Method and device for predicting internal force of dynamic system based on structure-preserving deep learning

Abstract

The application discloses a kind of based on the internal force prediction method and equipment of dynamics system of structure-preserving deep learning, the method includes: for the dynamics system to be analyzed, construct the mechanical neural network model according to its inherent physical characteristics;Response data of the dynamics system is obtained, and network training data set is constructed;Mechanical neural network model is embedded in the control equation of dynamics system, based on the initial response of network training data set, the response of subsequent time step of dynamics system is calculated using high-precision numerical integration method;Based on the predicted response obtained by the integration of mechanical neural network model and the real response in training data set, a loss function is constructed to train the model;Finally, the trained model is applied to the prediction of the motion behavior of the dynamics system.The application can identify the non-ideal constraint of the dynamics system with strong nonlinear characteristics, without pre-assuming the empirical model compared to the traditional identification method, and then stably predict the behavior of the dynamics system.

Description

Technical Field

[0001] This invention belongs to the field of internal force identification and prediction of dynamic systems, and relates to a method and device for predicting internal forces of dynamic systems based on structure-preserving deep learning. Background Technology

[0002] Accurate prediction of dynamic response is beneficial for system state monitoring and high-precision control, which is of great significance in engineering fields such as aerospace and vehicles. However, in practical engineering applications, it is usually necessary to accurately identify the key models and parameters of dynamic systems. In particular, for dynamic systems, errors in manufacturing and assembly can lead to non-ideal properties such as stiffness and damping, which act on the system itself in the form of internal forces, thus affecting the system's response. Therefore, accurate identification and precise prediction of the internal force model of a dynamic system is of great importance.

[0003] With the improvement of computing power and the development of optimization algorithms, optimization-based dynamic model identification methods have been widely used. Traditional model identification usually relies on parameterized physical models and identifies unknown parameters by minimizing the error between experimental data and model predictions. Optimization-based model identification methods are effective and widely adopted in engineering. However, the identification effect depends to some extent on the empirical selection of the model, and the generalization of the identification results needs further verification. Moreover, the optimization may produce results that exceed the physical meaning. Therefore, accurate identification of complex nonlinear systems remains a challenge.

[0004] In recent years, with the development of artificial intelligence technology, various deep learning models have been widely applied in the study of dynamic problems. The powerful high-dimensional nonlinear fitting capabilities of neural networks have provided new means for the identification and prediction of complex nonlinear systems, especially the hybrid approach combining data-driven methods and physical models, which has become a research hotspot. Physical Information Neural Networks (PINNs) embed known physical equations into the loss function during neural network training, enabling the model to maintain physical consistency even with sparse data. This method exhibits strong generalization ability in various physical inverse problems, and is particularly suitable for some observational or noisy experimental data. However, the addition of physical loss increases the difficulty of the model training process, leading to a tendency to converge to local optima. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a method and device for predicting internal forces in dynamic systems based on structure-preserving deep learning. A neural network model characterizing the internal loads of the dynamic system is designed and then embedded in the dynamic time integral to predict the system response. By constructing a loss and training model between this model and the actual dynamic response, the internal force model of the system is identified. This strategy eliminates the need for pre-assumed internal force models and leverages the ability of neural networks to capture complex nonlinear patterns in data. Furthermore, the identification method proposed in this invention avoids the high cost of directly measuring internal forces by learning the response derived from the network's dynamic integral, while preserving the dynamic evolution characteristics of the system. The identified model possesses stronger physical interpretability, thus offering greater advantages in dynamic response prediction.

[0006] The technical solution adopted in this invention is as follows:

[0007] A method for predicting internal forces in a dynamic system based on structure-preserving deep learning, characterized by the following steps:

[0008] S1. For the mechanical or structural dynamics system to be analyzed, a mechanical neural network model is constructed based on the inherent physical characteristics of the dynamics system. The model is used to characterize the nonlinear mapping relationship between the internal forces generated by the non-ideal constraints of the system and the system response.

