Simulation prediction method based on reduced-order model machine learning

Abstract

The invention discloses a simulation prediction method based on reduced-order model machine learning, and relates to the technical field of crossing of computer-aided engineering simulation and machine learning, in particular to a simulation prediction method based on reduced-order model machine learning, which comprises the following steps: firstly, performing finite element simulation on automobile parts (such as an anti-collision beam) to obtain simulation data; secondly, selecting sample points by adopting a Latin hypercube sampling method, and verifying that a data set meets an order reduction requirement; then, carrying out dimension reduction processing on the data by applying an order reduction model (such as intrinsic orthogonal decomposition (POD) or singular value decomposition (SVD)); and finally, predicting the data after order reduction by using a Kriging method machine learning model, and evaluating the prediction precision by using a decision coefficient R2 and a root mean square error RMSE. According to the method, through combination of the reduced-order model and machine learning, the simulation calculation efficiency is effectively improved, meanwhile, the accuracy of a prediction result is ensured, and the method is suitable for rapid simulation optimization in automobile design.

Description

Technical Field

[0001] This invention relates to the field of computer-aided engineering simulation and machine learning, specifically to a simulation prediction method based on reduced-order model machine learning. Background Technology

[0002] In the field of mechanical design and manufacturing, structural optimization analysis is a core step in improving product performance, reducing costs, and shortening development cycles. Traditionally, engineers have relied primarily on computer-aided engineering (CAE) techniques, such as finite element analysis, to optimize the topology, dimensions, and shape of structures. This method, through mathematical modeling and simulation, can efficiently generate accurate and reliable optimization solutions to a certain extent, solving complex problems that are difficult to handle manually, thereby improving design reliability and reducing the cost of physical testing. Structural topology optimization is generally divided into two categories: discrete structures (such as plates and trusses) and continuous structures (such as planes and shells). CAE technology plays an important role in both types of optimization, for example, by using software such as Hypermesh for mesh generation and load case settings to achieve rapid iteration.

[0003] However, with the development of engineering technology, the structural scale and system complexity of modern components have increased significantly, highlighting the limitations of traditional CAE methods. First, the design process requires manual pre-specification of the designable area, setting optimization objectives, loads, and constraints, resulting in a large workload and low level of automation. Second, optimization design involves numerous parameters (such as material properties, geometric dimensions, and loading conditions), and these parameters are coupled, leading to extensive finite element iterative calculations that are time-consuming. For example, in the simulation of automotive crash beams, changes in parameters such as thickness, elastic modulus, and impact velocity require multiple sampling and simulations. Each sample point may involve data extraction from tens of thousands of nodes, consuming significant computational resources. Specifically, the simulation model of a crash beam typically contains tens of thousands of nodes, uses shell elements for meshing, and configures mass blocks and impact velocity parameters, making a single simulation take several hours or even longer, which is insufficient for rapid optimization needs.

[0004] In recent years, the rise of machine learning has provided new ideas for structural optimization. Researchers have attempted to combine machine learning with CAE, utilizing its high-dimensional mapping capabilities to approximate complex physical relationships, thereby reducing computational costs. For example, compressing high-dimensional data using reduced-order models (such as intrinsic orthogonal decomposition (POD) or singular value decomposition (SVD)) and then combining it with surrogate models such as Kriging for prediction can significantly accelerate the process. However, existing methods still face challenges: key information may be lost during data dimensionality reduction, the accuracy of machine learning models depends on sample quality, and parameter estimation (such as maximum likelihood estimation) is complex and prone to prediction errors. Although traditional methods can obtain stress contour maps and deformation data in crash beam simulations, their sampling efficiency is low (e.g., Latin hypercube sampling requires 27 sets of sample points), and the computational burden of full-order models is heavy. Summary of the Invention

[0005] The purpose of this invention is to provide a simulation prediction method based on reduced-order model machine learning. By combining Latin hypercube sampling, singular value decomposition for order reduction, and Kriging machine learning, it can achieve rapid and accurate prediction of deformation and stress of automotive parts, thereby optimizing the design process, reducing testing costs, and improving engineering efficiency.

