CN104698837A - Method and device for identifying operating modal parameters of linear time-varying structure and application of the device - Google Patents
Method and device for identifying operating modal parameters of linear time-varying structure and application of the device Download PDFInfo
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Abstract
The invention relates to method for identifying operating modal parameters of a linear time-varying structure based on memory-restricted principal component analysis. According to the method, the operating modal parameters of a dynamical system with time-varying structural characteristics can be identified by only using unsteady vibration response signals, the operating modal parameters of the structure are identified, and the dynamical variation characteristics of the system can be effectively monitored in real time, thus the method can be applied to vibration control, equipment fault diagnosis, health monitoring, and system structure analysis and optimization. The method is characterized in that the parameter characteristics of the system are identified by only using actual measured response signals, load signals aren't measured, and the method is proven according to mathematical theoretical analysis and experiment, so that a physical significance is endowed to the method. The invention further relates to an operating modal measuring device based on the method, and the device is used for measuring vibration response signals and identifying the operating modal parameters to obtain the real-time online dynamical characteristic change of the system structure, thus the device can be applied to fault diagnosis and health monitoring analysis of a large complex engineering structure (bridge, rail and the like).
Description
Technical Field
The invention relates to a time-varying linear structure working modal parameter identification method based on limited memory principal component analysis, application of the method in structural fault diagnosis and health state monitoring, and a time-varying linear structure working modal parameter identification device based on limited memory principal component analysis.
Background
The analysis of the vibration characteristics of structures is highly regarded in the fields of aerospace vehicles, submarines, civil engineering and construction, ships, automobiles, and the like, particularly modal analysis. The modal analysis provides an effective way for researching various vibration characteristics. The accurate identification of modal parameters (modal frequency, modal shape and damping ratio) is an important guarantee for the safety and maintainability of the system structure, and is an important method for structure dynamic design and fault diagnosis. The traditional test mode analysis method is mainly based on applying artificial excitation to a measurement structure in a laboratory, and by measuring excitation and response signals, a frequency response function curve of a system is solved by using a mode analysis theory, so that the mode parameters are estimated. In recent years, as the research on the large and complex structures, the excitation load of the structures is difficult to measure, and the conventional method of applying artificial excitation is difficult to implement, so that a working mode parameter identification method is created. Such as wind loads to which the bridge is subjected, wave loads to which large marine structures are subjected, and the like. If a dynamic model of the structure is to be built, only a working modal parameter identification method (only the modal parameters of the system are identified from the measured response signals) can be adopted. The working modal parameter identification method belongs to the second inverse problem in engineering mechanics, is high in research difficulty and is an important research direction. At present, the theory and technology are still immature, and deep research and development are needed.
In practical engineering, the structural parameters (mass, stiffness, damping, etc.) of the system are not constant, with time-varying characteristics. For example, during the flight of an aircraft such as a rocket, a missile and the like, fuel is consumed rapidly, and the mass of the aircraft has a time-varying characteristic; as high speed trains can cause severe vibration of bridges, the structural systems of bridges and trains are time-varying. For such a time-varying structure, if a linear time-invariant recognition model is still used, the estimated parameters will deviate from the true values seriously or even diverge, which brings great difficulty to the analysis and control of the system. Therefore, the study of the time-varying structure is urgent. The research of the time-varying structure is a leading problem, particularly an inverse problem (in the case of unknown excitation) in the structure dynamics, and the current theoretical technology is not mature. For the problem research, scholars at home and abroad also make a great deal of research at present, for example, McLamore and the like extract modal frequency by using a peak value method based on fast fourier transform, but the method has the problem that intensive modes cannot be identified; the subspace method provided by Kalman and the like extracts a signal subspace by using methods such as matrix decomposition and the like to obtain an equivalent system, the method is suitable for parameter identification of a linear time-varying structure under stable excitation, has certain anti-interference capability on output noise, but the order determination of a random subspace model is more complicated, the calculated amount is large, and a false mode is easy to identify; the method is a local identification method, is difficult to completely analyze the overall characteristics of the system, and is easy to influence the identification precision due to the limitation of the filtering capability to the problem of dense modes.
