Defect-based test bench performance attenuation modeling method

Abstract

The invention provides a test bench performance attenuation modeling method based on defects, and belongs to the technical field of aero-engines, and the method comprises the steps: obtaining the initial defect information of a test bench according to the structural characteristics of the test bench; defects needing to be considered in the modeling process are determined based on the initial defect information; the method comprises the following steps: constructing a defect-containing test bed structure finite element model, respectively carrying out static finite element analysis and dynamic finite element analysis to obtain a static finite element displacement field and a dynamic finite element displacement field, and respectively constructing a static order reduction model and a dynamic order reduction model; based on the static order reduction model and the dynamic order reduction model, obtaining a stress tensor of the test bench; and based on the stress tensor, establishing an incidence relation between the defect and the key performance index, and obtaining a performance attenuation model of the test bench. The method can achieve the purposes of rapid damage prediction and failure early warning in the operation process of the rack, and remarkably improves the efficiency and predictability of rack performance evaluation.

Description

Technical Field

[0001] This application relates to the field of aero-engine technology, and in particular to a defect-based test bench performance degradation modeling method. Background Technology

[0002] With the increasing demand for aerospace equipment testing, test benches play a crucial role in the performance verification of components such as engines, electronic equipment, and structural parts. However, long-term operation in extreme environments such as high altitude, low temperature, and low pressure can easily lead to defects such as material aging, weld fatigue, loose connections, and corrosion, resulting in a gradual degradation of structural strength, stiffness, and stability.

[0003] Currently, most existing test bench performance evaluation methods rely on periodic testing and manual experience, lacking quantitative modeling tools for structural defects. This makes it difficult to predict performance degradation trends, posing safety risks and wasting resources. Therefore, there is an urgent need for a method that can establish a test bench performance degradation model based on defect type and evolution characteristics to support predictive maintenance and reliability assessment. Summary of the Invention

[0004] In view of this, embodiments of this application provide a defect-based test bench performance degradation modeling method, which can realize quantitative analysis of the impact of different types of structural defects on test bench performance, establish a defect-driven reduced-order numerical model, and then quickly predict the remaining life of the structure and the degradation trend of key performance indicators.

[0005] This application provides a defect-based method for modeling the performance degradation of a test bench, the method comprising: Based on the structural characteristics of the test bench, non-destructive testing technology was used to obtain the initial defect information of the test bench; Determine the defects to be considered during the modeling process based on the initial defect information; A finite element model of the test bench structure with defects was constructed. Static finite element analysis and dynamic finite element analysis were performed based on the finite element model of the test bench structure to obtain the static finite element displacement field and the dynamic finite element displacement field respectively. A static reduced-order model is constructed based on a static finite element displacement field, and a dynamic reduced-order model is constructed based on a dynamic finite element displacement field. The stress tensor of the test bench is obtained based on the static or dynamic order reduction model. Based on the stress tensor, the correlation between defects and key performance indicators is established to obtain a performance degradation model of the test bench.

[0006] According to a specific implementation of an embodiment of this application, the step of determining the defects to be considered during the modeling process based on initial defect information includes: Data such as defect type, defect location, defect size, and defect shape features are extracted from the initial defect information, and the defects that need to be considered in the modeling process are determined based on the extracted data.

[0007] According to a specific implementation of an embodiment of this application, the construction of a finite element model of a test bench structure containing defects includes: Based on the 3D digital model and design drawings, the 3D geometric model of the test bench containing defects is inspected and repaired. The inspected and repaired 3D geometric model is meshed and discretized into finite element methods. Based on the finite element method, material properties are defined, boundary conditions are set, and loads are applied to obtain a finite element model of the test bench structure containing defects.

[0008] According to a specific implementation of an embodiment of this application, the step of constructing a static reduced-order model based on a static finite element displacement field includes: Singular value decomposition is performed on the static finite element displacement field to obtain the first singular value matrix and the first singular vector matrix. Based on the first singular value matrix and the first singular vector matrix, the basis functions for constructing the low-dimensional space are obtained; Based on the basis functions, the static finite element displacement field is projected onto the POD space to obtain a static reduced-order model.

