results as the basis for design and optimization. The accuracy of the dynamic response directly affects the reliability of structural safety assessments, while computational efficiency determines the feasibility of the analysis method in engineering practice. Balancing these two aspects remains a key research focus in this field.

[0053] Traditional methods for calculating dynamic response primarily rely on numerical integration methods, such as the Newmark-β method and the central difference method. These methods discretize the time history into several time steps and iteratively solve for the displacement, velocity, and acceleration of the structure. In engineering, two strategies are commonly used: "large time steps" and "small time steps." Large time steps reduce computational load by increasing the time interval, suitable for rapid simulations, but due to larger truncation errors, they struggle to capture high-frequency components of the load and the instantaneous response of the structure. Small time steps improve accuracy by reducing the time interval, reflecting the detailed dynamic characteristics of the structure, but require tens or even hundreds of times more computational cost, especially in complex structures or long-time-history analyses, where their efficiency bottleneck is particularly prominent. This inherent contradiction between accuracy and efficiency makes traditional numerical methods unable to meet the dual demands of high accuracy and high efficiency in modern engineering.

[0054] With the development of artificial intelligence technology, data-driven dynamic response calculation methods have gradually become a research hotspot. These methods utilize the powerful time-series fitting capabilities of neural networks, such as recurrent neural networks (RNNs) and long short-term memory networks (LSTMs), to directly predict the dynamic behavior of structures under new loads by learning from a large amount of historical response data. For example, some studies train neural networks by inputting load sequences and outputting corresponding displacement responses, which can significantly shorten computation time in specific scenarios. However, purely data-driven methods have significant limitations: on the one hand, their prediction results depend on the coverage of the training data, resulting in poor generalization to unseen complex loads; on the other hand, due to the lack of constraints on physical laws, they may output non-physical results that violate the dynamic equilibrium equations, such as contradictions between the dynamic characteristics of displacement and load, making them difficult to use for engineering decision-making.

[0055] To overcome the shortcomings of purely data-driven methods, analytical methods that fuse physical and data-driven approaches, such as physical information neural networks, have emerged. These methods embed structural motion equations as constraints into the network training, thus ensuring physical consistency of the results to a certain extent. However, existing fusion methods still have significant limitations: some methods deeply couple the numerical integration step with the neural network, such as by embedding time steppers, resulting in complex network structures, high training difficulty, and difficulty in adapting to different numerical integration formats; other methods, while introducing physical constraints, struggle to balance the constraint strength with the data fitting accuracy, failing to achieve a synergy between high precision, high efficiency, and high reliability.

[0056] Based on the above, current dynamic response calculation methods still have many problems to be solved: traditional numerical methods are limited by the inherent properties of time steps and cannot overcome the contradiction between accuracy and efficiency; pure data-driven methods lack physical constraints, resulting in insufficient reliability and generalization; existing fusion methods are either complex with module coupling and poor engineering adaptability, or have unreasonable constraint design and are difficult to balance constraint strength and data fitting accuracy.

[0057] There are many methods and theories for correcting the calculation results of structural dynamic response under large time step conditions. The first is the pure numerical correction method based on interpolation. This type of method does not rely on data or physical laws, but only uses mathematical interpolation to compensate for the truncation error of large time steps. For example, for displacement sequences calculated under large time step conditions, linear interpolation, cubic spline interpolation, etc., are used to insert several virtual points between adjacent time points, and then smoothing is used to "correct" the rough results; in engineering, this is often used as a "post-processing module" of finite element software. However, this type of method lacks physical basis: the correction relies only on mathematical smoothing and does not consider the influence of structural dynamic characteristics, such as mass and stiffness, on the error. For example, for structures under high-frequency impact, the large time step error stems from the failure to capture the high-frequency components of the load, and interpolation can only smooth the curve, but cannot restore the true instantaneous response peak; at the same time, its adaptability is relatively poor, only suitable for scenarios with gradual load changes. For variable amplitude or abrupt loads, such as seismic waves and mechanical impacts, interpolation will "smooth out" key dynamic characteristics and introduce new errors.