[0009] S2. Obtain the response data of the dynamic system, the response data including displacement and velocity, and use the response data to construct a network training dataset;

[0010] S3. Embed the mechanical neural network model into the control equations of the dynamic system, and calculate the response of the dynamic system at subsequent time steps based on the initial response data of the network training dataset using a high-precision numerical integration method;

[0011] S4. Construct a loss function based on the predicted response obtained by integrating the mechanical neural network model and the real response in the training dataset, and iteratively train the parameters of the mechanical neural network model using the loss function;

[0012] S5. Apply the trained mechanical neural network model to predict the motion behavior of the dynamic system.

[0013] Furthermore, in step S1, the input of the mechanical neural network model is the system state, including displacement and velocity, and the output is the equivalent internal force under non-ideal constraints.

[0014] Furthermore, in step S2, the response data of the dynamic system is obtained through testing or simulation. The network training dataset includes several sets of data pairs. Each set of data pairs consists of initial response data and subsequent response data. The initial response data consists of initial displacement and initial velocity, and the subsequent response data consists of displacement and velocity one time step after the initial response data.

[0015] Furthermore, in step S3, the dynamic equation of the system is:

[0016] ,

[0017] in, Represents the mass matrix of the dynamic system. , and These represent the displacement, velocity, and acceleration of the dynamic system, respectively. A mechanical neural network model representing the i-th non-ideal constraint of a dynamic system. This represents the parameters of the neural network to be trained. This represents the external load acting on the dynamic system.

[0018] Furthermore, in step S3, based on the initial response data of the network training dataset, a high-precision numerical integration method is used to calculate the response of the dynamic system at subsequent time steps, specifically including:

[0019] Under the same external load conditions as during data collection, a high-precision numerical integration algorithm is used to calculate the predicted response of the dynamic system at subsequent time steps based on the initial response in the network training dataset.

[0020] Furthermore, the high-precision numerical integration method is the fourth-order Runge-Kutta method.

[0021] Furthermore, in step S4, the loss function is:

[0022]

[0023] in, This represents the predicted displacement and velocity after one time step. This represents the actual displacement and velocity after a time step. This represents the number of training samples in the network training dataset. This represents the loss function.

[0024] Furthermore, the loss function is either the L1 loss function or the MSE loss function.

[0025] Furthermore, step S5 specifically includes: under the given external load and initial response of the actual working condition, applying the trained mechanical neural network model to the dynamic equation, and solving the motion response of the dynamic system by numerical integration.

[0026] A computer device, characterized in that the computer device comprises:

[0027] One or more processors;

[0028] Memory, used to store one or more programs;

[0029] When the one or more programs are executed by the one or more processors, the one or more processors implement the above-described method for predicting internal forces in dynamic systems based on structure-preserving deep learning.

[0030] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0031] The method provided by this invention can identify the internal forces of a dynamic system with strong nonlinear characteristics, which does not require prior assumptions of empirical models compared to traditional identification methods. Furthermore, this invention's method learns from the integrated response of network dynamics, avoiding the high cost of directly measuring internal forces, and ensures the structure-preserving characteristics of system dynamic evolution prediction. The identified model has stronger physical interpretability, thus offering greater advantages in dynamic response prediction. Attached Figure Description

[0032] Figure 1 This is a flowchart of the method in an embodiment of the present invention.

[0033] Figure 2 External load in the embodiments of the present invention The response prediction results under (N) are shown, where (a) and (b) represent the system displacement and velocity, respectively.

[0034] Figure 3 External load in the embodiments of the present invention The response prediction results under (N) are shown, where (a) and (b) represent the system displacement and velocity, respectively. Detailed Implementation

[0035] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0036] like Figure 1 As shown, a method for predicting internal forces in a dynamic system based on structure-preserving deep learning is presented. This method does not require prior assumptions about the internal force model and leverages the ability of neural networks to capture complex nonlinear patterns in data. Furthermore, the identification method proposed in this invention avoids the high cost of directly measuring internal forces by learning the response derived from the network's dynamic integration, while preserving the dynamic evolution characteristics of the system. The identified model possesses stronger physical interpretability, thus offering advantages in dynamic response prediction. The method includes the following steps:

[0037] S1. For the dynamic system to be analyzed, including mechanical or structural dynamic systems, a mechanical neural network model is constructed based on the inherent physical properties of the dynamic system, such as stiffness, friction, and damping. Specifically, This represents the mechanical neural network model that characterizes the i-th non-ideal constraint of the system. The parameters of the neural network to be trained are represented. The model is used to characterize the nonlinear mapping relationship between the internal forces generated by the non-ideal constraints of the system and the system response. Its input is the system state, including displacement and velocity, and its output is the equivalent internal force under non-ideal constraints.

