CN104698837A - Method and device for identifying operating modal parameters of linear time-varying structure and application of the device - Google Patents

Abstract

The invention relates to a time-varying structure working modal parameter identification method based on limited memory principal component analysis, which can only use non-stationary vibration response signals for dynamic systems with time-varying structural characteristics to identify working modal parameters and identify the structure The working mode parameters can effectively monitor the dynamic characteristics of the system in real time, and can be used for vibration control, equipment fault diagnosis, health monitoring, and system structure analysis and optimization. This method only recognizes the parameter characteristics of the system by the measured response signal, without measuring the load signal, and it is proved from mathematical theory analysis and experiment, giving the method a physical meaning. The present invention also relates to a working mode measurement device based on the above method, which measures the vibration response signal and identifies the working mode parameters, obtains the real-time online dynamic characteristic changes of the system structure, and uses it for large complex engineering structures (bridges, Rails, etc.) in fault diagnosis and health monitoring analysis.

Description

A time-varying linear structure working mode parameter identification method, device and application

technical field

The present invention relates to a time-varying linear structural working modal parameter identification method based on limited memory principal component analysis, and the application of the method in structural fault diagnosis and health state monitoring, and also relates to a time-varying linear structure based on limited memory principal component analysis. A variable linear structure working mode parameter identification device.

Background technique

The analysis of vibration characteristics of structures is highly valued in the fields of aerospace vehicles, submarines, civil engineering, ships, automobiles, etc., especially the modal analysis. Modal analysis provides an effective way to study various vibration characteristics. Accurate identification of modal parameters (modal frequency, mode shape, damping ratio) is an important guarantee for the safety and maintainability of the system structure, and an important method for structural dynamic design and fault diagnosis. The traditional experimental modal analysis method is mainly based on applying artificial excitation to the measurement structure in the laboratory. By measuring the excitation and response signals, the modal analysis theory is used to obtain the frequency response function curve of the system, thereby estimating the modal parameters. In recent years, with the increase in size and complexity of the research structure, it is difficult to measure the excitation load of the structure, and it is difficult to realize the method of applying artificial excitation in the past, so the identification method of the working mode parameters was born. For example, wind loads on bridges, wave loads on large marine structures, etc. If you want to establish a dynamic model of the structure, you can only use the method of identifying the working modal parameters (only identify the modal parameters of the system from the measured response signal). The identification method of working modal parameters belongs to the second type of inverse problem in engineering mechanics. This method is difficult to study and is an important research direction. At present, its theory and technology are still immature and need to be further studied and developed.

In actual engineering, the structural parameters (mass, stiffness, damping, etc.) of the system are not constant and have time-varying characteristics. For example, during the flight of rockets, missiles and other aircraft, the fuel is consumed rapidly, and its mass has time-varying characteristics; another example is that high-speed trains will cause severe vibration of bridges, and the structural systems of bridges and trains are time-varying. For this time-varying structure, if the linear time-invariant identification model is still used, the estimated parameters will seriously deviate from the real value or even diverge, which will bring great difficulty to the analysis and control of the system. Therefore, the research on the time-varying structure is imminent. The study of time-varying structures is a frontier problem in structural dynamics, especially the inverse problem (in the case of unknown excitation), and the current theory and technology are still very immature. Scholars at home and abroad have also done a lot of research on this problem. For example, McLamore et al. used the peak method to extract the modal frequency based on the fast Fourier transform, but this method has the problem of not being able to identify dense modes; the subspace method proposed by Kalman et al. , using matrix decomposition and other methods to extract the signal subspace to obtain an equivalent system, this method is suitable for parameter identification of linear time-varying structures under stationary excitation, and has a certain anti-interference ability to output noise, but the determination of the order of the stochastic subspace model It is relatively cumbersome, with a large amount of calculation, and it is easy to identify false modes; there are also methods such as wavelet transform and Hilbert-Huang transform based on time-frequency analysis, which analyze signal characteristics from both time domain and frequency domain, but these methods are a This kind of local recognition method is difficult to do a complete analysis of the overall characteristics of the system, and for dense mode problems, the recognition accuracy is easily affected due to the limitation of filtering capabilities.

