Armored vehicle floor-occupant-seat local model equivalent loading modeling method
By improving the kernel principal component analysis and Bayesian optimization methods, the problem of efficient evaluation of armored vehicle crew protection systems under explosive impact was solved, and accurate data dimensionality reduction and loading of floor node groups were achieved, thus improving evaluation efficiency and accuracy.
Patent Information
- Application Number
- CN202510590578.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-08
- Publication Date
- 2026-03-17
- Estimated Expiration
- 2045-05-08
AI Technical Summary
Existing armored vehicle crew protection systems suffer from wasted computational resources and time costs in performance evaluation under blast impact. Traditional loading methods cannot accurately capture the motion anisotropy of multi-degree-of-freedom node groups on the floor, resulting in large response errors and making it difficult to perform efficient iterative optimization.
By employing an improved kernel principal component analysis method and a Bayesian optimization method, and through data dimensionality reduction and loading error quantization, the optimal coordinates of the equivalent principal component node group of the floor node group are determined, thereby achieving equivalent loading of the local finite element model.
It significantly improves the efficiency of occupant protection system performance evaluation, shortens the evaluation cycle, ensures the equivalence of loading accuracy and physical magnitude, and breaks through the engineering adaptability limitations of traditional methods.
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Figure CN120430118B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of armored vehicle protection, and specifically relates to an equivalent loading modeling method for a local model of the floor, crew, and seats of an armored vehicle. Background Technology
[0002] In modern warfare, military armored vehicles primarily face the threat of explosions from under-vehicle devices, such as improvised explosive devices (IEDs), on asymmetric battlefields. Under explosive impact conditions, the optimal design and selection of occupant protection systems often requires multiple rounds of optimization and verification, necessitating repeated armored vehicle explosion simulations or tests. Full-scale vehicle numerical simulation is a crucial method for analyzing the performance of armored vehicle occupant protection systems under explosive impact, offering advantages in cost and efficiency compared to explosion testing. However, it should be noted that numerical simulation efficiency is a significant factor affecting the development cycle of armored vehicle occupant protection system performance under explosive impact. In explosion simulations requiring iterative optimization, the boundary condition excitations experienced by the occupants and their protection systems are essentially the same, leading to a significant waste of computational resources and time. Solving the complete occupant response in a full-scale vehicle model on a typical local server generally takes several days, which is unacceptable for occupant response evaluation problems requiring iterative optimization. Evaluating and optimizing the physiological response of occupants and the performance of occupant protection systems independently of the full-scale vehicle model, with low cost and high efficiency, is a crucial aspect of current armored vehicle occupant protection performance development.
[0003] The floor-occupant-seat local loading model provides a solution for rapidly evaluating the performance of occupant protection systems, replacing full-scale vehicle numerical simulation. By separating the whole vehicle model and the occupant-seat local model, and extracting the floor acceleration coordinates of occupant feet, seat mounting points, etc., from the whole vehicle numerical simulation model, and loading it onto the occupant-seat local model, the evaluation efficiency of occupant protection systems such as protective foot pads and buffer partitions can be significantly improved. However, the rationality and error of loading thin-walled floors in the local model cannot be ignored.
[0004] There are currently three main loading methods for local models: The first is to extract the acceleration of all nodes on the floor, average it, and synthesize the average acceleration as the boundary condition for floor loading in the local model, and then make certain corrections to the acceleration curve based on experimental data. This is the most commonly used loading method, but it ignores the anisotropy of motion of multi-degree-of-freedom particles in a plane, and there is no unified and rigorous correction method for the average acceleration curve, so the resulting response error remains unresolved. The second method is to divide the floor into several relatively small blocks and calculate the average acceleration of each block for loading. This method is essentially an improvement on the first method, but it still suffers from loading error problems caused by the uncertainty of the number of floor blocks and the non-uniqueness of block area. The third method is to use triangular or sine wave loading, and deduce the characteristic parameters of the triangular or sine wave from the occupant response in full-scale vehicle numerical simulation. This method is only suitable for solving specific engineering problems and lacks feasibility in scientific research. Summary of the Invention
[0005] The purpose of this invention is to provide a method for dimensionality reduction and equivalent loading modeling of local finite element model data of floor-occupant-seat, which improves the development efficiency of occupant protection system while ensuring solution accuracy and interpretability.
