Modal recognition method based on unsupervised optimization covariance random subspace method

Abstract

The invention discloses a modal recognition method based on an unsupervised optimization covariance random subspace method. The modal recognition method comprises the following steps: arranging an acceleration sensor on a to-be-detected structure to obtain a structural dynamic response; a covariance matrix # imgabs0 # is calculated, and a Toeplitz matrix is constructed based on the # imgabs1 #; an expanded observable matrix # imgabs2 # and an expanded controllable matrix # imgabs3 # are calculated; defining the range of the row block number i and the model order N of the Toeplitz matrix; analyzing the sensitivity of the row block number i of the Toeplitz matrix and the model order N based on a parameter optimization index # imgabs4 #; the singular entropy increment of the Toeplitz matrix # imgabs5 # is calculated; the singular entropy increment curvature of a Toeplitz matrix # imgabs6 # is calculated, and a critical model order # imgabs7 # is determined; calculating a cumulative parameter optimization index # imgabs10 # value from a minimum model order # imgabs8 # to a critical model order # imgabs9 # under the condition of different row block numbers i of the Toeplitz matrix; selecting a parameter combination # imgabs11 # corresponding to the minimum parameter as an optimal parameter; identifying a system matrix and determining modal parameters, and drawing an original stability diagram; and cleaning false modals in the original stability graph based on a hard index criterion. A corresponding system is also disclosed.

Description

Technical Field

[0001] The present invention relates to the technical field of structural dynamics and operational modal analysis, and particularly relates to a modal identification method based on an unsupervised optimized covariance stochastic subspace method, which is an unsupervised algorithm for parameter optimization in the covariance-driven stochastic subspace identification (SSI-Cov) method, and is used to improve the accuracy and robustness of modal parameter identification, thereby providing a scientific basis for structural health monitoring. Background Art

[0002] In the field of structural health monitoring and condition assessment, accurately identifying structural modal parameters is crucial for ensuring the safe operation of infrastructure; and the covariance stochastic subspace method (SSI-Cov), as a parametric system identification method, has been widely applied in practical engineering due to its superior robustness and efficiency. Its accuracy mainly depends on two user-defined parameters, namely the model order N and the number of row blocks i of the Toeplitz matrix (or Hankel matrix). On the one hand, the model order should theoretically be equal to the number of non-zero singular values of the Toeplitz matrix. However, in practical engineering, due to the presence of noise, it is difficult to determine the number of non-zero singular values. Therefore, a model order within a certain range and overestimated is usually selected and substituted into SSI-Cov to identify the system, and then the calculation results are plotted as a stability diagram with frequency as the abscissa and model order as the ordinate. Among them, a stable vertical polar axis formed at a certain frequency after calculating multiple model orders is identified as a certain physical mode of the structure, and vice versa is a false mode. However, too high a model order will not only increase the computational amount, but also lead to a higher probability of false modes; too low a model order may result in modal omission or taking the linear combination of modes as a single identified mode, thereby introducing identification bias. On the other hand, the size of the number of row blocks i of the Toeplitz matrix will not only affect the calculation speed, but also affect the accuracy of modal identification. Especially for the damping ratio, its relatively large uncertainty level is usually of the same order of magnitude as the size of its estimated value, thus affecting the reliability of the identification result. Therefore, the above input parameters seriously affect the accuracy and reliability of the SSI-Cov method in identifying modes, and are crucial for applications such as the state or damage assessment and health monitoring of damage-sensitive indicators based on modal parameter changes or derivatives.

[0003] In recent years, structural operational modal analysis based on the Stochastic Subspace Identification (SSI) method has been widely applied. For example, the invention patent application CN118673348A discloses a method and system for identifying structural modal parameters based on intelligent clustering of modal features; the invention patent CN115200700B discloses a method for identifying modal parameters based on the Welch method and the covariance stochastic subspace method; the invention patent application CN116796615A discloses a method for identifying structural modal parameters based on stochastic subspace deep learning; the invention patent application CN118820718A discloses a method, system and medium for identifying structural modal parameters; the invention patent CN115357853B discloses a method for identifying modal parameters of engineering structures based on fast stochastic subspace, etc. However, at present, the parameter setting of the SSI-Cov method mainly depends on the professional experience of technicians, which is difficult to avoid manual intervention and subjectivity, directly affecting the accuracy and consistency of modal identification results. Therefore, it is urgent to develop an SSI-Cov modal identification method based on unsupervised optimization of key parameters to automatically determine the optimal model order and the number of row blocks of the Toeplitz matrix, thereby eliminating the uncertainty brought by manual parameter tuning. Through the unsupervised optimization algorithm, the input parameters are intelligently screened and optimized, significantly improving the accuracy and robustness of the identification results, and providing more reliable data support for subsequent damage assessment and health monitoring based on modal parameter identification. Summary of the Invention

[0004] The object of the present invention is to provide a modal identification method and system based on unsupervised optimization of the covariance stochastic subspace method for the defects of the prior art. Aiming at the problems that the parameter setting in the modal identification process of the traditional covariance-driven stochastic subspace identification (SSI-Cov) method depends on manual experience, is affected by noise interference, and the model order is not properly selected, a parameter optimization method based on sensitivity analysis is proposed. This method constructs a parameter optimization index by using the product of the condition numbers of the extended observable matrix and the extended controllable matrix, and automatically calculates the optimal model order N and the number of row blocks i of the Toeplitz matrix by calculating the first derivative and curvature spectrum of the singular entropy increment, thus significantly improving the accuracy and robustness of modal identification.

