CN113589795A - Multi-oscillation detection method based on intelligent optimization nonlinear chirp modal decomposition algorithm - Google Patents

Multi-oscillation detection method based on intelligent optimization nonlinear chirp modal decomposition algorithm Download PDF

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CN113589795A
CN113589795A CN202110880349.9A CN202110880349A CN113589795A CN 113589795 A CN113589795 A CN 113589795A CN 202110880349 A CN202110880349 A CN 202110880349A CN 113589795 A CN113589795 A CN 113589795A
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吴夏来
张宁
林灵
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Abstract

The invention discloses a multiple oscillation detection method based on an intelligent optimization nonlinear chirp modal decomposition algorithm, which comprises the following steps: (1) collecting a loop output signal of an industrial process to be detected; (2) decomposing the signal by using an NCMD method to obtain a plurality of initial decomposition modes; (3) calculating the fitness of each decomposition mode, and obtaining an optimal parameter pair of the NCMD method through intelligent optimization, wherein the optimal parameter pair comprises a mode number and a bandwidth parameter; (4) decomposing the loop output signals again by using the optimized NCMD method to obtain a plurality of optimized decomposition modes; (5) calculating a normalized correlation coefficient and a sparse index of each optimized decomposition mode, and reserving the decomposition modes meeting oscillation detection indexes as final modes so as to detect oscillation; (6) estimating the oscillation frequency of each final mode by using a power weighted average; (7) the frequency relationship between the different final modes is studied to characterize the oscillation type. The invention has better anti-mixed mode, detection precision and reliability.

Description

Multi-oscillation detection method based on intelligent optimization nonlinear chirp modal decomposition algorithm
Technical Field
The invention belongs to the field of performance evaluation and fault diagnosis in an industrial control system, and particularly relates to a multiple oscillation detection method based on an intelligent optimization nonlinear chirp modal decomposition algorithm.
Background
The detection and characterization of multiple oscillations is still a challenging problem due to the presence of non-linearities, non-stationarity, and noise. Naghosi and Huang combined the clustering algorithm and the autocovariance function to detect multiple oscillations and estimate the corresponding oscillation frequencies. Since multiple oscillations can be seen as frequency components contained in the data, researchers and engineers prefer to employ fourier power spectra to detect the full process range of oscillations. But fourier transform is only suitable for processing linearly stationary signals, which is difficult to satisfy in practical applications.
Huang et al propose Empirical Mode Decomposition (EMD) with a recursive screening process to extract the eigenmode functions. Srinivasan et al applied EMD to characterize oscillations. The chinese patent publication CN105698922A discloses a transformer vibration fault feature extraction method based on improved EMD and spectral kurtosis, which can effectively solve the problem that the conventional empirical mode decomposition generates false components through an improved empirical mode decomposition method based on energy moment ratio and variance contribution rate, and the empirical mode component (IMF) obtained after EMD denoising and signal reconstruction can accurately reflect the original signal feature information. However, EMD often has modal aliasing and end-point effects, which compromise the decomposition performance, reducing the accuracy and reliability of the detection results. Although some EMD improvement techniques, such as EEMD and CEEMD, were subsequently developed to compensate for these problems, the above detection schemes are subjective and lack theoretical criteria by using signal decomposition methods.
Starting from Variational Modal Decomposition (VMD), methods based on optimization theory have become a focus of research. For example, chinese patent publication No. CN108983058A discloses a transformer partial discharge ultrahigh frequency signal denoising method based on improved variational mode and singular value decomposition, which includes the following steps: the method comprises the steps of collecting partial discharge signals of transformer oil paper insulation by using an ultrahigh frequency detection method, carrying out variation modal decomposition on the collected partial discharge signals, optimizing parameters of the variation modal decomposition algorithm by using an evolutionary algorithm, introducing a kurtosis index, and filtering out narrow-band noise. Although VMDs have good modal-mixing-resistant performance and robustness, they are limited to decomposition of narrow-band signals and cannot be represented time-frequency.