[0006] The technical solution for achieving the present invention is: an equivalent loading modeling method for a local model of an armored vehicle floor-crew-seat system, comprising:
[0007] S1: Data extraction, i.e., constructing the whole vehicle finite element model, and the acceleration matrix A of the floor node group at the occupant's feet.
[0008] S2: Data dimensionality reduction, which involves using an improved kernel principal component analysis method to reduce the dimensionality of the floor node group acceleration matrix A, thereby obtaining the equivalent principal component acceleration matrix of the floor node group. .
[0009] S3: Coordinate determination, i.e., extracting the floor-occupant-seat local finite element model from the whole vehicle finite element model, and based on this local finite element model, using the time-domain response error quantization-Bayesian optimization joint method to determine the equivalent principal component acceleration matrix of the floor node group. The optimal coordinate vector of the equivalent principal component node group. .
[0010] S4: Load modeling, convert the floor node group into equivalent principal component acceleration matrix The equivalent node group acceleration data in the model is processed according to the optimal equivalent principal component node group coordinate vector. The coordinates in the model are loaded onto the occupant's foot floor in the local finite element model of floor-occupant-seat, completing the equivalent loading modeling.
[0011] S1 includes: constructing a finite element model of the entire vehicle under explosive impact, and extracting the acceleration matrix of the floor node group at the occupant's feet from the finite element model of the entire vehicle. , The form is:
[0012]
[0013] In the formula, The length of the time series. For node dimensions; For time series indexing, ; Indexed by node dimension, ; for The acceleration vector of the node group at time t.
[0014] S2 includes: S21: Principal component analysis dimensionality reduction of the acceleration matrix A of the floor node group and S22: Order of magnitude restoration of the dimensionality reduction result.
[0015] S21: Principal component analysis for dimensionality reduction of the acceleration matrix A of the floor node group includes:
[0016] Kernel principal component analysis (KPCA) was employed, introducing a kernel function. To quantify Correlation between the accelerations of nodal groups at different times:
[0017]
[0018] In the formula, For time series indexes different from i, ; for The row vector of the node group acceleration at time t; The dynamic variable bandwidth of the Gaussian kernel function is calculated as follows:
[0019]
[0020] in The correlation coefficient is calculated as follows:
[0021]
[0022] In the formula, for The Value ; for The Value ;
[0023] Then the kernel matrix contains the correlation between the accelerations of all node groups at different times in A. It can be represented as:
[0024]
[0025] To remove the effects of data offset, If centralized processing is performed, then the centralized kernel matrix... It can be represented as:
[0026]
[0027] in For an idempotent symmetric matrix, the calculation method is as follows:
[0028]
[0029] In the formula, It is an m-order identity matrix; It is an m-dimensional vector of all 1s.
[0030] Solve eigenvalues and eigenvectors :
[0031]
[0032] Obtain the eigenvalue matrix and eigenvector matrix :
[0033]
[0034]
[0035] In the formula, For the first eigenvalues The corresponding feature vector, Sort in descending order of numerical value.
[0036] Calculate the principal component acceleration matrix B of the floor node group:
[0037]
[0038] In the formula for The former The principal component eigenvalue matrix, composed of eigenvalues, is in the form of:
[0039]
[0040] for The former The principal component eigenvector matrix, composed of eigenvectors, is in the form of:
[0041]
[0042] in, The dimensionality reduction order is determined using the Cumulative Variance Contribution Rate (CVCR):
[0043]
[0044] In the formula, The coefficient of determination is usually taken as 0.9.
[0045] In equation (11), B takes the form:
[0046]
[0047] In the formula, for The acceleration vectors of the principal components of the node group at time t. At this point, data dimensionality reduction has been completed, and... Middle node group Each node, reduced to dimensionality Middle principal component node group There are principal component nodes, but The acceleration data of the principal component node group has no actual physical meaning and needs to be restored to its magnitude.