[0009] According to a specific implementation of an embodiment of this application, the expression for the singular value decomposition is: , Among them, U km The static finite element displacement field is obtained by performing static finite element analysis on the finite element model of the test bench structure containing the kth defect under the mth load. W1 is the first left singular vector matrix, V1 is the first right singular vector matrix, and Σ is the first singular value matrix. The first singular vector matrix includes the first left singular vector matrix and the first right singular vector matrix. The basis functions are constructed by extracting the first r singular values ​​of the first singular value matrix Σ and the first r columns of the first left singular vector matrix W1. The expression for the static order reduction model is: , Among them, a b For projection coefficients, This is the static displacement field after order reduction. Let b be a basis function, where b = 1, 2, ..., r.

[0010] According to a specific implementation of an embodiment of this application, the construction of a dynamically reduced-order model based on a dynamic finite element displacement field includes: Construct dynamic equations and solve them using the finite element method to obtain the dynamic finite element displacement field; The dynamic finite element displacement field is discretized over time to obtain solutions at multiple time points; Construct leading snapshot matrix and lagging snapshot matrix based on solutions at multiple time points; The step matrix is ​​calculated based on the leading snapshot matrix and the lagging snapshot matrix; Singular value decomposition is performed on the hysteresis snapshot matrix to obtain the second singular value matrix and the second singular vector matrix. Based on the second singular value matrix, the second singular vector matrix, and the leading snapshot matrix, an approximate matrix of the step matrix is ​​obtained; The approximate matrix is ​​reduced in order to obtain a reduced-order matrix. Based on the reduced-order matrix, construct the basis matrix, and then construct the dynamic reduced-order model based on the basis matrix.

[0011] According to a specific implementation of this application, the expression of the dynamic equation is: , Where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, t is time, and F(t) is the dynamic load. The dynamic finite element displacement field is calculated for the finite element model of the test bench structure containing the k-th defect under the i-th load. The expression for the time-discrete dynamic finite element displacement field is: , Among them, u n This represents the solution at time n.

[0012] According to a specific implementation of an embodiment of this application, the formula for calculating the step matrix is ​​as follows: U + =AU - , Where A is the step matrix, U + For the ahead snapshot matrix, U + =[u2,...,u l ], U - U is the hysteresis snapshot matrix. - =[u1,...,u l-1 ], u l Let u represent the solution at time l. l-1 Let l represent the solution at time l-1. <n; The formula for calculating the singular value decomposition is as follows: U - ≈W2ΩV2 * , Where W2 is the second left singular vector matrix, Ω is the second singular value matrix, V2 is the second right singular vector matrix, and the superscript * indicates complex conjugate. The second singular vector matrix includes the second left singular vector matrix and the second right singular vector matrix. The formula for calculating the approximate matrix is: , in, It is an approximate matrix; The formula for calculating the reduced-order matrix is: , , in, It is a reduced-order matrix.

[0013] According to a specific implementation of an embodiment of this application, the step of constructing a basis matrix based on the reduced-order matrix and constructing a dynamic reduced-order model based on the basis matrix includes: Calculate the eigenvalues ​​and eigenvectors of the reduced-order matrix to obtain the eigenvalue matrix and eigenvector matrix. The calculation formula is as follows: , Where X is the eigenvector matrix. It is the eigenvalue matrix; Based on the eigenvector matrix, the leading snapshot matrix, the second right singular vector matrix, and the second singular value matrix, the basis matrix is ​​obtained. The formula for calculating the basis matrix is: , in, The basis matrix; A dynamic order reduction model is constructed based on the basis matrix. The expression for the dynamic order reduction model is as follows: , in, This represents the reduced-order dynamic displacement field, where Δt is the time interval. for The Moore-Penrose pseudo-inverse matrix, with u0 as the initial value.

[0014] According to a specific implementation of an embodiment of this application, the expression for the stress tensor is: , , , Where σ is the stress tensor, D is the elasticity matrix, and ε is the small strain tensor. is the gradient operator, u is the static displacement field after order reduction in the static order reduction model or the dynamic displacement field after order reduction in the dynamic order reduction model, E is the Young's modulus of the material, and v is Poisson's ratio.

[0015] Beneficial effects: The defect-based test bench performance degradation modeling method in this application involves constructing a finite element model of a test bench structure containing defects, and performing dynamic and static finite element analyses on the model to construct dynamic and static reduced-order models. Based on these models, a test bench performance degradation model is built. This model enables rapid damage prediction and failure early warning during test bench operation, significantly improving the efficiency and predictability of test bench performance evaluation. Furthermore, this modeling method can integrate multi-source data and dynamically correct the degradation model, possessing modeling capabilities oriented towards defect types and evolution characteristics, providing decision support for intelligent maintenance of test equipment. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 A flowchart of a defect-based test bench performance degradation modeling method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a test bench defect according to an embodiment of the present invention; Detailed Implementation The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0018] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0020] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0021] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0022] This application provides a defect-based method for modeling the performance degradation of test benches, which will be described below with reference to... Figures 1 to 2 Provide a detailed description.

