Joint diagonalization-based spectral density near-frequency modal parameter identification automation method

Abstract

The invention discloses a spectral density near-frequency modal parameter identification automation method based on joint diagonalization, and the method comprises the steps: obtaining a response power spectral density matrix of a detected system, and determining a frequency peak point; and determining the natural vibration frequency and the damping ratio according to a rotation matrix determined by the response power spectral density matrix. According to the method, the joint diagonalization technology is utilized, automatic identification of the near-frequency modal parameters is achieved, meanwhile, the identification accuracy of the modal shape is improved, the joint diagonalization technology is adopted to process the power spectrum density matrix of the near-frequency modal, the natural vibration frequency and the damping ratio of the detected system are automatically extracted, and the detection accuracy is improved. And the modal shape of the detected system can be determined according to the natural vibration frequency and the damping ratio, so that efficient identification of a near-frequency modal is automatically realized through an algorithm, human intervention is reduced, the analysis efficiency is greatly improved, and the method is suitable for online monitoring and modal analysis of a large-scale structure. The method is widely applied to the technical field of control.

Description

Technical Field

[0001] The present invention relates to the field of control technology, and in particular to an automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization. Background Art

[0002] Modal parameter identification is one of the key technologies in the fields of structural dynamics and health monitoring. Its goal is to extract the natural frequency (self-vibration frequency), damping ratio, and modal shape of a structure from vibration responses. These parameters can effectively characterize the dynamic performance of the structure and provide important bases for fault diagnosis, fatigue analysis, and life assessment.

[0003] Current modal parameter identification techniques generally use frequency-domain data of Fourier transform for modal parameter identification. This method requires an assumption about the initial damping ratio. In actual engineering, it is very difficult to estimate the damping ratio, and in many cases, it is impossible to obtain an accurate estimate of the damping ratio. During the parameter identification process, the accuracy of the initial damping ratio directly affects the identification result. Moreover, current modal parameter identification techniques usually require manual determination of the frequency bandwidth of dense near-frequencies. This process depends on observing the resonance frequency band of the spectral density image near the near-frequency mode. However, in actual measurements, the coupling of multiple modal frequencies may cause the resonance bandwidth of the near-frequency mode to be not obvious on the spectral density diagram, thus increasing the difficulty of manually selecting the frequency band. In addition, the number of dense near-frequency modes also needs to be determined manually, which poses relatively high requirements for non-professional operators or the analysis of complex systems and may lead to errors or inefficiencies. On the other hand, due to the very small interval between frequencies, dense near-frequency modes may cause modal responses to overlap in the frequency domain, thus increasing the difficulty of modal parameter identification and making it difficult to distinguish near-frequency modes. Summary of the Invention

[0004] Aiming at the technical problems such as difficult damping ratio estimation, dependence on manual observation which is inefficient and error-prone, and difficulty in distinguishing near-frequency modes when performing modal parameter identification, the purpose of the present invention is to provide an automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization.

[0005] Embodiments of the present invention include an automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization. The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization includes the following steps:

[0006] Obtain the kinematic information of the system to be detected;

[0007] Determine the response power spectral density matrix according to the kinematic information;

[0008] Determine the frequency peak points and the existence state of dense near-frequencies according to the response power spectral density matrix;

[0009] When the existence state of dense near - frequencies indicates the presence of dense near - frequencies, determine whether the frequency peak point belongs to the resonance frequency band;

[0010] When the frequency peak point belongs to the resonance frequency band, determine the rotation matrix according to the response power spectral density matrix;

[0011] Determine the natural vibration frequency and damping ratio of the detected system according to the rotation matrix.

[0012] Further, the obtaining of the kinematic information of the detected system includes:

[0013] Detect the detected system through an accelerometer sensor to obtain acceleration response data;

[0014] Use the acceleration response data as the kinematic information.