At present, the parameter identification method for studying time-varying structures is mainly based on the idea of "time freezing", that is, it is assumed that the system is frozen at a certain moment, and in this short time range, the system is regarded as a linear time-invariant system. Then use the theory of time-invariant structure to analyze. Existing studies mainly include two types: one is based on the limited memory method, that is, the data is divided into small time segments, and the structural parameters are regarded as time-invariant in each time segment, and then the identified data in each data segment The other is the online or recursive technology, the data at each moment must be considered, the old data is gradually forgotten, and the new data is continuously added, and the parameter value is calculated at each moment. Amendment, this method needs to consider how to select the observation data and forgetting factor.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art, to provide an improved time-varying structural work modal parameter identification method based on limited memory principal component analysis, and time-varying structural work modal parameter identification based on limited memory principal component analysis The device also provides the application of the identification method of time-varying structural operating mode parameters based on limited memory principal component analysis in equipment fault diagnosis and health status monitoring.

Technical scheme of the present invention is as follows:

A time-varying linear structure operating modal parameter identification method based on limited memory principal component analysis, which only uses the time-domain vibration response signals of multiple sensor measurement points of the time-varying linear structure, combined with the idea of limited memory and principal component analysis algorithm, using The statistical characteristics of the principal component analysis algorithm in each limited memory period can obtain the transient operating mode parameters at each time, and then the operating mode parameters obtained at each time are connected to perform curve fitting, so as to realize the time-varying linear structure. Modal parameter identification.

Preferably, the specific steps are as follows:

Step 1) Set the measured original time-domain vibration response data X(t) matrix of the time-varying linear structure under white noise excitation as:

Among them, M represents the number of vibration sensor measuring points arranged on the time-varying linear structure, N represents the number of sampling points in the time domain, 1≤j≤M; 1≤i≤N, the length of the selected limited memory data rectangular window is L , initialize i=1;

Step 2) Continuously intercept the time-domain vibration response signal of length L in sequence

Find its autocorrelation matrix ${\mathrm{\ψ}}_{x_L^{\left(i\right)}{x}_L^{\left(i\right)T}}=e\left[x_L^{\left(i\right)}{x}_L^{\left(i\right)T}\right]\∈R^{m\×m};$

Step 3) According to linear algebra and matrix theory, the real symmetric square matrix uniquely decomposes into Among them, V ⁽ⁱ⁾ ∈ R ^M×M satisfies V ^(i)T V ⁽ⁱ⁾ ＝I _M×M , I _M×M is an M-dimensional identity matrix, and Υ ⁽ⁱ⁾ ∈ ^{R M×M} is derived from the real Symmetrical square matrix The eigenvalues of are arranged in order from large to small to form a diagonal square matrix;

Step 4) Based on principal component analysis, uniquely decomposes into Establish the PCA initialization model, where V ⁽ⁱ⁾ ∈ R ^{M × M} is the transformation matrix in the principal component analysis, is the intercepted time-domain vibration response signal of length L The principal components of , each principal component is not correlated with each other;

Step 5) For any time-domain vibration response signal of length L that is continuously intercepted in sequence Expressed in modal coordinates as $x_L^{\left(i\right)}\≈{\mathrm{\Φ}}^{\left(i\right)}{Q}_L^{\left(i\right)};$

where the regularized mode shape matrix ${\mathrm{\Φ}}^{\left(i\right)}=[{\mathrm{\φ}}_1^{\left(i\right)}\left(L\right),{\mathrm{\φ}}_2^{\left(i\right)}\left(L\right),\·\&Center\; Dot;\·,{\mathrm{\φ}}_j^{\left(i\right)}\left(L\right),\·\&Center\; Dot;\&Center\; Dot;{\mathrm{\φ}}_m^{\left(i\right)}\left(L\right)]{\∈R}^{m\×m}$ Satisfy Φ ^(i)T Φ ⁽ⁱ⁾ ＝I _M×M , modal coordinate response matrix

Among them, the modal responses of each order Independent;

Φ ⁽ⁱ⁾ ∈ ^{R M×M} is the statistical average mode of the time-varying linear structure from sampling time point i to i+L-1;

is the modal coordinate response of the time-varying linear structure from the sampling time point i to i+L-1, using single-degree-of-freedom modal identification technology to identify the modal coordinate response from the sampling time point i to i+L-1 The instantaneous modal natural frequency at the most intermediate moment $W_L^{\left(i\right)}={[w_1^{\left(i\right)}\left(L\right),w_2^{\left(i\right)}\left(L\right),\&Center\; Dot;\·\·,w_j^{\left(i\right)}\left(L\right),\·\·\·,w_m^{\left(i\right)}\left(L\right)]}^T\∈R^{m\×1};$

Step 6) Because they are independent of each other and must not be correlated, based on the principal component analysis, the regularized mode shape matrix Φ ⁽ⁱ⁾ ∈ R ^M×M corresponds to the linear aliasing matrix V ⁽ⁱ⁾ ∈ R ^M× in the principal component analysis ^M , the modal response matrix of each order Principal Components in Principal Component Analysis