[0006] To achieve the above objectives, this invention employs the following technical solution: a simulation prediction method based on reduced-order model machine learning. This method includes finite element simulation analysis of automotive components. Specifically, a geometric model is built using the 3D software NX. Taking an automotive anti-collision beam as an example, its length, width, and height are 1400mm, 33mm, and 100mm respectively, with a thickness of 2.5mm. During the modeling process, details such as bolts and welded nuts are removed to simplify the model, thereby improving mesh quality and reducing computation time. Subsequently, Hypermesh software is used for mesh generation, employing shell elements with a size of 6.6mm, resulting in a total of 13118 elements and 12968 nodes. The loading condition settings include establishing a cylindrical rigid wall at the front end of the anti-collision beam and placing a 0.2t mass block at the rear end, impacting the wall at a speed of 15m / s to simulate actual engineering conditions. The stress and deformation contour maps obtained after simulation analysis show that the maximum deformation displacement is 118.9 mm, the X-direction intrusion point is 37.01 mm, and the maximum stress is 280.7 MPa, mainly concentrated at the collision point. These simulation data provide a foundation for subsequent steps, ensuring the accuracy and representativeness of the data.

[0007] Furthermore, the Latin hypercube sampling method is used to select sample points, with parameters including the thickness of the anti-collision beam, the elastic modulus, and the impact velocity. The thickness sampling interval is set to [1mm, 5mm], the elastic modulus interval to [68GPa, 76GPa], and the impact velocity interval to [10m / s, 20m / s]. A total of 27 sample points are used. This method ensures that the samples uniformly cover the high-dimensional parameter space, avoiding duplication or missed detections. After sampling, displacement sample data in the X-axis direction at 271,142 nodes are extracted from the simulation data to form a dataset. The advantage of Latin hypercube sampling lies in its ability to effectively reduce the correlation between samples, improve the representativeness of the dataset, and lay the foundation for the validation of the reduced-order model.

[0008] Furthermore, the reduced-order model employs the Singular Value Decomposition (SVD) method, the formula of which is:

[0009] Q=U×∑×V T Where Q is the response matrix, U is the left singular matrix, Σ is the singular value matrix, and V is the right singular matrix. In implementation, the SVD method is used to reduce the dimensionality of high-dimensional datasets. When the number of response points far exceeds the operating conditions, the matrix Q is solved... T The eigenvalues ​​of Q are used to simplify the calculation. Eigenvalue λ i With singular value σ i satisfy The relationship is 2, where i = 1, 2, ..., I. This method is equivalent to intrinsic orthogonal decomposition (POD), but it is more efficient when the data dimensionality is low. After dimensionality reduction, the data is projected into a lower-dimensional space, reducing computation while preserving key features.

[0010] Furthermore, in the SVD method, the eigenvalue λ i via Matrix QQ T With Q T Solve for the relationship of Q, satisfying... This relationship ensures the accuracy of the eigenvalues, providing a mathematical basis for order reduction. In specific calculations, the eigenvector φ i Through formula Obtain, where λ i For Q T The eigenvectors of Q are used to construct an orthonormal basis for the column space of the response matrix.

[0011] Furthermore, the feature vector is calculated using the formula Implementation, where φ i As QQ TThe eigenvectors are used to form an orthonormal basis. This step ensures the accurate construction of the column space of the response matrix, thus maintaining the intrinsic relationships of the data during dimensionality reduction. This method effectively handles differences in spatial dimensions. When the time dimension n is lower than the spatial dimension m, the eigenvector solution is optimized using the SVD method to reduce computational complexity. The orthogonality of the eigenvectors guarantees the robustness of the reduced-order model, providing clean data input for machine learning predictions.

[0012] Furthermore, the reduced-order model also includes a modal truncation step, using the formula...

[0013] The data information completeness level *p* is calculated. The *p* value represents the proportion of information from the full-order data contained in the reduced-order data. Typically, *p* ≥ 0.95 is required to ensure that the modal basis functions can well approximate the full-order model. In practice, the cumulative variance contribution rate reached 99.9%, indicating that the data information is fully preserved after reduction. This step reduces computational costs by truncating secondary modes while maintaining prediction accuracy, making the method more suitable for large-scale simulations.

[0014] Furthermore, the surrogate function of the Kriging machine learning model is...

[0015] Y(x) = β0 + Z(x), where H(x,x′) is the correlation function, and its expression is:

[0016] The correlation function decreases as the distance between sample points increases, reflecting spatial autocorrelation. The parameter vector θ is optimized using maximum likelihood estimation to ensure the model fits the data distribution. This function effectively handles high-dimensional inputs, such as the multi-parameter variables of a crash barrier beam, improving the smoothness and accuracy of predictions.