[0015] Further, the determining of the response power spectral density matrix according to the kinematic information includes:

[0016] According to the formula

[0017]

[0018] Perform calculations; where G yy (ω k ) is the response power spectral density matrix, N is the total number of sampling points of the kinematic information, Δt is the sampling time interval of the kinematic information, y α and y β are the acceleration response data.

[0019] Further, the determining of the frequency peak point and the existence state of dense near - frequencies according to the response power spectral density matrix includes:

[0020] According to the formula

[0021]

[0022] Perform singular value decomposition on the response power spectral density matrix;

[0023] Use an automatic peak - picking algorithm to extract the frequency peak point ω k .

[0024] Further, the determining of the frequency peak point and the existence state of dense near - frequencies according to the response power spectral density matrix includes:

[0025] According to the result of the singular value decomposition of the response power spectral density matrix, obtain the local extreme points of the third - order singular value, the local extreme points of the second - order singular value, and the maximum value of the first - order singular value;

[0026] Determine a first ratio by comparing the local extreme point of the third-order singular value with the maximum value of the first-order singular value;

[0027] When the first ratio is greater than a first threshold, determine that there are 3 dense near frequencies; otherwise, determine a second ratio by comparing the local extreme point of the second-order singular value with the maximum value of the first-order singular value;

[0028] When the second ratio is greater than a second threshold, determine that there are 2 dense near frequencies; otherwise, determine that there are no dense near frequencies.

[0029] Further, determining whether the frequency peak point belongs to the resonance frequency band includes:

[0030] Obtain the first-order singular value vector i k at the frequency peak point ω k1 and the second-order singular value vector u k2 ;

[0031] According to the formula

[0032]

[0033] determine the transformation matrix A; where, is the conjugate matrix of u k1 and is the conjugate matrix of u k2 ;

[0034] According to the formula

[0035]

[0036] determine u j1 and u j2 ;

[0037] According to the formula

[0038]

[0039] MAC clo

[0040] calculate;

[0041] MAC clo

[0042] When it is greater than a third threshold, determine that the frequency peak point belongs to the resonance frequency band; otherwise, determine that the frequency peak point does not belong to the resonance frequency band.

[0043] Further, determining the rotation matrix according to the response power spectral density matrix includes:

[0044] Using the Jacobi rotation algorithm to determine the rotation matrix.

[0045] Further, using the Jacobi rotation algorithm to determine the rotation matrix includes:

[0046] According to the formula

[0047]

[0048] Determine the input matrix Λ k , k = 1, ..., N f , where U i , S i Are the singular values obtained by performing singular value decomposition on the response power spectral density matrix;

[0049] Set the threshold ∈ s ;

[0050] Set the initial value R of the rotation matrix 0 = I m ;

[0051] Let i = 1: m - 1, when |s| ≥ ∈ s , loop through the following steps (1)-(3):

[0052] (1) Let j = i + 1: m, loop through the following steps (101)-(105):

[0053] (101) According to the formula

[0054] v k = [(Λ k ) ii -(Λ k ) jj , (Λ k ) ij +(Λ k ) ji , i((Λ k ) ji -(Λ k ) ij ))], k = 1, 2, ..., N f ;

[0055] Perform the calculation;

[0056] (102) According to the formula

[0057]

[0058] Perform the calculation;

[0059] (103) Take the normalized eigenvector [x, y, z] corresponding to the maximum eigenvalue of G T , where x ≥ 0;

[0060] (104) Calculate the rotation parameters

[0061] (105) According to the formula

[0062] (R o ) ii =(R o ) jj = c, (R o ) ji =-s

[0063] Construct the rotation matrix R o ;

[0064] (2) Update according to the formula ;

[0065] (3) Update according to the formula ;

[0066] Output the R obtained by the last execution of steps (1)-(3) i , as the rotation matrix.

[0067] Furthermore, determining the natural vibration frequency and damping ratio of the system to be detected according to the rotation matrix includes:

[0068] According to the formula

[0069]

[0070] Calculate to determine the matrix L k ;

[0071] According to the matrix L k , determine the natural vibration frequency and the damping ratio.