Recently, Chen et al proposed a Nonlinear Chirped Modal Decomposition (NCMD) algorithm, which is a recent development in the field of signal decomposition. NCMD is based on the conversion of a wideband signal into a set of narrowband signals. It defines the signal decomposition problem as a demodulation problem and extracts multiple modes simultaneously. NCMD is widely used because it exhibits good decomposition performance even when modes are close to or crossed. However, the performance of NCMD depends on the choice of the number of modes Q and the bandwidth parameter α. How to select these two parameters is an important issue, but has not been studied.
Disclosure of Invention
The invention provides a multiple oscillation detection method based on an intelligent optimization nonlinear chirp modal decomposition algorithm, which has better performances in the aspects of anti-aliasing, detection precision, reliability and the like compared with the existing method.
A multiple oscillation detection method based on an intelligent optimization nonlinear chirp modal decomposition algorithm comprises the following steps:
(1) collecting a loop output signal of an industrial process to be detected;
(2) decomposing the acquired loop output signals by using a nonlinear chirp mode decomposition NCMD method to obtain a plurality of initial decomposition modes;
(3) calculating the fitness of each initial decomposition mode, and obtaining an optimal parameter pair of the NCMD method through intelligent optimization, wherein the optimal parameter pair comprises a mode number and a bandwidth parameter;
(4) decomposing the loop output signals again by using the optimized NCMD method to obtain a plurality of optimized decomposition modes;
(5) calculating a normalized correlation coefficient and a sparse index of each optimized decomposition mode, and reserving the decomposition modes meeting oscillation detection indexes as final modes so as to detect oscillation;
(6) estimating the oscillation frequency of each final mode by using a power weighted average;
(7) the frequency relationship between the different final modes is studied to characterize the oscillation type.
The specific process of the step (2) is as follows:
(2-1) assume that the loop output signal of the industrial process to be tested consists of several modes, which are expressed as follows:
Figure BDA0003191994000000031
wherein Q is a mode number; m isi(t) is modal; a isiIs the instantaneous amplitude; f. ofiIs the instantaneous frequency; phi is aiIs the initial phase; η (t) is noise;
(2-2) demodulating the signal into a dechirped form as follows:
Figure BDA0003191994000000032
wherein:
Figure BDA0003191994000000033
is the estimated instantaneous frequency; in the above formula, ui(t) and vi(t) are all demodulated signals, represented as follows:
Figure BDA0003191994000000034
(2-3) when the estimated instantaneous frequency
Figure BDA0003191994000000041
With the true instantaneous frequency fiWhen the signals are equal, the demodulated signals have the narrowest bandwidth, and the optimal demodulation problem at this time is represented as:
Figure BDA0003191994000000042
wherein epsilon is the reconstruction tolerance;
(2-4) since the actually sampled signal is discrete, the corresponding discrete form is as follows:
Figure BDA0003191994000000043
Figure BDA0003191994000000044
wherein t is t0，…，tN-1Is a time vector, and N is the number of samples;
ui＝[ui(t0)，…，ui(tN-1)]T；uirepresents the demodulated signal 1;
vi＝[vi(t0)，…，vi(tN-1)]T；virepresents the demodulated signal 2;
fi＝[fi(t0)，…，fi(tN-1)]T；fia discrete form representing the instantaneous frequency;
s＝[s(t0)，…，s(tN-1)]T(ii) a s represents a discrete form of the loop output signal of the industrial process to be detected;
Figure BDA0003191994000000045
Figure BDA0003191994000000046
Figure BDA0003191994000000047
Figure BDA0003191994000000048
represents the phase;
Λ represents a second order difference operator, specifically as follows:
Figure BDA0003191994000000051
(2-5) converting the inequality constraint optimization problem into an equality constraint optimization problem by introducing an auxiliary variable omega, wherein the form is as follows:
Figure BDA0003191994000000052
Figure BDA0003191994000000053
wherein, alpha is a quadratic compensation coefficient, namely a bandwidth parameter; λ is the Lagrange multiplier;
(2-6) solving the equality constraint optimization problem by an Alternative Direction Multiplier Method (ADMM).