[0005] The first aspect of the present invention lies in providing a modal identification method based on unsupervised optimization of the covariance stochastic subspace method, including:

[0006] S1, arranging acceleration sensors on the structure to be measured that needs modal identification, wherein the acceleration sensors are used to obtain the structural dynamic response of the structure to be measured;

[0007] S2, calculating the covariance matrix based on the structural dynamic response, and constructing a Toeplitz matrix from and ;

[0008] S3. Calculate the extended observable matrix and the extended controllable matrix according to the Toeplitz matrix; ;

[0009] S4. Define the ranges of the number of row blocks i of the Toeplitz matrix and the model order N;

[0010] S5. Analyze the sensitivity of the number of row blocks i of the Toeplitz matrix and the model order N based on the parameter optimization index ;

[0011] S6. Calculate the singular entropy increment of the Toeplitz matrix ;

[0012] S7. Calculate the singular entropy increment curvature of the Toeplitz matrix based on the singular entropy increment of the Toeplitz matrix to determine the critical model order ;

[0013] S8. Calculate the cumulative parameter optimization index from the minimum model order to the critical model order for different numbers of row blocks i of the Toeplitz matrix; Select the parameter combination corresponding to the minimum value of the cumulative parameter optimization index as the optimal parameters;

[0014] S9. Identify the system matrix and determine the modal parameters using the optimized optimal parameters ; Draw the original stability diagram according to the system matrix and the modal parameters; Among them, the modal parameters include the natural frequency, damping ratio, and mode shape coefficient;

[0015] S10. Clean the false modes in the original stability diagram based on the hard criterion.

[0016] Preferably, the S2 includes:

[0017] S21. Assume that the output data is ergodic, and calculate the covariance matrix based on the structural dynamic response; The covariance matrix is expressed as Equation (1):

[0018] (1);

[0019] In Equation (1), , representing the observation vector of the N - degree - of - freedom (DOF) system at discrete time instant k, i.e., the acceleration, velocity, or displacement within the time history of the measurement signal, where is the number of row - blocks of the Toeplitz matrix; j corresponds to the total length of the measurement data;

[0020] S22, constructing a Toeplitz matrix based on the covariance matrix , expressed as Equation (2):

[0021] (2);

[0022] S23, constructing a Toeplitz matrix based on the covariance matrix , expressed as Equation (3):

[0023] (3);

[0024] In Equations (2) and (3), the parameter represents the number of row - blocks of the Toeplitz matrix, and the dimension of the matrix is , which is smaller than the dimension of the original Hankel matrix .

[0025] Preferably, the S3 includes:

[0026] S31, calculating the small singular values, where the small singular values are equal to the number of singular values obtained from the singular - value decomposition of the Toeplitz matrix , as shown in Equation (4):

[0027] (4);

[0028] In Equation (4), and are orthogonal matrices, and are orthogonal matrices, is a diagonal matrix; is a non - singular matrix;

[0029] S32, taking the non - singular matrix as the identity matrix, i.e., T = I, and calculating the extended observable matrix and the extended controllable matrix based on the Toeplitz matrix , as shown in Equations (5) and (6) respectively:

[0030] (5);

[0031] (6);

[0032] In equations (5) and (6), and are the extended observable matrix and the extended controllable matrix respectively; l is the identity matrix.

[0033] Preferably, the S4 includes:

[0034] S41. Determine the lower limit value i of the number of row blocks i of the Toeplitz matrix based on the sampling frequency and the structural fundamental frequency min , as shown in equation (7-1); determine the lower limit value of the model order N based on the PSD peak value , as shown in equation (7-2);

[0035] (7-1);

[0036] (7-2);

[0037] In the formula, is the number of PSD peak values of the structural dynamic response signal, is the structural fundamental frequency, is the sampling frequency;

[0038] S42. Based on equation (8) and the constraint condition li min ≥ respectively determine the upper limit value i of the number of row blocks i of the Toeplitz matrix max and the upper limit value of the model order N , thereby determining the value range of the parameters {i, N} :

[0039] (8);

[0040] In the formula, ; l is the identity matrix.

[0041] Preferably, the S5 includes:

[0042] Based on the value range of the parameters {i, N} , through equation (9), calculate the optimization index for each pair of parameters {i, N} within this value range. That is, calculate the product of the condition numbers of the extended observable matrix and the extended controllable matrix , :

[0043] (9);

[0044] In equation (9), represents the matrix condition number; refers to the pseudo-inverse of the matrix; it should be noted that the proposed is a generalized expression, and for the 2-norm condition number, is also equal to the ratio of the largest singular value of the matrix to the Nth singular value.