[0058] The solution method based on dynamically adjusting the time step is also a common approach. The core idea is to dynamically adjust the time step based on the degree of load change. Small time steps are used for calculations during periods of rapid load change or high frequency, while large time steps are used during periods of stable load or low frequency. This aims to shorten the calculation time while ensuring the accuracy of the results. However, this method has the disadvantages of requiring manual preset of a large number of parameters, repeated adjustment of parameters for specific structures and load types, and difficulty in determining the load change index.

[0059] Neural network-based computational methods have become increasingly popular recently. However, most neural networks, such as RNNs and LSTMs, directly predict the response by learning the relationship between force and response; for example, a force with a small time step predicts a response with a small time step, and a force with a large time step predicts a response with a large time step. Furthermore, physics-driven computational methods incorporate physics knowledge into the neural network structure, making the network's training and prediction more consistent with physical laws. Therefore, current research has not yet delved into how to use neural networks to correct large-time-step computation results to improve the quality of dynamic response analysis of engineering structures.

[0060] Therefore, developing a dynamic response correction method that can retain the efficiency advantage of large time steps, ensure accuracy through physical constraints, and is easy to implement in engineering is the key to resolving the above contradictions.

[0061] Based on the above analysis, this embodiment integrates the data-driven method in deep learning with the concept of physical modeling. Under the condition of large time step, it utilizes the ability of Long Short-Term Memory (LSTM) network to extract the temporal features of non-stationary force loads, performs feature mining of dynamic correlation of external force sequences, constructs a loss function training network with residual dynamic equilibrium equation as constraint, and finally obtains high-precision dynamic response results by superimposing the dynamic response results under the condition of large time step with the residual results predicted by the neural network, so as to solve the above technical problems.

[0062] Reference Figure 1 , Figure 1 This is a flowchart of the dynamic response calculation method based on physical constraints and time step amplification provided in this embodiment.

[0063] like Figure 1 As shown, this embodiment discloses a dynamic response calculation method based on physical constraints and time step amplification, applied to the dynamic response analysis of engineering structures, wherein the engineering structure includes at least a linear elastic engineering structure, and the method includes:

[0064] Step 1: Define the time step. Set the interval before time step magnification as the small time step and the interval after magnification as the large time step. The small time step and the large time step are in a multiple relationship.

[0065] Step 2: Based on large time steps, collect load sequences of the target engineering structure under multiple sets of different dynamic loads to obtain load data;

[0066] Step 3: Based on the inherent parameters and load data of the target engineering structure, obtain the dynamic response results over a large time step, including at least the displacement response, velocity response, and acceleration response over a large time step; among which, the inherent parameters include at least mass, damping, and stiffness.

[0067] Step 4: Based on the load data, predict the residuals using a long short-term memory neural network embedded with structural dynamic laws to obtain the predicted residual results; wherein, the residual is the difference between the dynamic response results at the same time step and the dynamic response results at the same time step, and includes at least the predicted values ​​corresponding to the displacement residual, velocity residual and acceleration residual;

[0068] Step 5: Add the dynamic response results of the large time step to the corresponding predicted residual results to obtain the corresponding displacement correction results, velocity correction results, or acceleration correction results, which can be applied to the dynamic response analysis of engineering structures.

[0069] Based on the above, this embodiment solves the technical problems of structural dynamic response calculation methods struggling to balance computational accuracy, efficiency, and physical reliability, as well as the poor engineering adaptability or unreasonable physical constraint design of existing fusion methods of physical-driven and data-driven approaches. Furthermore, this embodiment can be applied to linear elastic engineering structures, including but not limited to trusses.

[0070] In practical applications, common dynamic responses include displacement response, velocity response, and acceleration response. To further illustrate the technical problem solved by the technical solution of this embodiment, this embodiment uses the displacement response of a structure as an example. It is understood that the technical effects produced by the technical solution of this embodiment can be extended to velocity and acceleration.

[0071] Reference Figure 2 , Figure 2 The network scheme based on residual long short-term memory neural network (RES-LSTM) provided in this embodiment.

[0072] like Figure 2 As shown, specifically, the long short-term memory neural network is a residual long short-term memory neural network, and the loss function of the residual long short-term memory neural network incorporates structural dynamics.