At present, a parameter identification method for researching a time-varying structure is mainly based on the thought of 'time freezing', namely, a system is assumed to be frozen at a certain moment, and in a short time range, the system is regarded as a linear time-invariant system, and then the theory of the time-invariant structure is utilized for analysis. The existing research mainly includes two types: one is based on a limited memory method, namely, dividing data into small time periods, regarding the structural parameters as time-invariant in each time period, and then fitting the value curves identified in the data periods to obtain a parameter time-variant rule; another is an online or recursive technique, where data at various times are considered, old data is gradually forgotten, new data is continuously added, and parameter values are corrected at each time.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides an improved time-varying structure working mode parameter identification method based on limited memory principal component analysis, a time-varying structure working mode parameter identification device based on limited memory principal component analysis, and application of the time-varying structure working mode parameter identification method based on limited memory principal component analysis in equipment fault diagnosis and health state monitoring.
The technical scheme of the invention is as follows:
a time-varying linear structure working modal parameter identification method based on limited memory principal component analysis only utilizes time domain vibration response signals of a plurality of sensor measuring points of a time-varying linear structure, combines the thought of limited memory and a principal component analysis algorithm, utilizes the statistical characteristics of the principal component analysis algorithm in each limited memory time period to obtain transient working modal parameters of each moment, and then connects the working modal parameters obtained at each moment to perform curve fitting, thereby realizing the time-varying linear structure working modal parameter identification.
Preferably, the method comprises the following specific steps:
step 1) setting an original time domain vibration response data X (t) matrix of a measured time-varying linear structure under white noise excitation as follows:
wherein M represents the number of measuring points of the vibration sensor arranged on the time-varying linear structure, N represents the number of time domain sampling points, and j is more than or equal to 1 and less than or equal to M; i is more than or equal to 1 and less than or equal to N, the length of a selected limited memory data rectangular window is L, and i is initialized to 1;
step 2) continuously intercepting time domain vibration response signals with length of L according to sequence
Computing its autocorrelation matrix <math>
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Step 3) according to the linear algebra and the matrix theory, the real symmetric square matrixIs only decomposed intoWherein, V(i)∈RM×MSatisfy V(i)TV(i)＝IM×M，IM×MIs the unit matrix of M dimension, gamma(i)∈RM×MIs composed of a real symmetrical square matrixIs composed of characteristic values arranged in descending orderA diagonal matrix;
step 4) based on the principal component analysis,is only decomposed intoEstablishing a PCA initialization model, wherein V(i)∈RM×MIs a transformation matrix in the principal component analysis,is a truncated time-domain vibration response signal of length LThe principal components of (a), the principal components being uncorrelated with each other;
step 5) for time domain vibration response signals with length of L and continuously intercepted in any orderExpressed as in modal coordinates <math>
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Wherein the mode shape matrix is normalized <math>
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</math> Satisfies phi(i)TΦ(i)＝IM×MResponse matrix of modal coordinates
Wherein each order of modal responseAre independent of each other;
Φ(i)∈RM×Mis the statistical average mode of the time-varying linear structure from the sampling time point i to the time period of i + L-1;
the modal coordinate response of the time-varying linear structure in the time period from the sampling time point i to the i + L-1 is realized, and the instantaneous modal natural frequency of the most intermediate moment in the time period from the sampling time point i to the i + L-1 is identified by utilizing the single-degree-of-freedom modal identification technology <math>
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Step 6) regularizing the mode shape matrix phi based on principal component analysis because of mutual independence and certain irrelevance(i)∈RM×MLinear aliasing matrix V in corresponding principal component analysis(i)∈RM×MModal response matrix of each orderIs a principal component in principal component analysis
Step 7) accumulating contribution rate according to principal elementDetermining the number p of main elements, wherein, CPVpAccumulating contribution rates for variances of the first p principal components;
step 8) quantitatively evaluating the accuracy of vibration mode identification by adopting a modal confidence parameter MAC, which specifically comprises the following steps:
wherein,is the j-th mode shape at time i identified,the jth mode shape representing the true time i,andrespectively representAndthe transpose of (a) is performed,represents the inner product of two vectors and represents the inner product of the two vectors,to representAndto the extent of the similarity in the direction of the line,if the value is closer to 1, the vibration mode identification accuracy is higher;
and 9) returning to the step 2) until i is N + 1-L.
Preferably, the transient operating mode parameters at each time include a mode natural frequency and a mode natural mode shape of each order.