[0072] Furthermore, determining the natural vibration frequency and the damping ratio according to the matrix L k includes:

[0073] According to the formula

[0074]

[0075] Determine the natural vibration frequency ω i and the damping ratio ζ i .

[0076] The beneficial effects of the present invention are as follows: The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization in the embodiment utilizes the joint diagonalization technique to achieve automated identification of near-frequency modal parameters and simultaneously improve the identification accuracy of modal shapes. Specifically, by using the joint diagonalization technique to process the power spectral density matrix of near-frequency modes, it realizes the automated extraction of the natural vibration frequency and damping ratio of the detected system. Based on the natural vibration frequency and damping ratio, the modal shape of the detected system can be determined, thereby achieving efficient identification of near-frequency modes through algorithms automatically, reducing human intervention, significantly improving the analysis efficiency, and being applicable to online monitoring and modal analysis of large-scale structures. Description of the Drawings

[0077] Figure 1 It is a schematic diagram of the steps of the automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization in the embodiment;

[0078] Figure 2 It is a schematic flow diagram of the automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization in the embodiment;

[0079] Figure 3 It is a schematic diagram of the principle of steps S3 - S6 in the embodiment. Detailed Embodiment

[0080] Term Explanation:

[0081] Joint diagonalization: A linear algebra technique used to simultaneously transform multiple sets of matrices into an approximately diagonal form. This method can be applied to signal processing, blind source separation, modal analysis, and other fields that require extracting useful information from matrix features. The mathematical basis of this technique is to find an optimal solution that makes multiple sets of matrices as close to diagonal matrices as possible after unified transformation while maintaining the inherent characteristics of the data structure.

[0082] Power spectral density: A quantitative description of a signal or system in the frequency domain, usually used to analyze the distribution of the energy or power of a signal at different frequencies.

[0083] Modal parameter identification: Modal parameter identification is a technique used to analyze and extract the dynamic characteristics of a structure or system. By studying the input-output relationship of the system, parameters such as its natural frequency, damping ratio, and modal shape are determined. These parameters can describe the vibration behavior of the system under dynamic loading and are commonly used in engineering vibration analysis, structural health monitoring, and mechanical system design. Modal parameter identification can effectively evaluate the dynamic characteristics of a structure or system and plays an important role in dynamic design optimization, fault diagnosis, vibration control, and system reliability assessment.

[0084] Automation: Utilizing automated tools or algorithms to achieve the high-efficiency and intelligentization of the modal parameter identification process and reduce human intervention.

[0085] Closely spaced near frequencies: Refers to a phenomenon in modal parameter identification where the natural frequencies of different modes are very close to each other. This situation usually occurs in complex structures or systems, such as mechanical, aerospace, and civil engineering structures with high symmetry or strong coupling.

[0086] In this embodiment, referring to Figure 1 , the automated method for identifying closely spaced near-frequency modal parameters based on joint diagonalization includes the following steps:

[0087] S1. Obtain the kinematic information of the system to be detected;

[0088] S2. Determine the response power spectral density matrix according to the kinematic information;

[0089] S3. Determine the frequency peak points and the presence state of closely spaced near frequencies according to the response power spectral density matrix;

[0090] S4. When the presence state of closely spaced near frequencies indicates the existence of closely spaced near frequencies, determine whether the frequency peak points belong to the resonance frequency band;

[0091] S5. When the frequency peak points belong to the resonance frequency band, determine the rotation matrix according to the response power spectral density matrix;

[0092] S6. Determine the natural vibration frequency and damping ratio of the system to be detected according to the rotation matrix.

[0093] Steps S1 - S6 can be executed by a computer. The flow of steps S1 - S6 is as Figure 2 shown.

