Operational modal analysis method based on composite frequency domain decomposition

Abstract

The present application is an operational modal analysis method based on composite frequency domain decomposition, and specifically relates to the technical field of modal analysis. The method includes: obtaining multi-channel structural vibration response data and calculating the cross-power spectrum matrix; performing singular value decomposition on the cross-power spectrum matrix to obtain a frequency vector function; selecting the peak frequency of the target order according to the frequency vector function; obtaining the enhanced frequency domain complex function of the target order according to the peak frequency of the target order; based on the enhanced frequency domain complex function of the target order, using a second-order orthogonal polynomial fraction to fit the natural frequency and modal damping ratio of the target order. Based on the above scheme, an enhanced frequency domain complex function can be obtained, and the enhanced frequency domain complex function contains amplitude and phase information; without any approximation, the numerator complex orthogonal polynomial and the denominator complex orthogonal polynomial are used to fit the natural frequency and damping ratio of the structure, thereby improving the stability and noise resistance of modal parameter identification.

Description

Technical Field

[0001] The present application relates to the field of modal analysis, and in particular to an operational modal analysis method based on composite frequency domain decomposition. Background Art

[0002] Frequency domain decomposition modal parameter identification algorithms are widely used in operational modal analysis. They have the advantages of stable algorithms, fast calculation speed, and the ability to identify repeated frequency modes.

[0003] The traditional frequency domain decomposition method FDD does not have the ability to identify the modal damping ratio parameters, and the accuracy of the identified modal frequency depends on the frequency resolution of the singular value curve. In order to solve the above problems, a variety of variant methods have been developed, the most mature of which are the enhanced frequency domain decomposition method EFDD and the frequency domain space domain decomposition method FSDD. Among them, the EFDD method performs an inverse Fourier transform on the singular values ​​in a narrow frequency band near the peak selected by the original FDD method to obtain a single-mode correlation function, extract the attenuation envelope and zero-crossing curve of the correlation function, and use a straight-line fitting method to estimate the modal damping ratio and natural frequency respectively. The FSDD method is based on the FDD method, and uses the singular vectors at the peak frequency to perform weighted calculation on the overall cross-power spectrum matrix to obtain an enhanced power spectrum function, and uses the real least squares algorithm to identify the natural frequency and modal damping ratio in a narrow frequency band.

[0004] All identification processes of the FSDD method are carried out in the frequency domain, which easily leads to skewness errors when identifying modal parameters, especially damping ratio parameters. Summary of the invention

[0005] The present application provides an operational modal analysis method based on composite frequency domain decomposition, which improves the stability and noise resistance of modal parameter identification. The technical solution is as follows.

[0006] In one aspect, an operational modal analysis method based on composite frequency domain decomposition is provided, the method comprising:

[0007] Obtain multi-channel structural vibration response data and calculate the cross-power spectrum matrix;

[0008] Performing singular value decomposition on the cross power spectrum matrix to obtain a frequency vector function;

[0009] According to the frequency vector function, selecting the peak frequency of the target order;

[0010] According to the peak frequency of the target order, obtaining an enhanced frequency domain complex function of the target order;

[0011] Based on the enhanced frequency domain complex function of the target order, the natural frequency and modal damping ratio of the target order are fitted using a second-order orthogonal polynomial fraction.

[0012] In another aspect, an operational modal analysis device based on composite frequency domain decomposition is provided, the device comprising:

[0013] A cross-power spectrum matrix calculation module is used to obtain multi-channel structural vibration response data and calculate the cross-power spectrum matrix;

[0014] A singular value decomposition module, used for performing singular value decomposition on the cross power spectrum matrix to obtain a frequency vector function;

[0015] A frequency peak selection module, used to select the peak frequency of the target order according to the frequency vector function;

[0016] A complex function selection module, used for obtaining an enhanced frequency domain complex function of a target order according to the peak frequency of the target order;

[0017] A fitting module is used to fit the natural frequency and modal damping ratio of the target order based on the enhanced frequency domain complex function of the target order using a second-order orthogonal polynomial fraction.

[0018] In a possible implementation, the multi-channel structure vibration response data y(nΔt) is:

[0019] y(nΔt)=[y1(nΔt) y2(nΔt) … y no (nΔt)] T

[0020] Where Δt is the sampling interval, n is the sampling point number, and the superscript T indicates transposition.