A method for diagnosing equipment faults and monitoring health states is based on the method for identifying the working modal parameters of a time-varying linear structure based on limited memory principal component analysis, and comprises the following steps:
step a), collecting a group of response data on line, carrying out normalization processing, and establishing an initial principal component model;
b) determining the number of the pivot elements according to the pivot element accumulated contribution rate, and identifying modal parameters;
step d) analyzing and comparing the measured working modal parameters with modal parameters before the equipment to be tested fails, and determining whether the equipment fails or not and the position of the failure;
and d) if no fault occurs, iterating, reestablishing the principal component model, and then carrying out modal parameter identification analysis.
Preferably, in step 2), the modal parameters include frequency and mode shape.
A time-varying linear structure working modal parameter recognition device based on limited memory principal component analysis is used for realizing the time-varying linear structure working modal parameter recognition method based on limited memory principal component analysis; the device comprises a signal input module, a signal conditioning module, a data acquisition unit, an A/D data acquisition and conversion module, a DSP, a control module, a storage module, a power supply and a reset module; the system comprises a signal input module, a signal conditioning module, an A/D data acquisition and conversion module, a DSP (digital signal processor), a control module and an upper computer, wherein the DSP, the control module and the upper computer are in bidirectional communication connection; the data acquisition unit is connected between the DSP and the signal conditioning module, the storage module is connected with the control module, and the power supply and the reset module are respectively connected with the DSP and the control module.
Preferably, the working steps are as follows:
firstly, an upper computer sends information acquisition parameters to a control module through an Ethernet; the control module sends the instruction to the DSP through the SPI, and the DSP drives the data collector to collect data;
then, the DSP analyzes the time-frequency domain of the collected data according to the instruction sent by the upper computer, and 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 stores the data format and transmits the data format to the upper computer for analysis and display through the Ethernet.
The invention has the following beneficial effects:
the time-varying structure working modal parameter identification method based on the limited memory principal component analysis can perform real-time online parameter identification on a structure with time-varying characteristics, identify working modal parameters (modal shape and modal frequency) of a system, effectively monitor the dynamic variation characteristics of the system in real time, and can be used for equipment fault diagnosis, health monitoring and system structure analysis and optimization. The method is a working modal parameter identification method (the characteristics of the system can be identified only by actually measured response signals), and is proved from mathematical theory analysis and experiments, so that the method is endowed with physical explanation, and has greater advantages compared with the traditional experimental modal parameter identification technology which needs to measure excitation and response signals simultaneously. The method has the main ideas that firstly, a group of data is collected on line, a PCA initialization model is established, the idea of principal component analysis is utilized to find out the corresponding relation between the modal shape and the linear aliasing matrix and between each order of modal response and the principal component, the modal parameters of the system are identified, the existence, uniqueness and certainty of the modal parameters are proved through principal component decomposition, and the algorithm physical significance is definite; and then when a new group of data is collected, updating and iterating the data matrix and the covariance matrix, and updating and iterating the PCA model, so as to identify the modal parameters of the system structure on line in real time.
The time-varying structure working modal parameter identification device based on the limited memory principal component analysis arranges a plurality of vibration sensor devices on key points of a measurement structure, monitors the dynamic characteristic change of a system structure by identifying the working modal parameters of a measured vibration response signal, and is applied to fault diagnosis and health state monitoring of a large-scale engineering structure. The working modal parameter monitoring device takes ARM and DSP as cores and forms a plurality of units such as a signal input module, a signal conditioning module, a data acquisition unit, an A/D data acquisition and conversion module, the DSP, a control module, a storage module, a power supply and a reset module. The design of the device makes full use of the mode that the ARM chip has low power consumption, high processing speed and flexible task scheduling and the capability of DSP algorithm design and data processing analysis, and the two are effectively combined to realize real-time online acquisition, processing, transmission and analysis of vibration signals. Meanwhile, the Ethernet is adopted for data transmission, so that the rapid and efficient transmission of data is realized, the loss of signals in transmission is avoided, remote diagnosis and monitoring and resource sharing are realized, and the defects of offline and delay of traditional data acquisition are overcome. The design of the device effectively combines a signal processing technology, a circuit design, a computer technology, an algorithm design and a fault analysis technology, realizes the digitization, the automation and the intellectualization of a diagnosis system, and has potential application value.
