CN110657882B - Bridge real-time safety state monitoring method utilizing single-measuring-point response - Google Patents

Bridge real-time safety state monitoring method utilizing single-measuring-point response Download PDF

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CN110657882B
CN110657882B CN201910898394.XA CN201910898394A CN110657882B CN 110657882 B CN110657882 B CN 110657882B CN 201910898394 A CN201910898394 A CN 201910898394A CN 110657882 B CN110657882 B CN 110657882B
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CN110657882A (en
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聂振华
沈兆丰
谢永康
邓杰龙
刘思雨
赵晨
马宏伟
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Jinan University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups

Abstract

The invention discloses a bridge real-time safety state monitoring method utilizing single-measuring-point response, which comprises the following steps: s1, arranging an acceleration sensor on the bridge; s2, measuring the acceleration response of the bridge vibration; s3, defining a moving time window, intercepting the measured signal, and reconstructing the signal in the window into an embedded state space matrix X by a time delay methodi(ii) a S4, and state space matrix XiPerforming principal component analysis; s5, defining bridge safety evaluation index R1(i) (ii) a S6, obtaining R in the window by moving the time window1(i) A time series of (a); s7, according to R1(i) And whether the curve is mutated or not is judged so as to judge whether the safety state of the bridge structure is changed or not. According to the method, a finite element model with an accurate structure is not needed to be used as a reference for comparison, and whether the damage degree of the bridge structure changes or not can be effectively reflected in real time only by utilizing the response measured by a single acceleration sensor.

Description

Bridge real-time safety state monitoring method utilizing single-measuring-point response
Technical Field
The invention relates to the technical field of structural safety monitoring, in particular to a bridge real-time safety state monitoring method utilizing single-point response.
Background
The current bridge structure health monitoring faces the problems of too many measuring points and huge monitoring data. In the existing bridge structure health monitoring system, after the construction of the bridge structure is completed, a large number of sensors are installed on the bridge structure and various structural characteristics are monitored in real time, so that the information quantity stored by the bridge structure monitoring system is too large. On one hand, the total amount of sensor equipment installed in the existing bridge structure greatly increases the initial investment and daily operation and maintenance cost of a bridge operator; on the other hand, the monitoring data is redundant, so that the difficulty of structure monitoring is increased.
Disclosure of Invention
The invention aims to solve the defects in the prior art and provides a bridge real-time safety state monitoring method by using single-measuring-point response.
The purpose of the invention can be achieved by adopting the following technical scheme:
a bridge real-time safety state monitoring method utilizing single-point response comprises the following steps:
s1, installing an acceleration sensor at any position on the bridge;
s2, measuring acceleration response of bridge vibration to obtain an acceleration signal x (i), wherein i is 1,2, …, N and N are signal sampling point lengths;
s3, defining a moving time window, intercepting the measured signal, and reconstructing the signal in the window into an embedded state space matrix X by a time delay methodiThe expression is as follows:
Figure BDA0002211009410000021
wherein i is the ith observation position after the window moves, l is the window length, r is the delay time, and n is the embedding dimension;
s31, determining the delay time r by the autocorrelation function of the signal. The autocorrelation function is:
Figure BDA0002211009410000022
wherein
Figure BDA0002211009410000023
The time k corresponding to the first zero point of the autocorrelation function is the delay time r.
And S32, determining the embedding dimension n by using the accumulated contribution rate obtained by the principal component analysis method. The measured signal is first reconstructed into an embedding state space a of:
Figure BDA0002211009410000024
where r is the delay time determined in step S31 and p is the temporary embedding dimension. p is determined by the bandwidth limiting frequency f in the fourier spectrum of the signal x, which means that there are no significant frequencies of energy in the frequency bands larger than f in the fourier spectrum. And p is the number of frequencies with significant energy in the frequency bands less than or equal to f plus 1. And (3) carrying out principal component analysis calculation on the state space matrix A:
PCA(A)＝[U,Y,Λ] (4)
wherein U is the eigenvector matrix, Y is the principal component score matrix, Λ is the eigenvalue matrix, Λ is the diagonal matrix, does:
Figure BDA0002211009410000031
the obtained cumulative contribution rate is:
Figure BDA0002211009410000032
and taking the value of n corresponding to the first accumulated contribution rate greater than or equal to 90%, namely the finally determined embedding dimension n.