[0021] In a possible implementation, the cross-power spectrum matrix calculation module is used to perform calculation according to the following formula:

[0022]

[0023] Among them, the cross power spectrum matrix G yy (ω k ) is the auto-power spectrum, and the other elements are the cross-power spectrum, ω k represents the circular frequency corresponding to the kth spectral line, p i,i (ω) is the autopower spectrum of the i-th channel data, p i,j (ω) is the cross power spectrum of the i-th channel and the j-th channel data.

[0024] In a possible implementation, the singular value decomposition module is further used to:

[0025] The cross power spectrum matrix is ​​subjected to singular value decomposition using the following formula:

[0026]

[0027] Among them, U k is the matrix composed of the left singular vectors on the kth spectral line, Σ(ω k ) is a diagonal matrix composed of singular values, V k is the matrix composed of the right singular vectors on the kth spectral line, and the superscript H represents the conjugate transpose.

[0028] In a possible implementation, the singular value decomposition module is further used to:

[0029] Taking the diagonal elements of the singular value matrix on the k-th spectral line in the cross-power spectrum matrix, and arranging them in descending order, to obtain a singular value sequence corresponding to the k-th spectral line;

[0030] In the singular value sequences corresponding to all the spectrum lines in the cross-power spectrum matrix, singular values ​​in a specified order are selected to form a singular value function curve.

[0031] In a possible implementation, the peak frequency selection module is further used to:

[0032] On the singular value function curve, select the r-th order peak and record the spectral line index corresponding to the r-th order peak;

[0033] The frequency f corresponding to the r-th order peak is selected according to the spectral line index r .

[0034] In a possible implementation, the complex function acquisition module includes:

[0035] A response function acquisition unit, used for acquiring an enhanced response function of a target order according to a peak frequency of the target order;

[0036] The complex function acquisition unit is used to acquire the enhanced frequency domain complex function of the target order according to the enhanced response function of the target order.

[0037] In a possible implementation, the response function acquisition unit is further configured to:

[0038] From the cross power spectrum matrix, calculate the left singular vector u corresponding to the r-th order peak r ;

[0039] The left singular vector corresponding to the r-th order peak is used to perform weighted calculation on the multi-channel response data to obtain the r-th order enhanced response y r (nΔt):

[0040]

[0041] Among them, Re() means taking the real part;

[0042] The autocorrelation calculation is performed on the r-th order enhanced response:

[0043]

[0044] Where L is the enhanced response function y r The sample length of (nΔt);

[0045] Then we get the enhanced correlation function of positive delay and negative delay:

[0046]

[0047] Among them, a r is the amplitude coefficient, the superscript * indicates conjugation, λ r represents the r-th order pole, which can be expressed as:

[0048]

[0049] Among them, f r is the rth order natural frequency, ξ r is the r-th order modal damping ratio.

[0050] In a possible implementation, the complex function acquisition unit is further configured to:

[0051] The enhanced frequency domain complex function is expressed as a second-order orthogonal polynomial fraction:

[0052]

[0053] Among them, β i , α i are the numerator and denominator orthogonal polynomials of order i, c i d i are the corresponding polynomial coefficients.

[0054] On the other hand, a computer device is provided, comprising a processor and a memory, wherein the memory stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the above-mentioned operational modal analysis method based on composite frequency domain decomposition.

[0055] On the other hand, a computer-readable storage medium is provided, wherein at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement the above-mentioned operational modal analysis method based on composite frequency domain decomposition.

[0056] In another aspect, a computer program product or a computer program is provided, wherein the computer program product or the computer program includes computer instructions, and the computer instructions are stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device performs the above-mentioned operational modal analysis method based on composite frequency domain decomposition.

[0057] The technical solution provided by this application may have the following beneficial effects:

[0058] First, the multi-channel structural vibration response data of the object is obtained, and its cross-power spectrum matrix is ​​calculated. The cross-power spectrum matrix is ​​decoupled by the singular vector at the target order peak, and based on the decoupled enhanced response function, the enhanced frequency domain complex function is obtained. The enhanced frequency domain complex function contains amplitude and phase information. Without any approximation, the numerator complex orthogonal polynomial and the denominator complex orthogonal polynomial are used to fit the natural frequency and damping ratio of the structure, thereby improving the stability and noise resistance of modal parameter identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the specific implementation methods of the present application or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0060] Figure 1 It is a schematic structural diagram of a mechanical structure vibration analysis system according to an exemplary embodiment.

[0061] Figure 2 The present invention is a flowchart of an operational modal analysis method based on composite frequency domain decomposition according to an exemplary embodiment.