[0045] Preferably, the S6 includes:

[0046] For each parameter i, calculate the singular entropy increment of the constructed Toeplitz matrix according to Equation (10):

[0047] (10);

[0048] wherein, refers to the singular entropy increment, and refers to the eigenvalues of the matrix .

[0049] Preferably, the S7 includes:

[0050] S71, calculate the curvature spectrum of the singular entropy increment, including:

[0051] For each parameter i, calculate the curvature spectrum of the singular entropy increment according to Equation (11):

[0052] (11);

[0053] wherein in (11), and indicate that when calculating the singular entropy increment of discrete data, the derivative terms in Equation (11) are replaced by the corresponding difference formulas, as shown in Equations (12) and (13) respectively:

[0054] (12);

[0055] (13);

[0056] S72, calculate the critical model order according to the curvature spectrum of the singular entropy increment , including:

[0057] For different i values, the model order when the curvature spectrum drops to the asymptotic threshold is determined as the critical model order , where = 1e -5 .

[0058] Preferably, the S8 includes:

[0059] Calculate the cumulative parameter optimization index from the minimum model order to the critical model order for different numbers of row blocks i of the Toeplitz matrix; select the parameter combination corresponding to the minimum value of the cumulative parameter optimization index as the optimal parameters, as shown in Equation (14):

[0060] (14);

[0061] wherein, is the critical model order for the specified value of i calculated according to step S72.

[0062] Preferably, the S9 includes:

[0063] S91, identify the system matrix using the optimized optimal parameters , including: expressing the system matrix A as Equation (15) as follows:

[0064] (15);

[0065] The modal parameters of the discrete-time system are obtained from the system matrix A and the output matrix C, where the output matrix C is equal to the first l rows in Equation (5) ;

[0066] S92, determine the modal parameters, including:

[0067] (1) Decompose the system matrix A through eigenvalue decomposition to obtain Equation (16):

[0068] (16);

[0069] wherein, is a diagonal matrix composed of the system poles of the discrete-time system; corresponds to the right eigenvector of matrix A; and the continuous-time eigenvalue and the eigenvalue in the discrete state satisfy the following relationship, as shown in Equation (17):

[0070] (17);

[0071] wherein, represents the sampling time interval;

[0072] (2) Determine the natural frequency , damping ratio and mode shape coefficient ;

[0073] (18);

[0074] S93. Draw the original stability diagram according to the system matrix and the modal parameters.

[0075] Preferably, the S10 includes: according to the hard index judgment criterion, regarding the candidate modes that do not simultaneously satisfy Equation (19) as false modes and eliminating them to obtain the cleaned stability diagram, where:

[0076] (19);

[0077] In the formula, is the eigenvalue obtained by eigenvalue decomposition of the system matrix A in the discrete state, is conjugate.

[0078] The second aspect of the present invention lies in providing a modal identification system based on an unsupervised optimized covariance stochastic subspace method for implementing the method of the first aspect, including:

[0079] A structural dynamic response acquisition module (101) for arranging acceleration sensors on the structure to be measured that needs modal identification, where the acceleration sensors are used to acquire the structural dynamic response of the structure to be measured;

[0080] A Toeplitz matrix construction module (102) for calculating the covariance matrix based on the structural dynamic response, and constructing the Toeplitz matrices and and ;

[0081] An observable matrix and controllable matrix calculation module (103) for calculating the extended observable matrix and the extended controllable matrix and ;

[0082] A parameter range definition module (104) for defining the range of the number of row blocks i of the Toeplitz matrix and the model order N;

[0083] An optimization index sensitivity analysis module for parameters (105) for analyzing the sensitivity of the number of row blocks i of the Toeplitz matrix and the model order N based on the parameter optimization index ;

[0084] A singular entropy increment calculation module (106) for calculating the Toeplitz matrix Singular entropy increment;

[0085] A critical model order determination module (107) for calculating the singular entropy increment curvature of the Toeplitz matrix based on the singular entropy increment of the Toeplitz matrix, thereby determining the critical model order of the Toeplitz matrix to determine the critical model order ;

[0086] An optimal parameter combination determination module (108) for calculating the cumulative parameter optimization index value from the minimum model order to the critical model order in the case of different numbers of row blocks i of the Toeplitz matrix; selecting the parameter combination corresponding to the minimum value of the cumulative parameter optimization index to the critical model order as the optimal parameter; value; selecting the parameter combination corresponding to the minimum value of the cumulative parameter optimization index as the optimal parameter; as the optimal parameter;

[0087] A mode identification module (109) based on the optimized parameters for identifying the system matrix and determining the mode parameters using the optimized optimal parameters, and drawing an original stability diagram according to the system matrix and the mode parameters; wherein the mode parameters include natural frequency, damping ratio, and mode shape coefficient; to identify the system matrix and determine the mode parameters, and draw an original stability diagram according to the system matrix and the mode parameters; wherein the mode parameters include natural frequency, damping ratio, and mode shape coefficient;

[0088] A false mode cleaning module (110) for cleaning the false modes in the original stability diagram based on a hard criterion.