Step 7) Accumulate the contribution rate according to the pivot Determine the number of principal components p, where CPV _p is the variance cumulative contribution rate of the first p principal components;

Step 8) Use the modal confidence parameter MAC to quantitatively evaluate the accuracy of mode shape identification, specifically:

in, is the identified mode shape of the jth mode at time i, represents the jth mode shape at the real time i, and Representing and the transposition of represents the inner product of two vectors, express and degree of similarity, If its value is closer to 1, the accuracy of mode shape identification is higher;

Step 9) i=i+1, return to step 2), until i=N+1-L.

Preferably, the transient operating mode parameters at each moment include the natural frequencies and natural mode shapes of modes of each order.

A method for equipment fault diagnosis and health status monitoring, based on the above-mentioned identification method of time-varying linear structure operating mode parameters based on limited memory principal component analysis, the steps are as follows:

Step a) collecting a set of response data online, performing normalization processing, and establishing an initial principal component model;

Step b) determining the number of pivots by the cumulative contribution rate of the pivots, and identifying the modal parameters;

Step d) Analyzing and comparing the measured working modal parameters with the modal parameters of the device under test before failure to determine whether the equipment is faulty and where the fault is located;

Step d) If no fault occurs, iterations are performed to re-establish the principal element model, and then the modal parameter identification analysis is performed.

Preferably, in step 2), the modal parameters include frequency and mode shape.

A time-varying linear structure operating mode parameter identification device based on limited memory principal component analysis, used to realize the above-mentioned time-varying linear structure operating mode parameter identification method based on limited memory principal component analysis; including a signal input module, a signal conditioning Module, data collector, A/D data acquisition conversion module, DSP, control module, storage module, power supply and reset module; signal input module, signal conditioning module, A/D data acquisition conversion module, DSP, control module, upper computer Two-way communication connection is carried out; the data collector is connected between the DSP and the signal conditioning module, the storage module is connected with the control module, and the power supply and reset module are respectively connected with the DSP and the control module.

As preferably, the working steps are as follows:

First, the host computer sends the information collection parameters to the control module through Ethernet; the control module then sends instructions to the DSP through SPI, and the DSP drives the data collector to collect data;

Then, the DSP analyzes the collected data in the time-frequency domain according to the instructions sent by the host computer, and then sends the collected original data and the data analyzed by the DSP to the control module through the SPI, and the control module restores and saves the data format, and passes through Ethernet transmission to the host computer for analysis and display.

The beneficial effects of the present invention are as follows:

The time-varying structure operating mode parameter identification method based on limited memory principal component analysis described in the present invention can carry out real-time online parameter identification for structures with time-varying characteristics, and identify the operating mode parameters (mode shape) of the system , modal frequency), real-time effective monitoring of the dynamic characteristics of the system, which can be used for equipment fault diagnosis, health monitoring, and system structure analysis and optimization. And this method is a method of identification of working modal parameters (the characteristics of the system can be identified only by the measured response signal), and it is proved from mathematical theoretical analysis and experiments, and the method is given a physical explanation, compared with the traditional The experimental modal parameter identification technology that needs to measure the excitation and response signals at the same time has great advantages. The main idea of this method is to first collect a set of data online, establish a PCA initialization model, and use the idea of principal component analysis to find out the correspondence between the mode shape and the linear aliasing matrix, as well as between the modal responses of each order and the principal components. relationship, identify the modal parameters of the system, prove the existence, uniqueness and certainty of the modal parameters through principal component decomposition, and the physical meaning of the algorithm is clear; then whenever a new set of data is collected, the data matrix and covariance matrix are updated The PCA model is updated and iterated accordingly, and then the modal parameters of the system structure are identified online in real time.

In the time-varying structure operating mode parameter identification device based on limited memory principal component analysis of the present invention, a plurality of vibration sensor devices are arranged on the key points of the measurement structure, and the operating mode parameters are determined by the vibration response signal obtained from the measurement. Identify and monitor the dynamic characteristic changes of the system structure, and apply it to the fault diagnosis and health status monitoring of large-scale engineering structures. The working mode parameter monitoring device takes ARM and DSP as the core, and forms a signal input module, a signal conditioning module, a data collector, an A/D data acquisition conversion module, DSP, a control module, a storage module, a power supply and a reset module and many other units. The design of the device makes full use of the ARM chip's low power consumption, fast processing speed, and flexible task scheduling, as well as the ability of DSP algorithm design and data processing and analysis, and effectively combines the two to realize real-time online acquisition, processing, transmission and analyze. At the same time, Ethernet is used for data transmission to realize fast and efficient data transmission, avoid signal loss during transmission, achieve remote diagnosis and monitoring, and resource sharing, which is superior to the shortcomings of traditional data collection such as offline and delay. The design of the device effectively combines signal processing technology, circuit design, computer technology, algorithm design and fault analysis technology, realizes the digitization, automation and intelligence of the diagnosis system, and has potential application value.