[0062] Figure 3 The present invention is a flowchart of an operational modal analysis method based on composite frequency domain decomposition according to an exemplary embodiment.

[0063] Figure 4 It is a schematic diagram of a singular value function curve of an operational modal analysis method based on composite frequency domain decomposition according to an exemplary embodiment.

[0064] Figure 5 It is a schematic diagram of a fitting curve of an operational modal analysis method based on composite frequency domain decomposition according to an exemplary embodiment.

[0065] Figure 6It is a structural block diagram of an operational modal analysis device based on composite frequency domain decomposition according to an exemplary embodiment.

[0066] Figure 7 It is a structural block diagram of a computer device according to an exemplary embodiment. DETAILED DESCRIPTION

[0067] The technical solution of the present application will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present application.

[0068] It should be understood that the "indication" mentioned in the embodiments of the present application can be a direct indication, an indirect indication, or an indication of an association relationship. For example, A indicates B, which can mean that A directly indicates B, for example, B can be obtained through A; it can also mean that A indirectly indicates B, for example, A indicates C, and B can be obtained through C; it can also mean that there is an association relationship between A and B.

[0069] In the description of the embodiments of the present application, the term "corresponding" may indicate a direct or indirect correspondence between two items, or an association relationship between the two items, or a relationship between indication and being indicated, configuration and being configured, and the like.

[0070] In an embodiment of the present application, "predefinition" can be achieved by pre-saving corresponding codes, tables or other methods that can be used to indicate relevant information in a device (for example, including a terminal device and a network device). The present application does not limit its specific implementation method.

[0071] Figure 1 1 is a schematic diagram of a mechanical structure vibration analysis system according to an exemplary embodiment. The mechanical structure vibration analysis system includes a data processing device 110 and a data acquisition device 120 .

[0072] Optionally, the data acquisition device 120 includes a vibration sensor, which can collect vibrations of a target object, thereby obtaining vibration data of the target object.

[0073] Optionally, the data acquisition device 120 further includes a data storage device. When the vibration sensor in the data acquisition device performs vibration acquisition on the target object and obtains the vibration data of the target object, the vibration data can be stored in the data storage device.

[0074] Optionally, the data processing device 110 may be a computer device with high computing power, and the data processing device is used to analyze the collected vibration data of the target object to obtain the vibration characteristics of the target object.

[0075] Optionally, the data processing device 110 may be a terminal device installed with vibration analysis software. When the terminal device receives an instruction to analyze vibration data, the terminal device may read corresponding vibration data from a data storage device in the data acquisition device 120, and analyze the vibration data to obtain the vibration characteristics of the target object.

[0076] Optionally, the terminal device can perform modal analysis on the vibration data of the target object to obtain the specific natural frequency, damping ratio and modal vibration shape of each mode of the target object, that is, the vibration characteristics of the target object, to complete the vibration analysis of the target object.

[0077] Optionally, the data processing device 110 may also be a server installed with vibration analysis software, and the data acquisition device may be a terminal device. When the vibration sensor in the terminal device collects vibration data of the target object, the vibration data may be transmitted to the server to complete the vibration analysis of the target object.

[0078] Optionally, the data processing device 110 and the data acquisition device 120 may be communicatively connected via a wired or wireless network.

[0079] Optionally, the above-mentioned server can be a server cluster or a distributed system composed of multiple physical servers, or it can be a cloud server that provides cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, CDN, as well as big data and artificial intelligence platforms and other technical computing services.

[0080] Optionally, the system may further include a management device, which is used to manage the system (such as managing the connection status between each module and the server, etc.), and the management device is connected to the server via a communication network. Optionally, the communication network is a wired network or a wireless network.

[0081] Optionally, the above-mentioned wireless network or wired network uses standard communication technology and / or protocol. The network is usually the Internet, but it can also be any other network, including but not limited to any combination of local area network, metropolitan area network, wide area network, mobile, limited or wireless network, private network or virtual private network. In some embodiments, the technology and / or format including hypertext markup language, extensible markup language, etc. are used to represent the data exchanged through the network. In addition, conventional encryption technologies such as secure socket layer, transport layer security, virtual private network, Internet protocol security, etc. can also be used to encrypt all or some links. In other embodiments, customized and / or dedicated data communication technology can also be used to replace or supplement the above-mentioned data communication technology.

