A method for generating reduced-order models of nonlinear systems by integrating physical constraints and digital twins

Abstract

The present invention relates to a method for generating a reduced-order model of a nonlinear system that integrates physical constraints and digital twins, and belongs to the field of digital twin technology. The method comprises: sparsely sampling high-dimensional dynamic response data, extracting the dominant modes of high-fidelity model data, and retaining the modes of the physical mutation area through physical field gradient constraints during the extraction process; combining high-fidelity finite element models with low-fidelity simplified models to construct a hybrid reduced-order framework based on multi-fidelity proxy models; based on the hybrid reduced-order framework, in the data-physics joint-driven model training and optimization, data-driven errors and physical mechanism residuals are integrated, and the basis functions of the dominant modes are updated based on online streaming data; the outputs of the high-fidelity finite element model and the reduced-order model are cross-validated, and the accuracy of the reduced-order model is improved through iterative optimization strategies. The problem of intelligent model reduction is realized, and the accuracy and speed of the reduced-order model are guaranteed.

Description

Technical Field

[0001] The present invention belongs to the field of digital twin technology, and specifically relates to a method for generating a reduced-order model of a nonlinear system by integrating physical constraints and digital twins. Background Art

[0002] Currently, structural durability simulation based on finite element models in large structures such as automobiles and engineering equipment faces numerous challenges. Firstly, the complex structures of these structures, including numerous components and their interactions, make establishing accurate finite element models extremely difficult and time-consuming. Secondly, structural nonlinearities, such as material nonlinearity, geometric nonlinearity, and contact nonlinearity, further increase the difficulty and complexity of simulation.

[0003] For example, when simulating the durability of the suspension system during vehicle driving, it is necessary to consider the hyperelastic deformation of the rubber bushing, the large displacement of the metal parts, and the complex contact relationship between the components. These nonlinear factors are coupled with each other, which greatly increases the difficulty of solving the finite element equations.

[0004] Furthermore, durability simulations typically require extensive cyclic load analysis, resulting in cumbersome calculations and single simulations taking hours or even days, severely limiting the speed of design iterations. Furthermore, high-degree-of-freedom finite element models place extremely high demands on computing power and storage resources. A typical durability simulation of a large-scale engineering machinery structure can have finite element models with hundreds of thousands to millions of degrees of freedom, requiring the support of high-performance computer clusters and occupying significant storage space to store intermediate results and calculation data.

[0005] Under these circumstances, traditional durability simulation methods are no longer able to meet the demands of rapid product iteration and optimization in modern industry. Therefore, there is an urgent need for an efficient method for generating reduced-order models of nonlinear systems that integrates physical constraints with digital twins. This method can address the low computational efficiency and high resource consumption faced by existing finite element-based structural durability simulations, thereby providing stronger technical support for the structural durability design and optimization of large-scale mechanical equipment.

[0006] Currently, the dynamic response prediction of large-scale mechanical equipment (such as cranes, gas turbines, and aircraft engines) faces the dual challenges of high-dimensional nonlinear systems:

[0007] 1. Computational efficiency bottleneck: The full-order DOF of finite element (FEM) or CFD models can reach millions, and a single simulation takes hours to days, making it difficult to meet the millisecond-level real-time requirements of digital twins.

[0008] 2. Physics-Data Contradiction:

[0009] Purely physical models (such as Galerkin projection) rely on rigorous mathematical derivations. Although they can preserve conservation laws, the computational complexity of strong nonlinear terms is still high;

[0010] Although pure data-driven models (such as POD + Gaussian process) can achieve rapid predictions, they are not subject to the constraints of physical laws and are prone to non-physical solutions (such as negative pressure and vorticity distortion) in extrapolated scenarios.

[0011] 3. Poor adaptability to dynamic working conditions: In scenarios such as equipment damage and sudden load changes, traditional reduced-order models (ROMs) cannot be updated in real time due to offline training and fixed modal bases, resulting in accumulated prediction errors. Summary of the Invention

[0012] In order to solve the above problems existing in the prior art, the present invention provides a method for generating a reduced-order model of a nonlinear system by integrating physical constraints and digital twins;

[0013] The purpose of the present invention can be achieved through the following technical solutions:

[0014] S1: Collect high-dimensional dynamic response data through the sensor network of the digital twin system, sparsely sample the high-dimensional dynamic response data to obtain high-fidelity model data, extract the dominant mode of the high-fidelity model data, and retain the mode of the physical mutation area through physical field gradient constraints during the extraction process;

[0015] S2: Combining a high-fidelity finite element model with a low-fidelity simplified model, a hybrid order reduction framework based on a multi-fidelity surrogate model is constructed, dense sampling is performed in the physical mutation region, and number space preprocessing is performed on the nonlinear terms;

[0016] S3: Based on the hybrid order reduction framework, data-driven errors and physical mechanism residuals are integrated in data-physics-driven model training and optimization, and the basis functions of the dominant modes are updated based on online streaming data.