In the step (3), the specific process of the intelligent optimization is as follows:
(3-1) defining a fitness function for quantifying the decomposition performance of the NCMD, wherein the fitness function is specifically described as follows:
Figure BDA0003191994000000054
wherein i is a modality index; PECC is a fitness function of a defined NCMD mode; q is the mode number of NCMD; alpha is the bandwidth parameter of NCMD;
(3-2) initializing a set of particles in a solution space;
(3-3) calculating the fitness of each particle, and searching individual extremum and group extremum;
and (3-4) updating the position and the speed of each particle, and continuously iterating until an optimal solution is found.
In the step (3-1), the fitness function PECC formula of the NCMD modality is:
Figure BDA0003191994000000055
wherein ρ is a correlation coefficient; NH is the normalized permutation entropy.
In the step (5), the normalized correlation coefficient is used for identifying and eliminating spurious modes, and is calculated as follows:
Figure BDA0003191994000000061
wherein λ isiQ is the number of modes of NCMD, which is the correlation coefficient of the decomposition modes.
The correlation coefficient of the decomposition mode is used for quantifying the correlation between the original signal and the decomposition mode, and the formula is as follows:
Figure BDA0003191994000000062
wherein Cov (·) represents covariance; σ represents the standard deviation; s (t) a loop output signal representing the industrial process to be examined, mi(t) represents the mode of s (t).
In the step (5), the sparse index is used for quantifying the oscillation degree, and the formula is as follows:
Figure BDA0003191994000000063
wherein N is the data length;
Figure BDA0003191994000000064
representing a fourier transform; m isiIs a decomposition mode.
The oscillation detection indexes are as follows:
Figure BDA0003191994000000065
wherein, betaiIs a normalized correlation coefficient; gamma rayiIs a sparseness index.
In the step (6), the oscillation frequency of each mode is estimated by using a power weighted average, and the calculation formula is as follows:
Figure BDA0003191994000000066
wherein: f. ofi(t) is the instantaneous frequency obtained for the NCMD; a isi(t) is the instantaneous amplitude obtained for NCMD.
In the step (7), if the following conditions are met, the higher harmonic is considered to be detected, and the nonlinear oscillation is indicated to exist:
Figure BDA0003191994000000071
in the formula, betaiRepresents and betajNormalized correlation coefficient, f, representing the corresponding modei osciAnd fj osciRepresenting the instantaneous frequency of the corresponding mode obtained by a power weighted average algorithm.
Compared with the prior art, the invention has the following beneficial effects:
the invention searches the two parameters by using the intelligent optimization algorithm, thereby successfully improving the performance of the original NCMD algorithm.
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FIG. 1 is a block diagram of a multi-oscillation detection method based on an intelligent optimized nonlinear chirp modal decomposition algorithm according to the present invention;
FIG. 2 is a flow chart of an embodiment of the present invention.
Detailed Description
The invention will be described in further detail below with reference to the drawings and examples, which are intended to facilitate the understanding of the invention without limiting it in any way.
The invention combines an intelligent optimization algorithm with Nonlinear Chirp Modal Decomposition (NCMD) and provides a novel oscillation detector. Since the performance of NCMD depends on the choice of the number of modes Q and the bandwidth parameter α, an intelligent optimization algorithm is used to search for the optimal parameter pair. Then, a plurality of modalities contained in the process variable are extracted using the optimized NCMD algorithm. And respectively eliminating stray modes and the quantitative oscillation degree by adopting the normalized correlation coefficient and the sparse index. After detection, the multi-oscillation type can be accurately represented by utilizing the time-frequency information provided by the oscillation mode and carrying out power weighted average. Through comparison, the superiority of the method is verified, the decomposition performance of the original NCMD is effectively improved, and the multi-oscillation detection method based on the intelligent optimization nonlinear chirp modal decomposition algorithm is provided, and the specific frame of the method is shown in figure 1.
As shown in fig. 2, the multiple oscillation detection method based on the intelligent optimized nonlinear chirp modal decomposition algorithm of the present embodiment includes the following steps:
(1) collecting a loop output signal of an industrial process to be detected;
in this embodiment, the loop output signal form of the industrial process to be detected is as follows:
s(t)＝cos(2πt)+cos(10πt)+2cos(16πt+40πt2)+η(t)
wherein: η (t) ∈ N (0, 0.1) is noise.