[0082] Figure 2 is a flowchart of an operational modal analysis method based on composite frequency domain decomposition according to an exemplary embodiment. The method is executed by a computer device, which may be Figure 1 The data processing device 110 shown in FIG. Figure 2 As shown, the operational modal analysis method of the composite frequency domain decomposition may include the following steps:

[0083] Step 201: Acquire multi-channel structural vibration response data and calculate the cross-power spectrum matrix.

[0084] Modal analysis is a method for studying the dynamic characteristics of structures, and is generally used in the field of engineering vibration. Among them, mode refers to the natural vibration characteristics of mechanical structures, and each mode has a specific natural frequency, damping ratio, and modal vibration shape. Operational modal analysis refers to the use of the output response of the structure to perform modal analysis, that is, to analyze the natural vibration characteristics of the mechanical structure.

[0085] In the embodiment of the present application, when analyzing the inherent vibration characteristics of the mechanical structure, multi-channel structural vibration response data can be obtained first.

[0086] Optionally, in the multi-channel structural vibration response data, the data between the channels may be independent of each other or may be related to each other. For example, the data of some channels may be obtained through the data of other channels.

[0087] The source of the multi-channel structural vibration response data may be a house, a bridge, a ship, an airplane, or an earthquake or a typhoon. That is to say, the multi-channel structural vibration response data may be obtained based on electrical signals, magnetic signals, or sound wave signals.

[0088] After acquiring the multi-channel structural vibration response data, the computer equipment can calculate the cross-power spectrum matrix based on the multi-channel structural vibration response data. The cross-power spectrum can describe the statistical correlation between two different signals in the frequency domain. Any element in the cross-power spectrum matrix is ​​the statistical correlation between two different signals or between a signal and itself. For example, the cross-power spectrum matrix can be calculated according to the periodogram method.

[0089] Among them, the periodogram method can also be a piecewise average periodogram method, a windowed average periodogram method, a Welch periodogram method, a multi-window periodogram method, a maximum entropy periodogram method, or a multi-signal classification periodogram method.

[0090] Step 202: perform singular value decomposition on the cross-power spectrum matrix to obtain a frequency vector function.

[0091] In a possible implementation, the computer device may first perform singular value decomposition on the cross-power spectrum matrix. The singular value decomposition may be applied to matrices with unequal numbers of row and column elements. The singular value decomposition may be calculated by a single machine or in parallel. Then, according to the singular value decomposition result, the diagonal elements of each spectrum line in the singular value matrix are arranged in a target order to obtain a singular value sequence corresponding to each spectrum line. In the singular value sequence corresponding to each spectrum line, singular values ​​of the target order are selected to obtain a frequency vector function.

[0092] Step 203: Select the peak frequency of the target order according to the frequency vector function.

[0093] In one possible implementation, after obtaining the frequency vector function, the frequency vector function is represented in a coordinate system to form a singular value function curve, and then the peak value of the target order is selected from the singular value function curve and the spectral line index corresponding to the peak value of the target order is recorded, and the frequency of the target order corresponding to the peak value of the target order is selected according to the spectral line index.

[0094] Step 204: Obtain an enhanced frequency domain complex function of the target order according to the peak frequency of the target order.

[0095] In one possible implementation, a computer device can calculate the left singular vectors of the target order based on the cross-power spectrum matrix of the target order, and use the left singular vectors of the target order to perform weighted calculation on the multi-channel structural vibration response data to obtain an enhanced response function of the target order; then, the enhanced response function of the target order is autocorrelated to obtain enhanced correlation functions of positive and negative delays of the target order, and the enhanced correlation function of the positive delay of the target order is discrete Fourier transformed to obtain an enhanced frequency domain complex function of the target order.

[0096] Step 205 : Based on the enhanced frequency domain complex function of the target order, a second-order orthogonal polynomial fraction is used to fit the natural frequency and modal damping ratio of the target order.

[0097] In one possible implementation, after obtaining the enhanced frequency domain complex function of the target order, the enhanced frequency domain complex function is expressed as a second-order orthogonal polynomial fraction, and then the coefficient solution equation is obtained by the least squares method. The coefficient solution equation is solved to obtain the solution of the denominator coefficient and the numerator coefficient, and then the natural frequency and modal damping ratio of the target order are fitted.

[0098] In summary, this method first obtains the multi-channel structural vibration response data of the object and calculates its cross-power spectrum matrix. The cross-power spectrum matrix is ​​decoupled by the singular vector at the target order peak, and based on the decoupled enhanced response function, the enhanced frequency domain complex function is obtained. The enhanced frequency domain complex function contains amplitude and phase information. Without any approximation, the numerator complex orthogonal polynomial and the denominator complex orthogonal polynomial are used to fit the natural frequency and damping ratio of the structure, thereby improving the stability and noise resistance of modal parameter identification.