[0017] S4: Cross-validate the outputs of the high-fidelity finite element model and the reduced-order model, including global error evaluation and focused analysis of local physical mutation areas. Build an adaptive error threshold feedback mechanism based on the error quantification results, and improve the accuracy of the reduced-order model through iterative optimization strategies.

[0018] Specifically, the sparse sampling method is:

[0019] A physical field gradient amplitude matrix is ​​constructed to identify high-gradient areas. The high-gradient areas are densely sampled using a Gaussian random measurement matrix, and the low-gradient areas are sparsely sampled using a Bernoulli random matrix. In the time dimension, three sampling frequencies are set: transient stage, transition stage, and steady-state stage.

[0020] Specifically, the dominant mode of the high-fidelity model data is a set of low-dimensional basis functions that characterize key dynamic characteristics of the system.

[0021] Specifically, the dominant mode extraction method includes: physical constraint mode decomposition, mutation region mode retention, multi-scale mode selection, and dynamic mode update; wherein the physical constraint mode decomposition adopts intrinsic orthogonal decomposition combined with physical field gradient weighting function to construct a weighted inner product space to ensure that the extracted mode satisfies both data statistical characteristics and physical field gradient constraints; the dynamic mode update detects the new mode energy ratio through online streaming data, and triggers incremental basis function update according to the new mode energy ratio.

[0022] Specifically, the high-fidelity finite element model is a physically accurate model constructed based on a full-order finite element discretization method, and the low-fidelity simplified model is a lightweight proxy model generated by projection reduction and data-physics joint driving.

[0023] Specifically, the hybrid order reduction framework includes a multi-fidelity data fusion module, a physical constraint embedding module, a nonlinear term preprocessing module, a dynamic resource allocation module, and a stride error feedback link;

[0024] The multi-fidelity data fusion module adjusts the mixing weights in real time according to the distribution differences between the high-fidelity finite element model and the low-fidelity simplified model, and constructs a smooth transition field by interpolation in the boundary area;

[0025] The physical constraint embedding module introduces a gradient sensitivity weight matrix to reconstruct the projection equation in the traditional projection and adds a residual term to the low-fidelity simplified model training loss function;

[0026] The nonlinear term preprocessing module uses discrete empirical interpolation and convolutional autoencoder to perform number space preprocessing on the nonlinear term;

[0027] The dynamic resource allocation module adjusts the computing resource ratio of the high-fidelity finite element model and the low-fidelity simplified model in real time based on the error feedback mechanism, and triggers local recalculation of the high-fidelity finite element model in the mutation area.

[0028] Specifically, the method of number space preprocessing is:

[0029] Decompose the nonlinear term into a steady-state component and a transient pulsating component:

[0030] ,

[0031] Wherein, F(u) is a nonlinear term, the transient pulsating component is expressed as ΔF(u), Fmean is the steady-state component, is the correlation coefficient between the spatial basis function and the temporal basis function, and m is the total number of basis functions in the transient pulsating part;

[0032] The transient pulsation component is sparsely sampled to obtain key feature points of the transient pulsation component, and the key feature points are encoded and decoded through a convolutional autoencoder to achieve efficient representation of nonlinear terms in a low-dimensional space.

[0033] Specifically, the data-driven error is a statistical deviation between a low-fidelity simplified model and a high-fidelity finite element model in dynamic response prediction.

[0034] Specifically, the physical mechanism residual is the degree of deviation of the low-fidelity simplified model from the constraints of mass, momentum, energy and physical field gradient.

[0035] Specifically, the method of iterative optimization strategy includes:

[0036] When the global error exceeds a preset threshold, the source of the error is located through residual dominant mode analysis, and the dominant mode basis function is updated based on the online stream data in S3 to supplement the missing high-order modes;

[0037] When the gradient mutation of the local physical mutation area exceeds a preset threshold, the physical constraint is strengthened in the hybrid order reduction framework of S2, and the sampling density of the corresponding local physical mutation area is increased through gradient sensitivity analysis.