[0073] Specifically, the structural dynamics laws include at least the residual dynamic equilibrium conditions corresponding to the residuals. These residual dynamic equilibrium conditions are expressed as residual dynamic equilibrium equations, which are:

[0074]

[0075] in: For the quality of the engineering structure; Damping for engineering structures; For the stiffness of the engineering structure; In the first Time nodes Below, the displacement residuals of the displacement response at small time steps and the displacement response at large time steps; In the first Time nodes Below, the velocity residual between the small time step velocity response and the large time step velocity response; In the first Time nodes Below, the acceleration residuals between the small-time-step acceleration response and the large-time-step acceleration response; To discretize the continuous time and use it for dynamic response calculation Each time point;

[0076] In practical applications, we embed the residual dynamic equilibrium equation as a physical constraint into the loss function. The derivation of the residual dynamic equilibrium equation is as follows:

[0077] For engineering structures, regardless of whether the calculation is based on a large time step or a small time step, in any corresponding... The dynamic equilibrium equations are satisfied at all times:

[0078] For large time steps:

[0079] For small time steps:

[0080] At the same time, and They are equal; subtracting them gives:

[0081]

[0082] in, For displacement residuals, Corresponding velocity residual, Corresponding acceleration residual.

[0083] Specifically, obtaining the training dataset for the residual long short-term memory neural network includes:

[0084] Using finite element analysis software, based on the inherent parameters of the target engineering structure, the dynamic response results of large time steps and small time steps under various dynamic loads are calculated respectively, and the residuals are then calculated as training labels; among them, the inherent parameters include at least mass, damping and stiffness.

[0085] In practical applications, finite element analysis software such as ANSYS and MATLAB are used to establish training datasets using numerical integration algorithms, such as the Newmark-β numerical integration algorithm. The training set contains the dynamic responses of the structure under different dynamic loads with large time steps. The load sequences sampled at large time steps serve as the input to the residual prediction module, and the residuals of the dynamic responses between large and small time steps serve as the training labels for the residual prediction module. Let the large time step interval and the small time step interval be denoted as . (Small time step is a large time step) (times), calculate the coarse displacement response at large time steps respectively. and fine displacement response at small time steps Calculate the residual between the two. Simultaneously extract the mass of the structure. Damping and stiffness And simultaneously calculate the velocity residual. and acceleration residual This serves as the physical constraint for the subsequent residual prediction module. It should be noted that in this embodiment, the coarse and fine displacement responses are defined as effects corresponding to large and small time steps, respectively, and they correspond to the large and small time step dynamic responses.

[0086] Based on the above description, the specific total loss function of the residual long short-term memory neural network is as follows:

[0087]

[0088] in: This is the total loss function; For data loss function; For physical loss function; and This refers to the weight of the corresponding item. This weight is set based on the actual training requirements.

[0089] Specifically, the data loss function is as follows:

[0090]

[0091] in, For prediction type Predicted values ​​of residuals, prediction type Including displacement prediction, velocity prediction, and acceleration prediction. For prediction type The true value of the residual between the large-time-step dynamic response results and the small-time-step dynamic response results.

[0092] Specifically, the physical loss function is as follows:

[0093]

[0094] Where: formula This represents the physical loss function when the prediction type is displacement prediction. This is the predicted value of the displacement residual. This represents the true value of the velocity residual. The true value of the acceleration residual; Equation This represents the physical loss function when the prediction type is velocity prediction. This represents the true value of the displacement residual. The predicted value of the velocity residual; Equation This represents the physical loss function when the prediction type is acceleration prediction. The predicted value is the acceleration residual; and the physical loss function corresponds to the prediction type in the data loss function.

[0095] In practical applications, load data corresponding to the dynamic load sequence with a large time step that needs to be predicted is obtained through sensors or external systems. In the numerical integration stage, according to The displacement sequence under large time steps was calculated based on the Newmark-β numerical integration algorithm, where the initial displacement, initial velocity, and initial acceleration were all 0.

[0096]

[0097]

[0098]

[0099] in, and For control parameters, usually , , This refers to the time interval under a large time step condition.

[0100] Then, The input is fed into the trained residual prediction module to obtain the corresponding predicted residual sequence.

[0101] Specifically, the correction results in step five are based on Add them together; where, For prediction type The results of the large time step dynamic response are as follows. For prediction type The predicted residual results are as follows. For prediction type The following are the corrected results.

