Nonlinear modal data drive identification method based on physical fusion deep learning

Abstract

The invention provides a nonlinear modal data drive identification method based on physical fusion deep learning, and the method employs a deep learning technology, and can identify a nonlinear modal only depending on the response data of a nonlinear system. The process strictly follows the definition of a nonlinear regular mode, the physical interpretability of the recognition process is ensured, and the method is suitable for various nonlinear systems. Compared with a traditional non-linear modal recognition method, the method effectively solves the problems that non-linear modal recognition is high in calculation complexity, the prior knowledge of non-linear behaviors depends on, and the recognition method lacks physical interpretation.

Description

Technical Field

[0001] The present invention relates to the field of deep learning technology, and in particular to a nonlinear modal data driven recognition method based on physical fusion deep learning. Background Art

[0002] Nonlinear modal identification has a wide range of applications in engineering and scientific research. Commonly used methods include the Koopman operator method and the harmonic balance method. Although these methods can achieve satisfactory results when dealing with specific nonlinear problems, they are limited in their universal applicability and clarity of physical interpretation. Constructing a finite-dimensional approximation in the Koopman operator method is a very challenging task; although the harmonic balance method is applicable to strongly nonlinear systems, it is computationally complex and lacks a clear physical interpretation. Summary of the invention

[0003] The purpose of the present invention is to provide a nonlinear modal data-driven recognition method based on physical fusion deep learning to solve the problems raised in the above background technology. To achieve the above purpose, the present invention provides the following technical solutions: A nonlinear modal data-driven recognition method based on physical fusion deep learning includes the following steps: S1: Obtain training data; S2: construct a deep learning framework, the deep learning framework includes an encoder, a decoder, and a power encoder, initialize the parameters of the encoder, the decoder, and the power encoder, and perform cyclic training on the encoder, the decoder, and the power encoder based on the training data; S3: Encode the system response based on the trained encoder to identify the nonlinear modal space; S4: The decoder accurately reconstructs the identified nonlinear mode back to its original state space; S5: Predicting the results of future states through the dynamic encoder.

[0004] Furthermore, in S2, the following calculations are performed during the cyclic training process: S21: Through encoder Displace and speed Response decomposition into displacements in modal space and speed response; S22: Through the decoder ) The displacement of the modal space and speed The responses are reconstructed back into the original state space, thus constructing the manifold of a specific mode; S23: In modal space, through the dynamic encoder According to displacement and speed Perform time evolution advancement and predict and , to achieve dynamic evolution prediction, where the latent space dynamic expression ; S24: The dynamics of the latent space in step S23 is expressed by a dynamics decoder ; S25: Substitute the values ​​obtained in steps S21, S22, S23 and S24 into the autoencoder loss function , correlation loss function , modal dynamic loss function , A dynamic encoder loss function , B-dynamic encoder loss function To obtain the corresponding losses; among them, ; ; ; ; ; S26: Calculate the model gradient using the corresponding loss function and neural network weight obtained in step S25 through a conventional back propagation algorithm; S27: Update the model gradient obtained in step S26 by conventional gradient descent , , Parameters in .

[0005] Furthermore, in step S1, the vibration response data of the system is obtained as training data by solving the dynamic equation.

[0006] Furthermore, the system comprises: The dynamics of a two-degree-of-freedom linear system is:

[0007] .

[0008] The kinematic equation of the undamped cubic nonlinear stiffness Duffing system is:

[0009] .

[0010] The kinematic equation of the damped cubic nonlinear stiffness Duffing system is:

[0011] .

[0012] Furthermore, in step S2, a deep learning framework is constructed through the Tensorflow machine learning platform. Beneficial Effects