[0048] S22: Dimensionality reduction result order of magnitude restoration includes:
[0049] By introducing a correction factor to perform order-of-magnitude restoration, the equivalent principal component acceleration matrix of the floor node group is solved. :
[0050]
[0051] In the formula, To and Correction matrices of the same order, i.e. for and The Hadamard; This is a correction factor.
[0052] Among them, the correction factor Solve by minimizing the following expression:
[0053]
[0054] at this time, The intermediate principal component node group contains Each equivalent principal component node has practical physical meaning, but middle The coordinates of the equivalent principal component node group need to be further determined.
[0055] S3 includes: S31: quantization of equivalent loading error and S32: determination of coordinates of equivalent principal component node group.
[0056] S31: Equivalent loading error quantification includes:
[0057] Extracting occupant response data from the finite element model of the vehicle. .
[0058] Extract the floor-occupant-seat local finite element model from the whole vehicle finite element model.
[0059] Using the Design of Experiment (DOE) method, for The coordinates of all equivalent principal component nodes in the equivalent principal component node group are combined and sampled to obtain multiple equivalent principal component node group coordinate vectors. .
[0060] The coordinate vector of each equivalent principal component node group Load the data into the local finite element model of the floor-occupant-seat configuration and obtain the data for each occupant. The corresponding local finite element model is loaded with occupant response data. .
[0061] Calculate phase error :calculate and cross-relationships between :
[0062]
[0063] In the formula, To calculate the corresponding Phase shift during time.
[0064] Calculated using the following formula and Phase error between :
[0065]
[0066] Calculate amplitude error Define the distance cost matrix The distance cost element is calculated using the Euclidean distance in the following formula. :
[0067]
[0068] Define distance cost matrix The regular path W on:
[0069]
[0070] In the formula, Let p be the p-th point on the regularized path W. It represents middle and middle Euclidean cost distance between two points .
[0071] calculate and Amplitude error between :
[0072]
[0073] Calculate the comprehensive loading error of the local finite element model :
[0074]
[0075] In the formula, and These are the phase error weighting factor and the amplitude error weighting factor, respectively.
[0076] S32: Determining the coordinates of the equivalent principal component node group includes:
[0077] The coordinate vectors of multiple equivalent principal component nodes are combined. Combination effect principal component node group coordinate vector set , to combine multiple with each Corresponding Combined into a local finite element model loading comprehensive error set F Together they constitute the training dataset. .
[0078] Using the training dataset , build about Gaussian Process (GP) Prior Distribution Approximate Surrogate Model Its form is:
[0079]
[0080] In the formula, for China is different Another equivalent principal component node group coordinate vector; ,for The mean distribution; is the covariance kernel function.
[0081] Determine the approximate surrogate model of the current prior distribution. middle, maximum value Does it exceed 80%? The new equivalent principal component node group coordinate vector is determined by the Expected Improvement (EI) acquisition function. :
[0082]
[0083] The coordinate vector of the new equivalent principal component node group is obtained by solving the following formula. posterior distribution :
[0084]
[0085] In the formula, The prior distribution defined for the Gaussian process is solved by equation (24); For the observation likelihood, it is usually assumed to be Gaussian noise. .
[0086] Further solve for the posterior distribution The predicted mean and predicted covariance ,in .
[0087] In acquiring posterior distribution After obtaining the predicted value, an iterative optimization process is performed, repeating the Bayesian optimization steps described in S32 until... At this time The optimal equivalent principal component node group coordinate vector .
[0088] S4 includes: converting the floor node group into an equivalent principal component acceleration matrix. The equivalent nodal group acceleration data in the middle, according to The coordinates in the model are loaded onto the occupant's foot floor in the local finite element model of floor-occupant-seat, completing the equivalent loading modeling.
[0089] Compared with the prior art, the significant advantages of this invention are:
[0090] (1) The present invention adopts the kernel principal component analysis method that considers dynamic variable bandwidth, which solves the problem of ignoring the anisotropy of the motion of the multi-degree-of-freedom node group of the floor in the existing average method. The nonlinear acceleration correlation of the floor node group can be accurately captured by the dynamic variable bandwidth, and the dimension of the node group can be significantly reduced while retaining the information characteristics of the original node group acceleration matrix.