[0023] In one embodiment, refer to Figure 1 and Figure 2 A defect-based test bench performance degradation modeling method is provided, the method comprising: Step S101: Based on the structural characteristics of the test bench, use non-destructive testing technology to obtain the initial defect information of the test bench; Step S102: Determine the defects to be considered in the modeling process based on the initial defect information; Step S103: Construct a finite element model of the test bench structure containing defects, and perform static finite element analysis and dynamic finite element analysis based on the finite element model of the test bench structure to obtain the static finite element displacement field and the dynamic finite element displacement field respectively. Step S104: Construct a static reduced-order model based on the static finite element displacement field, and construct a dynamic reduced-order model based on the dynamic finite element displacement field; Step S105: Obtain the stress tensor of the test bench based on the static or dynamic order reduction model. Step S106: Based on the stress tensor, establish the correlation between defects and key performance indicators to obtain the test bench performance degradation model.

[0024] Furthermore, the determination of defects to be considered during the modeling process based on initial defect information includes: Data such as defect type, defect location, defect size, and defect shape features are extracted from the initial defect information, and the defects that need to be considered in the modeling process are determined based on the extracted data.

[0025] In practice, based on the structural characteristics of the test bench, non-destructive testing techniques such as ultrasonic, infrared, or 3D scanning are used to acquire initial defect information, including defect type (e.g., cracks, corrosion, loosening), location, size, and shape. Image processing and signal processing algorithms (e.g., edge detection, wavelet transform, morphological operations) are used to extract key geometric parameters of the defects, including defect type (cracks, corrosion, loosening, delamination, etc.), defect location (3D coordinates relative to the structural coordinate system), size information (length, width, depth), and shape features (crack opening degree, sharpness, corrosion spot morphology factor, etc.). Simultaneously, combined with collected recent fault and maintenance records of the test bench system, the frequency of occurrence of the above defects is categorized and statistically analyzed to establish a defect priority list, identifying multiple defects that need to be considered in the modeling.

[0026] In one embodiment, before constructing the finite element model of the test bench structure, it is also necessary to determine the test bench and load conditions, including: Static load: Simulated load-bearing or sealing test, typical load level is 20kN-100kN; Dynamic load: periodic vibration and impact loading, frequency range 1Hz-50Hz, amplitude range 0.5mm - 5mm; Environmental coupling loads: temperature range, atmospheric pressure conditions.

[0027] Furthermore, the construction of the finite element model of the test bench structure containing defects includes: Based on the 3D digital model and design drawings, the 3D geometric model of the test bench containing defects is inspected and repaired. The inspected and repaired 3D geometric model is meshed and discretized into finite element methods. Based on the finite element method, material properties are defined, boundary conditions are set, and loads are applied to obtain a finite element model of the test bench structure containing defects.

[0028] In practice, during the construction of the finite element model of the test bench structure, the finite element model of the bench structure conforms to the actual test task, including typical welded frames, hinged supports, load-bearing beams, ducts, and other components. The following steps are also included: Geometric model preparation: Based on the 3D digital model and design drawings, inspect and repair the 3D geometric model (such as repairing bad surfaces, gaps, singularities, etc. in the 3D model). Perform appropriate geometric simplification according to the stress characteristics of the test bench (removing small holes, rounding corners, merging fragmented geometric surfaces, etc.). Create the mesh for the test bench: Discretize the prepared geometric model into finite element elements (such as tetrahedral, hexahedral, shell elements, etc.) to ensure that the size and quality of the mesh meet the analysis requirements; Model assembly: If it is necessary to assemble different parts of the test bench using appropriate connection methods (bolts, connection units, binding, multi-point constraints, etc.); Material property definition: Input the material's elastic modulus, Poisson's ratio, density, coefficient of thermal expansion, etc. Boundary condition settings: Define the fixed supports and constraints of the model; Load application: Apply static or dynamic loads according to actual working conditions, including gravity, engine thrust, vibration excitation, temperature, etc. By setting appropriate solution parameters (analysis type, solver options, convergence criteria, etc.) and running static and dynamic finite element solution software, the displacement field on the test bench can be obtained.