Drawings
FIG. 1 is a block diagram of a design system of a working modal parameter measurement device;
FIG. 2 is a functional block diagram of a host computer;
FIG. 3 is a three degree-of-freedom vibration system excited by a simulated environment;
FIG. 4 is a diagram of a model selected based on data defining a length L of a memory data window;
FIG. 5 is a flow chart of an algorithm based on a finite memory principal component analysis;
FIG. 6 is a white noise excitation and time domain displacement response signal;
fig. 7(1) is a natural frequency variation curve of the three-degree-of-freedom time-varying structure, and fig. 7(2) is a frequency variation curve of the three-degree-of-freedom time-varying structure identified by PCA;
fig. 8(1) to 8(5) are graphs showing comparisons between the three free system eigenmodes and the PCA identification modes at times 50.025s, 500s, 950s, 1400s, and 1987.225s, respectively, and contributions from the principal components at each time.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
A time-varying linear structure working modal parameter identification method based on limited memory principal component analysis only utilizes time domain vibration response signals of a plurality of sensor measuring points of a time-varying linear structure, combines the thought of limited memory and a principal component analysis algorithm, utilizes the statistical characteristics of the principal component analysis algorithm in each limited memory period to estimate transient working modal parameters (including modal natural frequency and modal natural vibration type) of each moment, and then connects the working modal parameters obtained at each moment to perform curve fitting, thereby realizing the time-varying linear structure working modal parameter identification.
The method comprises the following specific steps:
step 1) setting an original time domain vibration response data X (t) matrix of a measured time-varying linear structure under white noise excitation as follows:
wherein M represents the number of measuring points of the vibration sensor arranged on the time-varying linear structure, N represents the number of time domain sampling points, and j is more than or equal to 1 and less than or equal to M; i is more than or equal to 1 and less than or equal to N, the length of a selected limited memory data rectangular window is L, and i is initialized to 1;
step 2) continuously intercepting time domain vibration response signals with length of L according to sequence
Computing its autocorrelation matrix <math>
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Step 3) according to the linear algebra and the matrix theory, the real symmetric square matrixCan be uniquely decomposed intoWherein, V(i)∈RM×MSatisfy V(i)TV(i)＝IM×M，IM×MIs the unit matrix of M dimension, gamma(i)∈RM×MIs composed of a real symmetrical square matrixThe characteristic values of the matrix are arranged in a diagonal matrix from big to small;
step 4) based on the principal component analysis,can be uniquely decomposed intoEstablishing a PCA initialization model, wherein V(i)∈RM×MIs a transformation matrix in the principal component analysis,is a truncated time-domain vibration response signal of length LThe principal components of (a), the principal components being uncorrelated with each other;
step 5) for time domain vibration response signals with length of L and continuously intercepted in any orderExpressed as in modal coordinates <math>
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Wherein the mode shape matrix is normalized <math>
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Wherein each order of modal responseAre independent of each other;
Φ(i)∈RM×Mis the statistical average mode of the time-varying linear structure from the sampling time point i to the period of i + L-1 (length L), and can be regarded as the most middle time (i.e. i + (L-1)) in the period from the sampling time point i to the sampling time point i + L-1 (length L)Time/2) is estimated from the time of the second phase.
The modal coordinate response of the time-varying linear structure in a time period from a sampling time point i to i + L-1 (the length is L) is realized, and the instantaneous modal natural frequency of the most intermediate time (i.e. the time of i + (L-1)/2) in the time period from the sampling time point i to the time point of i + L-1 (the length is L) can be identified by utilizing a single-degree-of-freedom modal identification technology (the highest peak value corresponds to the modal frequency through Fourier transformation) <math>
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Step 6) regularizing the mode shape matrix phi based on principal component analysis because of mutual independence and certain irrelevance(i)∈RM×MLinear aliasing matrix V in corresponding principal component analysis(i)∈RM×MModal response matrix of each orderIs a principal component in principal component analysis
Step 7) accumulating contribution rate according to principal elementDetermining the number p of main elements, wherein, CPVpAccumulating contribution rates for variances of the first p principal components;
step 8) quantitatively evaluating the accuracy of vibration mode identification by adopting a modal confidence parameter MAC, which specifically comprises the following steps:
wherein,is the j-th mode shape at time i identified,the jth mode shape representing the true time i,andrespectively representAndthe transpose of (a) is performed,represents the inner product of two vectors and represents the inner product of the two vectors,to representAndto the extent of the similarity in the direction of the line,if the value is closer to 1, the vibration mode identification accuracy is higher;
and 9) returning to the step 2) until i is N + 1-L.