S33, defining a convergence function to determine the window length l. Firstly, the signal x is reconstructed into an embedding state space B (m) by using the delay time r and the embedding dimension n determined in the steps S31 and S32
Figure BDA0002211009410000033
Where m is a positive integer variable, L ═ mfs/f1,fsFor the sampling frequency of the signal under test, f1The fundamental frequency of the measured signal can be derived from the fourier spectrum of the signal. And (c) performing principal component analysis calculation on the B (m) to obtain an eigenvalue matrix Λ (m), and calculating a first principal component contribution rate function through the Λ (m), namely a first principal component contribution rate convergence function, which is defined as:
Figure BDA0002211009410000034
wherein λ is1(m) is the first characteristic when the variable is mAnd (5) feature value. Obtaining a first principal component contribution rate convergence spectrum through the formula (8), determining that a corresponding M value is a multiple M of a corresponding period of the optimal fundamental frequency when the function converges to a stable value through the convergence spectrum, and finally determining that the window length of the moving time is:
Figure BDA0002211009410000035
s4, determining the parameters, and obtaining the state space matrix X in the formula (1)iPerforming principal component analysis:
PCA(Xi)＝[Ui,Yi,Λi] (10)
obtaining a feature vector matrix U in the windowiPrincipal component score matrix YiMatrix of eigenvalues Λi。
S5, passing the eigenvalue matrix Lambda in the windowiDefining the bridge safety evaluation indexes as follows:
Figure BDA0002211009410000041
wherein
Figure BDA0002211009410000042
Refers to the first-order characteristic value of the image,
Figure BDA0002211009410000043
comprises the following steps:
Figure BDA0002211009410000044
wherein
Figure BDA0002211009410000045
Refer to the j-th order eigenvalue.
S6, moving the time window along with the development of time from the current time of the time shaft of the measured signal, wherein the moving step length is the period corresponding to the fundamental frequency, and the moving step length is repeated onceRepeating the steps S4 and S5 to obtain R1(i) Time profile.
S7 passing index R1(i) And (5) evaluating the safety state of the bridge by using the curve. When the bridge structure is damaged or abnormal behaviors occur, R1(i) The value will suddenly change, thereby monitoring the safety state of the bridge in real time.
Compared with the prior art, the invention has the following advantages and effects:
1) in the invention, three important parameters of delay time r, embedding dimension n and moving window length l which are required to be determined for reconstructing the embedding state space are determined only once, namely data of one day is collected after the sensor is installed and is used as basic data to determine the parameters. Once the parameters are determined, the monitoring process may be continued only by moving the window as time progresses. The method does not need to move the window once and determine the parameters once, and the characteristic can ensure that the calculation speed is high, accurately capture the safety change and abnormal behavior of the bridge and achieve the effect of real-time monitoring.
2) The invention does not need to compare by taking a finite element model with an accurate structure as a reference, only needs to directly analyze a measured signal, does not need to carry out a model correction process required in the traditional monitoring method, belongs to a data driving method, and is suitable for the engineering application of an actual bridge. The traditional method requiring a finite element model is difficult and serious in practical engineering application, the modeling of complex bridges such as a large-span suspension bridge, a cable-stayed bridge and a rigid truss bridge is a difficult problem, and the model must have larger deviation with a practical structure. However, various model correction methods require a large amount of iterative computation, and particularly, a large complex bridge takes too long time to achieve a real-time effect.
3) The invention can judge the structural damage of the bridge by only a single sensor, greatly reduces the number of monitoring sensors and the storage amount of monitoring data, effectively reduces the calculation amount of the monitoring data, solves the problem that a large number of sensors are needed for monitoring the structural damage, is beneficial to reducing the cost of monitoring equipment and improves the real-time monitoring efficiency of the bridge structure.