[0091] (2) This invention innovatively introduces a process to restore the magnitude of the dimensionality reduction result, ensuring that the acceleration data of the node group after dimensionality reduction is strictly equivalent to the original data in terms of physical magnitude and dynamic characteristics.
[0092] (3) This invention proposes a joint method of time-domain response error quantization and Bayesian optimization, which determines the coordinates of the optimal equivalent principal component node group based on objective error assessment.
[0093] (4) The local model equivalent loading modeling method proposed in this invention greatly shortens the evaluation cycle of the occupant protection system performance while ensuring the solution progress, and breaks through the engineering adaptability limitations of traditional average loading and triangular wave loading methods. Attached Figure Description
[0094] Figure 1 shows the overall framework of the local finite element model equivalent loading modeling method.
[0095] Figure 2 is a flowchart of the acceleration matrix dimensionality reduction method.
[0096] Figure 3 is a schematic diagram of the joint method of time-domain response error quantization and Bayesian optimization.
[0097] Figure 4 is a schematic diagram of equivalent loading modeling. Detailed Implementation
[0098] The example will now be described in further detail with reference to the accompanying drawings.
[0099] Please see Figure 1-4 The present invention provides a method for dimensionality reduction and equivalent loading modeling of local finite element model data of armored vehicle floor-crew-seat.
[0100] Please see the appendix Figure 1 The equivalent loading modeling method for the armored vehicle floor-crew-seat local model described in this invention includes:
[0101] S1: Data extraction, i.e., constructing the whole vehicle finite element model, and the acceleration matrix A of the floor node group at the occupant's feet.
[0102] S2: Data dimensionality reduction, which involves using an improved kernel principal component analysis method to reduce the dimensionality of the floor node group acceleration matrix A, thereby obtaining the equivalent principal component acceleration matrix of the floor node group. .
[0103] S3: Coordinate determination, i.e., extracting the floor-occupant-seat local finite element model from the whole vehicle finite element model, and based on this local finite element model, using the time-domain response error quantization-Bayesian optimization joint method to determine the equivalent principal component acceleration matrix of the floor node group. The optimal coordinate vector of the equivalent principal component node group. .
[0104] S4: Load modeling, convert the floor node group into equivalent principal component acceleration matrix The equivalent nodal group acceleration data in the middle, according to The coordinates in the model are loaded onto the occupant's foot floor in the local finite element model of floor-occupant-seat, completing the equivalent loading modeling.
[0105] Please see the appendix Figure 1 S1 includes: constructing a finite element model of the whole vehicle under explosive impact, and extracting the acceleration matrix of the floor node group at the foot of the occupants from the finite element model of the whole vehicle. , The form is:
[0106]
[0107] In the formula, The length of the time series. For node dimensions; For time series indexing, ; Indexed by node dimension, ; for The acceleration vector of the node group at time t.
[0108] Please see the appendix Figure 1 and attached Figure 2 S2 includes: S21: Principal component analysis dimensionality reduction of the acceleration matrix A of the floor node group and S22: Order of magnitude restoration of the dimensionality reduction result.
[0109] S21: Principal component analysis for dimensionality reduction of the acceleration matrix A of the floor node group includes:
[0110] Because the acceleration of the nodal group is affected by the dynamic response of the floor impact, it exhibits a Gaussian-like attenuation characteristic in space. Therefore, kernel principal component analysis (KPCA) is adopted, introducing a Gaussian kernel function. To quantify Correlation between the accelerations of nodal groups at different times:
[0111]
[0112] In the formula, It is also a time series index. ; for The row vector of the node group acceleration at time t; The dynamic variable bandwidth of the Gaussian kernel function is calculated as follows:
[0113]
[0114] in The correlation coefficient is calculated as follows:
[0115]
[0116] In the formula, for The Value ; for The Value ;
[0117] Then the kernel matrix contains the correlation between the accelerations of all node groups at different times in A. It can be represented as:
[0118]
[0119] kernel matrix It is an m-order positive semi-definite symmetric matrix, which contains The similarity between the acceleration vectors of the node groups at different times is calculated from all feature information in the data.