[0038] The beneficial effects of the present invention are:

[0039] The method provided by the present invention can significantly improve the computational efficiency and accuracy of dynamic response prediction of large-scale mechanical equipment. Specifically, this method combines the advantages of physical constraints and digital twins, effectively solving the problems of high computational complexity of pure physical models and lack of physical law constraints of pure data-driven models. Through sparse sampling and dominant mode extraction, the present invention can efficiently obtain the key features of high-fidelity model data while retaining the modal information of physical mutation areas. The hybrid reduced-order framework constructed by combining high-fidelity finite element models with low-fidelity simplified models further improves the adaptability of the model under complex dynamic conditions.

[0040] The data-physics-driven model training and optimization process integrates data-driven errors and physical mechanism residuals, enabling comprehensive assessment and precise localization of model errors. By updating the dominant mode basis functions with online streaming data and employing an iterative optimization strategy based on error quantification, the reduced-order model continuously improves itself, gradually enhancing prediction accuracy.

[0041] Furthermore, the proposed method offers excellent versatility and scalability, making it suitable for dynamic response prediction of a wide range of large-scale mechanical equipment. By flexibly adjusting the sampling strategy, dominant mode extraction method, and the specific implementation of the hybrid order reduction framework, the proposed method can meet the specific needs of different application scenarios, providing strong technical support for the development of digital twin technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] To facilitate understanding by those skilled in the art, the present invention is further described below with reference to the accompanying drawings.

[0043] Figure 1 Schematic diagram of a flow chart of a method for generating a reduced-order model of a nonlinear system by integrating physical constraints and digital twins according to the present invention;

[0044] Figure 2 Schematic diagram of state timing of a method for generating a reduced-order model of a nonlinear system that integrates physical constraints and digital twins. DETAILED DESCRIPTION

[0045] In order to further illustrate the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the specific implementation methods, structures, features and effects of the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments.

[0046] See also Figure 1-2 , a method for generating reduced-order models of nonlinear systems that integrates physical constraints and digital twins, including:

[0047] S1: Collect high-dimensional dynamic response data through the sensor network of the digital twin system, sparsely sample the high-dimensional dynamic response data to obtain high-fidelity model data, extract the dominant mode of the high-fidelity model data, and retain the mode of the physical mutation area through physical field gradient constraints during the extraction process;

[0048] S2: Combining a high-fidelity finite element model with a low-fidelity simplified model, a hybrid order reduction framework based on a multi-fidelity surrogate model is constructed, dense sampling is performed in the physical mutation region, and number space preprocessing is performed on the nonlinear terms;

[0049] S3: Based on the hybrid order reduction framework, data-driven errors and physical mechanism residuals are integrated in data-physics-driven model training and optimization, and the basis functions of the dominant modes are updated based on online streaming data.

[0050] S4: Cross-validate the outputs of the high-fidelity finite element model and the reduced-order model, including global error evaluation and focused analysis of local physical mutation areas. Build an adaptive error threshold feedback mechanism based on the error quantification results, and improve the accuracy of the reduced-order model through iterative optimization strategies.

[0051] Specifically, the sparse sampling method is:

[0052] A physical field gradient amplitude matrix is ​​constructed to identify high-gradient areas. The high-gradient areas are densely sampled using a Gaussian random measurement matrix, and the low-gradient areas are sparsely sampled using a Bernoulli random matrix. In the time dimension, three sampling frequencies are set: transient stage, transition stage, and steady-state stage.

[0053] In this embodiment, an adaptive sampling strategy driven by the physical field gradient is constructed. The sampling density is set according to the gradient change rate, including full sampling (sampling density 100%), exponential distribution sampling (density 50%-80%), and Latin hypercube sampling (density ≤30%). In the time dimension, a three-stage sampling frequency is set within the characteristic time constant, and in the spatial dimension, sampling points are dynamically allocated based on the KL divergence.

[0054] Specifically, the dominant mode of the high-fidelity model data is a set of low-dimensional basis functions that characterize key dynamic characteristics of the system.