[0017] Furthermore, in the maximum likelihood estimation method, the likelihood function is:

[0018] Used to solve for the surrogate function parameters. Variance estimate.

[0019] σ 2 The calculation formula is: The formula for calculating the global trend value β0 is as follows: Where F = [1, 1, ..., 1] T This method optimizes model parameters by maximizing the likelihood function, ensuring consistency between predicted and actual values. This step, applied to the Kriging model, improves the efficiency of parameter estimation; for example, in the crash beam example, the calculation of β0 simplifies the determination of the global trend.

[0020] Furthermore, the evaluation of the prediction results uses the decision coefficient R. 2 The root mean square error (RMSE) index.2 The calculation formula is: The formula for calculating RMSE is as follows:

[0021] When R 2 A value close to 1 indicates high accuracy of the prediction model.

[0022] This invention provides a simulation prediction method based on reduced-order model machine learning, which has the following beneficial effects:

[0023] 1. Dimensionality reduction of high-dimensional finite element simulation data is achieved through model reduction (such as Singular Value Decomposition (SVD)). This simplifies complex calculations requiring the processing of a large number of nodes (e.g., 271,142 nodes) into efficient computations in a low-dimensional space. Specifically, in the case of automotive crash beams, 27 sets of sample points were selected using Latin hypercube sampling, and key eigenvalues ​​were extracted using SVD, significantly reducing the data dimensionality. This effectively reduces computational resource consumption and simulation time, avoiding iterative calculation delays caused by parameter coupling in traditional CAE analysis. For example, after dimensionality reduction, only a few principal components (e.g., PC1, PC2, and PC3, with a cumulative variance contribution rate of 99.9%) need to be processed, retaining most of the information and accelerating the optimization design process. This method is particularly suitable for large-scale engineering problems, such as collision simulation of automotive crash beams, helping engineers quickly obtain prediction results, shortening the design-to-verification cycle, and improving overall development efficiency.

[0024] 2. Construct a surrogate function using a Kriging machine learning model and validate it with reduced-order data (such as decision coefficient R). 2 By measuring the root mean square error (RMSE), this invention enables accurate prediction of simulation results. In the crash beam example, the predicted values ​​of the test set (such as samples 5, 19, and 22) closely match the actual values, and R0... 2 Coefficients close to 1 (e.g., 98.962%) and low RMSE values ​​(e.g., 0.5563) indicate small model errors and high fit. This high accuracy stems from the reduced-order model's complete preservation of data information (e.g., p-value greater than 0.95) and the Kriging method's effective capture of spatial correlations. This method accurately reflects the displacement and stress distribution of the crash beam during a collision, avoiding the biases caused by insufficient samples or model simplification in traditional methods. Therefore, it provides a reliable basis for structural optimization and reduces design risks.

[0025] 3. By employing the Latin hypercube sampling method to select parameter variables (such as the thickness of the anti-collision beam, elastic modulus, and impact velocity), this invention ensures a uniform distribution of samples in high-dimensional space, avoiding duplicate or missed detections. The sampling intervals are reasonably set (e.g., thickness [1mm, 5mm], elastic modulus [68GPa, 76GPa]), and the 27 sample points cover the key parameter ranges, thereby maximizing data diversity. This strategy improves the representativeness of the dataset, enabling the reduced-order model to more comprehensively capture full-order features. The variance contribution rate shown indicates that the first three principal components contain 99.9% of the information. Compared to random sampling, this method reduces the required sample size while improving the model's generalization ability, laying a solid foundation for subsequent machine learning, and is particularly suitable for complex engineering scenarios with multiple coupled parameters.

[0026] 4. By replacing some physical testing with finite element simulation and machine learning prediction, this invention significantly reduces the need for physical prototypes. In the case of crash beams, traditional CAE analysis is time-consuming and costly, while this invention only requires a small amount of simulation data (e.g., 27 sets of samples) to complete the prediction, avoiding a large number of repetitive experiments. The combination of the reduced-order model and the Kriging method makes it possible to quickly evaluate different design parameters (such as thickness and material) in a digital environment, thereby optimizing structural performance without increasing manufacturing costs. For example, the prediction results can guide the selection of crash beam dimensions and materials, saving on experimental materials and labor costs. When this method is extended to other automotive parts, it can significantly reduce R&D investment and improve economic efficiency.