[0089] A third aspect of the present invention provides an electronic device, including a processor and a memory, where the memory stores multiple instructions, and the processor is configured to read the instructions and execute the method described in the first aspect or the second aspect.

[0090] A fourth aspect of the present invention provides a computer-readable storage medium storing multiple instructions that can be read and executed by a processor to execute the method described in the first aspect or the second aspect.

[0091] Advantages of the method, system, electronic device, and computer-readable storage medium of the present invention:

[0092] By constructing a parameter optimization index that is the product of the condition numbers of the extended observable matrix and the extended controllable matrix, and based on the sensitivity analysis of the singular entropy increment and its curvature spectrum, the optimal model order N and the number of row blocks of the Toeplitz matrix are automatically determined, thus significantly improving the identification accuracy and robustness of modal parameters (natural frequency, damping ratio, mode shape coefficient), and avoiding the uncertainties brought by relying on expert experience, overestimating the model order, and noise interference in traditional methods. This method and system not only optimize key parameters and achieve unsupervised selection of optimized parameters, but also provide a more reliable scientific basis for structural health monitoring and damage assessment. Description of the Drawings

[0093] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the related art, the following will briefly introduce the drawings required for use in the description of the specific embodiments or the related art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0094] Figure 1 Flowchart of the modal identification method based on the unsupervised optimized covariance stochastic subspace method according to an embodiment of the present invention;

[0095] Figure 2 System architecture diagram of the modal identification based on the unsupervised optimized covariance stochastic subspace method according to an embodiment of the present invention;

[0096] Figure 3 Power spectral density of the structural response in the numerical example of Embodiment 1 of the present invention.

[0097] Figure 4 7-degree-of-freedom mass-spring-damper system in Embodiment 1 of the present invention;

[0098] Figure 5 Based on the parameter optimization index in Embodiment 1 of the present invention Results of the sensitivity analysis;

[0099] Figure 6 Critical model order determined based on the singular entropy increment curvature spectrum in Embodiment 1 of the present invention;

[0100] Figure 7 Singular entropy increment curvature spectrum (taking the optimal i value as an example) in Embodiment 1 of the present invention;

[0101] Figure 8 Results diagram of the optimal parameters unsupervised determined based on the sensitivity analysis in Embodiment 1 of the present invention;

[0102] Figure 9It is the stability diagram after the hard index cleaning in Embodiment 1 of the present invention;

[0103] Figure 10 It is the structural diagram of the electronic device provided according to the embodiment of the present invention. Specific Embodiments

[0104] Next, the technical solutions of the present invention will be clearly and completely described in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0105] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be understood as a limitation to the present invention. In addition, the terms "first", "second", and "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0106] In the description of the present invention, it should be noted that unless otherwise clearly specified and limited, the terms "installation", "connection", and "connection" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0107] Embodiment 1

[0108] As Figure 1 shown, this embodiment provides a modal identification method based on an unsupervised optimized covariance random subspace method, including:

[0109] S1, arranging acceleration sensors on the structure to be measured that needs modal identification, where the acceleration sensors are used to obtain the structural dynamic response of the structure to be measured;

[0110] S2, calculating the covariance matrix based on the structural dynamic response, and constructing Toeplitz matrices and and ;

[0111] S3. Calculate the extended observable matrix and the extended controllable matrix according to the Toeplitz matrix ; and the extended controllable matrix ;

[0112] S4. Define the range of the number of row blocks i of the Toeplitz matrix and the model order N;

[0113] S5. Analyze the sensitivity of the number of row blocks i of the Toeplitz matrix and the model order N based on the parameter optimization index ;

[0114] S6. Calculate the singular entropy increment of the Toeplitz matrix ;

[0115] S7. Calculate the singular entropy increment curvature of the Toeplitz matrix based on the singular entropy increment of the Toeplitz matrix to determine the critical model order ;

[0116] S8. Calculate the cumulative parameter optimization index value from the minimum model order to the critical model order for different numbers of row blocks i of the Toeplitz matrix; select the parameter combination corresponding to the minimum cumulative parameter optimization index value as the optimal parameters;

[0117] S9. Identify the system matrix and determine the modal parameters using the optimized optimal parameters , and draw the original stability diagram according to the system matrix and the modal parameters; wherein, the modal parameters include natural frequency, damping ratio and mode shape coefficient;

[0118] S10. Clean the false modes in the original stability diagram based on the hard criterion.

[0119] As a preferred implementation manner, the S2 includes:

[0120] S21. Assume that the output data is ergodic, and calculate the covariance matrix based on the structural dynamic response; the covariance matrix is expressed as Equation (1):

[0121] (1);

[0122] In Equation (1), , representing the observation vector of an N-degree-of-freedom (DOF) system at discrete time instant k, i.e., acceleration, velocity, or displacement within the time history of the measurement signal, where is the number of row blocks of the Toeplitz matrix, which corresponds to the number of test channels; j corresponds to the total length of the measurement data;

[0123] S22, based on the covariance matrix construct the Toeplitz matrix , expressed as Equation (2):

[0124] (2);

[0125] S23, based on the covariance matrix construct the Toeplitz matrix , expressed as Equation (3):

[0126] (3);

[0127] In Equations (2) and (3), the parameter represents the number of row blocks of the Toeplitz matrix, and the dimension of the matrix is , which is smaller than the dimension of the original Hankel matrix , thus reducing the computational amount and memory requirement.