(2) Decomposing the signal by using an NCMD method;
in this embodiment, the NCMD algorithm includes the following steps:
and (2-1) assuming that a loop output signal of the industrial process to be detected consists of several modes, and the modes are represented as follows:
Figure BDA0003191994000000081
wherein: q is a mode number; m isi(t) is modal; a isiIs the instantaneous amplitude; f. ofiIs the instantaneous frequency; phi is aiIs the initial phase; η (t) is noise.
Step (2-2), the signal is demodulated and changed into a chirp-removing form, which comprises the following specific steps:
Figure BDA0003191994000000082
wherein:
Figure BDA0003191994000000083
is the estimated instantaneous frequency;
in the above formula, u in this examplei(t) and vi(t) are all demodulated signals, represented as follows:
Figure BDA0003191994000000091
step (2-3), when the estimated instantaneous frequency
Figure BDA0003191994000000092
With the true instantaneous frequency fiWhen the signals are equal, the demodulated signals have the narrowest bandwidth, and the optimal demodulation problem at this time is represented as:
Figure BDA0003191994000000093
Figure BDA0003191994000000094
wherein: epsilon is the reconstruction tolerance;
step (2-4), since the actually sampled signal is discrete, the corresponding discrete form is as follows:
Figure BDA0003191994000000095
Figure BDA0003191994000000096
wherein: t is t0，…，tN-1Is a time vector, and N is the number of samples;
ui＝[ui(t0)，…，ui(tN-1)]T；
vi＝[vi(t0)，…，vi(tN-1)]T；
fi＝[fi(t0)，…，fi(tN-1)]T；
s＝[s(t0)，…，s(tN-1)]T；
Figure BDA0003191994000000097
Figure BDA0003191994000000098
Figure BDA0003191994000000101
Λ represents a second order difference operator, specifically as follows:
Figure BDA0003191994000000102
step (2-5), in this embodiment, the inequality constraint optimization problem is converted into an equality constraint optimization problem by introducing an auxiliary variable ω, in the following form:
Figure BDA0003191994000000103
Figure BDA0003191994000000104
wherein: α is a quadratic compensation coefficient, which is referred to as a bandwidth parameter in this embodiment; λ is the Lagrange multiplier;
and (2-6) solving the equality constraint optimization problem by an Alternative Direction Multiplier Method (ADMM).
(3) Calculating the fitness of each decomposition mode, and obtaining an optimal parameter pair through intelligent optimization: number of modes and bandwidth parameters.
In this embodiment, the intelligent optimization algorithm comprises the following steps:
step (3-1), in this embodiment, a reasonable fitness function of the NCMD is defined for quantifying the decomposition performance of the NCMD, and the specific description is as follows:
Figure BDA0003191994000000105
wherein: i is a modal index; PECC is a fitness function of the NCMD mode defined by the invention; q is the mode number of NCMD; α is the bandwidth parameter of the NCMD.
Further preferably, the fitness function of the NCMD modality is as follows:
Figure BDA0003191994000000111
wherein: rho is a correlation coefficient; NH is the normalized permutation entropy.
Step (3-2), initializing a group of particles in a solution space;
step (3-3), calculating the fitness of each particle, and searching an individual extreme value and a group extreme value;
and (3-4) updating the position and the speed of each particle, and continuously iterating until an optimal solution is found, wherein the iteration process is as follows:
Figure BDA0003191994000000112
Figure BDA0003191994000000113
wherein: superscript d is the solution space dimension; subscript j is the number of particles; the subscript b indicates the best position (individual extremum) found in this iteration; subscript g indicates that it was found in this iterationThe optimal global solution (group extrema) of the population of particles; vj dIs the amount of change in magnitude and direction in the next iteration;
Figure BDA0003191994000000114
for each particle's current location; r is1、r2Is distributed in [0, 1 ]]The random number of (2); weighting factor: firstly
Figure BDA0003191994000000117
②c1＝1.4；③c1＝1.4。
(4) Re-decomposing the signal with the optimized NCMD;
(5) calculating a normalized correlation coefficient and a sparse index of each decomposition mode, and reserving the modes meeting oscillation detection indexes so as to detect oscillation;
in this embodiment, the normalized correlation index is used to identify and reject spurious modes, and the formula is as follows:
Figure BDA0003191994000000115
wherein: lambda [ alpha ]iIs the correlation coefficient.