[0099] Figure 3 is a flowchart of an operational modal analysis method based on composite frequency domain decomposition according to an exemplary embodiment. The method is executed by a computer device, which may be Figure 1 The data processing equipment in the modal analysis system shown in FIG. Figure 3 As shown, the operational modal analysis method based on composite frequency domain decomposition may include the following steps:

[0100] Step 301: Acquire multi-channel structural vibration response data and calculate the cross-power spectrum matrix.

[0101] Optionally, the multi-channel structural vibration response data y(nΔt) is:

[0102] y(nΔt)=[y1(nΔt) y2(nΔt) … y no (nΔt)] T

[0103] Among them, Δt is the sampling interval, its reciprocal is the sampling frequency, n is the sampling point number, and the superscript T indicates transposition.

[0104] Optionally, the computer device may calculate the cross-power spectrum matrix by the following steps:

[0105]

[0106] Among them, the cross power spectrum matrix G yy (ω k ) is the auto-power spectrum, and the other elements are the cross-power spectrum, ω krepresents the circular frequency corresponding to the kth spectral line, p i,i (ω) is the autopower spectrum of the i-th channel data, p i,j (ω) is the cross power spectrum of the i-th channel and the j-th channel data. Exemplarily, the Welch periodogram method can be used to calculate the cross power spectrum matrix.

[0107] Step 302: Perform singular value decomposition on the cross-power spectrum matrix to obtain a frequency vector function.

[0108] Optionally, the computer device may perform singular value decomposition of the cross power spectrum matrix using the following formula:

[0109]

[0110] Among them, U k is the matrix composed of the left singular vectors on the kth spectral line, Σ(ω k ) is a diagonal matrix composed of singular values, V k is the matrix composed of the right singular vectors on the kth spectral line, and the superscript H represents the conjugate transpose.

[0111] Furthermore, the computer device may take the diagonal elements of the singular value matrix on the kth spectral line in the cross-power spectrum matrix and arrange them in descending order to obtain a singular value sequence corresponding to the kth spectral line.

[0112] In the singular value sequence corresponding to all spectral lines in the cross-power spectrum matrix, select the singular values ​​in the specified order to form a singular value function curve. Please refer to Figure 4 , which shows a schematic diagram of a singular value function curve involved in an embodiment of the present application.

[0113] Step 303: Select the peak frequency of the target order according to the frequency vector function.

[0114] Optionally, the computer device selects the r-th order peak on the singular value function curve and records the spectral line index corresponding to the r-th order peak; selects the frequency f corresponding to the r-th order peak according to the spectral line index r .

[0115] Step 304: Obtain an enhanced response function of the target order according to the peak frequency of the target order.

[0116] Optionally, the computer device calculates the left singular vector u corresponding to the r-th order peak from the cross power spectrum matrix r , and use the left singular vector corresponding to the r-th order peak to perform weighted calculation on the multi-channel response data to obtain the r-th order enhanced response y r (nΔt):

[0117]

[0118] Among them, Re() means taking the real part;

[0119] Calculate the autocorrelation of the r-th order enhancement response:

[0120]

[0121] Where L is the enhanced response function y r (nΔt) sample length;

[0122] Then we get the enhanced correlation function of positive delay and negative delay:

[0123]

[0124] Among them, a r is the amplitude coefficient, the superscript * indicates conjugation, λ r represents the r-th order pole, which contains the natural frequency and damping ratio information of the structure and can be expressed as:

[0125]

[0126] Among them, f r is the rth order natural frequency, ξ r is the r-th order modal damping ratio.

[0127] Step 305: Obtain an enhanced frequency domain complex function of the target order according to the enhanced response function of the target order.

[0128] Optionally, the computer device may take the positively delayed enhanced correlation function and perform a discrete Fourier transform to obtain an enhanced frequency domain complex function g r (jω k ):

[0129]

[0130] in,

[0131] Step 306 : Based on the enhanced frequency domain complex function of the target order, a second-order orthogonal polynomial fraction is used to fit the natural frequency and modal damping ratio of the target order.

[0132] Optionally, the computer device may represent the enhanced frequency domain complex function using a second-order orthogonal polynomial fraction:

[0133]

[0134] Among them, β i , α i are the numerator and denominator orthogonal polynomials of order i, c i d i are the corresponding polynomial coefficients.