[0128] As a preferred embodiment, the S3 includes:

[0129] S31, calculate the small singular values, where the small singular values are equal to the number of singular values obtained from the singular value decomposition of the Toeplitz matrix , as shown in Equation (4):

[0130] In this embodiment, the model order N is another parameter that needs to be defined by the user. By ignoring the small singular values, the small singular values are equal to the number of singular values obtained from the singular value decomposition (Equation (4)) of the Toeplitz matrix ;

[0131] (4);

[0132] In Equation (4), and are orthogonal matrices, and are orthogonal matrices, is a diagonal matrix; is a non-singular matrix;

[0133] S32, take the non-singular matrix as the identity matrix, i.e., T = I, according to the Toeplitz matrix Calculate the extended observable matrix and the extended controllable matrix , as shown in Equations (5) and (6) respectively:

[0134] (5);

[0135] (6);

[0136] In Equations (5) and (6), and are the extended observable matrix and the extended controllable matrix respectively; l is the identity matrix.

[0137] As a preferred embodiment, the S4 includes:

[0138] S41, determine the lower limit value i min of the number of rows i of the Toeplitz matrix based on the sampling frequency and the structural fundamental frequency, as shown in Equation (7-1); determine the lower limit value of the model order N based on the PSD peak , as shown in Equation (7-2);

[0139] (7-1);

[0140] (7-2);

[0141] In the formula, is the number of PSD peak values of the structural dynamic response signal, is the structural fundamental frequency, is the sampling frequency;

[0142] S42, determine the upper limit value i min ≥ of the number of rows i of the Toeplitz matrix and the upper limit value max of the model order N respectively based on Equation (8) and the constraint condition li , so as to determine the value range of the parameters {i, N} :

[0143] (8);

[0144] In the formula, ; l is the identity matrix.

[0145] As a preferred embodiment, the S5 includes:

[0146] Based on the value range of the parameters {i, N} , through Equation (9), calculate the optimization index for each pair of parameters {i, N} within this value range. That is, calculate the extended observable matrix and the extended controllable matrix product of condition numbers of :

[0147] (9);

[0148] In formula (9), represents the condition number of the matrix; refers to the pseudo-inverse of the matrix; It should be noted that the proposed is a generalized expression. For the 2-norm condition number, is also equal to the ratio of the largest singular value to the Nth singular value of the matrix .

[0149] As a preferred implementation, the S6 includes:

[0150] For each parameter i, calculate the singular entropy increment of the constructed Toeplitz matrix according to formula (10) :

[0151] (10);

[0152] In the formula, refers to the singular entropy increment, and refer to the eigenvalues of the matrix .

[0153] As a preferred implementation, the S7 includes:

[0154] S71, calculate the curvature spectrum of the singular entropy increment, including:

[0155] For each parameter i, calculate the curvature spectrum of the singular entropy increment according to formula (11):

[0156] (11);

[0157] In it (11), and indicate that when calculating the singular entropy increment of discrete data, the derivative terms in formula (11) are replaced by the corresponding difference formulas, as shown in formulas (12) and (13) respectively: (12); (13);

[0158] S72, calculate the critical model order according to the curvature spectrum of the singular entropy increment , including:

[0159] For different i values, the curvature spectrum drops to the asymptotic threshold The model order at which ,in =1e -5 .

[0160] As a preferred embodiment, the S8 includes:

[0161] Optimization Index The resulting surface will be determined by the critical model order at different values ​​of i The projection of the composed space curve on the (i, N) plane is divided into two different regions. Among them, the region with a smaller model order represents the effective model order range for identifying physical modes in the stability diagram; while the region with a larger model order often contains interference from false modes caused by overestimation of the model order. Calculate the case of different Toeplitz matrix row block numbers i, starting from the minimum model order To the critical model order Cumulative parameter optimization index Value; Select cumulative parameter optimization indicator The parameter combination corresponding to the minimum value As the optimal parameter, as shown in formula (14):

[0162] (14);

[0163] In the formula, is the critical model order at the specified i value calculated in step S72.

[0164] As a preferred implementation, the S9 includes:

[0165] S91, using the optimized optimal parameters Identifying a system matrix includes: expressing the system matrix A as equation (15) as follows:

[0166] (15);

[0167] The modal parameters of the discrete-time system are obtained from the system matrix A and the output matrix C, where the output matrix C is equal to The first l lines of ;

[0168] S92, determining modal parameters, including:

[0169] (1) Decompose the system matrix A by eigenvalue to obtain equation (16):

[0170] (16);

[0171] In the formula, is a diagonal matrix composed of the system poles of a discrete-time system ; corresponding to the right eigenvectors of matrix A; while the continuous-time eigenvalues and the eigenvalues in the discrete state satisfy the following relationship, as shown in Equation (17):

[0172] (17);

[0173] wherein, represents the sampling time interval;

[0174] (2) Determine the natural frequency , damping ratio and mode shape coefficient of the system from Equation (18);

[0175] (18);

[0176] S93. Draw the original stability diagram according to the system matrix and modal parameters.