Further preferably, a correlation index is used to quantify the correlation between the composite signal and the sub-signal, and the formula is as follows:
Figure BDA0003191994000000116
wherein: cov (·) denotes covariance; σ denotes the standard deviation.
In this embodiment, the sparse index is used to quantify the oscillation degree, and the formula is as follows:
Figure BDA0003191994000000121
wherein: n is the data length;
Figure BDA0003191994000000122
representing a fourier transform; m isiIs a decomposition mode.
Preferably, in step (5), the oscillation detection index is as follows:
Figure BDA0003191994000000123
wherein: beta is aiIs a normalized correlation coefficient; gamma rayiIs a sparseness index.
(6) Estimating the oscillation frequency of each mode by using a power weighted average;
in this embodiment, the power weighted average algorithm is as follows:
Figure BDA0003191994000000124
wherein: f. ofi(t) is the instantaneous frequency obtained for the NCMD; a isi(t) is the instantaneous amplitude obtained for NCMD.
(7) The frequency relationship between the different modes is studied to characterize the type of oscillation.
In the present embodiment, the detection of a higher harmonic is considered to indicate the presence of nonlinear oscillation when the following conditions are satisfied:
Figure BDA0003191994000000125
the embodiments described above are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only specific embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions and equivalents made within the scope of the principles of the present invention should be included in the scope of the present invention.

Claims (10)

1. A multiple oscillation detection method based on an intelligent optimization nonlinear chirp modal decomposition algorithm is characterized by comprising the following steps:
(1) collecting a loop output signal of an industrial process to be detected;
(2) decomposing the acquired loop output signals by using a nonlinear chirp mode decomposition NCMD method to obtain a plurality of initial decomposition modes;
(3) calculating the fitness of each initial decomposition mode, and obtaining an optimal parameter pair of the NCMD method through intelligent optimization, wherein the optimal parameter pair comprises a mode number and a bandwidth parameter;
(4) decomposing the loop output signals again by using the optimized NCMD method to obtain a plurality of optimized decomposition modes;
(5) calculating a normalized correlation coefficient and a sparse index of each optimized decomposition mode, and reserving the decomposition modes meeting oscillation detection indexes as final modes so as to detect oscillation;
(6) estimating the oscillation frequency of each final mode by using a power weighted average;
(7) the frequency relationship between the different final modes is studied to characterize the oscillation type.
2. The multiple oscillation detection method based on the intelligent optimized nonlinear chirp modal decomposition algorithm according to claim 1, wherein the specific process of the step (2) is as follows:
(2-1) assume that the loop output signal of the industrial process to be tested consists of several modes, which are expressed as follows:
Figure FDA0003191993990000011
wherein Q is a mode number; m isi(t) is modal; a isiIs the instantaneous amplitude; f. ofiIs the instantaneous frequency; phi is aiIs the initial phase; η (t) is noise;
(2-2) demodulating the signal into a dechirped form as follows:
Figure FDA0003191993990000021
wherein:
Figure FDA0003191993990000022
is the estimated instantaneous frequency; in the above formula, ui(t) and vi(t) are all demodulated signals, represented as follows:
Figure FDA0003191993990000023
(2-3) when the estimated instantaneous frequency
Figure FDA0003191993990000024
With the true instantaneous frequency fiWhen the signals are equal, the demodulated signals have the narrowest bandwidth, and the optimal demodulation problem at this time is represented as:
Figure FDA0003191993990000025
Figure FDA0003191993990000026
wherein epsilon is the reconstruction tolerance;
(2-4) since the actually sampled signal is discrete, the corresponding discrete form is as follows:
Figure FDA0003191993990000027
Figure FDA0003191993990000028
wherein t is t0，…，tN-1Is a time vector, and N is the number of samples;
ui＝[ui(t0)，…，ui(tN-1)]T；
vi＝[vi(t0)，…，vi(tN-1)]T；
fi＝[fi(t0)，…，fi(tN-1)]T；
s＝[s(t0)，…，s(tN-1)]T；
Figure FDA0003191993990000031
Figure FDA0003191993990000032
Figure FDA0003191993990000033
a represents a second order difference operator, which is specifically as follows:
Figure FDA0003191993990000034
(2-5) converting the inequality constraint optimization problem into an equality constraint optimization problem by introducing an auxiliary variable omega, wherein the form is as follows:
Figure FDA0003191993990000035
Figure FDA0003191993990000036
wherein, alpha is a quadratic compensation coefficient, namely a bandwidth parameter; λ is the Lagrange multiplier;
(2-6) solving the equality constraint optimization problem by an Alternative Direction Multiplier Method (ADMM).