[0029] In one embodiment, a rapid computational model (static order-reduced model and dynamic order-reduced model) is constructed based on the calculation results of the finite element solution software for real-time rapid calculation. The construction of the static order-reduced model based on the static finite element displacement field includes: Singular value decomposition is performed on the static finite element displacement field to obtain the first singular value matrix and the first singular vector matrix. Based on the first singular value matrix and the first singular vector matrix, the basis functions for constructing the low-dimensional space are obtained; Based on the basis functions, the static finite element displacement field is projected onto the POD (Proper Orthogonal Decomposition) space to obtain a static reduced-order model.

[0030] Furthermore, the expression for the singular value decomposition is: , Among them, U km To obtain the static finite element displacement field for a finite element model of a test bench structure containing the k-th defect under the m-th load, in specific implementation, multiple static finite element displacement fields under different loads (various loads experienced by the test bench during the test) can be obtained for each defect. U kmIt is represented as an n x m real matrix, where W1 is the first left singular vector matrix, W1 is an m-order unitary matrix, V1 is the first right singular vector matrix, V1 is an n-order unitary matrix, Σ is the first singular value matrix, Σ is an m x n real matrix, and the first singular vector matrix includes the first left singular vector matrix and the first right singular vector matrix. The basis functions are constructed by extracting the first r singular values ​​(the first r principal elements of the first singular value matrix Σ) and the first r columns of the first left singular vector matrix W1; The expression for the static order reduction model is: , Among them, a b These are the projection coefficients, calculated using Newton's method. This is the static displacement field after order reduction. Let b be a basis function, where b = 1, 2, ..., r.

[0031] In one embodiment, the construction of a dynamically reduced-order model based on a dynamic finite element displacement field includes: Construct dynamic equations and solve them using the finite element method to obtain the dynamic finite element displacement field; The dynamic finite element displacement field is discretized over time to obtain solutions at multiple time points; Construct leading snapshot matrix and lagging snapshot matrix based on solutions at multiple time points; The step matrix is ​​calculated based on the leading snapshot matrix and the lagging snapshot matrix; Singular value decomposition is performed on the hysteresis snapshot matrix to obtain the second singular value matrix and the second singular vector matrix. Based on the second singular value matrix, the second singular vector matrix, and the leading snapshot matrix, an approximate matrix of the step matrix is ​​obtained; The approximate matrix is ​​reduced in order to obtain a reduced-order matrix. Based on the reduced-order matrix, construct the basis matrix, and then construct the dynamic reduced-order model based on the basis matrix.

[0032] Specifically, the expression for the dynamic equation is: , Where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, t is time, and F(t) is the dynamic load. The dynamic finite element displacement field is calculated for the finite element model of the test bench structure containing the k-th defect under the i-th load. The expression for the time-discrete dynamic finite element displacement field is: , Among them, u nLet n represent the solution at time n, where n is time nΔt and Δt is the time interval.

[0033] Furthermore, the formula for calculating the step matrix is ​​as follows: U + =AU - , Where A is the step matrix, U + For the ahead snapshot matrix, U + =[u2,...,u l ], U - U is the hysteresis snapshot matrix. - =[u1,...,u l-1 ], u l Let u represent the solution at time l. l-1 Let l represent the solution at time l-1. <n; The formula for calculating the singular value decomposition is as follows: U - ≈W2ΩV2 * , Where W2 is the second left singular vector matrix, W2 is an n-order unitary matrix, Ω is the second singular value matrix, V2 is the second right singular vector matrix, V2 is an r-order unitary matrix, and the superscript * indicates complex conjugate. The second singular vector matrix includes the second left singular vector matrix and the second right singular vector matrix. The hysteresis snapshot matrix U is calculated using singular value decomposition. - The pseudo-inverse matrix is ​​obtained, and then the approximate matrix of the step matrix A is obtained. The formula for calculating the approximate matrix is: , in, It is an approximate matrix; The formula for calculating the reduced-order matrix is: , , in, It is a reduced-order matrix.