[0038] S2. Obtain the response data of the dynamic system, which includes displacement and velocity, and use the response data to construct a network training dataset. Specifically, this includes:

[0039] Obtain through testing or simulation, etc. Group Initial displacement and velocity of degrees of freedom ( ) and displacement and velocity after one time step ( The initial response data and the corresponding subsequent response data are grouped into several data pairs, thus forming the training dataset.

[0040] S3. Embed the aforementioned mechanical neural network model into the control equations of the dynamic system:

[0041] ,

[0042] in, Represents the mass matrix of the dynamic system. , and These represent the displacement, velocity, and acceleration of the dynamic system, respectively. A mechanical neural network model representing the i-th non-ideal constraint of a dynamic system. This represents the parameters of the neural network to be trained. This represents the external load acting on the dynamic system.

[0043] Then, under the same external load conditions as during data collection, based on the initial displacement and velocity from the network training dataset... A high-precision numerical integration algorithm is used to calculate the predicted response of the dynamic system at subsequent time steps. The high-precision numerical integration algorithm can be the fourth-order Runge-Kutta method, for forms such as A system of differential equations, in which Indicates time, Representing generalized displacement and velocity, Represents the system characteristic function. Indicates the initial displacement. In terms of time step... Discretize, then the... The displacement for each time step can be calculated as follows.

[0044]

[0045] in, , They represent the first and Displacement at each time step These are intermediate calculation variables for the algorithm.

[0046] S4. Construct a loss function based on the predicted response obtained by integrating the mechanical neural network model and the real response in the training dataset, and iteratively train the parameters of the mechanical neural network model using the loss function.

[0047] The training loss function can be expressed as:

[0048] in, This represents the predicted displacement and velocity after one time step. This represents the actual displacement and velocity after a time step. This represents the number of training samples in the network training dataset. The loss function can be represented by L1, MSE, or other loss function models. The parameters of the neural network can be trained using optimizers such as Adam until the loss function converges.

[0049] S5. Under the given external load and initial response of the actual working condition, the trained mechanical neural network model is applied to the dynamic equation, and the motion response of the dynamic system is solved by numerical integration.

[0050] Example 1

[0051] To illustrate the application process and prediction results of the method in detail, the following describes the application of the present invention in detail using a specific practical situation as an example.

[0052] For a two-degree-of-freedom mechanical dynamic system with nonlinear damping and stiffness characteristics, its mass matrix... (kg). Its nonlinear damping force:

[0053] (N)

[0054] and nonlinear stiffness loads:

[0055] (N)

[0056] The prediction will proceed step by step below:

[0057] Step 1: Design a mechanical neural network model to characterize the system's stiffness and damping. and The mechanical neural network models are all fully connected layer networks with 4 hidden layers, 16 neurons, and ReLU activation function.

[0058] Step 2: Determine the time step Under constant load Under (N), 2560 initial responses are randomly generated, and the 4th-order Runge-Kutta algorithm is applied to calculate the response after one time step as the true value, thereby constructing the network training dataset.

[0059] Step 3: Embed the mechanical neural network model into the dynamic equation, and calculate the response predicted by the network model under the corresponding initial conditions and loads, using the L1 loss function.

[0060] Step 4: The training process is divided into training and validation sets in a 9:1 ratio. In each round, training is performed with a batch size of 128. The Adam optimizer is used for 8000 rounds of training until the loss function tends to converge.