Description of drawings

Figure 1 is a block diagram of the design system of the working mode parameter measurement device;

Fig. 2 is a functional structure diagram of the upper computer;

Figure 3 is a three-degree-of-freedom vibration system for simulating environmental excitation;

Fig. 4 is based on the data selection model of limited memory data window length L;

Fig. 5 is the algorithm flowchart based on limited memory principal component analysis;

Fig. 6 is white noise excitation time domain displacement response signal;

Fig. 7 (1) is the natural frequency variation curve of the three-degree-of-freedom time-varying structure, and Fig. 7 (2) is the frequency transformation curve of the three-degree-of-freedom time-varying structure identified by PCA;

Figures 8(1) to 8(5) are the comparison of the natural mode shapes of the three-freedom system at the time of 50.025s, 500s, 950s, 1400s, and 1987.225s, respectively, and the PCA identification mode shapes, and the contribution of each principal component at each time volume chart.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

A time-varying linear structure operating modal parameter identification method based on limited memory principal component analysis, which only uses the time-domain vibration response signals of multiple sensor measurement points of the time-varying linear structure, combined with the idea of limited memory and principal component analysis algorithm, using Based on the statistical characteristics of the principal component analysis algorithm in each limited memory period, the transient operating modal parameters (including the natural frequency and mode shape of each order mode) are estimated at each time, and then the operating modal parameters obtained at each time Connect them together and perform curve fitting, so as to realize the identification of time-varying linear structure working mode parameters.

Specific steps are as follows:

Step 1) Set the measured original time-domain vibration response data X(t) matrix of the time-varying linear structure under white noise excitation as:

Among them, M represents the number of vibration sensor measuring points arranged on the time-varying linear structure, N represents the number of sampling points in the time domain, 1≤j≤M; 1≤i≤N, the length of the selected limited memory data rectangular window is L , initialize i=1;

Step 2) Continuously intercept the time-domain vibration response signal of length L in sequence

Find its autocorrelation matrix ${\mathrm{\ψ}}_{x_L^{\left(i\right)}{x}_L^{\left(i\right)T}}=e\left[x_L^{\left(i\right)}{x}_L^{\left(i\right)T}\right]\∈R^{m\×m};$

Step 3) According to linear algebra and matrix theory, the real symmetric square matrix can be uniquely decomposed into Among them, V ⁽ⁱ⁾ ∈ R ^M×M satisfies V ^(i)T V ⁽ⁱ⁾ ＝I _M×M , I _M×M is an M-dimensional identity matrix, and Υ ⁽ⁱ⁾ ∈ ^{R M×M} is derived from the real Symmetrical square matrix The eigenvalues of are arranged in order from large to small to form a diagonal square matrix;

Step 4) Based on principal component analysis, can be uniquely decomposed into Establish the PCA initialization model, where V ⁽ⁱ⁾ ∈ R ^{M × M} is the transformation matrix in the principal component analysis, is the intercepted time-domain vibration response signal of length L The principal components of , each principal component is not correlated with each other;

Step 5) For any time-domain vibration response signal of length L that is continuously intercepted in sequence Expressed in modal coordinates as $x_L^{\left(i\right)}\≈{\mathrm{\Φ}}^{\left(i\right)}{Q}_L^{\left(i\right)};$

where the regularized mode shape matrix ${\mathrm{\Φ}}^{\left(i\right)}=[{\mathrm{\φ}}_1^{\left(i\right)}\left(L\right),{\mathrm{\φ}}_2^{\left(i\right)}\left(L\right),\·\·\&Center\; Dot;,{\mathrm{\φ}}_j^{\left(i\right)}\left(L\right),\·\·\·{\mathrm{\φ}}_m^{\left(i\right)}\left(L\right)]{\∈R}^{m\×m}$ Satisfy Φ ^(i)T Φ ⁽ⁱ⁾ ＝I _M×M , modal coordinate response matrix

Among them, the modal responses of each order Independent;

Φ ⁽ⁱ⁾ ∈ ^{R M×M} is the statistical average mode of the time-varying linear structure from sampling time point i to i+L-1 (length L), which can be considered as An approximate estimate of the instantaneous mode shape at the most intermediate moment (i+(L-1)/2 moment) within the period of L-1 (length L).