[0027] 5. This invention uses an automotive anti-collision beam as an example, but the method framework is universal and can be easily adapted to other automotive parts or mechanical structures. The claims emphasize the use of standard tools (such as NX, Hypermesh, and Matlab), making the implementation process easy to replicate and extend. The parameter setting and verification process (such as the range adjustment of elastic modulus and impact velocity) demonstrates the flexibility of the method, enabling it to address different design requirements. The modular design of the reduced-order model and machine learning model allows users to adjust parameters according to specific problems without having to redevelop the entire system. This scalability ensures the long-term applicability of the method in complex scenarios such as continuum topology optimization, providing the industry with a sustainable solution. Attached Figure Description

[0028] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0029] Figure 1This is a flowchart of the overall method of the present invention;

[0030] Figure 2 This is a detailed flowchart of the finite element simulation analysis of the present invention;

[0031] Figure 3 This is a flowchart of the SVD order reduction and modal truncation process of the present invention;

[0032] Figure 4 This is a flowchart of the Kriging model construction and prediction process of this invention;

[0033] Figure 5 This is a flowchart of the model verification and evaluation process for this invention. Detailed Implementation

[0034] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses consistent with some aspects of this disclosure as detailed in the appended claims.

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0036] Example 1: Implementation of the overall method based on claim 1

[0037] This embodiment corresponds to the simulation prediction method based on reduced-order model machine learning as described in claim 1, focusing on the implementation details of the overall process. This method aims to improve the efficiency of simulation prediction for automotive parts through reduced-order models and machine learning, using an automotive anti-collision beam as an example.

[0038] First, finite element simulation analysis was performed: a geometric model of the crash beam was built using the 3D software NX, with dimensions of 1400mm long, 33mm wide, 100mm high, and 2.5mm thick. To improve mesh quality, the model was simplified by removing non-critical components such as bolts and welded nuts. Then, Hypermesh software was used for mesh generation, employing shell elements with a mesh size of 6.6mm, resulting in a mesh model with 13118 elements and 12968 nodes. In the loading condition settings, a 0.2t mass block was placed at the rear end of the crash beam to simulate the actual connecting components, impacting a cylindrical rigid wall at a speed of 15m / s. After the simulation, the response data was extracted as the base dataset.

[0039] Secondly, the Latin hypercube sampling method was used to select sample points. The parameters included the thickness of the crash beam (sampling interval [1mm, 5mm]), the elastic modulus (interval [68GPa, 76GPa]), and the impact velocity (interval [10m / s, 20m / s]), generating a total of 27 sample points. After the sample data was validated, it was ensured that it met the order reduction requirements, such as data uniformity and coverage.

[0040] Next, a dimensionality reduction model is applied to the dataset. This embodiment uses Singular Value Decomposition (SVD), with the formula Q = U × Σ × V. T Σ is the singular value matrix, where Q is the response matrix, U and V are the left and right singular matrices respectively, and Σ is the singular value matrix. SVD projects high-dimensional data into a low-dimensional space, reducing computational complexity.

[0041] Finally, a Kriging machine learning model is used to predict the reduced-order data. The surrogate function is represented as Y(x) = β0 + Z(x), where β0 is the global trend value and Z(x) is a stochastic process. The prediction results are expressed using decision coefficients R0. 2 The root mean square error (RMSE) is used for evaluation. 2 A value close to 1 indicates high prediction accuracy. This embodiment, through the above steps, realizes the entire process from simulation to prediction, significantly improving computational efficiency.

[0042] Example 2: Implementation of Finite Element Simulation Analysis Based on Claim 2

[0043] This embodiment corresponds to claim 2, and describes in detail the specific implementation process of finite element simulation analysis, taking an automobile anti-collision beam as an example. Finite element simulation is the foundation of this method, aiming to obtain high-precision physical field data.

[0044] First, in the geometric modeling stage: the geometric model of the crash beam was created using the 3D software NX. The dimensions are 1400mm (length), 33mm (width), and 100mm (height), with a thickness of 2.5mm. The material chosen is aluminum alloy, with an elastic modulus of 72GPa, a Poisson's ratio of 0.34, and a density of 2.7g / cm³. 3 To optimize computation, the model was simplified by removing detailed components such as bolts and welded nuts to reduce the number of meshes and improve mesh quality. After simplification, the model focuses on the main structure, ensuring that simulation accuracy is not affected.