[0135] Furthermore, a frequency band is selected, and the number of spectral lines contained in the frequency band is N, then:

[0136]

[0137]

[0138] v=[g(jω -N )α2(jω -N ) … g(jω -1 )α2(jω -1 ) g(jω1)α2(jω1) … g(jω N )α2(jω N )] T

[0139] According to the least squares method, the coefficients are obtained to solve the equation:

[0140]

[0141] Among them, I1 and I2 are unit matrices, B = -Re(P H Q), C=P H P, D = Q H Q,x=Re(P H v), c=[c0 c1 c2] T , d=[d0 d1 d2] T ;

[0142] The denominator coefficient solution d and the numerator coefficient solution c in the coefficient solution equation are:

[0143] d=-(I2-B T B) -1 B T x

[0144] c=x-Bd

[0145] The roots of the quadratic equation consisting of the coefficients of the denominator polynomial are the conjugate poles λ of the structure r and The amplitude and phase of the enhanced frequency domain complex function within the frequency band can be synthesized from the numerator polynomial and the denominator polynomial. Figure 5 , which shows a schematic diagram of a fitting curve involved in an embodiment of the present application.

[0146] In summary, this method first obtains the multi-channel structural vibration response data of the object and calculates its cross-power spectrum matrix. The cross-power spectrum matrix is ​​decoupled by the singular vector at the target order peak, and based on the decoupled enhanced response function, the enhanced frequency domain complex function is obtained. The enhanced frequency domain complex function contains amplitude and phase information. Without any approximation, the numerator complex orthogonal polynomial and the denominator complex orthogonal polynomial are used to fit the natural frequency and damping ratio of the structure, thereby improving the stability and noise resistance of modal parameter identification.

[0147] Figure 6 1 is a block diagram of a structure of an operational modal analysis device based on composite frequency domain decomposition according to an exemplary embodiment. The operational modal analysis device based on composite frequency domain decomposition includes:

[0148] A cross-power spectrum matrix calculation module 601 is used to obtain multi-channel structural vibration response data and calculate the cross-power spectrum matrix;

[0149] A singular value decomposition module 602 is used to perform singular value decomposition on the cross power spectrum matrix to obtain a frequency vector function;

[0150] A frequency peak selection module 603 is used to select a peak frequency of a target order according to the frequency vector function;

[0151] A complex function selection module 604 is used to obtain an enhanced frequency domain complex function of a target order according to the peak frequency of the target order;

[0152] The fitting module 605 is used to fit the natural frequency and modal damping ratio of the target order using a second-order orthogonal polynomial fraction based on the enhanced frequency domain complex function of the target order.

[0153] In a possible implementation, the multi-channel structure vibration response data y(nΔt) is:

[0154] y(nΔt)=[y1(nΔt) y2(nΔt) … y no (nΔt)] T

[0155] Where Δt is the sampling interval, n is the sampling point number, and the superscript T indicates transposition.

[0156] In a possible implementation, the cross-power spectrum matrix calculation module is used to perform calculation according to the following formula:

[0157]

[0158] Among them, the cross power spectrum matrix G yy (ω k ) is the auto-power spectrum, and the other elements are the cross-power spectrum, ωk represents the circular frequency corresponding to the kth spectral line, p i,i (ω) is the autopower spectrum of the i-th channel data, p i,j (ω) is the cross power spectrum of the i-th channel and the j-th channel data.

[0159] In a possible implementation, the singular value decomposition module is further used to:

[0160] The cross power spectrum matrix is ​​subjected to singular value decomposition using the following formula:

[0161]

[0162] Among them, U k is the matrix composed of the left singular vectors on the kth spectral line, Σ(ω k ) is a diagonal matrix composed of singular values, V k is the matrix composed of the right singular vectors on the kth spectral line, and the superscript H represents the conjugate transpose.

[0163] In a possible implementation, the singular value decomposition module is further used to:

[0164] Taking the diagonal elements of the singular value matrix on the k-th spectral line in the cross-power spectrum matrix, and arranging them in descending order, to obtain a singular value sequence corresponding to the k-th spectral line;

[0165] In the singular value sequences corresponding to all the spectrum lines in the cross-power spectrum matrix, singular values ​​in a specified order are selected to form a singular value function curve.