[0094] In step S1, the system to be detected can be a structure that may vibrate in the fields of machinery, aerospace, civil engineering, etc., such as gears, rotating shafts, etc.

[0095] In step S1, the kinematic information to be obtained can be the displacement, velocity, or acceleration of the system to be detected, etc. In this embodiment, the acceleration response data of the system to be detected is taken as an example of the kinematic information for illustration. Specifically, when executing step S1, an accelerometer sensor can be used to detect the system to be detected to obtain the acceleration response data y(t) as the kinematic information of the system to be detected. Wherein, t represents time.

[0096] In step S2, the welch method can be used to calculate the response power spectral density matrix G yy (ω k ) according to the kinematic information y(t). Specifically, the calculation can be performed according to the following formula:

[0097]

[0098] Among them, G yy (ω k ) is the response power spectral density matrix, N is the total number of sampling points for kinematic information, Δt is the sampling time interval for kinematic information, and j and l are parameters in the calculation process. y α and y β are both functional forms of the acceleration response data y(t), and different variables are distinguished by α and β.

[0099] In step S3, the response power spectral density matrix G yy (ω k ) is subjected to singular value decomposition to obtain the frequency peak points. Specifically, according to the formula

[0100]

[0101] the response power spectral density matrix G yy (ω k ) is subjected to singular value decomposition, so as to obtain u k1 , s k1 and and other singular values, and the automatic peak picking algorithm is used to extract the frequency peak point ω k .

[0102] In step S3, it is also possible to determine the presence state of dense near frequencies according to the response power spectral density matrix G yy (ω k ), such as whether there are dense near frequencies in the vibration spectrum of the system to be detected, and the number of dense near frequencies in the case of the presence of dense near frequencies.

[0103] For the determination of the number of near frequencies, it can be achieved by observing the singular values to determine the presence and quantity of the dense near frequency modes. For example, when there are no near frequencies, the first-order singular value is significantly greater than other-order singular values. Similarly, when there are dense near frequency modes, the number of larger singular values corresponds to the number of dense near frequency modes. The above process can be achieved manually. In this embodiment, based on the characteristics of the above process, a criterion for automatically detecting the number of near frequency modes is designed, so as to be applied to automatically detect the number of dense near frequency modes near a specific frequency when performing step S3.

[0104] In this embodiment, the principles of steps S3-S6 are as Figure 3 shown.

[0105] Specifically, in step S3, for any specific frequency in the vibration spectrum of the system to be detected:

[0106] First step, find out the response power spectral density matrix G yy (ω kAmong the decomposed singular values, find the local extreme point S of the third-order singular value at this specific frequency j3 , the local extreme point S of the second-order singular value j2 and the maximum value S of the first-order singular value j1 ;

[0107] Second step, compare the local extreme point S of the third-order singular value j3 with the maximum value S of the first-order singular value j1 to determine the first ratio

[0108] Third step, judge the magnitude of the first ratio . If is greater than the first threshold (specifically, it can be 0.2), then it can be determined that there are three dense near-frequency modes near this specific frequency in the vibration spectrum of the detected system. If is less than or equal to the first threshold, then the judgment can be continued;

[0109] Fourth step, compare the local extreme point S of the second-order singular value j2 with the maximum value S of the first-order singular value j1 to determine the second ratio

[0110] Fifth step, judge the magnitude of the second ratio . If is greater than the second threshold (specifically, it can be 0.2), then it can be determined that there are two dense near-frequency modes near this specific frequency in the vibration spectrum of the detected system. If is less than or equal to the second threshold, then it can be determined that there are no dense near-frequency modes near this specific frequency point.

[0111] When it is determined in step S3 that there are dense near-frequencies (for example, there exists a frequency point ω j , and there are three or two dense near-frequencies near it), execute step S4 to judge whether the frequency peak point ω k belongs to the resonance frequency band, that is, whether the frequency points near the frequency peak point ω k in the spectrum are within the resonance frequency band.