3. The multiple oscillation detection method based on the intelligent optimized nonlinear chirp modal decomposition algorithm according to claim 1, wherein in the step (3), the specific process of the intelligent optimization is as follows:
(3-1) defining a fitness function for quantifying the decomposition performance of the NCMD, wherein the fitness function is specifically described as follows:
Figure FDA0003191993990000041
wherein i is a modality index; PECC is a fitness function of a defined NCMD mode; q is the mode number of NCMD; alpha is the bandwidth parameter of NCMD;
(3-2) initializing a set of particles in a solution space;
(3-3) calculating the fitness of each particle, and searching individual extremum and group extremum;
and (3-4) updating the position and the speed of each particle, and continuously iterating until an optimal solution is found.
4. The multiple oscillation detection method based on the intelligent optimized nonlinear chirp modal decomposition algorithm according to claim 3, wherein in the step (3-1), the fitness function PECC formula of NCMD mode is as follows:
Figure FDA0003191993990000042
wherein ρ is a correlation coefficient; NH is the normalized permutation entropy.
5. The method for detecting multiple oscillations based on intelligent optimized nonlinear chirp modal decomposition algorithm of claim 1, wherein in step (5), said normalized correlation coefficient is used for identifying and rejecting spurious modes, and is calculated as follows:
Figure FDA0003191993990000043
wherein λ isiQ is the number of modes of NCMD, which is the correlation coefficient of the decomposition modes.
6. The method of claim 5, wherein the correlation coefficient of the decomposed mode is used to quantify the correlation between the original signal and the decomposed mode, and the formula is as follows:
Figure FDA0003191993990000044
wherein Cov (·) represents covariance; σ represents the standard deviation; s (t) a loop output signal representing the industrial process to be examined, mi(t) represents the mode of s (t).
7. The multiple oscillation detection method based on the intelligent optimized nonlinear chirp modal decomposition algorithm according to claim 6, wherein in the step (5), the sparsity index is used for quantifying the oscillation degree, and the formula is as follows:
Figure FDA0003191993990000051
wherein N is the data length;
Figure FDA0003191993990000052
representing a fourier transform; m isiIs a decomposition mode.
8. The multiple oscillation detection method based on the intelligent optimized nonlinear chirp modal decomposition algorithm according to claim 7, wherein in the step (5), the oscillation detection indexes are as follows:
Figure FDA0003191993990000053
wherein, betaiIs a normalized correlation coefficient; gamma rayiIs a sparseness index.
9. The multiple oscillation detection method based on the intelligent optimized nonlinear chirp modal decomposition algorithm according to claim 1, wherein in the step (6), the oscillation frequency of each mode is estimated by using a power weighted average, and the calculation formula is as follows:
Figure FDA0003191993990000054
wherein: f. ofi(t) is the instantaneous frequency obtained for the NCMD; a isi(t) is the instantaneous amplitude obtained for NCMD.
10. The multiple oscillation detection method based on the intelligent optimized nonlinear chirp modal decomposition algorithm according to claim 1, wherein in the step (7), the detection of the higher harmonic is considered to indicate the existence of the nonlinear oscillation if the following conditions are satisfied:
Figure FDA0003191993990000055
in the formula, betaiRepresents and betajA normalized correlation coefficient representing the corresponding mode shape,
Figure FDA0003191993990000056
and
Figure FDA0003191993990000057
representing the instantaneous frequency of the corresponding mode obtained by a power weighted average algorithm.
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