[0102] Specifically, the calculation method for obtaining the large time step dynamic response result in step three includes at least a numerical integration algorithm, which includes at least the Newmark-β numerical integration algorithm, and the initial conditions for obtaining the large time step response sequence are that the initial displacement, initial velocity, and initial acceleration are all 0.

[0103] Reference Figure 3 , Figure 3 The flowchart shows the architecture for dynamic response calculation based on physical constraints and time step amplification provided in this embodiment.

[0104] like Figure 3As shown, this embodiment constructs a Long Short-Term Memory (LSTM) network module as a residual prediction module to learn and predict the residuals between the calculation results of large and small time steps. By constructing the residual dynamic balance equation of the structure and embedding the loss function of the LSTM, the physical consistency condition of the structure is forced to be satisfied, thereby enhancing the physical interpretability and accuracy of the model. Furthermore, a numerical integration module is constructed to calculate the dynamic response under large time step conditions based on the Newmark-β numerical integration algorithm. Finally, the results of the two modules are superimposed to obtain the corrected dynamic response under large time step conditions.

[0105] Reference Figure 4 , Figure 4 This is a block diagram of the dynamic response calculation system based on physical constraints and time-step amplification provided in this application. To achieve the above objectives, as... Figure 4 As shown, this embodiment provides a dynamic response calculation system based on physical constraints and time step amplification, applied to the dynamic response calculation method based on physical constraints and time step amplification as described above. The system includes:

[0106] The time step definition module is used to define time steps, setting the interval before time step amplification as a small time step and the interval after amplification as a large time step, with the small time step and the large time step being a multiple of each other;

[0107] The data acquisition module is used to collect load sequences of the target engineering structure under multiple sets of different dynamic loads based on a large time step, and obtain load data.

[0108] The numerical integration module is used to obtain large-time-step dynamic response results based on the inherent parameters and load data of the target engineering structure, including at least large-time-step displacement response, large-time-step velocity response, and large-time-step acceleration response; wherein the inherent parameters include at least mass, damping, and stiffness.

[0109] The residual prediction module is used to predict residuals based on load data by using a long short-term memory neural network embedded with structural dynamic laws, and obtain the predicted residual results. The residual is the difference between the dynamic response results at the same time step and the dynamic response results at the same time step, and includes at least the predicted values ​​corresponding to displacement residual, velocity residual and acceleration residual.

[0110] The response correction module is used to add the dynamic response results of large time steps to their corresponding predicted residual results to obtain the corresponding displacement correction results, velocity correction results, or acceleration correction results, which can be applied to the dynamic response analysis of engineering structures.

[0111] Example 1

[0112] To analyze the displacement response of a single-story shear-type building under horizontal seismic load, the dynamic response calculation method based on physical constraints and time step amplification provided in this embodiment is adopted, and the specific analysis is as follows:

[0113] Single-story shear-type buildings under horizontal seismic loads can be approximately simplified to a single-degree-of-freedom structural model; refer to Figure 5 , Figure 5 This provides a simplified single-degree-of-freedom structural model and its parameters for a single-story shear-type building.

[0114] like Figure 5 As shown, 500 sets of artificial seismic loads with a duration of 90s were randomly generated and divided into training and test sets in a 4:1 ratio. The small time step interval was 0.005s, i.e., 18001 time steps, and the large time step was 0.05s, i.e., 1801 time steps. The training dataset of the structure was constructed using the numerical integration algorithm (Newmark-β numerical integration algorithm) in finite element software, and the residual prediction module was trained using the training dataset to obtain the trained residual prediction module.

[0115] A numerical integration module based on the Newmark-β numerical integration algorithm calculates the displacement response of the structure over a large time step under artificial seismic loads from the test set. Then, the artificial seismic loads from the test set are input into the residual prediction module. The residual prediction parameters of the physically constrained RES-LSTM-based residual prediction module in this embodiment are compared with those of the traditional LSTM without physical constraints, with reference to... Figure 6 , Figure 6 The comparison results of the indicator parameters provided in this embodiment.