[0166] In a possible implementation, the peak frequency selection module is further used to:

[0167] On the singular value function curve, select the r-th order peak and record the spectral line index corresponding to the r-th order peak;

[0168] The frequency f corresponding to the r-th order peak is selected according to the spectral line index r .

[0169] In a possible implementation, the complex function acquisition module includes:

[0170] A response function acquisition unit, used for acquiring an enhanced response function of a target order according to a peak frequency of the target order;

[0171] The complex function acquisition unit is used to acquire the enhanced frequency domain complex function of the target order according to the enhanced response function of the target order.

[0172] In a possible implementation, the response function acquisition unit is further configured to:

[0173] From the cross power spectrum matrix, calculate the left singular vector u corresponding to the r-th order peak r ;

[0174] The left singular vector corresponding to the r-th order peak is used to perform weighted calculation on the multi-channel response data to obtain the r-th order enhanced response y r (nΔt):

[0175]

[0176] Among them, Re() means taking the real part;

[0177] The autocorrelation calculation is performed on the r-th order enhanced response:

[0178]

[0179] Where L is the enhanced response function y r The sample length of (nΔt);

[0180] Then we get the enhanced correlation function of positive delay and negative delay:

[0181]

[0182] Among them, a r is the amplitude coefficient, the superscript * indicates conjugation, λ r represents the r-th order pole, which can be expressed as:

[0183]

[0184] Among them, f r is the rth order natural frequency, ξ r is the r-th order modal damping ratio.

[0185] In a possible implementation, the complex function acquisition unit is further configured to:

[0186] The enhanced frequency domain complex function is expressed as a second-order orthogonal polynomial fraction:

[0187]

[0188] Among them, β i , α i are the numerator and denominator orthogonal polynomials of order i, c i d i are the corresponding polynomial coefficients.

[0189] In summary, the multi-channel structural vibration response data of the object is first obtained, and its cross-power spectrum matrix is ​​calculated. The cross-power spectrum matrix is ​​decoupled by the singular vector at the target order peak, and based on the decoupled enhanced response function, the enhanced frequency domain complex function is obtained. The enhanced frequency domain complex function contains amplitude and phase information. Without any approximation, the numerator complex orthogonal polynomial and the denominator complex orthogonal polynomial are used to fit the natural frequency and damping ratio of the structure, thereby improving the stability and noise resistance of modal parameter identification.

[0190] Figure 7 The structural block diagram of a computer device 700 shown in an exemplary embodiment of the present application is shown. The computer device can be implemented as a server in the above-mentioned solution of the present application. The computer device 700 includes a central processing unit (CPU) 701, a system memory 704 including a random access memory (RAM) 702 and a read-only memory (ROM) 703, and a system bus 705 connecting the system memory 704 and the central processing unit 701. The computer device 700 also includes a large-capacity storage device 706 for storing an operating system 709, an application program 710 and other program modules 711.

[0191] The mass storage device 706 is connected to the central processing unit 701 via a mass storage controller (not shown) connected to the system bus 705. The mass storage device 706 and its associated computer readable medium provide non-volatile storage for the computer device 700. That is, the mass storage device 706 may include a computer readable medium (not shown) such as a hard disk or a compact disc read-only memory (CD-ROM) drive.

[0192] Without loss of generality, the computer-readable medium may include computer storage media and communication media. Computer storage media include volatile and non-volatile, removable and non-removable media implemented by any method or technology for storing information such as computer-readable instructions, data structures, program modules or other data. Computer storage media include RAM, ROM, Erasable Programmable Read Only Memory (EPROM), Electronically-Erasable Programmable Read-Only Memory (EEPROM) flash memory or other solid-state storage technology, CD-ROM, Digital Versatile Disc (DVD) or other optical storage, cassette, tape, disk storage or other magnetic storage devices. Of course, those skilled in the art will know that the computer storage medium is not limited to the above. The above-mentioned system memory 704 and mass storage device 706 can be collectively referred to as memory.

[0193] According to various embodiments of the present disclosure, the computer device 700 can also be connected to a remote computer on the network through a network such as the Internet. That is, the computer device 700 can be connected to the network 708 through the network interface unit 707 connected to the system bus 705, or the network interface unit 707 can be used to connect to other types of networks or remote computer systems (not shown).

[0194] The memory further includes at least one computer program, which is stored in the memory. The central processing unit 701 implements all or part of the steps in the methods shown in the above embodiments by executing the at least one computer program.