It is the modal coordinate response of the time-varying linear structure from the sampling time point i to i+L-1 (length L), using single-degree-of-freedom modal identification technology (through Fourier transform, the highest peak corresponds to the modal frequency ), which can identify the instantaneous modal natural frequency of the most intermediate moment (that is, i+(L-1)/2 moment) in the period from the sampling time point i to i+L-1 (length L) $W_L^{\left(i\right)}={[w_1^{\left(i\right)}\left(L\right),w_2^{\left(i\right)}\left(L\right),\·\·\·,w_j^{\left(i\right)}\left(L\right),\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;,w_m^{\left(i\right)}\left(L\right)]}^T\∈R^{m\×1};$

Step 6) Because they are independent of each other and must not be correlated, based on the principal component analysis, the regularized mode shape matrix Φ ⁽ⁱ⁾ ∈ R ^M×M corresponds to the linear aliasing matrix V ⁽ⁱ⁾ ∈ R ^M× in the principal component analysis ^M , the modal response matrix of each order Principal Components in Principal Component Analysis

Step 7) Accumulate the contribution rate according to the pivot Determine the number of principal components p, where CPV _p is the variance cumulative contribution rate of the first p principal components;

Step 8) Use the modal confidence parameter MAC to quantitatively evaluate the accuracy of mode shape identification, specifically:

in, is the identified mode shape of the jth mode at time i, represents the jth mode shape at the real time i, and Representing and the transposition of represents the inner product of two vectors, express and degree of similarity, If its value is closer to 1, the accuracy of mode shape identification is higher;

Step 9) i=i+1, return to step 2), until i=N+1-L.

A method for equipment fault diagnosis and health status monitoring, a time-varying linear structure work mode parameter identification method based on limited memory principal component analysis, the steps are as follows:

Step a) collecting a set of response data online, performing normalization processing, and establishing an initial principal component model;

Step b) determining the number of pivots by the cumulative contribution rate of the pivots, and identifying the modal parameters, including frequency and mode shape;

Step c) analyzing and comparing the measured working modal parameters with the modal parameters before the failure of the equipment under test to determine whether the equipment fails and the location of the failure;

Step d) If no fault occurs, iterations are performed to re-establish the principal element model, and then the modal parameter identification analysis is performed.

A time-varying structure operating mode parameter identification device based on limited memory principal component analysis, used to realize the time-varying linear structure operating mode parameter identification method based on limited memory principal component analysis; including a signal input module, a signal conditioning Module, data collector, A/D data acquisition conversion module, DSP, control module, storage module, power supply and reset module; signal input module, signal conditioning module, A/D data acquisition conversion module, DSP, control module, upper computer Two-way communication connection is carried out; the data collector is connected between the DSP and the signal conditioning module, the storage module is connected with the control module, and the power supply and reset module are respectively connected with the DSP and the control module.

First, the upper computer sends the information collection parameters to the control ARM control module through Ethernet; the control module then sends instructions to the DSP through SPI, and the DSP drives the data collector to collect data;

Then, the DSP analyzes the collected data in the time-frequency domain according to the instructions sent by the host computer, and then sends the collected original data and the data analyzed by the DSP to the control module through the SPI, and the control module restores and saves the data format, and passes through Ethernet transmission to the host computer for analysis and display.

Example

As shown in Figure 1, the time-varying structure operating mode parameter identification device based on limited memory principal component analysis of the present invention includes a signal input module, a signal conditioning module, a data collector, an A/D data acquisition conversion module, and a DSP , control module, storage module, power supply and reset module. In order to achieve high-speed, real-time data collection and processing, the system design adopts ARM+DSP dual-core architecture, DSP unit realizes data collection, analysis and processing, and ARM realizes multi-thread work, responsible for data storage, monitoring management, network transmission and other tasks, fully Give full play to the ability of DSP signal processing and ARM control.

Data acquisition is completed by signal input module, signal conditioning module, data collector, A/D data acquisition conversion module, DSP, etc. This device filters, amplifies, and samples the collected signals with a certain sampling method and data organization form. And so on, and transmitted to DSP for processing. The data processing is mainly done by the DSP unit. The DSP analyzes the collected data in the time domain, frequency domain and algorithm based on the improved limited memory principal component analysis, and then sends the data to the ARM control module through the SPI interface. The control module mainly completes the real-time storage of data, saves the stored data in a certain format, and then transmits the processed data and original data to the host computer for analysis and display through Ethernet.