[0045] Secondly, mesh generation and load condition settings: Finite element analysis was performed using Hypermesh software. Shell elements were used as the mesh type, with a size of 6.6 mm, resulting in a total of 13,118 elements and 12,968 nodes. A cylindrical rigid wall was constructed at the front end of the crash beam to simulate a collision scenario. In the loading condition, a 0.2t mass block was placed at the rear end of the crash beam to represent the actual connected heavy components, and the impact velocity was set to 15 m / s. This setting realistically reflects the dynamic response of the crash beam during a collision.

[0046] After the simulation was run, stress and deformation contour maps were obtained. The results showed that the maximum deformation displacement of the anti-collision beam was 118.9 mm, and the main intrusion point in the X direction was the collision contact point, with an intrusion amount of 37.01 mm. The stress distribution showed that the maximum stress was located at the collision point, with a value of 280.7 MPa, which is consistent with the engineering expectations.

[0047] Finite element simulation not only verified the effectiveness of the model but also provided a high-quality dataset for subsequent data reduction and machine learning. This embodiment emphasizes the implementation of simulation details to ensure the reliability of the data source.

[0048] Example 3: Implementation of Latin hypercube sampling based on claim 3

[0049] This embodiment corresponds to claim 3, focusing on the application of the Latin hypercube sampling method in data acquisition. This method is used to efficiently select sample points, ensuring the representativeness and uniformity of the dataset.

[0050] The sampling parameters include three variables: the thickness of the crash beam, the elastic modulus, and the impact velocity. The thickness sampling interval is [1mm, 5mm], the elastic modulus interval is [68GPa, 76GPa], and the impact velocity interval is [10m / s, 20m / s]. Latin hypercube sampling, based on statistical principles, ensures a uniform distribution of sample points within each parameter interval, avoiding duplication or omission, making it particularly suitable for high-dimensional problems. This embodiment generates 27 sets of sample points, each corresponding to a complete simulation condition.

[0051] After sampling, dataset validation was performed. X-axis displacement samples were extracted from 271,142 nodes in the simulation data to ensure sufficient data volume. Analysis of variance was used to verify that the dataset met the requirements for order reduction, such as minimizing the covariance between samples, to ensure the stability of the subsequent order-reduced model. The 27 sets of samples largely preserved data characteristics, with a cumulative variance contribution rate of 99.9%, demonstrating the effectiveness of the sampling.

[0052] The variance contribution plot shows that the contribution rates of principal components PC1, PC2, and PC3 are 43.5%, 34.1%, and 22.3%, respectively, with a cumulative contribution rate close to 100%, indicating complete sample information. This embodiment provides high-quality input for the reduced-order model through detailed sampling steps.

[0053] Example 4: Implementation based on the reduced-order model of claims 4-6

[0054] This embodiment, based on claims 4-6, describes specific applications of the order reduction model, including singular value decomposition (SVD) and modal truncation. The order reduction model aims to reduce data dimensionality and improve computational efficiency.

[0055] First, the response matrix Q is decomposed using the SVD method, with the formula Q = U × Σ = V. T Among them, the eigenvalue λ i With singular value σ i Satisfying Relationships λ i For Matrix QQ T and Q T The eigenvalues ​​of Q. The eigenvectors are obtained through the formula... Calculate φ i The response matrix column space is constructed using an orthonormal basis. In this embodiment, the response matrix is ​​constructed based on the displacement data of 27 sample points. The spatial dimension m is much larger than the time dimension n, therefore SVD can efficiently solve for the eigenvalues.

[0056] Secondly, modal truncation is performed to reduce computational costs. This is achieved through the formula... The data information completeness p is calculated, where k is the number of truncated modes. The closer the p value is to 1, the more complete the full-order information contained in the reduced-order data; this embodiment requires p ≥ 0.95 to ensure the approximation effect.

[0057] Example 5: Implementation of machine learning prediction and evaluation based on claims 7-10

[0058] This embodiment corresponds to claims 7-10, describing the prediction process and evaluation metrics of the Kriging machine learning model. This method is used to predict data after order reduction and to verify its accuracy.

[0059] The surrogate function model is Y(x) = β0 + Z(x), where β0 is the global trend value, obtained through the formula... Calculate (F is a vector of all 1s). Z(x) is a static random process with covariance function cov(Z(x),Z(x′))=σ 2 H(x,x′), the correlation function H(x,x′) is expressed as The parameter θ is solved using the maximum likelihood estimation method, and the likelihood function is: variance

[0060] σ 2 The calculation formula is

[0061] In the prediction, 24 out of 27 samples were selected as the training set, and samples 5, 19, and 22 were selected as the test set. The prediction results were expressed using the decision coefficient R0. 2 Root Mean Square Error (RMSE) Evaluation: R 2 The calculation formula is RMSE is R of the test sample 2 All are close to 1 (e.g., R for sample 5) 2 =98.962%), and a small RMSE (e.g., 0.5563mm) indicates high prediction accuracy.