A method for diagnosing equipment faults and monitoring health states is a time-varying linear structure working mode parameter identification method based on limited memory principal component analysis, and comprises the following steps:
step a), collecting a group of response data on line, carrying out normalization processing, and establishing an initial principal component model;
b) determining the number of principal elements according to the accumulated contribution rate of the principal elements, and identifying modal parameters including frequency and vibration mode;
step c) analyzing and comparing the measured working modal parameters with modal parameters before the equipment to be tested fails, and determining whether the equipment fails or not and the position of the failure;
and d) if no fault occurs, iterating, reestablishing the principal component model, and then carrying out modal parameter identification analysis.
A time-varying structure working modal parameter recognition device based on limited memory principal component analysis is used for realizing the time-varying linear structure working modal parameter recognition method based on limited memory principal component analysis; the device comprises a signal input module, a signal conditioning module, a data acquisition unit, an A/D data acquisition and conversion module, a DSP, a control module, a storage module, a power supply and a reset module; the system comprises a signal input module, a signal conditioning module, an A/D data acquisition and conversion module, a DSP (digital signal processor), a control module and an upper computer, wherein the DSP, the control module and the upper computer are in bidirectional communication connection; the data acquisition unit is connected between the DSP and the signal conditioning module, the storage module is connected with the control module, and the power supply and the reset module are respectively connected with the DSP and the control module.
Firstly, an upper computer sends information acquisition parameters to a control ARM control module through an Ethernet; the control module sends the instruction to the DSP through the SPI, and the DSP drives the data collector to collect data;
then, the DSP analyzes the time-frequency domain of the collected data according to the instruction sent by the upper computer, and 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 stores the data format and transmits the data format to the upper computer for analysis and display through the Ethernet.
Examples
As shown in fig. 1, the time-varying structure working mode parameter identification apparatus based on limited memory principal component analysis according to the present invention includes a signal input module, a signal conditioning module, a data acquisition device, an a/D data acquisition and conversion module, a DSP, a control module, a storage module, a power supply, and a reset module. In order to realize high-speed and real-time data acquisition and processing, an ARM + DSP dual-core architecture is adopted in system design, a DSP unit realizes data acquisition and analysis processing, ARM realizes multi-thread work and is responsible for tasks of data storage, monitoring management, network transmission and the like, and the signal processing and ARM control capacity of the DSP is fully exerted.
The data acquisition is accomplished by signal input module, signal conditioning module, data collection station, AD data acquisition conversion module, DSP etc. and this device is with certain sampling mode, data organization form, handles such as filtering, enlargies, sampling with the signal of gathering to transmit DSP to handle. The DSP unit is mainly used for processing the data, and the DSP unit is used for carrying out time domain and frequency domain analysis on the acquired data and algorithm analysis based on improved limited memory principal component analysis, and then sending the data to the ARM control module through the SPI interface. The control module is mainly used for storing data in real time, storing the stored data in a certain format, and transmitting the processed data and the original data to the upper computer through the Ethernet for analysis and display.
As shown in fig. 2, the upper computer software management mainly completes ethernet communication setting, transmission of sampling data, sampling format, data encapsulation setting, various waveform display of data and storage management of data.
As shown in FIG. 3, the system is a three-freedom-degree spring oscillator system excited by a simulated environment, and the system is a time-varying system with weak damping, wherein the mass m of an object block 11Is time-varying, to simulate a time-varying quality system; the external excitation uses gaussian white noise with a mean of 0 and a variance of 1 (in many practical problems, the environment that is difficult to measure externally is often modeled with white noise to solve the problem).