[0177] As a preferred embodiment, the S10 includes: according to the hard index judgment criterion, regarding the candidate modes that do not simultaneously satisfy Equation (19) as false modes and eliminating them to obtain the stability diagram after cleaning, wherein:

[0178] (19);

[0179] wherein, is the eigenvalue obtained by eigenvalue decomposition of the system matrix A in the discrete state, is conjugate of.

[0180] Embodiment 2

[0181] As Figure 2 shown, this embodiment provides a modal identification system based on the unsupervised optimized covariance stochastic subspace method for implementing the method of Embodiment 1, including:

[0182] A structural dynamic response acquisition module 101, configured to arrange acceleration sensors on the structure to be measured that needs modal identification, wherein the acceleration sensors are used to acquire the structural dynamic response of the structure to be measured;

[0183] A Toeplitz matrix construction module 102, configured to calculate the covariance matrix based on the structural dynamic response, and construct the Toeplitz matrix and from ;

[0184] The observable matrix and controllable matrix calculation module 103 is used to calculate the extended observable matrix according to the Toeplitz matrix and the extended controllable matrix ; ;

[0185] The parameter range definition module 104 is used to define the ranges of the number of row blocks i of the Toeplitz matrix and the model order N;

[0186] The sensitivity analysis module 105 of the optimization index to parameters is used to analyze the sensitivity of the number of row blocks i of the Toeplitz matrix and the model order N based on the parameter optimization index ;

[0187] The singular entropy increment calculation module 106 is used to calculate the singular entropy increment of the Toeplitz matrix ;

[0188] The critical model order determination module 107 is used to calculate the singular entropy increment curvature of the Toeplitz matrix based on the singular entropy increment of the Toeplitz matrix so as to determine the critical model order ; ;

[0189] The optimal parameter combination determination module 108 is used to calculate the cumulative parameter optimization index from the minimum model order to the critical model order when different numbers of row blocks i of the Toeplitz matrix are used; select the parameter combination corresponding to the minimum value of the cumulative parameter optimization index as the optimal parameter; ;

[0190] The mode identification module 109 based on the optimized parameters is used to identify the system matrix and determine the mode parameters by using the optimized optimal parameters and draw the original stability diagram according to the system matrix and the mode parameters; wherein, the mode parameters include natural frequency, damping ratio and mode shape coefficient;

[0191] The false mode cleaning module 110 is used to clean the false modes in the original stability diagram based on the hard index criterion.

[0192] In Embodiment 1, a 7-degree-of-freedom mass-spring-damper system ( Figure 3 ) was constructed by using MATLAB for the operational modal analysis under ambient excitation. In the model, the mass of each layer was set to 1 unit, the stiffness was set to 10 units, and Rayleigh damping was adopted, and its damping matrix was Cn = 0.01M n + 0.003K n (where M n and K n are the mass matrix and the stiffness matrix respectively). By applying excitations to each layer, Gaussian white noise with a mean of 0 and a variance of 1 is input using the lsim function in MATLAB to simulate ambient excitation, and noise with a signal-to-noise ratio of 10 dB is introduced using the awgn function to simulate random interference in actual dynamic tests. Finally, the output response y i (t) of each layer is obtained. The acceleration responses of each layer are recorded at a sampling frequency of 5 Hz according to the sampling theorem, and the duration is 3000 seconds.

[0193] The specific implementation steps for identifying the structural modal parameters are as follows:

[0194] Based on the output response signal y i (t) of each layer, the structural dynamic response under ambient excitation is obtained.

[0195] Calculate the covariance matrix based on the dynamic response and construct the Toeplitz matrix and and .

[0196] Based on the Toeplitz matrix calculate the extended observable matrix and the extended controllable matrix .

[0197] Based on the response spectrum result with 10 dB noise interference ( Figure 4 ), the fundamental frequency of this numerical model is 0.105 Hz, and there are at least 6 different peaks ( = 6). Thus, according to Equation the lower limit of the model order is determined to be 12. According to , the minimum number of block rows i of the Toeplitz matrix can be set to 25.

[0198] Determine the value range of the parameters {i, N} as , where the increments of the two parameters i and N are set to 5 and 4 respectively.

[0199] Calculate the optimization index for each parameter combination {i, N} to obtain the sensitivity analysis result ( Figure 5 ).

[0200] Based on the curvature spectrum of the singular entropy increment of the matrix , the critical model order at different i values is obtained ( Figure 6 ).

[0201] Taking the optimal i opt = 50 as an example, its singular entropy increment curvature spectrum is as Figure 7 shown.

[0202] The optimization parameters automatically determined based on the corresponding algorithm of the present invention are {i opt = 50, N opt = 38}, and the corresponding cumulative logarithmic minimum value is 24.26 ( Figure 8 ).