[0013] This invention breaks through the reliance of traditional nonlinear modal identification on dynamic background knowledge. By adopting a deep learning method, it realizes modal identification technology that does not require expert experience and only relies on the system's response data. With limited data, this invention demonstrates a strong generalization ability and effectively identifies time-varying modal frequencies in nonlinear systems, the relationship between frequency and energy, and the invariant manifold of nonlinear modes. The present invention proposes a loss function based on physical information constraints, which can ensure that the identified nonlinear modes meet the definition of nonlinear regular modes proposed by Shaw and Pierre, showing high universality in nonlinear system analysis. Compared with the classical harmonic balance method, this method is not limited by the degree of nonlinearity and can provide non-periodic solutions, thus broadening the application scope of nonlinear system analysis; The method proposed in the present invention not only improves the accuracy of recognition in the process of nonlinear modal identification, but also enhances the physical interpretability. Compared with traditional methods, this method can provide a more intuitive physical explanation, making the identification results easier to understand and verify. In addition, this method also allows for a more in-depth analysis and prediction of the dynamic behavior of nonlinear systems, providing a powerful tool for engineering design and system optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 It is a schematic diagram of nonlinear mode identification of the present invention; Figure 3 This is the first nonlinear mode identification result of the present invention; Figure 4 is the nonlinear mode identification result of the second type of the present invention; Figure 5 is a nonlinear modal frequency-energy relationship diagram of the third type of the present invention; Figure 6 is the invariant manifold of the second nonlinear mode of the present invention; Figure 7 This is the third decoding reconstruction and response prediction result of the present invention. DETAILED DESCRIPTION

[0015] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0016] See Figure 1 The present invention provides a nonlinear modal data-driven recognition method based on physical fusion deep learning, comprising the following steps: S1: Obtain training data; In one example, taking numerical simulation to obtain data as an example, the vibration response of the system is obtained by solving the dynamic equation as the input of the encoder model in the deep learning framework; in this embodiment, three cases are used, specifically: The first case is a two-degree-of-freedom linear system with the following kinematics: ; The second case is an undamped cubic nonlinear stiffness Duffing system, and the kinematic equation is: ; The third case is a damped cubic nonlinear stiffness Duffing system, and the kinematic equation is: .

[0017] In order to show the energy-frequency dependence of the modes in the nonlinear system, different initial conditions were selected to obtain the system motion trajectories at different energy levels. Specifically, 15 different energy levels from 10e-6 to 10e3 were considered. For each energy level, 100 vibration data samples were collected, of which 60 were used for model training, 20 for model validation, and the other 20 for model testing.

[0018] S2: construct a deep learning framework, which includes an encoder, a decoder, and a power encoder, initialize the parameters of the encoder, the decoder, and the power encoder, perform cyclic training on the encoder, the decoder, and the power encoder based on the training data, and perform the following calculations during the training process: S21: Through encoder Displace and speed Response decomposition into displacements in modal space and speed response; S22: Through the decoder ) The displacement of the modal space and speed The responses are reconstructed back into the original state space, thus constructing the manifold of a specific mode; S23: In modal space, through the dynamic encoder According to displacement and speed Perform time evolution advancement and predict and , to achieve dynamic evolution prediction, where the latent space dynamic expression ; S24: The dynamics of the latent space in step S23 is expressed by a dynamics decoder ; S25: Substitute the values ​​obtained in steps S21, S22, S23 and S24 into the autoencoder loss function , correlation loss function , modal dynamic loss function , A dynamic encoder loss function , B-dynamic encoder loss function To obtain the corresponding losses; among them, ; ; ; ; ; Among them, the autoencoder loss function is used to optimize the error between the reconstructed data and the original data, and the correlation loss function is used to constrain the coordinates in the modal space (displacement and speed ), the modal dynamic loss function is used to constrain the displacement of the modal space and speed The dynamic relationship between the dynamic encoder loss function 1 and the dynamic encoder loss function 2 respectively quantify the loss in the encoder under the temporal evolution of the modal space to ensure that the evolution of the modal space is consistent with the system response.

[0019] S26: Calculate the model gradient using the corresponding loss function and neural network weight model parameters obtained in step S25 through a conventional back propagation algorithm; S27: Update the model gradient obtained in step S26 by conventional gradient descent , , Parameters in ; In one example: You can build a deep learning framework using the Tensorflow machine learning platform, see Figure 1 , the deep learning framework is passed The current response state of the system is encoded into potential modal response coordinates and then The modal responses are decoded and reconstructed back into the original physical state space. To ensure that the latent modal space coordinates It can reflect the expected modal coordinates and integrate multiple physical information constraint loss functions in the deep learning framework. The total loss function is ,in is the weight of each loss function, , , They are respectively the autoencoder loss function, the correlation loss function, and the modal dynamics loss function. and With physical information constraints, the identified modes satisfy independence and the physical relationship between displacement and velocity.