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FIG. 1 is a flow chart of a bridge real-time safety state monitoring method using single-point acceleration response disclosed in the present invention;
FIG. 2 is a schematic view of a bridge model according to one embodiment;
FIG. 3 is a schematic diagram of a recombined acceleration signal and a moving window according to an embodiment;
FIG. 4 is a diagram of an autocorrelation function corresponding to the sensor 1 according to one embodiment;
FIG. 5 is a spectrum diagram of an acceleration signal corresponding to the sensor 1 in the first embodiment;
FIG. 6 is a graph of the corresponding principal component cumulative contribution rate of the sensor 1 in the first embodiment;
FIG. 7 is CCR of acceleration signals of the sensor 1 in the first embodiment1Convergence and popularization;
FIG. 8 shows R of the sensor 1 according to the first embodiment1(i) A graph;
FIG. 9 shows R of the sensor 2 according to the first embodiment1(i) A graph;
FIG. 10 is a schematic view of a large span suspension bridge of real time instance two;
FIG. 11 is a schematic diagram showing the arrangement positions of sensors in the second embodiment;
FIG. 12 is a diagram showing signals measured by the sensor 19 according to the second embodiment;
FIG. 13 is a diagram showing an autocorrelation function of a signal measured by the sensor 19 according to the second embodiment;
FIG. 14 is a frequency spectrum diagram of an acceleration signal corresponding to the sensor 19 in the second embodiment;
FIG. 15 is a graph showing the cumulative contribution of the principal component corresponding to the sensor 19 in the second embodiment;
FIG. 16 is CCR of acceleration signals of the sensor 19 in the second embodiment1Convergence and popularization;
FIG. 17 shows R of a sensor 19 according to the second embodiment1(i) A graph;
FIG. 18 is a graph showing the R values of the sensors 15 and 2 in the second embodiment1(i) Graph in which R of the sensor 15 in FIG. 18(a)1(i) Graph, R of sensor 2 in FIG. 18(b)1(i) Graph is shown.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example one
As shown in fig. 1, fig. 1 is a flowchart of a bridge real-time safety state monitoring method using single-point acceleration response disclosed in the embodiment of the present invention. The schematic representation of the steel bridge model used in this example is shown in fig. 2. The length l of the model beam is 20m, and the sampling frequency fsAt 200Hz, the lesion was located at 0.4l of the beam length.
The specific implementation process is as follows:
and S1, mounting an acceleration sensor at any position on the bridge. To illustrate the effectiveness of the present method in mounting the sensors at different locations, acceleration sensor 1 and acceleration sensor 2 are mounted at the bridge 6/10 and 1/10, respectively, as shown in fig. 2.
And S2, measuring the acceleration response x (i) of the bridge vibration, wherein i is 1,2, …, and N is the measured response length. In this embodiment, the test time for a single condition of the same sensor is 1250 seconds, and the data length is 250000. The acceleration signals are measured for bridge conditions with damage degrees of 0, 2/15, 3/15, 4/15 and 6/15 (section loss rate) by changing only the damage degree of the damage position of the bridge. The sensor signals at the same position with the bridge damage degrees of 0, 2/15, 3/15, 4/15 and 6/15 (section loss rate) are spliced in sequence from small to large according to the damage degree to obtain the response x (i) of a single sensor, namely the last monitoring time under each working condition is 1250 seconds, 2500 seconds, 3750 seconds, 5000 seconds and 6250 seconds in sequence, as shown in fig. 3.
S3, defining a moving time window, intercepting the measured signal, and reconstructing the signal in the window into an embedded state space matrix X by a time delay methodi。
Figure BDA0002211009410000071
Wherein i is the ith observation position after the window moves, l is the window length, r is the delay time, and n is the embedding dimension. The specific process of step S3 is as follows:
s31, determining the delay time r by the autocorrelation function of the signal. The autocorrelation function is:
Figure BDA0002211009410000072
wherein
Figure BDA0002211009410000073
The time k corresponding to the first zero point of the autocorrelation function is the delay time r. As shown in fig. 4, the delay time point r at which the sensor 1 signal is obtained is 11.