[0195] In an exemplary embodiment, a computer-readable storage medium is also provided, which is used to store at least one computer program, and the at least one computer program is loaded and executed by a processor to implement all or part of the steps in the above method. For example, the computer-readable storage medium can be a read-only memory (ROM), a random access memory (RAM), a compact disc read-only memory (CD-ROM), a magnetic tape, a floppy disk, an optical data storage device, etc.

[0196] In an exemplary embodiment, a computer program product or a computer program is also provided, the computer program product or the computer program comprising computer instructions, the computer instructions being stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device performs the above-mentioned Figure 2 or Figure 3 All or part of the steps of the method shown in any embodiment.

[0197] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the invention disclosed herein. The present application is intended to cover any modification, use or adaptation of the present application, which follows the general principles of the present application and includes common knowledge or customary techniques in the art that are not disclosed in the present application. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present application are indicated by the following claims.

[0198] It should be understood that the present application is not limited to the precise structures that have been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims

1. An operational modal analysis method based on composite frequency domain decomposition, characterized in that: The method comprises: Obtain multi-channel structural vibration response data and calculate the cross-power spectrum matrix; Performing singular value decomposition on the cross power spectrum matrix to obtain a frequency vector function; According to the frequency vector function, selecting the peak frequency of the target order; According to the peak frequency of the target order, obtaining an enhanced frequency domain complex function of the target order; Based on the enhanced frequency domain complex function of the target order, the natural frequency and modal damping ratio of the target order are fitted using a second-order orthogonal polynomial fraction; The step of obtaining an enhanced frequency domain complex function of a target order according to the peak frequency of the target order includes: According to the peak frequency of the target order, an enhanced response function of the target order is obtained; According to the enhanced response function of the target order, an enhanced frequency domain complex function of the target order is obtained; The step of obtaining the enhanced response function of the target order according to the peak frequency of the target order comprises: From the cross power spectrum matrix, we can calculate r The left singular vector corresponding to the order peak ; Adopt the r The left singular vector corresponding to the peak value is weighted to calculate the multi-channel response data, and the r Order Enhanced Response : Where Re( ) means taking the real part; For r The autocorrelation of the order-enhanced response is calculated: in, L is the enhanced response function The sample length of Get the enhanced correlation function for positive and negative delays: in, is the amplitude coefficient, the superscript represents conjugation, Indicates r The order pole is expressed as: in, For the r The natural frequency, For the r Damping ratio of the first mode; Obtaining the enhanced frequency domain complex function of the target order includes: Take the positive delayed enhanced correlation function and perform discrete Fourier transform to obtain the enhanced frequency domain complex function : in, .

2. The method according to claim 1, characterized in that The multi-channel structural vibration response data for: in, is the sampling interval, n is the sampling point number, and the superscript T indicates transposition.

3. The method according to claim 2, characterized in that The calculation of the cross power spectrum matrix comprises: Among them, the cross power spectrum matrix The diagonal elements of are the auto-power spectra, and the other elements are the cross-power spectra. Indicates k The circular frequency corresponding to the root spectrum line is For the i The autopower spectrum of the channel data is For the i Channels and j The cross power spectrum of the channel data.

4. The method according to claim 1, characterized in that Performing singular value decomposition on the cross power spectrum matrix includes: The cross power spectrum matrix is ​​subjected to singular value decomposition using the following formula: in, For the k The matrix composed of the left singular vectors on the root spectrum, is a diagonal matrix of singular values, For the k The matrix composed of the right singular vectors on the root spectral lines. The superscript H represents the conjugate transpose.

5. The method according to claim 4, characterized in that The frequency vector acquisition function comprises: Take the first k The diagonal elements of the singular value matrix on the root spectrum line are arranged in order from large to small to obtain the k The singular value sequence corresponding to the root spectral line; In the singular value sequences corresponding to all the spectrum lines in the cross-power spectrum matrix, singular values ​​in a specified order are selected to form a singular value function curve.

6. The method according to claim 5, characterized in that The peak frequency of the target order is selected as follows: On the singular value function curve, select r The peak value of the first r The spectral line index corresponding to the order peak; According to the spectral line index, the first r The frequency corresponding to the order peak .

7. The method according to claim 1, characterized in that Based on the enhanced frequency domain complex function of the target order, the natural frequency and modal damping ratio of the target order are fitted using a second-order orthogonal polynomial fraction, including: The enhanced frequency domain complex function is expressed as a second-order orthogonal polynomial fraction: in, , Respectively i The numerator and denominator are orthogonal polynomials of order, , are the corresponding polynomial coefficients.

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