As shown in fig. 4, based on a sliding data model defining a length L of the memory data window; as shown in fig. 5, the algorithm flow of the time-varying system working mode parameter identification based on the improved limited memory principal component analysis is as follows:
step 1: vibration response time domain displacement signal X (t) ═ x of small damping mechanical structure measured by M displacement sensors1(t) x2(t) … xM(t)]TSetting the main component threshold value as;
step 2: based on the selected data with limited memory length L asInitializing a PCA model;
and step 3: computingAutocorrelation matrixCharacteristic value ofAnd arranged in descending order such that <math>
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And 4, step 4: setting a counter k to be 1, and setting a k-th main component variance accumulated contribution rate CPV to be 0;
and 5: calculating characteristic valuesCorresponding feature vectorThen passing the characteristic valueCalculating principal components
Step 6: by the formulaCalculating and updating the variance cumulative contribution rate CPV ═ CPV + CPV (k);
and 7: when CPV (k)>When new data is added, i is i +1, and the PCA model and the data matrix are updatedReturning to the step 2 for calculation; when new data is not added, the loop is exited; when CPV (k)<And k is k +1, and the process returns to the step 5 to perform the principal component operation again.
In this embodiment, the time-varying structure working mode parameter identification device based on limited memory principal component analysis adopts a three-degree-of-freedom spring oscillator to simulate a time-varying structure, <math>
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</math> m2＝1kg，m3＝1kg；k1＝1000N/m，k2＝1000N/m，k3＝1000N/m；c1＝0.01N.s/m，c2＝0.01N.s/m，c30.01 n.s/m. The initial displacement and velocity are 0. The block 1 is excited by Gaussian white noise with mean 0 and variance 11. Based on Matlab/Simulink simulation, the sampling interval is 0.025s, the sampling frequency is 40Hz, the simulation time is 2000s, and the memory length is limited to be 1024.
As shown in fig. 6, is a displacement response signal measured based on a three-degree-of-freedom time-varying spring transducer (fig. 3) and a white noise excitation applied to the time-varying system.
As shown in fig. 7(1), the natural frequency of the third order time variation calculated by theory; as shown in fig. 7(2), it is a time-varying frequency variation curve identified by a Limited Memory Principal Component Analysis (LMPCA) algorithm; by comparing fig. 7(1) and fig. 7(2), it is found that the frequency variation characteristic can be well recognized, and the second-order and third-order frequency recognition processes recognized by the LMPCA algorithm are exchanged, which is a characteristic recognized by the PCA algorithm (when the contribution rates of the two main components are close to each other).
Based on the fact that all mode shapes are difficult to enumerate due to the change of modal mode shape time in the time-varying structure, 50.025s, 500s, 950s, 1400s and 1987.225s are randomly selected (the influence of random vibration is avoided, and data after 50s time is selected for calculation) in 2000s simulation time, as shown in fig. 8(1) -8 (5), the mode shapes of each order at 50.025s, 500s, 950s, 1400s and 1987.225s respectively are compared with the LMPCA algorithm identification through theoretical calculation and the accumulated contribution rate of each main component; as can be seen from the figures, the LMPCA algorithm can well identify each vibration mode, and the first main component accounts for the main component at each moment;
50.025s, 500s, 950s, 1400s, 1987.225s are shown in tables 1 to 5 for comparison of modal confidences (MACs) at respective times.
Table 1: comparing the natural mode at 50.025s with MCA of PCA recognition mode
| Order of natural mode | PCA recognition mode order | MAC |
| 1 | 1 | 1.0000 |
| 2 | 3 | 0.9999 |
| 3 | 2 | 0.9999 |
Table 2: comparing the natural vibration mode at 500s with MCA of PCA recognition vibration mode
| Order of natural mode | PCA recognition mode order | MAC |
| 1 | 1 | 0.9999 |
| 2 | 2 | 0.9856 |
| 3 | 3 | 0.9857 |
Table 3: comparing the natural vibration mode at 950s with MCA of PCA recognition vibration mode
| Order of natural mode | PCA recognition mode order | MAC |
| 1 | 1 | 0.9993 |
| 2 | 2 | 0.9794 |
| 3 | 3 | 0.9799 |
Table 4: comparing the natural vibration mode at 1400s with MCA of PCA recognition vibration mode
| Order of natural mode | PCA recognition mode order | MAC |
| 1 | 1 | 0.9993 |
| 2 | 3 | 0.9207 |
| 3 | 2 | 0.9201 |
Table 5: comparing the natural mode at 1987.225s with MCA of PCA recognition mode
| Order of natural mode | PCA recognition mode order | MAC |
| 1 | 1 | 1.0000 |
| 2 | 3 | 0.8870 |
| 3 | 2 | 0.8870 |
The recognition effect at each moment is good, and the vibration modes are very close; in tables 1, 4 and 5, the second and third identified mode shapes are identified by crossover because the second and third principal component contributions are very close.