[0116] like Figure 6 As shown, the residual displacement response predicted by the physically constrained RES-LSTM in this embodiment shows improvements in all prediction parameters compared to the prediction results of the traditional LSTM without physical constraints. Finally, the displacement response result at a large time step calculated by the numerical integration module is added to the residual displacement response obtained by the residual prediction module to obtain the corrected displacement response at a large time step, which is the final result of the method in this embodiment.

[0117] For one sample in the test set, refer to Figures 7 to 8 , Figure 7 The graphs show a comparison of the displacement responses calculated using the traditional numerical integration algorithm (Newmark-β numerical integration algorithm) with large and small time steps, respectively. Figure 8 A comparison diagram of the dynamic response calculation method based on physical constraints and time step amplification provided in this embodiment and the displacement response calculated by the traditional numerical integration algorithm using a small time step.

[0118] For the displacement response calculation of a single-story shear-type building under artificial seismic loads in the test set, the traditional numerical integration algorithm takes 2.98 s with a small time step of 0.005 s and 0.29 s with a large time step of 0.05 s. The method in this embodiment takes 0.34 s. (Comparison...) Figure 7 and Figure 8 It can be seen that the method in this embodiment achieves an accuracy close to that of a small time step calculation while having a computation time close to that of a traditional numerical integration algorithm with a large time step. This solves the inherent contradiction between accuracy and efficiency in traditional numerical integration methods and improves both the computation efficiency and accuracy of displacement response calculation for single-story shear-type buildings under horizontal seismic loads.

[0119] Example 2

[0120] To analyze the displacement response of a three-story shear-type building under horizontal seismic load, the dynamic response calculation method based on physical constraints and time step amplification provided in this embodiment is adopted. The specific analysis is as follows:

[0121] A three-story shear-type building under horizontal seismic load can be simplified into a three-degree-of-freedom structural model; such as Figure 9 The figure shows the simplified three-degree-of-freedom structural model and parameters of a three-story shear-type building. The mass matrix of this three-degree-of-freedom structure is:

[0122]

[0123] The stiffness matrix of the three-degree-of-freedom structure is:

[0124]

[0125] The three-degree-of-freedom structure uses Rayleigh damping, and the damping matrix is:

[0126]

[0127] in, and is the Rayleigh damping coefficient, whose value is determined based on the structure's natural frequency and its damping ratio.

[0128] 500 sets of artificial seismic loads with a duration of 90s were randomly generated and divided into training and test sets in a 4:1 ratio. The small time step interval was 0.005s, i.e., 18001 time steps, and the large time step was 0.05s, i.e., 1801 time steps. The training dataset for the structure was constructed using the numerical integration algorithm (Newmark-β numerical integration algorithm) in finite element software. The residual prediction module was then trained using the training dataset to obtain the trained residual prediction module.

[0129] A numerical integration module based on the Newmark-β algorithm calculates the displacement response of the structure over a large time step under artificial seismic loads from the test set. Then, the artificial seismic loads from the test set are input into the residual prediction module. The residual prediction parameters of the physically constrained RES-LSTM-based residual prediction module in this embodiment are compared with those of the traditional LSTM without physical constraints. Figure 10 .

[0130] like Figure 10 As shown, the residual displacement response predicted by the RES-LSTM with physical constraints in this embodiment shows improvements in all prediction parameters compared to the prediction results of the traditional LSTM without physical constraints.

[0131] The displacement response result calculated by the numerical integration module under a large time step is added to the residual displacement response obtained by the residual prediction module to obtain the large time step displacement response correction result, which is the final result of the method in this embodiment.

[0132] For one of the samples in the test set, such as Figure 11 The graphs show a comparison of the displacement responses calculated using the traditional numerical integration algorithm (Newmark-β numerical integration algorithm) with large and small time steps, respectively. Figure 12 This is a comparison chart of the displacement response calculated by the method in this embodiment and the displacement response calculated by the traditional numerical integration algorithm using a small time step.

[0133] For the displacement response calculation of a three-story shear-type building under artificial seismic loads in the test set, the traditional numerical integration algorithm takes 24.60 s with a small time step of 0.005 s and 2.49 s with a large time step of 0.05 s. The method in this embodiment takes 2.99 s. (Comparison...) Figure 11 and Figure 12 It can be seen that the method in this embodiment achieves an accuracy close to that of a small time step calculation while having a computation time close to that of a traditional numerical integration algorithm with a large time step. This solves the inherent contradiction between accuracy and efficiency in traditional numerical integration methods, and improves the efficiency and accuracy of displacement response calculation for three-story shear-type buildings under horizontal seismic loads. This results in the optimization of displacement response analysis of engineering structures under horizontal seismic loads.