[0112] For the case without near-frequencies, in modal parameter identification, the resonance frequency bandwidth can be automatically selected through the Modal Assurance Criterion (MAC). However, when there are near-frequency modes, calculating the MAC value is no longer applicable for automatically selecting the resonance frequency bandwidth, and step S4 is exactly executed in the case of dense near-frequencies. Therefore, other techniques are needed to judge whether the frequency peak point ω k belongs to the resonance frequency band.

[0113] For the case of near frequencies, near the frequency peak point ω k , there is always

[0114]

[0115] where u k1 is obtained according to the result of singular value decomposition of the response power spectral density matrix, and is the first-order singular value vector at the frequency peak point ω k , u k2 is the second-order singular value vector at the frequency peak point ω k . is the conjugate matrix of u k1 , is the conjugate matrix of u k2 . The transformation matrix A can be solved. Moreover, the transformation matrix A satisfies

[0116]

[0117] where u j1 is the first-order singular value vector at the frequency point ω j , u j2 is the second-order singular value vector at the frequency point ω j , ω j is the frequency point where dense near frequencies exist nearby, so that u and u can be solved according to the transformation matrix A. Then, through the formula

[0118] j1 j2

[0119]

[0120] the MAC clo can be calculated, and the magnitude of the MAC clo can be judged. In this embodiment, when the MAC clo is greater than the third threshold (specifically, it can be 0.2), it can be determined that the point near the peak ω k belongs to the resonance frequency band.

[0121] When there are near frequencies, the modal shape can be expressed as where, U i , S i are the singular values at the frequency ω i . Therefore, by constructing the matrix the value of R yy (ω k ) can be determined using the Jacobi rotation algorithm according to the response power spectral density matrix G i to obtain the modal shape.

[0122] Specifically, when using the Jacobi rotation algorithm to determine the rotation matrix, the following steps can be performed:

[0123] S501. According to the formula

[0124]

[0125] determine the input matrix Λ k , k = 1, ..., N f , where U i , S i are the singular values obtained by performing singular value decomposition on the response power spectral density matrix, and N f is the maximum frequency point in the frequency spectrum;

[0126] S502. Set the threshold ∈ s (specifically, it can be 10 -8 );

[0127] S503. Set the initial value R of the rotation matrix 0 = I m ; where I m is the m - order identity matrix;

[0128] S504. Let i = 1:m - 1. When |s| ≥ ∈ s , loop and execute the following steps (1)-(3) (that is, the range of the loop variable i is from 1 to m - 1. Each time steps (1)-(3) are executed, i is incremented by 1, and then the next execution of steps (1)-(3) is performed. When i exceeds m - 1 or |s| < ∈ s , the loop ends):

[0129] (1) Let j = i + 1:m, and loop and execute the following steps (101)-(105) (that is, the range of the loop variable j is from i + 1 to m. Each time steps (101)-(105) are executed, j is incremented by 1, and then the next execution of steps (101)-(105) is performed. When j exceeds m, the loop ends):

[0130] (101) According to the formula

[0131] v k = [(Λ k ) ii - (Λ k ) jj , (Λ k ) ij + (Λ k ) ji , i((Λ k ) ji - (Λ k ) ij ))], k = 1, 2, ..., Nf ;

[0132] Perform calculations;

[0133] (102) According to the formula

[0134]

[0135] Perform calculations;

[0136] (103) Take the normalized eigenvector [x, y, z] corresponding to the largest eigenvalue of G T , where x ≥ 0;

[0137] (104) Calculate the rotation parameters

[0138] (105) According to the formula

[0139] (R o ) ii =(R o ) jj = c, (R o ) ji =-s

[0140] Construct the rotation matrix R o ;

[0141] Thus, one round of steps (101)-(105) ends

[0142] (2) Update according to the formula ;

[0143] (3) Update according to the formula ;

[0144] Output the R obtained from the last execution of steps (1)-(3) i , as the rotation matrix

[0145] After obtaining the rotation matrix R i in step S5, when performing step S6, that is, determining the natural vibration frequency and damping ratio of the system to be detected according to the rotation matrix, first calculate according to the formula

[0146]

[0147] to determine the matrix L k . Where Λ(f k ) is the same as Λ k . Note that the natural vibration frequency and damping ratio are included in the matrix L k , and its form is

[0148]

[0149] where ζ i is the damping ratio, and ω i is the natural vibration frequency.