[0055] In this embodiment, the dominant modes of high-fidelity model data refer to a set of low-dimensional basis functions that can characterize the key dynamic characteristics of the system, extracted from sparsely sampled high-dimensional dynamic data through a modal decomposition method constrained by physical field gradients. Its core features include:

[0056] Dominance of physical mechanisms: The modes must satisfy conservation laws (mass and momentum conservation) and gradient constraints in the mutation region (shock waves and vortex cores) to avoid physical distortion caused by purely data-driven approaches.

[0057] Multi-scale separation capability: Separate steady-state modes (low frequency), transient modes (high frequency) and intermittent modes through time-frequency decoupling technology to ensure that the modal basis function can cover the full frequency domain dynamic behavior;

[0058] Compactness and completeness: While ensuring computational efficiency, the dominant mode must cover at least 95% of the system energy (POD energy cutoff criterion), and the energy contribution of the residual mode must not exceed a preset threshold.

[0059] Specifically, the dominant mode extraction method includes: physical constraint mode decomposition, mutation region mode retention, multi-scale mode selection, and dynamic mode update; wherein the physical constraint mode decomposition adopts intrinsic orthogonal decomposition combined with physical field gradient weighting function to construct a weighted inner product space to ensure that the extracted mode satisfies both data statistical characteristics and physical field gradient constraints; the dynamic mode update detects the new mode energy ratio through online streaming data, and triggers incremental basis function update according to the new mode energy ratio.

[0060] In this embodiment, the weighted inner product space can be expressed as:

[0061] ,

[0062] in, represents the inner product of vectors u and v in the weighted inner product space, N represents the dimension of vectors u and v, that is, the number of elements in the vector; represents the physical field value at the i-th position; represents the physical field gradient at the i-th position; tanh is the hyperbolic tangent function, which is used to map the modulus of the gradient to a specific range, and ui and vi are the components of the vectors u and v at the i-th position, respectively.

[0063] The gradient weighting mechanism introduces a hyperbolic tangent weight function to increase the modal energy of the physical mutation area where the gradient value exceeds the threshold by 2-3 orders of magnitude;

[0064] Multi-scale coupling: Global energy truncation is combined with local residual compensation to reduce local error to less than 5% while retaining 95% of the energy;

[0065] Dynamic update guarantee: The incremental POD algorithm reduces the computational complexity of modality update from O(N³) to O(kN²) (k is the number of newly added modalities);

[0066] Physical consistency: The weighted inner product space construction ensures that the extracted modes satisfy both data statistical characteristics and physical field gradient constraints.

[0067] Specifically, the high-fidelity finite element model is a physically accurate model constructed based on a full-order finite element discretization method, and the low-fidelity simplified model is a lightweight proxy model generated by projection reduction and data-physics joint driving.

[0068] In this embodiment, the high-fidelity finite element model uses anisotropic mesh encryption in the physical mutation region (vortex core, crack propagation path), verifies mesh convergence through gradient recovery technology (ZZ Error Estimator), and adopts Newton-Raphson iteration + line search for strong nonlinear problems (such as large deformation of hyperelastic materials), and introduces a quasi-static time step adaptive algorithm to avoid divergence; embeds a flux correction term (Flux-Corrected Transport, FCT) in the finite element weak form to ensure strict conservation of mass and momentum in the mutation region; the low-fidelity simplified model projects the full-order equation into a low-dimensional space based on the dominant mode basis function extracted by S1:

[0069] ,

[0070] Among them, the nonlinear force terms are sparsely sampled and reconstructed through DEIM, ɸ is the dominant mode basis function, and a is the coefficient vector in the low-dimensional space.

[0071] Specifically, the hybrid order reduction framework includes a multi-fidelity data fusion module, a physical constraint embedding module, a nonlinear term preprocessing module, a dynamic resource allocation module, and a stride error feedback link;

[0072] The multi-fidelity data fusion module adjusts the mixing weights in real time according to the distribution differences between the high-fidelity finite element model and the low-fidelity simplified model, and constructs a smooth transition field by interpolation in the boundary area;

[0073] The physical constraint embedding module introduces a gradient sensitivity weight matrix to reconstruct the projection equation in the traditional projection and adds a residual term to the low-fidelity simplified model training loss function;

[0074] The nonlinear term preprocessing module uses discrete empirical interpolation and convolutional autoencoder to perform number space preprocessing on the nonlinear term;

[0075] The dynamic resource allocation module adjusts the computing resource ratio of the high-fidelity finite element model and the low-fidelity simplified model in real time based on the error feedback mechanism, and triggers local recalculation of the high-fidelity finite element model in the mutation area.