[0120] To avoid the influence of acceleration matrix data shift on the principal component calculation in high-dimensional space, If centralized processing is performed, then the centralized kernel matrix... It can be represented as:
[0121]
[0122] in For an idempotent symmetric matrix, the calculation method is as follows:
[0123]
[0124] In the formula, It is an m-order identity matrix; It is an m-dimensional vector of all 1s; It remains an m-order positive semi-definite symmetric matrix.
[0125] Solve eigenvalues and eigenvectors :
[0126]
[0127] In the formula, Indicates the main direction of data projection. This represents the variance of the data along the main direction. The larger the value, the more information features are retained by the data projection in that direction. Obtain the eigenvalue matrix. and eigenvector matrix :
[0128]
[0129]
[0130] In the formula, For the first eigenvalues The corresponding feature vector, Sort in descending order of numerical value, then corresponding feature vector This is considered the primary direction, and so on.
[0131] Calculate the principal component acceleration matrix B of the floor node group:
[0132]
[0133] In the formula for The former The principal component eigenvalue matrix, composed of eigenvalues, is in the form of:
[0134]
[0135] for The former The principal component eigenvector matrix, composed of eigenvectors, is in the form of:
[0136]
[0137] in, The dimensionality reduction order is determined using the Cumulative Variance Contribution Rate (CVCR):
[0138]
[0139] In the formula, The coefficient of determination is typically set to 0.9. This means that when the cumulative variance contribution exceeds 90%, it is generally considered that... It can replace A in conducting research.
[0140] In equation (11), B takes the form:
[0141]
[0142] In the formula, for The acceleration vectors of the principal components of the node group at time t, and the acceleration matrix B of the principal components of the node group in preserving While providing the main acceleration information, it also has a higher... Lower node dimensionality. At this point, data dimensionality reduction has been completed, resulting in... Middle node group Each node, reduced to dimensionality Middle principal component node group There are principal component nodes, but The acceleration data of the principal component node group has no actual physical meaning and needs to be restored to its magnitude.
[0143] S22: Dimensionality reduction result order of magnitude restoration includes:
[0144] By introducing a correction factor to perform order-of-magnitude restoration, the equivalent principal component acceleration matrix of the floor node group is solved. :
[0145]
[0146] In the formula, To and Correction matrices of the same order, i.e. for and The Hadamard; This is a correction factor.
[0147] Among them, the correction factor Solve by minimizing the following expression:
[0148]
[0149] At this point, we have completed S2: dimensionality reduction of the floor acceleration matrix and determined the acceleration values for each principal component node. The intermediate principal component node group contains Each equivalent principal component node has practical physical meaning, but middle The coordinates of the equivalent principal component node group need to be further determined.
[0150] Please see the appendix Figure 1 and attached Figure 3 S3 includes: S31: quantization of equivalent loading error and S32: determination of coordinates of equivalent principal component node group.
[0151] S31: Equivalent loading error quantification includes:
[0152] Extracting occupant response data from the finite element model of the vehicle. .
[0153] Extract the floor-occupant-seat local finite element model from the whole vehicle finite element model.
[0154] Using the Design of Experiment (DOE) method, for The coordinates of all equivalent principal component nodes in the equivalent principal component node group are combined and sampled to obtain multiple equivalent principal component node group coordinate vectors. .
[0155] The coordinate vector of each equivalent principal component node group Load the data into the local finite element model of the floor-occupant-seat configuration and obtain the data for each occupant. The corresponding local finite element model is loaded with occupant response data. .
[0156] Calculate phase error :calculate and cross-relationships between :
[0157]
[0158] In the formula, To calculate the corresponding Phase shift over time. Cross-correlation coefficient. Capable of characterizing and The temporal phase correlation between them.
[0159] Calculated using the following formula and Phase error between :
[0160]
[0161] Right now When the value is at its maximum, and The correlation between them is the highest, at which point... The largest This is the phase error. .
[0162] Through phase error and After phase calibration, the amplitude error can be accurately quantified. .
[0163] Calculate amplitude error Define the distance cost matrix The distance cost element is calculated using the Euclidean distance in the following formula. :
[0164]
[0165] Define distance cost matrix The regular path W on:
[0166]
[0167] In the formula, Let p be the p-th point on the regularized path W. It represents middle and middle Euclidean cost distance between two points The starting point of the regularized path W is defined as... The destination is It possesses monotonicity and continuity that cannot cross nodes.