[0134] It should be noted that the dynamic response calculation system based on physical constraints and time step amplification in this embodiment corresponds to the aforementioned dynamic response calculation method based on physical constraints and time step amplification. Therefore, any content not specifically described in the dynamic response calculation system based on physical constraints and time step amplification in this embodiment, including but not limited to functional definitions, working principles, and technical effects, can be referred to the description in the aforementioned dynamic response calculation method based on physical constraints and time step amplification, and is not limited here.

[0135] In summary, the dynamic response calculation method and system based on physical constraints and time step amplification in this embodiment achieves at least the following technical effects:

[0136] (1) By embedding the residual dynamic equilibrium equation as a dedicated physical constraint into the LSTM loss function, physical constraints are applied only to the residuals, simplifying the complexity of the constraint conditions, reducing the difficulty of parameter tuning, and making the prediction results both consistent with the actual data and strictly follow the laws of structural dynamics, thus effectively improving the accuracy of residual prediction.

[0137] (2) A decoupled architecture of “RES-LSTM residual prediction + independent Newmark-β large time step calculation” is adopted. Newmark-β is used as an independent numerical tool to calculate the results under large time step conditions. The correction result is obtained by superimposing the residual predicted by RES-LSTM only in the final stage, thereby decoupling the network and numerical module and improving the adaptability to different numerical integration formats.

[0138] (3) Only the external force sequence sampled at a large time step is used as the input of the neural network. It does not need to rely on the high cost of small time step data, which significantly reduces the difficulty of obtaining training data. At the same time, it has good adaptability to untrained load conditions, and its practical value in engineering is greatly improved.

[0139] (4) By superimposing the large time step results and residual predictions, the accuracy of the results is close to that of the small time step while maintaining the high efficiency of the calculation under the large time step condition, thus solving the inherent contradiction between accuracy and efficiency in traditional numerical methods.

[0140] It should be understood that the above are merely illustrative examples and do not constitute any limitation on the technical solutions of the present invention. In specific applications, those skilled in the art can make settings as needed, and the present invention does not impose any restrictions on this.

[0141] It should be noted that the workflow described above is merely illustrative and does not limit the scope of protection of this invention. In practical applications, those skilled in the art can select some or all of the workflow to achieve the purpose of this embodiment according to actual needs, and no restrictions are imposed here.

[0142] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0143] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory / random access memory, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0144] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A dynamic response calculation method based on physical constraints and time step amplification, applied to the dynamic response analysis of engineering structures, wherein, The engineering structure includes at least a linear elastic engineering structure, characterized in that the method includes: Step 1: Define the time step. Set the interval before time step amplification as the small time step and the interval after amplification as the large time step. The small time step and the large time step are in a multiple relationship. Step 2: Based on the large time step, collect the load sequence of the target engineering structure under multiple sets of different dynamic loads to obtain load data; Step 3: Based on the inherent parameters of the target engineering structure and the load data, obtain the large-time-step dynamic response results, including at least the large-time-step displacement response, large-time-step velocity response, and large-time-step acceleration response; wherein, the inherent parameters include at least mass, damping, and stiffness; Step 4: Based on the load data, predict the residuals using a long short-term memory neural network embedded with structural dynamics laws to obtain the predicted residual results; wherein, the residual is the difference between the dynamic response results of the large time step and the dynamic response results of the small time step at the same moment, and includes at least the predicted values ​​corresponding to the displacement residual, velocity residual and acceleration residual; Step 5: Add the large time step dynamic response result to its corresponding prediction residual result to obtain the corresponding displacement correction result, velocity correction result or acceleration correction result, which can be applied to the dynamic response analysis of engineering structures. The long short-term memory neural network is a residual long short-term memory neural network, and the loss function of the residual long short-term memory neural network incorporates the structural dynamics law; The structural dynamics law includes at least the residual dynamic equilibrium condition corresponding to the residual, which is expressed as a residual dynamic equilibrium equation: in: For the quality of the engineering structure; Damping for engineering structures; For the stiffness of the engineering structure; In the first Time nodes Below, the displacement residuals of the displacement response at small time steps and the displacement response at large time steps; In the first Time nodes Below, the velocity residual between the small time step velocity response and the large time step velocity response; In the first Time nodes Below, the acceleration residuals between the small-time-step acceleration response and the large-time-step acceleration response; To discretize the continuous time and use it for dynamic response calculation Each time point.