[0203] Using the hard index modal criterion to clean the false modes, a stability diagram ( Figure 9 ) is obtained. Among them, the average normalized power spectral density (ANPSD) of each signal spectrum is superimposed as a comparison and verification. It represents that the stable polar axis variability of each physical mode is small and is consistent with the peak of the average normalized power spectral density. Figure 2

[0204] Table 1 lists the frequencies, damping ratios of all the first 7 identified modes and the statistical relative errors with their theoretical values. The results show that the errors of both the frequencies and the modal vibration modes are extremely small (the average errors are 0.001 and 0.004 respectively), and the average error of the damping ratio is 0.159.

[0205] Table 1 Theoretical Modes and Identified Modes of the Numerical Model

[0206]

[0207] The present invention also provides a memory storing multiple instructions for implementing the method as in Embodiment 1.

[0208] As Figure 10 shown, the present invention also provides an electronic device, including a processor 301 and a memory 302 connected to the processor 301. The memory 302 stores multiple instructions that can be loaded and executed by the processor so that the processor can execute the method as in Embodiment 1.

[0209] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A modal identification method based on unsupervised optimization covariance random subspace method, characterized in that: include: S1, arranging an acceleration sensor on a structure to be tested that needs to be subjected to modal identification, wherein the acceleration sensor is used to obtain a structural dynamic response of the structure to be tested; S2, calculate the covariance matrix based on the structural dynamic response , and by Constructing the Toeplitz Matrix and ; S3, according to the Toeplitz matrix Compute the extended observable matrix and extended controllable matrix ; S4, define the range of the number of Toeplitz matrix row blocks i and the model order N; S5, based on parameter optimization indicators Analyze the sensitivity of the Toeplitz matrix row block number i and the model order N; S6, Calculate the Toeplitz matrix The singular entropy increment of ; S7, based on the Toeplitz matrix The singular entropy increment of the Toeplitz matrix The singular entropy increment curvature of ; S8, calculate the minimum model order for different Toeplitz matrix row block numbers i To the critical model order Cumulative parameter optimization index Value; Select cumulative parameter optimization indicator The parameter combination corresponding to the minimum value As the optimal parameter; S9, using the optimized optimal parameters Identify the system matrix and determine the modal parameters, and draw an original stability diagram according to the system matrix and the modal parameters; wherein the modal parameters include natural frequency, damping ratio and vibration mode coefficient; S10, cleaning the false modes in the original stability diagram based on the hard index criterion.

2. The modal identification method based on unsupervised optimization covariance random subspace method according to claim 1, characterized in that: The S2 includes: S21, assuming that the output data undergoes various states, calculate the covariance matrix based on the structural dynamic response ; The covariance matrix It is expressed as formula (1): （1）； In formula (1), , represents the observation vector of the N-DOF system at discrete time k, that is, the acceleration, velocity or displacement in the measurement signal time history, where is the number of Toeplitz matrix row blocks, which is consistent with the number of test channels; j corresponds to the total length of the measured data; S22, based on the covariance matrix Constructing the Toeplitz Matrix , expressed as formula (2): （2）； S23, based on the covariance matrix Constructing the Toeplitz Matrix , expressed as formula (3): （3）； In formulas (2) and (3), the parameters Represents the number of Toeplitz matrix rows, matrix The dimension is , which is smaller than the dimension of the original Hankel matrix .

3. The modal identification method based on unsupervised optimization covariance random subspace method according to claim 2 is characterized in that: The S3 includes: S31, calculate small singular values, where the small singular values ​​are equal to the values ​​obtained from the Toeplitz matrix The number of singular values ​​obtained by the singular value decomposition of is shown in formula (4): （4）； In formula (4), and is an orthogonal matrix, and is an orthogonal matrix, is a diagonal matrix; is a non-singular matrix; S32, the non-singular matrix is ​​taken as the unit matrix, that is, T=I, according to the Toeplitz matrix Compute the extended observable matrix and extended controllable matrix , as shown in formula (5) and formula (6) respectively: （5）； （6）； In formulas (5) and (6), and are the extended observable matrix and the extended controllable matrix respectively; l is the unit matrix.

4. The modal identification method based on unsupervised optimization covariance random subspace method according to claim 3 is characterized in that: The S4 includes: S41, determine the lower limit value i of the number of Toeplitz matrix row blocks i based on the sampling frequency and the structural fundamental frequency min , as shown in formula (7-1); the lower limit of the model order N is determined based on the PSD peak value , as shown in formula (7-2); （7-1）； （7-2）； In the formula, is the number of PSD peaks of the structural dynamic response signal, is the structural fundamental frequency, is the sampling frequency; S42, based on formula (8) and constraint condition li min ≥ Determine the upper limit i of the number of row blocks i of the Toeplitz matrix max and the upper limit of the model order N , thereby determining the range of the parameter {i,N} : （8）； In the formula, ; l is the unit matrix.