[0168] When the total cost on the regularized path is equal to the Euclidean cost distance at each point... When the sum is minimized, the square root of the total cost is considered as and Amplitude error between :
[0169]
[0170] Calculate the comprehensive loading error of the local finite element model :
[0171]
[0172] In the formula, and These are the phase error weighting factor and the amplitude error weighting factor, respectively, and are generally taken as half of the equal weighted average.
[0173] S32: Determining the coordinates of the equivalent principal component node group includes:
[0174] The coordinate vectors of multiple equivalent principal component nodes are combined. Combination effect principal component node group coordinate vector set , to combine multiple with each Corresponding Combined into a local finite element model loading comprehensive error set F Together they constitute the training dataset. .
[0175] Using the training dataset , build about Gaussian Process (GP) Prior Distribution Approximate Surrogate Model Its form is:
[0176]
[0177] In the formula, for China is different Another equivalent principal component node group coordinate vector; ,for The mean distribution of represents the distribution of . The best estimate; The covariance kernel function defines the similarity between data points in a Gaussian process, and is used to construct... The key.
[0178] Determine the approximate surrogate model of the current prior distribution. middle, maximum value Does it exceed 80%? The new equivalent principal component node group coordinate vector is determined by the Expected Improvement (EI) acquisition function. :
[0179]
[0180] Right now Should make The value of is the largest.
[0181] The coordinate vector of the new equivalent principal component node group is obtained by solving the following formula. posterior distribution :
[0182]
[0183] In the formula, The prior distribution defined for the Gaussian process is solved by equation (24); For the observation likelihood, it is usually assumed to be Gaussian noise. .
[0184] Further solve for the posterior distribution The predicted mean and predicted covariance :
[0185]
[0186]
[0187] In the formula, for In matrix form, where .
[0188] In acquiring posterior distribution After obtaining the predicted value, an iterative optimization process is performed, repeating the Bayesian optimization steps described in S32 until... At this time The optimal equivalent principal component node group coordinate vector .
[0189] Please see the appendix Figure 4 S4 includes: converting the floor node group into equivalent principal component acceleration matrices. The equivalent nodal group acceleration data in the middle, according to The coordinates in the model are loaded onto the occupant's foot floor in the local finite element model of floor-occupant-seat, completing the equivalent loading modeling.
Claims
1. A method of modeling equivalent loading of an armored vehicle floor-occupant-seat local model, characterized in that, The method comprises the following steps: S1: data extraction: constructing a whole vehicle finite element model under explosion impact, and extracting a passenger foot floor node group acceleration matrix A; S2: data dimension reduction: using the improved kernel principal component analysis method, the data dimension of the floor node group acceleration matrix A is reduced to obtain the floor node group principal component acceleration matrix B, and the order of the floor node group principal component acceleration matrix B is restored to obtain the floor node group equivalent principal component acceleration matrix ; S3: Determine the coordinates: extract the floor-occupant-seat local finite element model from the whole vehicle finite element model, based on the local finite element model, use the time domain response error quantification-Bayes optimization joint method to determine the equivalent principal component acceleration matrix of the floor node group The equivalent principal component node group coordinates vector of the optimal equivalent principal component node group ; S4: Load modeling: load the equivalent node group acceleration data in the equivalent principal component node group acceleration matrix into the coordinates in the optimal equivalent principal component node group coordinate vector , and load into the passenger foot floor in the floor-passenger-seat local finite element model to complete the equivalent load modeling; Step S3 is specifically: S31: equivalent loading error quantification: Extracting vehicle occupant response data from a full vehicle finite element model ; extracting a floor-passenger-seat local finite element model from the whole vehicle finite element model; Using a design of experiment (DOE) method, an equivalent principal component node group acceleration matrix of a floor node group is obtained Combining the coordinates of all equivalent principal component nodes in a medium equivalent principal component node group to obtain a plurality of equivalent principal component node group coordinate vectors ; each equivalent principal component node group coordinate vector loaded into the floor-occupant-seat local finite element model, obtaining the corresponding local finite element model loading occupant response data of each equivalent principal component node group ; Computing phase error : Computing and cross-correlation coefficient between : In the formula, to calculate