And S32, determining the embedding dimension n by using the accumulated contribution rate obtained by the principal component analysis method. The measured signal is first reconstructed into an embedding state space a of:
Figure BDA0002211009410000074
where r is the delay time determined in step S31 and p is the temporary embedding dimension. p is determined by the bandwidth-limited frequency f in the fourier spectrum of the signal x, which means that there are no significant frequencies of energy in the frequency bands larger than f in the fourier spectrum. p is the number of frequencies with significant energy in the frequency band less than f plus 1. As shown in fig. 5, the spectrogram corresponding to the sensor 1 has 9 frequencies with significant energy in a frequency band less than or equal to the bandwidth limit frequency f, and thus the temporary embedding dimension p corresponding to the sensor 1 is determined to be 10. The state space matrix A corresponding to the sensor 1 is
Figure BDA0002211009410000075
Here, the signal length is 250000, and the response in the intact state is adopted, and the response in the lossy state is not adopted. Since the later monitoring data is used for evaluation in long-term monitoring, all parameters can be determined by using the currently measured signal and only once calculation is needed. And (3) carrying out principal component analysis calculation on a state space matrix A corresponding to the sensor 1:
PCA(A)＝[U,Y,Λ] (4)
wherein U is the eigenvector matrix, Y is the principal component score matrix, Λ is the eigenvalue matrix, Λ is the diagonal matrix, does:
Figure BDA0002211009410000081
the obtained cumulative contribution rate is:
Figure BDA0002211009410000082
and taking the value of n corresponding to the first accumulated contribution rate greater than or equal to 90%, namely the finally determined embedding dimension n. As shown in fig. 6, when n is 6, the cumulative contribution rate of the state space matrix a corresponding to the signal of the sensor 1 is greater than 90% for the first time; thus, the embedding dimension n of the sensor 1 signal is determined to be 6.
S33, a convergence function is defined to determine the window length l. First, the delay time r and the embedding dimension n determined in steps S31 and S32 are set to 11 and 6, and the signal x is reconstructed into an embedding state space b (m) of
Figure BDA0002211009410000083
Wherein m is a positive integer variable, wherein L ═ mfs/f1，f1The fundamental frequency of the signal is 1.12Hz, and L ═ m200/1.12 ═ 178m can be obtained. Performing principal component analysis calculation on B (m) to obtain an eigenvalue matrix Lambda (m), calculating a first principal component contribution rate function through Lambda (m),i.e. the convergence function of the first principal component contribution ratio, defined as:
Figure BDA0002211009410000091
wherein λ is1(m) is a first eigenvalue when the variable is m. The first eigenvalue converged spectrum obtained by equation (8) is shown in fig. 7, and the optimum fundamental frequency corresponding period multiple M can be determined to be 53. The calculation formula of the length of the available moving window is
Figure BDA0002211009410000092
The moving window length l 53 x 200/1.12 x 9464.3 can be calculated, taking the integer 9464.
S4, substituting the determined parameter r 11, n 6, l 9464 into the state space matrix X in the formula (1)iAnd performing principal component analysis:
PCA(Xi)＝[Ui,Yi,Λi] (10)
obtaining a feature vector matrix U in the windowiPrincipal component score matrix YiMatrix of eigenvalues Λi。
S5, passing the eigenvalue matrix Lambda in the windowiDefining the bridge safety evaluation indexes as follows:
Figure BDA0002211009410000093
wherein
Figure BDA0002211009410000094
Refers to the first-order characteristic value of the image,
Figure BDA0002211009410000095
comprises the following steps:
Figure BDA0002211009410000096
wherein
Figure BDA0002211009410000097
Refer to the j-th order eigenvalue.
S6, as shown in FIG. 3, moving the window from the current time of the time axis of the measured signal by the number f of sampling points in the period corresponding to the fundamental frequency of the signals/f1Namely 178. Repeating the processes of S4 and S5 every time of moving to obtain R1(i) Curves over time, as in fig. 8.
S7 passing index R1(i) And (5) evaluating the safety state of the bridge by using the curve. When the bridge structure is damaged or abnormal behaviors occur, R1(i) The value will suddenly change, thereby monitoring the safety state of the bridge in real time. As shown in FIG. 8, when the bridge is damaged and the safety state changes, R is1(i) The curve is suddenly stepped from one state level to another state level, the occurrence moment of the bridge damage is monitored in real time, and the purpose of real-time monitoring is achieved.
In this embodiment, in order to illustrate that it is equally effective to use sensors at different positions, the implementation process of the present invention is repeated by using the signals of the sensors 2, and the result is shown in fig. 9, and the curve can also accurately identify the occurrence time of the bridge damage. The method is equally effective, indicating that the sensor is mounted at a different location.