[0034] Furthermore, the construction of a basis matrix based on the reduced-order matrix, and the construction of a dynamic reduced-order model based on the basis matrix, includes: Calculate the eigenvalues ​​and eigenvectors of the reduced-order matrix to obtain the eigenvalue matrix and eigenvector matrix. The calculation formula is as follows: , Where X is the eigenvector matrix. It is the eigenvalue matrix; Based on the eigenvector matrix, the leading snapshot matrix, the second right singular vector matrix, and the second singular value matrix, the basis matrix is ​​obtained. The formula for calculating the basis matrix is: , in, The basis matrix; A dynamic order reduction model is constructed based on the basis matrix. The expression for the dynamic order reduction model is as follows: , in, This represents the reduced-order dynamic displacement field, where Δt is the time interval. for The Moore-Penrose pseudo-inverse matrix, with u0 as the initial value.

[0035] The static and dynamic reduced-order models obtained through the above process can be used to quickly calculate the static and dynamic displacement responses of the test bench under the condition of k types of defects.

[0036] In one embodiment, stress field calculation and performance degradation assessment of the test bench are performed. Based on the static and dynamic displacement calculation results, the small strain tensor is calculated by differentiation. The expression for the small strain tensor is: , For linear materials, the stress tensor can be calculated using the following relationship: , , Where σ is the stress tensor, D is the elasticity matrix, and ε is the small strain tensor. is the gradient operator, u is the static displacement field after order reduction in the static order reduction model or the dynamic displacement field after order reduction in the dynamic order reduction model, E is the Young's modulus of the material, and v is Poisson's ratio.

[0037] After stress calculations are completed, the performance degradation of the test bench is evaluated using static strength and fatigue strength criteria. A correlation is established between defects and key performance indicators (maximum load capacity, stiffness, natural frequencies, etc.) to obtain a complete performance degradation model for the test bench. Establishing this correlation involves calculating the stress response, stiffness changes, and modal frequency shifts under different defect parameters (such as crack length). This rapidly establishes a quantitative relationship between defect parameters and performance indicators (maximum load capacity, equivalent stiffness, and the first three natural frequencies), thereby achieving rapid damage prediction and failure early warning during test bench operation.

[0038] The embodiments provided by this invention involve constructing a finite element model of a test bench structure containing defects, and performing dynamic and static finite element analyses on the model to construct dynamic and static reduced-order models. Based on these models, a test bench performance degradation model is constructed. This model enables rapid damage prediction and failure early warning during test bench operation, significantly improving the efficiency and predictability of test bench performance evaluation. Furthermore, this modeling method can integrate multi-source data and dynamically correct the degradation model, possessing modeling capabilities oriented towards defect types and evolution characteristics, thus providing decision support for the intelligent maintenance of test equipment.

[0039] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A defect-based test bench performance degradation modeling method, characterized in that, The method includes: Based on the structural characteristics of the test bench, non-destructive testing technology was used to obtain the initial defect information of the test bench; Determine the defects to be considered during the modeling process based on the initial defect information; A finite element model of the test bench structure with defects was constructed. Static finite element analysis and dynamic finite element analysis were performed based on the finite element model of the test bench structure to obtain the static finite element displacement field and the dynamic finite element displacement field respectively. A static reduced-order model is constructed based on a static finite element displacement field, and a dynamic reduced-order model is constructed based on a dynamic finite element displacement field. The stress tensor of the test bench is obtained based on the static and dynamic order reduction models. Based on the stress tensor, the correlation between defects and key performance indicators is established to obtain a performance degradation model of the test bench.

2. The defect-based test bench performance degradation modeling method according to claim 1, characterized in that, The determination of defects to be considered in the modeling process based on initial defect information includes: Data such as defect type, defect location, defect size, and defect shape features are extracted from the initial defect information, and the defects that need to be considered in the modeling process are determined based on the extracted data.

3. The defect-based test bench performance degradation modeling method according to claim 1, characterized in that, The construction of the finite element model of the test bench structure containing defects includes: Based on the 3D digital model and design drawings, the 3D geometric model of the test bench containing defects is inspected and simplified; The inspected and simplified 3D geometric model is meshed and discretized into finite element model; Based on the finite element method, material properties are defined, boundary conditions are set, and loads are applied to obtain a finite element model of the test bench structure containing defects.

4. The defect-based test bench performance degradation modeling method according to claim 1, characterized in that, The static order reduction model constructed based on the static finite element displacement field includes: Singular value decomposition is performed on the static finite element displacement field to obtain the first singular value matrix and the first singular vector matrix. Based on the first singular value matrix and the first singular vector matrix, the basis functions for constructing the low-dimensional space are obtained; Based on the basis functions, the static finite element displacement field is projected onto the POD space to obtain a static reduced-order model.