2. The dynamic response calculation method based on physical constraints and time step amplification as described in claim 1, characterized in that, The acquisition of the training dataset for the residual long short-term memory neural network includes: Using finite element analysis software, based on the inherent parameters of the target engineering structure, the large-time-step dynamic response results and the small-time-step dynamic response results under various dynamic loads are calculated respectively, and the residuals are then calculated as training labels; wherein, the inherent parameters include at least mass, damping and stiffness.

3. The dynamic response calculation method based on physical constraints and time step amplification as described in claim 2, characterized in that, The total loss function of the residual long short-term memory neural network is: in: This is the total loss function; For data loss function; For physical loss function; and This represents the weight of the corresponding item.

4. The dynamic response calculation method based on physical constraints and time step amplification as described in claim 3, characterized in that, The data loss function is specifically as follows: in, For prediction type Predicted values ​​of residuals, prediction type Including displacement prediction, velocity prediction, and acceleration prediction. For prediction type The true value of the residual between the large-time-step dynamic response result and the small-time-step dynamic response result.

5. The dynamic response calculation method based on physical constraints and time step amplification as described in claim 4, characterized in that, The physical loss function is specifically as follows: Where: formula This indicates that the physical loss function is used when the prediction type is the displacement prediction. This is the predicted value of the displacement residual. This represents the true value of the velocity residual. The true value of the acceleration residual; Equation This indicates the physical loss function when the prediction type is the velocity prediction. This represents the true value of the displacement residual. The predicted value of the velocity residual; Equation This indicates that the prediction type is the physical loss function used for acceleration prediction. The predicted value is the acceleration residual; and the physical loss function corresponds to the prediction type in the data loss function.

6. The dynamic response calculation method based on physical constraints and time step amplification as described in claim 5, characterized in that, The correction result in step five is based on Add them together; where, For prediction type The following are the results of the large time step dynamic response. For prediction type The predicted residual results are as follows. For prediction type The following are the corrected results.

7. The dynamic response calculation method based on physical constraints and time step amplification as described in claim 1, characterized in that, The calculation method for obtaining the large time step dynamic response result in step three includes at least a numerical integration algorithm, which includes at least the Newmark-β numerical integration algorithm, and the initial conditions for obtaining the large time step response sequence are that the initial displacement, initial velocity, and initial acceleration are all 0.

8. A dynamic response calculation system based on physical constraints and time step amplification, applied to the dynamic response calculation method based on physical constraints and time step amplification as described in any one of claims 1-7, characterized in that, The system includes: The time step definition module is used to define time steps, setting the interval before time step amplification as a small time step and the interval after amplification as a large time step, wherein the small time step and the large time step are in a multiple relationship. The data acquisition module is used to collect load sequences of the target engineering structure under multiple sets of different dynamic loads based on the large time step, and obtain load data. The numerical integration module is used to obtain the large-time-step dynamic response results based on the inherent parameters of the target engineering structure and the load data, including at least the large-time-step displacement response, the large-time-step velocity response, and the large-time-step acceleration response; wherein the inherent parameters include at least mass, damping, and stiffness. The residual prediction module is used to predict residuals based on the load data by using a long short-term memory neural network embedded with structural dynamic laws, and to obtain the predicted residual results; wherein, the residual is the difference between the dynamic response results of the large time step and the dynamic response results of the small time step at the same moment, and includes at least the predicted values ​​corresponding to the displacement residual, velocity residual and acceleration residual; The response correction module is used to add the large time step dynamic response result to its corresponding prediction residual result to obtain the corresponding displacement correction result, velocity correction result or acceleration correction result, which can be applied to the dynamic response analysis of engineering structures.

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