[0076] Specifically, the method of number space preprocessing is:

[0077] Decompose the nonlinear term into a steady-state component and a transient pulsating component:

[0078] ,

[0079] Among them, F(u) is a nonlinear term, and the transient pulsation component is expressed as ΔF(u), F mean is the steady-state component, is the spatial basis function With time basis function The correlation coefficient of , m is the total number of basis functions in the transient pulsating part;

[0080] The transient pulsation component is sparsely sampled to obtain key feature points of the transient pulsation component, and the key feature points are encoded and decoded through a convolutional autoencoder to achieve efficient representation of nonlinear terms in a low-dimensional space.

[0081] In this embodiment, the greedy DEIM algorithm is used to select interpolation points for the transient component:

[0082] ,

[0083] Among them, U is the basis function, and interpolation points are preferentially selected in the physical mutation area. Local DEIM (LDEIM) is used to build a regional interpolation point library for multi-operating system. Gradient sensitivity weights are introduced in the interpolation matrix. In the convolutional autoencoder (CAE) latent space mapping, the encoder is designed to map the nonlinear terms compressed by DEIM to the latent space:

[0084] ,

[0085] The encoder uses convolutional layers to extract local nonlinear features and pooling layers to achieve dimensionality reduction; the decoder is reconstructed to recover the approximate value of the nonlinear term from the latent space.

[0086] Specifically, the data-driven error is a statistical deviation between a low-fidelity simplified model and a high-fidelity finite element model in dynamic response prediction.

[0087] Specifically, the physical mechanism residual is the degree of deviation of the low-fidelity simplified model from the constraints of mass, momentum, energy and physical field gradient.

[0088] In this embodiment, data-driven errors mainly include modal truncation error (loss of unmodeled modal energy due to POD energy truncation), sensor noise interference (noise pollution in the data collected by the digital twin system), and operating condition extrapolation error (boundary conditions or parameter variation domains not covered by the training data). The error quantification method evaluates the overall prediction accuracy through the global L2 error:

[0089] ,

[0090] Among them, ϵ data is the data-driven error, which represents the average relative error between the prediction results of the low-fidelity simplified model (ROM) and the high-fidelity finite element model (HFEM) in the time interval [0, T]; u ROM (t) represents the system state vector predicted by the low-fidelity simplified model at time t, u HFEM (t) represents the system state vector calculated by the high-fidelity finite element model at time t, which is usually regarded as the “true” solution; Represents the L2 norm, which is used to measure the size of a vector.

[0091] and focusing on the probability distribution differences of physical mutation regions through local KL divergence;

[0092] ,

[0093] Among them, D KL is the divergence, p ROM (x) and p HFEM (x) represents the probability density function at point x, p ROMrepresents the probability distribution based on the low-fidelity simplified model, p HFEM Represents the probability distribution based on a high-fidelity finite element model.

[0094] The physical mechanism residual refers to the degree of deviation of the reduced-order model from the conservation laws (mass, momentum, energy) and physical field gradient constraints, which must be enforced through regularization constraints;

[0095] A multi-objective loss function is constructed to jointly optimize the data-driven error and the physical mechanism residual.

[0096] Specifically, the method of iterative optimization strategy includes:

[0097] When the global error exceeds a preset threshold, the source of the error is located through residual dominant mode analysis, and the dominant mode basis function is updated based on the online stream data in S3 to supplement the missing high-order modes;

[0098] When the gradient mutation of the local physical mutation area exceeds a preset threshold, the physical constraint is strengthened in the hybrid order reduction framework of S2, and the sampling density of the corresponding local physical mutation area is increased through gradient sensitivity analysis.

[0099] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications 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 are still within the scope of the technical solution of the present invention.