Example two
To illustrate the practicability and effectiveness of the invention, in real-time safety monitoring of an actual large-span suspension bridge, an accident is successfully monitored by adopting the technology of the invention. The accident is that the bottom of the main span steel box girder of the bridge is slightly scratched by a sand boat mast, the occurrence time is 8 o' clock in the morning, the bridge vibrates to have abnormal behavior, and the response obtained by measurement has no any abnormal behavior. The object in this embodiment is a suspended bridge across the pearl river, as shown in fig. 10. Sampling frequency fsIs 200 Hz. The specific implementation process is as follows:
and S1, mounting an acceleration sensor at any position on the bridge. To illustrate the effectiveness of the method in mounting sensors at different locations, 24 sensors were mounted at different locations on the bridge, with the arrows being the direction of measurement, as shown in fig. 11.
And S2, measuring the acceleration response x (i) of the bridge vibration, wherein i is 1,2, … and N. And N is the measured response length. In this example, data from 6 to 10 am were analyzed. For convenience of illustration, taking the cross-midpoint 19 as an example, the measured response is shown in FIG. 12.
S3, defining a moving time window, intercepting the measured signal, and reconstructing the signal in the window into an embedded state space matrix X by a time delay methodiAs shown in formula (1) in example 1.
S31, determining the delay time r by the autocorrelation function of the signal. The autocorrelation function is shown in formula (2) in example 1. The time k corresponding to the first zero point of the autocorrelation function is the delay time r. As shown in fig. 13, the delay time point r at which the signal of the sensor 19 is obtained is 18.
And S32, determining the embedding dimension n by using the accumulated contribution rate obtained by the principal component analysis method. The measured signal is first reconstructed into an embedding state space a as shown in equation (3) of example 1. The temporary embedding dimension p is determined by the bandwidth limiting frequency f in the fourier spectrum of the signal x, the fourier spectrum of the sensor 19 is shown in fig. 14, in which there are 11 frequencies of significant energy in a frequency band less than or equal to the bandwidth limiting frequency, so that the temporary embedding dimension p corresponding to the sensor 19 is determined to be 12. The state space matrix a was subjected to principal component analysis calculation, and the cumulative contribution ratio was obtained by the calculation of formula (6) in example 1, as shown in fig. 15. And taking the value of n corresponding to the first cumulative contribution rate greater than or equal to 90%, namely the finally determined embedding dimension n, wherein n is determined to be 9.
S33, a convergence function is defined to determine the window length l. First, the delay time r and the embedding dimension n determined in steps S31 and S32 are set to 18 and 9, and the signal x is reconstructed into an embedding state space b (m), as shown in formula (7) in example 1. And (3) performing principal component analysis calculation on the B (M) to obtain an eigenvalue matrix Λ (M), calculating a first principal component contribution rate convergence function by using the formula (8) in the embodiment 1 through the Λ (M) to obtain a first eigenvalue convergence spectrum, wherein the first eigenvalue convergence spectrum is shown in fig. 16, and determining that the period multiple M corresponding to the optimal fundamental frequency is 159, and then calculating by using the formula (9) in the embodiment 1 to obtain a moving window length 265000.
S4, substituting the determined parameter r 18, n 9, l 265000 into the state space matrix X in formula (1)iAnd carrying out principal component analysis to obtain an eigenvalue matrix Lambda in the windowi。
S5, passing the eigenvalue matrix Lambda in the windowiThe bridge safety evaluation index is defined as shown in formula (11) in example 1.
And S6, moving the window from the time axis of the measured signal, wherein the moving step length is the number of sampling points in the corresponding period of the signal fundamental frequency. Repeating the processes of S4 and S5 every time of moving to obtain R1(i) The time-dependent curve is shown in FIG. 17.
S7 passing index R1(i) And (5) evaluating the safety state of the bridge by using the curve. When the bridge structure is abnormally acted, R1(i) The value will suddenly change, thereby monitoring the safety state of the bridge in real time. As shown in FIG. 17, R1(i) And (4) suddenly generating an obvious peak value at 8 o' clock in the curve, and monitoring the accident in real time.