As shown in Figure 2, the host computer software management mainly completes the Ethernet communication settings, the transmission of sampling data, sampling format, data packaging settings, and various waveform displays of data and data storage management.

As shown in Figure 3, it is a three-degree-of-freedom spring oscillator system that simulates environmental excitation. The system is a time-varying system with weak damping, in which the mass m ₁ of the object 1 is time-varying to simulate a time-varying mass system ; Gaussian white noise with a mean value of 0 and a variance of 1 is used for external excitation (in many practical problems, external environments that are difficult to measure are often simulated with white noise to solve problems).

As shown in Figure 4, the sliding data model based on the limited memory data window length L; as shown in Figure 5, it is based on the improved limited memory principal component analysis algorithm flow of the time-varying system working mode parameter identification:

Step 1: Use the vibration response time-domain displacement signal X(t)=[x ₁ (t) x ₂ (t) … x _M (t)] ^T of the small damping mechanical structure measured by M displacement sensors, and set the main The composition threshold is ε;

Step 2: The data data based on the selected limited memory length L is Initialize the PCA model;

Step 3: Calculate autocorrelation matrix The eigenvalues of and sorted in descending order such that ${\mathrm{\λ}}_1^{\left(i\right)}\&Greater\; Equal;{\mathrm{\λ}}_2^{\left(i\right)}\&Greater\; Equal;\·\·\&Center\; Dot;\&Greater\; Equal;{\mathrm{\λ}}_k^{\left(i\right)}\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;{\mathrm{\λ}}_{\mathrm{no}}^{\left(i\right)},k=\mathrm{1,2},\·\&Center\; Dot;\&Center\; Dot;\mathrm{no};$

Step 4: Set the counter k=1, the cumulative contribution rate of variance of the kth principal component CPV=0;

Step 5: Calculate Eigenvalues The corresponding eigenvector Then pass the eigenvalues Calculate principal components

Step 6: By the formula Calculate and update the variance cumulative contribution rate CPV=CPV+CPV(k);

Step 7: When CPV(k)>ε, the kth principal component satisfies the condition, when adding new data, i=i+1, update the PCA model and data matrix Return to step 2 for calculation; if no new data is added, exit the loop; when CPV(k)<ε, k=k+1, return to step 5 and perform principal component calculation again.

In this embodiment, the time-varying structure operating mode parameter identification device based on limited memory principal component analysis uses a three-degree-of-freedom spring oscillator to simulate a time-varying structure, wherein, $m_1=\left\{\begin{array}{c}1\mathrm{kg},t\&le;50\\ e^{-0.0005(t-50)},50<t\&le;2000\end{array}\right.,$ m ₂ = 1kg, m ₃ = 1kg; k ₁ = 1000N/m, k ₂ = 1000N/m, k ₃ = 1000N/m; c ₁ = 0.01Ns/m, c ₂ = 0.01Ns/m, c ₃ = 0.01Ns/m. The initial displacement and velocity are 0. Block 1 is excited by Gaussian white noise with mean value 0 and variance 1 F ₁ . Based on Matlab/Simulink simulation, the sampling interval is 0.025s, the sampling frequency is 40Hz, the simulation time is 2000s, and the limited memory length is L=1024.

As shown in Figure 6, it is the displacement response signal measured based on the three-degree-of-freedom time-varying spring oscillator (Figure 3) and the white noise excitation applied to the time-varying system.

As shown in Figure 7 (1), it is the natural frequency of the third-order time-varying by theoretical calculation; as shown in Figure 7 (2), it is the time-varying frequency curve identified by the limited memory principal component analysis (LMPCA) algorithm; Through the comparison of Figure 7(1) and Figure 7(2), it is found that the frequency change characteristics can be well identified, and the second-order and third-order frequency identification processes identified by the LMPCA algorithm are exchanged, which is identified by the PCA algorithm A characteristic (occurs when the two principal components contribute similarly).

Because the mode shapes in the time-varying structure change from time to time, it is difficult to list all the mode shapes. Based on this, in the 2000s simulation time, randomly select 50.025s, 500s, 950s, 1400s, 1987.225s (to avoid the influence of random vibration, choose 50s data after time), as shown in Fig. 8(1) to Fig. 8(5), the mode shapes of each order at each time of 50.025s, 500s, 950s, 1400s and 1987.225s are identified through theoretical calculation and LMPCA algorithm The comparison of each principal component and the cumulative contribution rate of each principal component; it can be seen from each figure that the LMPCA algorithm can identify each mode shape very well, and the first principal component is the main component at each moment;

The comparison of modal confidence (MAC) at each time of 50.025s, 500s, 950s, 1400s, and 1987.225s is shown in Table 1 to Table 5.