50.025s was compared with the third order natural frequency at time 1987.225s, and it was found that the frequency was changed as shown in Table 6.
Table 6: comparison of natural frequencies at times 50.025s and 1987.225s
| Natural frequency at time 50.025s | Natural frequency at time 1987.225s | Relative error |
| 2.2399 | 2.3133 | 3.173％ |
| 6.2760 | 7.2749 | 13.73％ |
| 9.0690 | 12.2951 | 26.24％ |
From table 6, it can be seen that the apparatus of the present invention has a time-varying system structure.
The above examples are provided only for illustrating the present invention and are not intended to limit the present invention. Changes, modifications, etc. to the above-described embodiments are intended to fall within the scope of the claims of the present invention as long as they are in accordance with the technical spirit of the present invention.
Claims (7)
1. A time-varying linear structure working modal parameter identification method based on limited memory principal component analysis is characterized in that transient working modal parameters of all moments are obtained by only utilizing time domain vibration response signals of a plurality of sensor measuring points of a time-varying linear structure and combining a limited memory idea and a principal component analysis algorithm and utilizing the statistical characteristics of the principal component analysis algorithm in all limited memory periods, and then working modal parameters obtained at all moments are connected for curve fitting, so that the time-varying linear structure working modal parameter identification is realized.
2. The method for identifying the working modal parameters of the time-varying linear structure based on the finite memory principal component analysis according to claim 1, is characterized by comprising the following specific steps:
step 1) setting an original time domain vibration response data X (t) matrix of a measured time-varying linear structure under white noise excitation as follows:
wherein M represents the number of measuring points of the vibration sensor arranged on the time-varying linear structure, N represents the number of time domain sampling points, and j is more than or equal to 1 and less than or equal to M; i is more than or equal to 1 and less than or equal to N, the length of a selected limited memory data rectangular window is L, and i is initialized to 1;
step 2) continuously intercepting time domain vibration response signals with length of L according to sequence
Computing its autocorrelation matrix <math>
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Step 3) according to the linear algebra and the matrix theory, the real symmetric square matrixIs only decomposed intoWherein, V(i)∈RM×MSatisfy V(i)TV(i)＝IM×M，IM×MIs an M-dimensional identity matrix, gamma(i)∈RM×MIs composed of a real symmetrical square matrixThe characteristic values of the matrix are arranged in a diagonal matrix from big to small;
step 4) based on the principal component analysis,is only decomposed intoEstablishing a PCA initialization model, wherein V(i)∈RM×MIs a transformation matrix in the principal component analysis,is a truncated time-domain vibration response signal of length LMain components of (2), each main component being different from each otherCorrelation;
step 5) for time domain vibration response signals with length of L and continuously intercepted in any orderExpressed as in modal coordinates <math>
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Wherein the mode shape matrix is normalized <math>
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Wherein each order of modal responseAre independent of each other;
Φ(i)∈RM×Mis the statistical average mode of the time-varying linear structure from the sampling time point i to the time period of i + L-1;
the modal coordinate response of the time-varying linear structure in the time period from the sampling time point i to the i + L-1 is realized, and the instantaneous modal natural frequency of the most intermediate moment in the time period from the sampling time point i to the i + L-1 is identified by utilizing the single-degree-of-freedom modal identification technology <math>
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</mrow>
</math>
Step 6) regularizing the mode shape matrix phi based on principal component analysis because of mutual independence and certain irrelevance(i)∈RM×MLinear aliasing matrix V in corresponding principal component analysis(i)∈RM×MModal response matrix of each orderIs a principal component in principal component analysis
Step 7) accumulating contribution rate according to principal elementDetermining the number p of main elements, wherein, CPVpAccumulating contribution rates for variances of the first p principal components;
step 8) quantitatively evaluating the accuracy of vibration mode identification by adopting a modal confidence parameter MAC, which specifically comprises the following steps:
wherein,is the j-th mode shape at time i identified,the jth mode shape representing the true time i,andrespectively representAndthe transpose of (a) is performed,represents the inner product of two vectors and represents the inner product of the two vectors,to representAndto the extent of the similarity in the direction of the line,if the value is closer to 1, the vibration mode identification accuracy is higher;
and 9) returning to the step 2) until i is N + 1-L.