the phase shift corresponding at time t; The phase error between and is calculated by the formula : Computing magnitude error : Defining distance cost matrix , the Euclidean distance in the following equation is used to compute the distance cost element : Defining a distance cost matrix W: a warping path on wherein is the p-th point on the regularized path W, represents in and in the Euclidean cost distance between two points ; Compute the amplitude error between and : Computing a local finite element model loading composite error : wherein and are the phase and amplitude error weight factors, respectively. S32: determining equivalent principal component node group coordinates: The coordinate vectors of multiple equivalent principal component nodes are combined. Combination effect principal component node group coordinate vector set , to combine multiple with each Corresponding Combined into a local finite element model loading comprehensive error set F Together they constitute the training dataset ; Using a training data set , a Gaussian process GP prior distribution approximation proxy model is constructed about the function in the form: wherein is different from another equivalent principal component node group coordinate vector; is the mean distribution; is the covariance kernel function; determining a current prior distribution approximation surrogate model in, maximum value whether it exceeds 80%, if determining a new equivalent principal component node group coordinate vector by improving the ei acquisition function by expectation : The new equivalent principal component node group coordinate vector is solved by the following formula posterior distribution of : where The prior distribution defined for the Gaussian process is solved by equation (24); is the observation likelihood, typically assumed to be Gaussian noise ; solving the posterior distribution the predictive mean and the predictive covariance where ; After obtaining the predictive values of the posterior distribution , an iterative optimization procedure is performed, repeating the Bayesian optimization step until , at which point is the optimal equivalent principal component node group coordinate vector .
2. The method of claim 1, wherein, The floor node group acceleration matrix in step S1 is of the form: wherein is the time series length, is the node dimension; is the time series index, ; is the node dimension index, ; is the node group acceleration vector at time instant 3. The method of claim 2, wherein, In step S2, "adopting an improved kernel principal component analysis method to perform data dimension reduction on the floor node group acceleration matrix A to obtain a floor node group principal component acceleration matrix B" is specifically: The kernel principal component analysis method KPCA is adopted, and a kernel function is introduced Quantifying the floor node group acceleration matrix Correlation between node group accelerations at different times wherein is a time series index different from i, ; is the acceleration vector of the node group at time instant t; is the acceleration vector of the node group at time instant t; is the dynamically variable bandwidth of the Gaussian kernel function, calculated as wherein is the correlation coefficient, calculated as: wherein is the th value is the th value A core matrix containing the correlation between all group accelerations of all nodes in the floor node group acceleration matrix A at different time instants is represented as: On the core matrix The centering process is performed to obtain the centered core matrix : wherein is a positive definite matrix, and the calculation method is as follows: wherein is an m x m identity matrix; is an m-dimensional all-one vector; Solving eigenvalues and eigenvectors of a centered kernel matrix : obtaining a matrix of eigenvalues and a matrix of eigenvectors : In the formula, is the first characteristic value corresponding eigenvector, arranged in descending order of numerical size; calculating the floor node group principal component acceleration matrix B: wherein is an eigenvalue matrix of the first principal eigenvalues consisting of the first p eigenvalues of the matrix is a matrix of principal component eigenvectors consisting of the first principal component eigenvectors of the feature vector matrix, in the form wherein is the number of dimensions, determined by the cumulative variance contribution rate: In the formula, R is the correlation coefficient. In formula (11), the floor node group principal component acceleration matrix B is in the form of: wherein is the principal component acceleration vector of the node group at the instant 4. The method of claim 3, wherein, "magnitude reduction of the floor node group principal component acceleration matrix B to obtain the floor node group equivalent principal component acceleration matrix B" in step S2 "specifically refers to: The magnitude reduction processing is introduced by using a correction factor to solve the equivalent principal component acceleration matrix of the floor node group : wherein is the acceleration matrix of the floor node group principal components is the acceleration matrix of the floor node group principal components is the acceleration matrix of the floor node group principal components and is the Hadamard product of is the correction factor where the correction factor Solve by minimizing the following: 。
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