[0150] Multiply both sides of the above equation by (ω k - ω di ), 2 +(ζ i ω i ), 2 to obtain

[0151] L k ((ω k - ω di ), 2 +(ζ i ω i )) 2 = d i ζ i ω i

[0152] where d i is a constant, ω di is the frequency with damping. According to the relationship between the damping ratio ζ i and the natural vibration frequency ω i

[0153]

[0154] it can be obtained that

[0155]

[0156] At this time, the natural vibration frequency ω i and the damping ratio ζ i can be calculated according to the formula, and the expressions

[0157]

[0158] can be obtained. That is, perform matrix calculations on the right side of the equation to obtain a matrix in the form of the left side of the equation, and extract the natural vibration frequency ω i and the damping ratio ζ i .

[0159] ​The automatic method for identifying near-frequency modal parameters of spectral density based on joint diagonalization in this embodiment uses the joint diagonalization technique to achieve automatic identification of near-frequency modal parameters and improve the identification accuracy of modal shapes. Specifically, the power spectral density matrix of near-frequency modes is processed using the joint diagonalization technique to automatically extract the natural vibration frequencies and damping ratios of the system to be detected. Based on the natural vibration frequencies and damping ratios, the modal shapes of the system to be detected can be determined, thus realizing efficient identification of near-frequency modes through an algorithm automatically, reducing human intervention, greatly improving the analysis efficiency, and being applicable to online monitoring and modal analysis of large-scale structures.

[0160] The automatic method for identifying near-frequency modal parameters of spectral density based on joint diagonalization in this embodiment has the following advantages:

[0161] 1. Automatic identification: It avoids the subjective errors caused by manually determining the frequency bandwidth of dense near-frequencies and reduces the difficulty of manually selecting frequency bands. In addition, a criterion for automatically identifying near-frequencies is proposed, improving the efficiency of the method.

[0162] 2. Identifying complex near-frequencies: The joint diagonalization technique is adopted, solving the situation where previous modal parameter identification methods can only identify orthogonal near-frequencies and making it possible to identify non-orthogonal near-frequencies.

[0163] 3. Efficiently estimating modal parameters: Existing modal parameter identification methods often estimate modal parameters by performing inverse Fourier transform on frequency-domain data to time-domain data. The present invention directly uses spectral density data for modal parameter identification, improving the identification efficiency.

[0164] A computer program implementing the automatic method for identifying near-frequency modal parameters of spectral density based on joint diagonalization in this embodiment can be written and stored in a computer device or storage medium. When the computer program is read and run, it executes the automatic method for identifying near-frequency modal parameters of spectral density based on joint diagonalization in this embodiment, thereby achieving the same technical effects as the automatic method for identifying near-frequency modal parameters of spectral density based on joint diagonalization in the embodiment.

[0165] It should be noted that, unless otherwise specified, when a certain feature is referred to as "fixed" or "connected" to another feature, it can be directly fixed or connected to the other feature, or indirectly fixed or connected to the other feature. In addition, the descriptions such as upper, lower, left, and right used in this disclosure are only relative to the mutual positional relationship of the components of this disclosure in the drawings. The singular forms of "a", "an", and "the" used in this disclosure are also intended to include the plural forms, unless the context clearly indicates otherwise. In addition, unless otherwise defined, all technical and scientific terms used in this embodiment have the same meaning as commonly understood by those skilled in the technical field of this technology. The terms used in the description of this embodiment of the specification are only for describing specific embodiments, rather than for limiting the present invention. The term "and / or" used in this embodiment includes any combination of one or more of the related listed items.