Claims

1. A method for generating a reduced-order model of a nonlinear system by integrating physical constraints and digital twins, characterized in that: include: S1: Collect high-dimensional dynamic response data through the sensor network of the digital twin system, sparsely sample the high-dimensional dynamic response data to obtain high-fidelity model data, extract the dominant mode of the high-fidelity model data, and retain the mode of the physical mutation area through physical field gradient constraints during the extraction process; S2: Combining a high-fidelity finite element model with a low-fidelity simplified model, a hybrid order reduction framework based on a multi-fidelity surrogate model is constructed, dense sampling is performed in the physical mutation region, and number space preprocessing is performed on the nonlinear terms; S3: Based on the hybrid order reduction framework, the data-driven error and physical mechanism residual are integrated in the data-physics joint driven model training and optimization, and the basis function of the dominant mode is updated based on the online streaming data to generate the optimized reduced-order model; S4: Cross-validate the outputs of the high-fidelity finite element model and the reduced-order model, including global error evaluation and focused analysis of local physical mutation areas. Build an adaptive error threshold feedback mechanism based on the error quantification results, and improve the accuracy of the reduced-order model through iterative optimization strategies.

2. The method according to claim 1, characterized in that The sparse sampling method is: Constructing a physical field gradient amplitude matrix, identifying high gradient regions, densely sampling the high gradient regions using a Gaussian random measurement matrix, and sparsely sampling the low gradient regions using a Bernoulli random matrix; In the time dimension, the sampling frequencies of three stages are set: transient stage, transition stage, and steady state stage.

3. The method according to claim 1, characterized in that The dominant mode of the high-fidelity model data is a set of low-dimensional basis functions that characterize the key dynamic characteristics of the system.

4. The method according to claim 1, wherein The dominant mode extraction method includes: physical constraint mode decomposition, mutation region mode retention, multi-scale mode selection, and dynamic mode update; wherein the physical constraint mode decomposition adopts intrinsic orthogonal decomposition combined with physical field gradient weighting function to construct a weighted inner product space, ensuring that the extracted mode satisfies both data statistical characteristics and physical field gradient constraints; the dynamic mode update detects the new mode energy ratio through online streaming data, and triggers incremental basis function update according to the new mode energy ratio.

5. The method according to claim 1, wherein The high-fidelity finite element model is a physically accurate model constructed based on a full-order finite element discretization method, and the low-fidelity simplified model is a lightweight proxy model generated by projection reduction and data-physics joint driving.

6. The method according to claim 1, characterized in that The hybrid order reduction framework includes a multi-fidelity data fusion module, a physical constraint embedding module, a nonlinear term preprocessing module, a dynamic resource allocation module, and a stride error feedback link; The multi-fidelity data fusion module adjusts the mixing weights in real time according to the distribution differences between the high-fidelity finite element model and the low-fidelity simplified model, and constructs a smooth transition field by interpolation in the boundary area; The physical constraint embedding module introduces a gradient sensitivity weight matrix to reconstruct the projection equation in the traditional projection and adds a residual term to the low-fidelity simplified model training loss function; The nonlinear term preprocessing module uses discrete empirical interpolation and convolutional autoencoder to perform number space preprocessing on the nonlinear term; The dynamic resource allocation module adjusts the computing resource ratio of the high-fidelity finite element model and the low-fidelity simplified model in real time based on the error feedback mechanism, and triggers local recalculation of the high-fidelity finite element model in the mutation area.

7. The method according to claim 6, characterized in that The method of number space preprocessing is: Decompose the nonlinear term into a steady-state component and a transient pulsating component: ， Among them, F(u) is a nonlinear term, and the transient pulsation component is expressed as ΔF(u), F mean is the steady-state component, is the spatial basis function With time basis function The correlation coefficient of , m is the total number of basis functions in the transient pulsating part; The transient pulsation component is sparsely sampled to obtain key feature points of the transient pulsation component, and the key feature points are encoded and decoded through a convolutional autoencoder to achieve efficient representation of nonlinear terms in a low-dimensional space.

8. The method according to claim 1, characterized in that The data-driven error is the statistical deviation between the low-fidelity simplified model and the high-fidelity finite element model in the dynamic response prediction.

9. The method according to claim 1, characterized in that The physical mechanism residual is the degree of deviation of the low-fidelity simplified model from the constraints of mass, momentum, energy and physical field gradient.

10. The method according to claim 1, characterized in that The method of iterative optimization strategy includes: When the global error exceeds a preset threshold, the source of the error is located through residual dominant mode analysis, and the dominant mode basis function is updated based on the online stream data in S3 to supplement the missing high-order modes; When the gradient mutation of the local physical mutation area exceeds a preset threshold, the physical constraint is strengthened in the hybrid order reduction framework of S2, and the sampling density of the corresponding local physical mutation area is increased through gradient sensitivity analysis.

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