5. The modal identification method based on unsupervised optimization covariance random subspace method according to claim 4 is characterized in that: The S5 includes: Based on the range of parameters {i,N} , through formula (9), each pair of parameters {i, N} in the value range is optimized Calculation; that is, calculation of the extended observable matrix and extended controllable matrix The product of the condition numbers of : （9）； In formula (9), represents the matrix condition number; refers to the pseudo-inverse of the matrix; it is worth noting that the proposed is a generalized expression, for the 2-norm condition number, It is also equal to the matrix The ratio of the largest singular value to the Nth singular value.

6. The modal identification method based on unsupervised optimization covariance random subspace method according to claim 5 is characterized in that: The S6 includes: For each parameter i, the constructed Toeplitz matrix is ​​calculated according to formula (10): The singular entropy increment of : （10）； In the formula, refers to the singular entropy increment, and Refers to the matrix The characteristic value of .

7. The modal identification method based on unsupervised optimization covariance random subspace method according to claim 6 is characterized in that: The S7 includes: S71, calculate the curvature spectrum of the singular entropy increment, including: For each parameter i, the curvature spectrum of the singular entropy increment is calculated according to formula (11): （11）； Among them (11), and It means that when calculating the singular entropy increment of discrete data, the derivative term in formula (11) is replaced by the corresponding differential formula, as shown in formula (12) and formula (13) respectively: （12）； （13）； S72, calculate the critical model order based on the curvature spectrum of the singular entropy increment ,include: For different values ​​of i, the curvature spectrum drops to the asymptotic threshold The model order at which ,in =1e -5 .

8. The modal identification method based on unsupervised optimization covariance random subspace method according to claim 7 is characterized in that: The S8 includes: Calculate the minimum model order for different Toeplitz matrix row block numbers i To the critical model order Cumulative parameter optimization index Value; Select cumulative parameter optimization indicator The parameter combination corresponding to the minimum value As the optimal parameter, as shown in formula (14): （14）； In the formula, is the critical model order at the specified i value calculated in step S72.

9. The modal identification method based on unsupervised optimization covariance random subspace method according to claim 8, characterized in that: The S9 includes: S91, using the optimized optimal parameters Identifying a system matrix includes: expressing the system matrix A as equation (15) as follows: （15）； The modal parameters of the discrete-time system are obtained from the system matrix A and the output matrix C, where the output matrix C is equal to The first l lines of ; S92, determining modal parameters, including: (1) Decompose the system matrix A by eigenvalue to obtain equation (16): （16）； In the formula, is the system pole of the discrete-time system The diagonal matrix composed of; corresponds to the right eigenvector of the matrix A; while the continuous-time eigenvalue and the eigenvalues ​​in the discrete state The following relationship is satisfied, as shown in formula (17): （17）； In the formula, Indicates the sampling time interval; (2) Determine the natural frequency of the system using equation (18): , Damping ratio and mode coefficients ; （18）； S93, drawing an original stability diagram according to the system matrix and modal parameters.

10. A modal identification method based on unsupervised optimization covariance random subspace method according to claim 9, characterized in that: The S10 includes: according to the hard index judgment criteria, the candidate modes that do not simultaneously satisfy equation (19) are regarded as false modes and are eliminated, and a cleaned stability map is obtained, wherein: （19）； In the formula, is the eigenvalue obtained by eigenvalue decomposition of the system matrix A in the discrete state, for The conjugation of.

11. A modal identification system based on unsupervised optimization covariance random subspace method, used to implement any method of claims 1-10, characterized in that: include: A structural dynamic response acquisition module (101) is used to arrange an acceleration sensor on a structure to be tested that needs to be subjected to modal identification, wherein the acceleration sensor is used to acquire the structural dynamic response of the structure to be tested; A Toeplitz matrix building module (102) is used to calculate the covariance matrix based on the structural dynamic response. , and by Constructing the Toeplitz Matrix and ; The observable matrix and controllable matrix calculation module (103) is used to calculate the Toeplitz matrix Compute the extended observable matrix and extended controllable matrix ; A parameter range definition module (104) is used to define the range of the number of Toeplitz matrix row blocks i and the model order N; The sensitivity analysis module (105) of the optimization index to the parameter is used to optimize the index based on the parameter. Analyze the sensitivity of the Toeplitz matrix row block number i and the model order N; Singular entropy increment calculation module (106) for calculating the Toeplitz matrix The singular entropy increment of ; A critical model order determination module (107) is used to determine the critical model order based on the Toeplitz matrix The singular entropy increment of the Toeplitz matrix The singular entropy increment curvature of ; The optimal parameter combination determination module (108) is used to calculate the optimal parameter combination from the minimum model order under different Toeplitz matrix row block numbers i. To the critical model order Cumulative parameter optimization index Value; Select cumulative parameter optimization indicator The parameter combination corresponding to the minimum value As the optimal parameter; A modal identification module (109) based on optimized parameters is used to utilize the optimized optimal parameters Identify the system matrix and determine the modal parameters, and draw an original stability diagram according to the system matrix and the modal parameters; wherein the modal parameters include natural frequency, damping ratio and vibration mode coefficient; The false mode cleaning module (110) is used to clean the false modes in the original stability diagram based on the hard index criterion.

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