[0166] It should be understood that although the terms first, second, third, etc. may be used in this disclosure to describe various elements, these elements should not be limited to these terms. These terms are only used to distinguish elements of the same type from each other. For example, without departing from the scope of this disclosure, the first element may also be referred to as the second element, and similarly, the second element may also be referred to as the first element. The use of any and all examples or exemplary language ("for example", "such as", etc.) provided in this embodiment is only intended to better illustrate the embodiments of the present invention, and unless otherwise required, will not impose a limitation on the scope of the present invention.

[0167] It should be recognized that the embodiments of the present invention can be implemented or carried out by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer-readable memory. The method can be implemented in a computer program using standard programming techniques - including a non-transitory computer-readable storage medium configured with the computer program, wherein the storage medium so configured causes the computer to operate in a specific and predefined manner - according to the methods and drawings described in the specific embodiments. Each program can be implemented in a high-level procedural or object-oriented programming language to communicate with the computer system. However, if desired, the program can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language. In addition, for this purpose, the program can run on a dedicated integrated circuit programmed for this purpose.

[0168] In addition, the operations of the processes described in this embodiment may be performed in any suitable order, unless this embodiment otherwise indicates or is otherwise clearly contradicted by the context. The processes described in this embodiment (or variations and / or combinations thereof) may be performed under the control of one or more computer systems configured with executable instructions and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) executed jointly on one or more processors, by hardware, or a combination thereof. A computer program includes a plurality of instructions executable by one or more processors.

[0169] Further, the method may be implemented in any type of computing platform operably connected, including but not limited to personal computers, minicomputers, mainframes, workstations, network or distributed computing environments, separate or integrated computer platforms, or communicating with charged particle tools or other imaging devices, etc. Aspects of the present invention may be implemented in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into the computing platform, such as a hard disk, optical read and / or write storage medium, RAM, ROM, etc., such that it is readable by a programmable computer and, when the storage medium or device is read by the computer, can be used to configure and operate the computer to perform the processes described herein. In addition, the machine-readable code, or portions thereof, may be transmitted via a wired or wireless network. When such media include instructions or programs that implement the above steps in conjunction with a microprocessor or other data processor, the invention of this embodiment includes these and other different types of non-transitory computer-readable storage media. When programmed according to the methods and techniques of the present invention, the present invention also includes the computer itself.

[0170] The computer program can be applied to the input data to perform the functions of this embodiment, thereby transforming the input data to generate output data stored in a non-volatile memory. The output information can also be applied to one or more output devices such as a display. In a preferred embodiment of the present invention, the transformed data represents physical and tangible objects, including a specific visual depiction of the physical and tangible objects generated on the display.

[0171] The above are only the preferred embodiments of the present invention. The present invention is not limited to the above-described embodiments. As long as it achieves the technical effects of the present invention by the same means, any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the scope of protection of the present invention. Within the scope of protection of the present invention, its technical solutions and / or implementation manners may have various different modifications and changes.

Claims

1. An automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization, characterized in that: The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization includes: Obtain kinematic information of the detected system; Determining a response power spectral density matrix based on the kinematic information; Determining the existence of frequency peak points and dense near frequencies according to the response power spectrum density matrix; When the existence state of dense close frequencies indicates the existence of dense close frequencies, determining whether the frequency peak point belongs to a resonant frequency band; When the frequency peak point belongs to the resonance frequency band, determining a rotation matrix according to the response power spectrum density matrix; According to the rotation matrix, the natural frequency and damping ratio of the detected system are determined.

2. The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization according to claim 1, characterized in that: The obtaining of kinematic information of the detected system includes: Detecting the detected system by using an accelerometer sensor to obtain acceleration response data; The acceleration response data is used as the kinematic information.