[0020] S3: Encode the system response based on the trained encoder to identify the nonlinear modal space; In one example, if Figure 2 As shown in Figure 1, first, the encoder is used to encode the system response to identify the nonlinear modal space. Each pair of modal vectors shows a unique modal spectrum. The above three cases all use the above identification method. Due to the differences in dynamic characteristics, the identified modes are different. The identification results of the first case are shown in Figure 1. Figure 3 As shown in . By reconstructing the components of each mode at different degrees of freedom, the invariant manifold identified by the system can be revealed. Figure 3 As shown in (d), the manifold of the linear system exhibits planar characteristics, and there is a linear relationship between the modal components of each degree of freedom. Figure 4 This is the recognition result of case three. Figure 4 (b) shows the time-varying modal frequency characteristics. Figure 4 (d) The manifold exhibits surface characteristics, and the modal components of each degree of freedom show a nonlinear relationship.

[0021] To further analyze the characteristics of the nonlinear manifold, we use the undamped case 2. The pre-prepared simulation data of different energy levels are used to obtain the manifold and construct the frequency-energy diagram, such as Figure 5 As shown in , the modal frequency shows a nonlinear relationship with the energy level. This feature is particularly obvious in the high energy region, which is consistent with the results of analytical calculation. Subsequently, the identified modes of Case 3 are further analyzed and their invariant manifolds are constructed, as shown in Figure 6 As shown, it presents a curved manifold, and colleagues point out that the system has energy-dependent nonlinearities.

[0022] S4: The decoder accurately reconstructs the identified nonlinear modality back to its original state space In one example, if Figure 7 As shown in (a), the comparison between the decoded system response and the true response shows that the reconstruction result fits the real data quite well.

[0023] S5: Predicting the results of future states through the dynamic encoder In one example, after integrating the dynamic encoder into the autoencoder recognition framework, end-to-end training can predict the future state of the system. Figure 7 The prediction results of future states after the introduction of the dynamics encoder are shown. Specifically, Figure 7 (b) Comparison of the predicted future modal space response with the actual situation, and Figure 7 (c) compares the predicted results of the future system state with the actual observed values. These comparison graphs clearly show the accuracy and reliability of the prediction results.

[0024] The above is only a preferred embodiment of the present invention, and does not limit the present invention in any form. The protection scope of the present invention shall be subject to the protection scope of the claims. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A nonlinear modal data-driven recognition method based on physical fusion deep learning, characterized in that: The following steps are involved: S1: Obtain training data; S2: construct a deep learning framework, the deep learning framework includes an encoder, a decoder, and a power encoder, initialize the parameters of the encoder, the decoder, and the power encoder, and perform cyclic training on the encoder, the decoder, and the power encoder based on the training data; S3: Encode the system response based on the trained encoder to identify the nonlinear modal space; S4: The decoder accurately reconstructs the identified nonlinear mode back to its original state space; S5: Predicting the results of future states through the dynamic encoder.

2. According to claim 1, a nonlinear modal data-driven identification method based on physical fusion deep learning is characterized in that: In S2, the following calculations are performed during the training cycle: S21: Through encoder Displace and speed Response decomposition into displacements in modal space and speed response; S22: Through the decoder ) The displacement of the modal space and speed The responses are reconstructed back into the original state space, thus constructing the manifold of a specific mode; S23: In modal space, through the dynamic encoder According to displacement and speed Perform time evolution advancement and predict and , to achieve dynamic evolution prediction, where the latent space dynamic expression ; S24: The dynamics of the latent space in step S23 is expressed by a dynamics decoder ; S25: Substitute the values ​​obtained in steps S21, S22, S23 and S24 into the autoencoder loss function , correlation loss function , modal dynamic loss function , A dynamic encoder loss function , B-dynamic encoder loss function To obtain the corresponding loss; among them, ; ； ； ； ； S26: Calculate the model gradient using the corresponding loss function and neural network weight obtained in step S25 through a conventional back propagation algorithm; S27: Update the model gradient obtained in step S26 by conventional gradient descent , , Parameters in .

3. The nonlinear modal data-driven identification method based on physical fusion deep learning according to claim 1 is characterized in that: In step S1 , the vibration response data of the system is obtained as training data by solving the dynamic equation.

4. The nonlinear modal data-driven identification method based on physical fusion deep learning according to claim 3 is characterized in that: The system comprises: The dynamics of a two-degree-of-freedom linear system is: ； The kinematic equation of the undamped cubic nonlinear stiffness Duffing system is: ； The kinematic equation of the damped cubic nonlinear stiffness Duffing system is: 。 5. The nonlinear modal data-driven identification method based on physical fusion deep learning according to claim 1 is characterized in that: In step S2, a deep learning framework is constructed through the Tensorflow machine learning platform.

Images