Table 1: MCA comparison between the natural mode shape at 50.025s and the PCA identification mode shape

natural mode order PCA to identify mode shape order MAC 1 1 1.0000 2 3 0.9999 3 2 0.9999

Table 2: MCA comparison between the natural mode shape at 500s and the PCA identification mode shape

natural mode order PCA to identify mode shape order MAC 1 1 0.9999 2 2 0.9856 3 3 0.9857

Table 3: MCA comparison between the natural mode shape at 950s and the mode shape identified by PCA

natural mode order PCA to identify mode shape order MAC 1 1 0.9993 2 2 0.9794 3 3 0.9799

Table 4: MCA comparison between the natural mode shape at 1400s and the PCA identification mode shape

natural mode order PCA to identify mode shape order MAC 1 1 0.9993 2 3 0.9207 3 2 0.9201

Table 5: MCA comparison between the natural mode shape at 1987.225s and the PCA identification mode shape

natural mode order PCA to identify mode shape order MAC 1 1 1.0000 2 3 0.8870 3 2 0.8870

It can be found that the recognition effect at each moment is relatively good, and the mode shapes are very close; among them, the second and third recognition mode shapes in Tables 1, 4 and 5 are exchanged and recognized because the contribution rates of the second and third principal components are very close.

The comparison results of the third-order natural frequency at 50.025s and 1987.225s show that the frequency has changed, as shown in Table 6.

Table 6: Comparison of natural frequencies at 50.025s and 1987.225s

Natural frequency at 50.025s Natural frequency at 1987.225s Relative error 2.2399 2.3133 3.173% 6.2760 7.2749 13.73% 9.0690 12.2951 26.24%

According to Table 6, it can be known that the device described in the present invention has a time-varying system structure.

The above-mentioned embodiments are only used to illustrate the present invention, but not to limit the present invention. As long as it is based on the technical spirit of the present invention, changes and modifications to the above embodiments will fall within the scope of the claims of the present invention.

Claims (7)