3. The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization according to claim 2, characterized in that: Determining a response power spectrum density matrix according to the kinematic information includes: According to the formula Calculate; where G yy (ω k ) is the response power spectrum density matrix, N is the total number of sampling points for the kinematic information, Δt is the sampling time interval for the kinematic information, y α and β is the acceleration response data.

4. The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization according to claim 3, characterized in that: Determining the existence state of frequency peak points and dense near frequencies according to the response power spectrum density matrix includes: According to the formula Performing singular value decomposition on the response power spectrum density matrix; Use the automatic peak picking algorithm to extract the frequency peak point ω k .

5. The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization according to claim 4, characterized in that: Determining the existence state of frequency peak points and dense near frequencies according to the response power spectrum density matrix includes: According to the result of singular value decomposition of the response power spectrum density matrix, local extreme value points of the third-order singular value, local extreme value points of the second-order singular value and the maximum value of the first-order singular value are obtained; Determine a first ratio by comparing the local extreme point of the third-order singular value with the maximum value of the first-order singular value; When the first ratio is greater than a first threshold, it is determined that there are three dense close frequencies, otherwise, a second ratio is determined by comparing the local extreme point of the second order singular value with the maximum value of the first order singular value; When the second ratio is greater than the second threshold, it is determined that there are two dense close frequencies; otherwise, it is determined that there are no dense close frequencies.

6. The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization according to claim 4 or 5, characterized in that: The determining whether the frequency peak point belongs to the resonance frequency band includes: According to the result of singular value decomposition of the response power spectrum density matrix, the frequency peak point ω is obtained. k The first-order singular value vector u at k1 and the second-order singular value vector u k2 ; According to the formula Determine the transformation matrix A; where, is u k1 The conjugate matrix of is u k2 The conjugate matrix of ; According to the formula Determine j1 and u j2 ; According to the formula MAC clo calculate; MAC clo When it is greater than the third threshold, it is determined that the frequency peak point belongs to the resonance frequency band; otherwise, it is determined that the frequency peak point does not belong to the resonance frequency band.

7. The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization according to claim 6, characterized in that: The step of determining a rotation matrix according to the response power spectrum density matrix comprises: The rotation matrix is ​​determined using a Jacobi rotation algorithm.

8. The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization according to claim 7, characterized in that: The method of using the Jacobi rotation algorithm to determine the rotation matrix includes: According to the formula Determine the input matrix Λ k ,k=1,...,N f , where U i , S i is a singular value obtained by performing singular value decomposition on the response power spectrum density matrix; Set the threshold ∈ s ; Set the initial value of the rotation matrix R0 = I m ; Let i = 1:m-1, when |s| ≥ ∈ s , the following steps (1)-(3) are executed cyclically: (1) Let j = i + 1: m, and loop through the following steps (101) to (105): (101) According to the formula v k =[(Λ k ) ii -(L k ) jj ,(L k ) ij +(L k ) ji ,i((Λ k ) ji -(L k ) ij ))],k=1,2,...,N f ; Perform calculations; (102) According to the formula Perform calculations; (103) Take the normalized eigenvector [x, y, z] corresponding to the maximum eigenvalue of G T , where x ≥ 0; (104) Calculate rotation parameters (105) According to the formula Construct the rotation matrix R o ; (2) According to the formula Make updates; (3) According to the formula Make updates; Output the R obtained by the last execution of steps (1)-(3) i , as the rotation matrix.

9. The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization according to claim 8, characterized in that: Determining the natural frequency and damping ratio of the detected system according to the rotation matrix includes: According to the formula Calculate and determine the matrix L k ; According to the matrix L k , determine the natural frequency and the damping ratio.

10. The automated method for identifying near-frequency modal parameters of spectral density based on joint diagonalization according to claim 9, characterized in that: According to the matrix L k , determining the natural frequency and the damping ratio, comprising: According to the formula Determine the natural frequency ω i and the damping ratio ζ i .

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