In order to illustrate that the sensors in different positions are also effective, the sensor 2, 1/4 in the tower top position is used to cross the sensor position 15, the result is shown in fig. 18(a) and 18(b), and the curve can also accurately monitor the occurrence time of the bridge accident. It is stated that the method works equally well with sensors installed at different locations.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (3)

1. A bridge real-time safety state monitoring method utilizing single-point response is characterized by comprising the following steps:
s1, installing an acceleration sensor at any position on the bridge;
s2, measuring acceleration response of bridge vibration to obtain an acceleration signal x (i), wherein i is 1,2, …, N and N are signal sampling point lengths;
s3, defining a moving time window, intercepting the measured signal, and reconstructing the signal in the window into an embedded state space matrix X by a time delay methodiThe expression is as follows:
Figure FDA0003015683970000011
wherein i is the ith observation position after the window moves, l is the window length, r is the delay time, and n is the embedding dimension;
in step S3, the embedding dimension n is determined by the accumulated contribution rate obtained by the principal component analysis method, and the measured signal is reconstructed into an embedding state space matrix a:
Figure FDA0003015683970000012
wherein r is delay time, p is a temporary embedding dimension, p is determined by bandwidth limit frequency f in a Fourier spectrum of a signal x, the bandwidth limit frequency means that no energy significant frequency exists in a frequency band which is greater than f in the Fourier spectrum, p is the number of the frequency with significant energy in the frequency bands which are less than or equal to f plus 1, and a state space matrix A is subjected to principal component analysis and calculation:
PCA(A)＝[U,Y,Λ] (4)
wherein U is the eigenvector matrix, Y is the principal component score matrix, Λ is the eigenvalue matrix, Λ is the diagonal matrix, does:
Figure FDA0003015683970000021
the obtained cumulative contribution rate is:
Figure FDA0003015683970000022
taking the value of n corresponding to the first accumulated contribution rate greater than or equal to 90%, namely the finally determined embedding dimension n;
s4, determining the parameters, and obtaining the state space matrix X in the formula (1)iPerforming principal component analysis:
PCA(Xi)＝[Ui,Yi,Λi] (10)
obtaining a feature vector matrix U in the windowiPrincipal component score matrix YiMatrix of eigenvalues Λi；
S5, passing the eigenvalue matrix Lambda in the windowiDefining the bridge safety evaluation indexes as follows:
Figure FDA0003015683970000023
wherein
Figure FDA0003015683970000024
Refers to the first-order characteristic value of the image,
Figure FDA0003015683970000025
comprises the following steps:
Figure FDA0003015683970000026
wherein
Figure FDA0003015683970000027
The j-th order characteristic value;
s6, moving the time window along with the development of time from the current time of the time axis of the measured signal, wherein the moving step length is the period corresponding to the fundamental frequency, and repeating the step S4 and the step S5 every time of moving to obtain R1(i) A time-dependent profile;
s7 passing index R1(i) The safety state of the bridge is evaluated by a curve, and when the bridge structure is damaged or abnormal behaviors occur, R1(i) The value will suddenly change, thereby monitoring the safety state of the bridge in real time.
2. The method for monitoring the real-time safety status of a bridge with single-point response according to claim 1, wherein in step S3, the delay time r is determined by an autocorrelation function of the signal, wherein the autocorrelation function is as follows:
Figure FDA0003015683970000031
wherein
Figure FDA0003015683970000032
The time k corresponding to the first zero point of the autocorrelation function is the delay time r.
3. The method for monitoring real-time safety status of bridge with single-point response as claimed in claim 1, wherein in step S3, the window length l is determined by defining a convergence function, and the signal x is first reconstructed into an embedding status space b (m) by using the determined delay time r and embedding dimension n
Figure FDA0003015683970000033
Where m is a positive integer variable, L ═ mfs/f1，fsFor the sampling frequency of the signal under test, f1Obtaining a fundamental frequency of a measured signal from a Fourier spectrum of the signal, performing principal component analysis calculation on B (m) to obtain an eigenvalue matrix Λ (m), and calculating a first principal component contribution rate function through Λ (m), namely a first principal component contribution rate convergence function, which is defined as:
Figure FDA0003015683970000034
wherein λ is1(M) is a first characteristic value when the variable is M, a first principal component contribution rate convergence spectrum is obtained through an equation (8), the corresponding M value is determined to be a multiple M of the corresponding period of the optimal fundamental frequency when the function is converged to a stable value through the convergence spectrum, and finally the window length of the movement time is determined to be:
Figure FDA0003015683970000035
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