[0062] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A simulation prediction method based on reduced-order model machine learning, characterized in that, Includes the following steps: Finite element simulation analysis is performed on automotive parts to obtain simulation data; The Latin hypercube sampling method was used to select sample points, and the simulation results of the sample points were used as the dataset. The dataset was then verified to meet the order reduction requirement. The dataset is reduced in dimensionality using a reduction model, which employs either intrinsic orthogonal decomposition (POD) or singular value decomposition (SVD). The Kriging machine learning model was used to predict the reduced-order data, and the prediction results were obtained. The reduced-order model employs the Singular Value Decomposition (SVD) method, and its formula is as follows: Q=U×∑×V T In the formula, Q is the response matrix, U is the left singular matrix, Σ is the singular value matrix, and V is the right singular matrix.

2. The simulation prediction method based on reduced-order model machine learning according to claim 1, characterized in that, The finite element simulation analysis includes: Geometric models of automotive parts were built using the 3D software NX, and the models were simplified to improve mesh quality. The Hypermesh finite element analysis software was used to generate the mesh and set the loading conditions. The mesh was generated using shell elements, and the mass block and impact velocity parameters were configured. Taking a car crash beam as an example, the crash beam has a length, width, and height of 1400mm, 33mm, and 100mm respectively, a thickness of 2.5mm, and is made of aluminum alloy with an elastic modulus of 72GPa, a Poisson's ratio of 0.34, and a density of 2.7g / cm³. 3 .

3. The simulation prediction method based on reduced-order model machine learning according to claim 1, characterized in that: In the Latin hypercube sampling method, the parameter variables include the thickness of the anti-collision beam, the elastic modulus, and the impact velocity; The thickness sampling range is set to [1mm, 5mm], the elastic modulus range is set to [68GPa, 76GPa], and the impact velocity range is set to [10m / s, 20m / s]. The number of sample points is 27, and the X-axis displacement sample data at node 271142 in the simulation data is extracted.

4. The simulation prediction method based on reduced-order model machine learning according to claim 1, characterized in that: In the reduced-order model, when the SVD method is used for solution, the eigenvalues ​​satisfy the following relationship: In the formula, λ i For Matrix QQ T With Q T The eigenvalues ​​of Q, σ i It is a singular value.

5. The simulation prediction method based on reduced-order model machine learning according to claim 4, characterized in that: In the SVD method, the feature vector is calculated using the following formula: In the formula, φ i For QQ T eigenvectors, φ i Construct the column space of the response matrix as an orthogonal basis.

6. The simulation prediction method based on reduced-order model machine learning according to claim 1, characterized in that: The reduced-order model also includes a modal truncation step, which calculates the data information completeness p using the following formula: In the formula, the p-value represents the completeness of the data information, and the reduced-order data it belongs to can contain the information of the full-order data.

7. The simulation prediction method based on reduced-order model machine learning according to claim 1, characterized in that: The surrogate function of the Kriging machine learning model is: Y(x) = β0 + Z(x) In the formula, β0 is the deterministic value of the global trend model, and Z(x) represents a static random process with a mean of 0 and a variance of σ.

8. The simulation prediction method based on reduced-order model machine learning according to claim 7, characterized in that: In the surrogate function, the covariance of the random variable at different spatial locations is expressed as: cov(Z(x),Z(x′))=σ 2 H(x,x′) In the formula, H(x,x′) is the correlation function, and its expression is: The θ vector is obtained by the maximum likelihood estimation method.

9. The simulation prediction method based on reduced-order model machine learning according to claim 1, characterized in that: In the maximum likelihood estimation method, the likelihood function is: variance estimate σ 2 The calculation formula is: The formula for calculating the global trend value β0 is: In the formula, F = [1, 1, ..., 1] T .

10. The simulation prediction method based on reduced-order model machine learning according to claim 1, characterized in that: The prediction results are evaluated using the decision coefficient R. 2 and the root mean square error (RMSE) index; Among them, R 2 The calculation formula is: The formula for calculating RMSE is: When R 2 When the value is close to 1, the prediction model has high accuracy.

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