1. A time-varying linear structure operating modal parameter identification method based on limited memory principal component analysis, characterized in that only the time-domain vibration response signals of a plurality of sensor measuring points of the time-varying linear structure are used, combined with the idea of limited memory and The principal component analysis algorithm uses the statistical characteristics of the principal component analysis algorithm in each limited memory period to obtain the transient operating mode parameters at each time, and then connects the operating mode parameters obtained at each time to perform curve fitting, thereby Realize the identification of working mode parameters of time-varying linear structures. 2. the time-varying linear structure operating mode parameter identification method based on limited memory principal component analysis according to claim 1, is characterized in that, concrete steps are as follows: Step 1) Set the measured original time-domain vibration response data X(t) matrix of the time-varying linear structure under white noise excitation as: Among them, M represents the number of vibration sensor measuring points arranged on the time-varying linear structure, N represents the number of sampling points in the time domain, 1≤j≤M; 1≤i≤N, the length of the selected rectangular window of limited memory data is L , initialize i=1; Step 2) Continuously intercept the time-domain vibration response signal of length L in sequence Find its autocorrelation matrix ${\mathrm{\&psi;}}_{x_L^{\left(i\right)}{x}_L^{\left(i\right)T}}=\mathrm{E.}\left[x_L^{\left(i\right)}{x}_L^{\left(i\right)T}\right]\&Element;R^{m\&times;m};$ Step 3) According to linear algebra and matrix theory, the real symmetric square matrix uniquely decomposes into Among them, V ⁽ⁱ⁾ ∈ R ^M×M satisfies V ^(i)T V ⁽ⁱ⁾ ＝I _M×M , I _M×M is the M-dimensional identity matrix, γ ⁽ⁱ⁾ ∈ R ^M×M is derived from the real Symmetrical square matrix The eigenvalues of are arranged in order from large to small to form a diagonal square matrix; Step 4) Based on principal component analysis, uniquely decomposes into Establish the PCA initialization model, where V ⁽ⁱ⁾ ∈ R ^{M × M} is the transformation matrix in the principal component analysis, is the intercepted time-domain vibration response signal of length L The principal components of , each principal component is not correlated with each other; Step 5) For any time-domain vibration response signal of length L that is continuously intercepted in sequence Expressed in modal coordinates as $x_L^{\left(i\right)}\&ap;{\mathrm{\&Phi;}}^{\left(i\right)}{Q}_L^{\left(i\right)};$ where the regularized mode shape matrix ${\mathrm{\&Phi;}}^{\left(i\right)}=[{\mathrm{\&phi;}}_1^{\left(i\right)}\left(L\right),{\mathrm{\&phi;}}_2^{\left(i\right)}\left(L\right),...,{\mathrm{\&phi;}}_j^{\left(i\right)}\left(L\right),...{\mathrm{\&phi;}}_m^{\left(i\right)}\left(L\right)]\&Element;R^{m\&times;m}$ Satisfy Φ ^(i)T Φ ⁽ⁱ⁾ ＝I _M×M , modal coordinate response matrix Among them, the modal responses of each order Independent; Φ ⁽ⁱ⁾ ∈ ^{R M×M} is the statistical average mode of the time-varying linear structure from sampling time point i to i+L-1; is the modal coordinate response of the time-varying linear structure from the sampling time point i to i+L-1, using single-degree-of-freedom modal identification technology to identify the modal coordinate response from the sampling time point i to i+L-1 The instantaneous modal natural frequency at the most intermediate moment $W_L^{\left(i\right)}={[w_1^{\left(i\right)}\left(L\right),w_2^{\left(i\right)}\left(L\right),...,w_j^{\left(i\right)}\left(L\right),...,w_m^{\left(i\right)}\left(L\right)]}^T\&Element;R^{m\&times;1};$ Step 6) Because they are independent of each other and must not be correlated, based on the principal component analysis, the regularized mode shape matrix Φ ⁽ⁱ⁾ ∈ R ^M×M corresponds to the linear aliasing matrix V ⁽ⁱ⁾ ∈ R ^M× in the principal component analysis ^M , the modal response matrix of each order Principal Components in Principal Component Analysis Step 7) Accumulate the contribution rate according to the pivot Determine the number of principal components p, where CPV _p is the variance cumulative contribution rate of the first p principal components; Step 8) Use the modal confidence parameter MAC to quantitatively evaluate the accuracy of mode shape identification, specifically: in, is the identified mode shape of the jth mode at time i, represents the jth mode shape at the real time i, and Representing and the transposition of represents the inner product of two vectors, express and degree of similarity, If its value is closer to 1, the accuracy of mode shape identification is higher; Step 9) i=i+1, return to step 2), until i=N+1-L. 3. the time-varying linear structure operating modal parameter identification method based on limited memory principal component analysis according to claim 1, is characterized in that, the transient operating modal parameters at each moment include each order modal natural frequency and modal Natural mode shape. 4. A device fault diagnosis and health status monitoring method, characterized in that, based on the time-varying linear structure operating mode parameter identification method based on the limited memory principal component analysis described in any one of claims 1 to 3, the steps are as follows: Step a) collecting a set of response data online, performing normalization processing, and establishing an initial principal component model; Step b) determining the number of pivots by the cumulative contribution rate of the pivots, and identifying the modal parameters; Step d) Analyzing and comparing the measured working modal parameters with the modal parameters of the device under test before failure to determine whether the equipment is faulty and where the fault is located; Step d) If no fault occurs, iterations are performed to re-establish the principal element model, and then the modal parameter identification analysis is performed. 5. The method for equipment fault diagnosis and health status monitoring according to claim 4, characterized in that, in step b), the modal parameters include frequency and mode shape. 6. A time-varying linear structure operating mode parameter identification device based on limited memory principal component analysis, characterized in that it is used to realize the time-varying linear structure based on limited memory principal component analysis described in any one of claims 1 to 3. Structural working mode parameter identification method; including signal input module, signal conditioning module, data collector, A/D data acquisition conversion module, DSP, control module, storage module, power supply and reset module; signal input module, signal conditioning module, A/D data acquisition and conversion module, DSP, control module, and upper computer are connected by two-way communication; the data collector is connected between the DSP and the signal conditioning module, the storage module is connected to the control module, and the power supply and reset module are respectively connected to the DSP and the control module connect. 7. The time-varying linear structure operating mode parameter identification device based on limited memory principal component analysis according to claim 6, wherein the working steps are as follows: First, the host computer sends the information collection parameters to the control module through Ethernet; the control module then sends instructions to the DSP through SPI, and the DSP drives the data collector to collect data; Then, the DSP analyzes the collected data in the time-frequency domain according to the instructions sent by the host computer, and then sends the collected original data and the data analyzed by the DSP to the control module through the SPI, and the control module restores and saves the data format, and passes through Ethernet transmission to the host computer for analysis and display.