5. The defect-based test bench performance degradation modeling method according to claim 4, characterized in that, The expression for the singular value decomposition is: ， Among them, U km The static finite element displacement field is obtained by performing static finite element analysis on the finite element model of the test bench structure containing the kth defect under the mth load. W1 is the first left singular vector matrix, V1 is the first right singular vector matrix, and Σ is the first singular value matrix. The first singular vector matrix includes the first left singular vector matrix and the first right singular vector matrix. The basis functions are constructed by extracting the first r singular values ​​of the first singular value matrix Σ and the first r columns of the first left singular vector matrix W1. The expression for the static order reduction model is: ， Among them, a b For projection coefficients, This is the static displacement field after order reduction. Let b be a basis function, where b = 1, 2, ..., r.

6. The defect-based test bench performance degradation modeling method according to claim 1, characterized in that, The construction of the dynamic order reduction model based on the dynamic finite element displacement field includes: Construct dynamic equations and solve them using the finite element method to obtain the dynamic finite element displacement field; The dynamic finite element displacement field is discretized over time to obtain solutions at multiple time points; Construct leading snapshot matrix and lagging snapshot matrix based on solutions at multiple time points; The step matrix is ​​calculated based on the leading snapshot matrix and the lagging snapshot matrix; Singular value decomposition is performed on the hysteresis snapshot matrix to obtain the second singular value matrix and the second singular vector matrix. Based on the second singular value matrix, the second singular vector matrix, and the leading snapshot matrix, an approximate matrix of the step matrix is ​​obtained; The approximate matrix is ​​reduced in order to obtain a reduced-order matrix. Based on the reduced-order matrix, construct the basis matrix, and then construct the dynamic reduced-order model based on the basis matrix.

7. The defect-based test bench performance degradation modeling method according to claim 6, characterized in that, The expression for the dynamic equation is: ， Where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, t is time, and F(t) is the dynamic load. The dynamic finite element displacement field is calculated for the finite element model of the test bench structure containing the k-th defect under the i-th load. The expression for the time-discrete dynamic finite element displacement field is: ， Among them, u n This represents the solution at time n.

8. The defect-based test bench performance degradation modeling method according to claim 7, characterized in that, The formula for calculating the step matrix is: IN + =AU - , Where A is the step matrix, U + For the ahead snapshot matrix, U + =[u2,...,u l ], U - U is the hysteresis snapshot matrix. - =[u1,...,u l-1 ], u l Let u represent the solution at time l. l-1 Let l represent the solution at time l-1. <n; The formula for calculating the singular value decomposition is as follows: IN - ≈W2ΩV2 * , Where W2 is the second left singular vector matrix, Ω is the second singular value matrix, V2 is the second right singular vector matrix, and the superscript * indicates complex conjugate. The second singular vector matrix includes the second left singular vector matrix and the second right singular vector matrix. The formula for calculating the approximate matrix is: ， in, It is an approximate matrix; The formula for calculating the reduced-order matrix is: ， ， in, It is a reduced-order matrix.

9. The defect-based test bench performance degradation modeling method according to claim 8, characterized in that, The construction of a basis matrix based on the reduced-order matrix, and the construction of a dynamic reduced-order model based on the basis matrix, include: Calculate the eigenvalues ​​and eigenvectors of the reduced-order matrix to obtain the eigenvalue matrix and eigenvector matrix. The calculation formula is as follows: ， Where X is the eigenvector matrix. It is the eigenvalue matrix; Based on the eigenvector matrix, the leading snapshot matrix, the second right singular vector matrix, and the second singular value matrix, the basis matrix is ​​obtained. The formula for calculating the basis matrix is: ， in, The basis matrix; A dynamic order reduction model is constructed based on the basis matrix. The expression for the dynamic order reduction model is as follows: ， in, This represents the reduced-order dynamic displacement field, where Δt is the time interval. for The Moore-Penrose pseudo-inverse matrix, with u0 as the initial value.

10. The defect-based test bench performance degradation modeling method according to claim 1, characterized in that, The expression for the stress tensor is: ， ， ， Where σ is the stress tensor, D is the elasticity matrix, and ε is the small strain tensor. is the gradient operator, u is the static displacement field after order reduction in the static order reduction model or the dynamic displacement field after order reduction in the dynamic order reduction model, E is the Young's modulus of the material, and v is Poisson's ratio.

Images