[0061] Step 5: Perform predictions on the trained mechanical neural network model under different working conditions to verify the model's accuracy and robustness. Figure 2 and Figure 3 These represent the response prediction results when the trained mechanical neural network model is applied to different working conditions. Figure 2 The dynamic response predicted using the same external load conditions as the training model shows that the identified model can accurately predict the system response over a long period of time. Figure 3 The prediction results of the model obtained by identification under other external load conditions show that the identification scheme of the present invention can accurately predict the system under different external loads. This indicates that the designed neural network accurately identifies the internal force characteristics of the system, and can then accurately predict the system response based on the time integration algorithm, rather than simply fitting the training set data. This verifies the superior generalization of the scheme of the present invention.

[0062] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0063] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0064] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0065] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0066] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0067] The above specific embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for predicting internal forces in a dynamic system based on structure-preserving deep learning, characterized in that, Includes the following steps: S1. For the mechanical or structural dynamics system to be analyzed, a mechanical neural network model is constructed based on the inherent physical characteristics of the dynamics system. The model is used to characterize the nonlinear mapping relationship between the internal forces generated by the non-ideal constraints of the system and the system response. S2. Obtain the response data of the dynamic system, the response data including displacement and velocity, and use the response data to construct a network training dataset; S3. Embed the mechanical neural network model into the control equations of the dynamic system, and calculate the response of the dynamic system at subsequent time steps based on the initial response data of the network training dataset using a high-precision numerical integration method; S4. Construct a loss function based on the predicted response obtained by integrating the mechanical neural network model and the real response in the training dataset, and iteratively train the parameters of the mechanical neural network model using the loss function; S5. Apply the trained mechanical neural network model to predict the motion behavior of the dynamic system; In step S4, the loss function is: in, This represents the predicted displacement and velocity after one time step. This represents the actual displacement and velocity after a time step. This represents the number of training samples in the network training dataset. This represents the loss function.

2. The method for predicting internal forces of a dynamic system based on structure-preserving deep learning according to claim 1, characterized in that, In step S1, the input of the mechanical neural network model is the system state, including displacement and velocity, and the output is the equivalent internal force under non-ideal constraints.

3. The method for predicting internal forces of a dynamic system based on structure-preserving deep learning according to claim 1, characterized in that, In step S2, the response data of the dynamic system is obtained through testing or simulation. The network training dataset includes several sets of data pairs. Each set of data pairs consists of initial response data and subsequent response data. The initial response data consists of initial displacement and initial velocity, and the subsequent response data consists of displacement and velocity one time step after the initial response data.

4. The method for predicting internal forces of a dynamic system based on structure-preserving deep learning according to claim 1, characterized in that, In step S3, the dynamic equation of the system is: ， in, Represents the mass matrix of the dynamic system. , and These represent the displacement, velocity, and acceleration of the dynamic system, respectively. A mechanical neural network model representing the i-th non-ideal constraint of a dynamic system. This represents the parameters of the neural network to be trained. This represents the external load acting on the dynamic system.

5. The method for predicting internal forces of a dynamic system based on structure-preserving deep learning according to claim 1, characterized in that, In step S3, based on the initial response data of the network training dataset, a high-precision numerical integration method is used to calculate the response of the dynamic system at subsequent time steps, specifically including: Under the same external load conditions as during data collection, a high-precision numerical integration algorithm is used to calculate the predicted response of the dynamic system at subsequent time steps based on the initial response in the network training dataset.

6. The method for predicting internal forces of a dynamic system based on structure-preserving deep learning according to claim 1, characterized in that, The high-precision numerical integration method described is the fourth-order Runge-Kutta method.

7. The method for predicting internal forces of a dynamic system based on structure-preserving deep learning according to claim 6, characterized in that, The loss function is either the L1 loss function or the MSE loss function.

8. The method for predicting internal forces of a dynamic system based on structure-preserving deep learning according to claim 1, characterized in that, Step S5 specifically includes: under the given external load and initial response of the actual working condition, applying the trained mechanical neural network model to the dynamic equation, and solving the motion response of the dynamic system by numerical integration.

9. A computer device, characterized in that, The computer device includes: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method for predicting internal forces of a dynamic system based on structure-preserving deep learning as described in any one of claims 1-8.

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