3. The method for identifying the working modal parameters of the time-varying linear structure based on the finite memory principal component analysis according to claim 1, wherein the transient working modal parameters at each moment comprise a modal natural frequency and a modal natural mode shape of each order.
4. A method for diagnosing equipment failure and monitoring health status, which is characterized in that based on any one of claims 1 to 3, the method for identifying the working modal parameters of the time-varying linear structure based on the finite memory principal component analysis comprises the following steps:
step a), collecting a group of response data on line, carrying out normalization processing, and establishing an initial principal component model;
b) determining the number of the pivot elements according to the pivot element accumulated contribution rate, and identifying modal parameters;
step d) analyzing and comparing the measured working modal parameters with modal parameters before the equipment to be tested fails, and determining whether the equipment fails or not and the position of the failure;
and d) if no fault occurs, iterating, reestablishing the principal component model, and then carrying out modal parameter identification analysis.
5. The method according to claim 4, wherein in step b), the modal parameters include frequency and mode shape.
6. A time-varying linear structure working modal parameter identification device based on limited memory principal component analysis, which is used for realizing the time-varying linear structure working modal parameter identification method based on limited memory principal component analysis according to any one of claims 1 to 3; the device comprises a signal input module, a signal conditioning module, a data acquisition unit, an A/D data acquisition and conversion module, a DSP, a control module, a storage module, a power supply and a reset module; the system comprises a signal input module, a signal conditioning module, an A/D data acquisition and conversion module, a DSP (digital signal processor), a control module and an upper computer, wherein the DSP, the control module and the upper computer are in bidirectional communication connection; the data acquisition unit is connected between the DSP and the signal conditioning module, the storage module is connected with the control module, and the power supply and the reset module are respectively connected with the DSP and the control module.
7. The device for identifying the parameters of the working mode of the time-varying linear structure based on the analysis of the finite memory principal components as claimed in claim 6 is characterized in that the working steps are as follows:
firstly, an upper computer sends information acquisition parameters to a control module through an Ethernet; the control module sends the instruction to the DSP through the SPI, and the DSP drives the data collector to collect data;
then, the DSP analyzes the time-frequency domain of the collected data according to the instruction sent by the upper computer, and 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 stores the data format and transmits the data format to the upper computer for analysis and display through the Ethernet.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1570629A (en) * | 2004-05-12 | 2005-01-26 | 浙江大学 | On-line soft measurement modeling method for 4-CBA content based on least square algorithm of restricted memory part |
| CN1904581A (en) * | 2006-08-01 | 2007-01-31 | 东北电力大学 | Oil gas water multiphase flow type identification method based on main component analysis and supporting vector machine |
| CN103207600A (en) * | 2013-03-07 | 2013-07-17 | 西安交通大学 | Multi-node network vibration abatement device and method |
| CN104112072A (en) * | 2014-07-15 | 2014-10-22 | 华侨大学 | Operating modal parameter identification method for principal component analysis on basis of wavelet threshold denoising |
-
2014
- 2014-12-11 CN CN201410763308.1A patent/CN104698837B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1570629A (en) * | 2004-05-12 | 2005-01-26 | 浙江大学 | On-line soft measurement modeling method for 4-CBA content based on least square algorithm of restricted memory part |
| CN1904581A (en) * | 2006-08-01 | 2007-01-31 | 东北电力大学 | Oil gas water multiphase flow type identification method based on main component analysis and supporting vector machine |
| CN103207600A (en) * | 2013-03-07 | 2013-07-17 | 西安交通大学 | Multi-node network vibration abatement device and method |
| CN104112072A (en) * | 2014-07-15 | 2014-10-22 | 华侨大学 | Operating modal parameter identification method for principal component analysis on basis of wavelet threshold denoising |
Non-Patent Citations (2)
| Title |
|---|
| 王成等: "利用主成分分析的模态参数识别", 《西安交通大学学报》 * |
| 高翔等: "基于限定记忆模式的递归PCA故障诊断法", 《仪器仪表学报》 * |
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