CN109542089B - Industrial process nonlinear oscillation detection method based on improved variational modal decomposition - Google Patents
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Abstract
An industrial process nonlinear oscillation detection method based on improved variational modal decomposition comprises the following steps: (1) collecting a group of loop output signals of the industrial process to be detected; (2) calculating the frequency spectrum of the loop output signal and the mean frequency spectrum of the phase correction signal, and determining the number of modes and the initial value of the central frequency; (3) setting a search range and a step length of a penalty coefficient; (4) calculating summation arrangement entropies obtained by VMD decomposition corresponding to different penalty coefficients, and determining an optimal penalty coefficient; (5) VMD decomposition is carried out by the determined mode number, the initial value of the central frequency and the punishment coefficient, and effective modes are selected; (6) and calculating whether a multiple relation exists between the center frequencies of the effective modes, and judging whether nonlinear oscillation exists. The invention can improve the nonlinear detection accuracy and reliability of the control loop of the industrial process, provide data support for performance evaluation and fault diagnosis and lay a foundation for the subsequent multi-loop nonlinear oscillation source positioning work.
Description
Technical Field
The invention belongs to the field of performance evaluation and fault diagnosis in an industrial control system, and particularly relates to an industrial process nonlinear oscillation detection method based on improved variational modal decomposition.
Background
With the rapid development of fault diagnosis and performance evaluation techniques for industrial control loops, oscillation detection is one of the main tasks of fault diagnosis for control loops. Due to the connections and couplings between the control system loops, oscillations generated in one loop will typically propagate to the other loop. These oscillations cause problems of energy loss, waste of raw materials and degradation of product quality. Valve sticking, controller misalignment, and external disturbances are three major causes of oscillation.
It is well documented that non-linear links in the control system, such as valve sticking, may be the primary cause of control loop oscillations. The strong demands for safety of the production process and product profits have greatly pushed the development of control system nonlinear oscillation detection techniques. Nonlinear oscillation detection methods can be roughly divided into two aspects, one is based on data driving, and the method does not need prior knowledge of the dynamic characteristics of a study object; another approach is to either require detailed process knowledge, user interaction or to learn a fairly precise process structure.
The data-driven nonlinear oscillation detection method includes shape-based viscosity detection, such as a phase characteristic method using an MV-OP diagram, a bicoherence method using a PV-OP diagram and an alternative data method; there are also techniques for detecting nonlinear oscillations based on cross-correlation, histogram, area calculation, curve fitting, and the like. Non-linear oscillation detection methods that require detailed process knowledge or precise process structure are model-based detection methods, detection methods based on output signal frequency knowledge, and the like.
In recent years, signal decomposition techniques have been developed rapidly, and research for applying these new signal processing techniques to processing data of an industrial control system has been underway. Bahji et al first detected and diagnosed non-linearities in industrial process control system data using HHT transforms. Aftab et al propose to use a non-linearity index to measure the degree of non-linearity. Recently, Aftab et al introduced multidimensional empirical mode decomposition into the field of nonlinear oscillation detection. These nonlinear oscillation detection methods based on the signal decomposition technique are performed based on the characteristic that nonlinear oscillation includes higher harmonics. If after a signal decomposition the higher harmonics can be detected by a non-linear detection algorithm, then the signal will have non-linear oscillations.
compared with the traditional methods such as EMD, L MD and the like, the variational modal decomposition method has the advantages of complete mathematical basis, difficulty in being influenced by endpoint effect and modal aliasing, capability of directly obtaining the frequency of each mode, high decomposition precision and the like.
Based on the background, aiming at the nonlinear oscillation signals in the industrial control system, an improved method for overcoming the problem that the basic variational modal decomposition depends on the parameters is found, the characteristic of high precision of the variational modal decomposition is utilized, the nonlinear oscillation is detected by analyzing the multiple relation of the central frequency of the effective mode obtained by the variational modal decomposition, and the method has very important practical value for accurately oscillating whether the nonlinear oscillation exists in the industrial process.
Disclosure of Invention
The invention provides an industrial process nonlinear oscillation detection method based on improved variational modal decomposition, which has high detection precision, only needs to obtain conventional operation data, and does not need process mechanism knowledge.
An industrial process nonlinear oscillation detection method based on improved variational modal decomposition comprises the following steps:
(1) Collecting a group of loop output signals of the industrial process to be detected;
(2) Calculating the frequency spectrum of the loop output signal and the mean frequency spectrum of the phase correction signal, and determining the number of modes and the initial value of the central frequency;
(3) Setting a search range and a step length of the penalty coefficient, calculating VMD decomposition corresponding to different penalty coefficients to obtain the sum of normalized arrangement entropies of each mode, and obtaining a summation arrangement entropy;
(4) Selecting a penalty coefficient corresponding to the minimum summation arrangement entropy as an optimal penalty coefficient;
(5) Performing VMD decomposition by using the mode number, the initial value of the central frequency and the selected penalty coefficient as parameters, and obtaining an effective mode according to the normalized permutation entropy and the correlation coefficient;
(6) And calculating whether the center frequencies of the effective modes have a multiple relation or not, and further judging whether nonlinear oscillation exists or not.
The method of the invention overcomes the problem that the decomposition effect of the basic variation modal decomposition depends on the modal quantity, the central frequency initialization value and the penalty coefficient seriously when processing the signal synthesized by harmonic waves, and infers whether nonlinear oscillation exists by detecting the central frequency of the effective mode obtained by improving the variation modal decomposition. The invention can improve the accuracy and reliability of nonlinear detection of the control loop in the industrial process, provide data support for performance evaluation and fault diagnosis, and lay the foundation for the subsequent multi-loop nonlinear oscillation detection.
The invention directly adopts measurable variables of the chemical process as process output signals, and all process output signals to be detected are acquired in real time on site.
The specific process of the step (2) is as follows:
(2-1) calculating a Fourier spectrum of an output signal x (t) in the process and a spectrum subjected to phase correction signal mean value processing;
(2-2) determining the number of modes K according to the following formula
K＝max{Kfft,KPRSA}+1
Wherein, K fftRepresenting the number of peaks, K, in the Fourier spectrum PRSAThe number of peaks of the frequency spectrum after the mean value processing of the phase correction signal is represented;
(2-3) taking the frequency values of all the peak values as the initialization value omega of the center frequency init。
In the step (3), the search range of the penalty coefficient is 100 to 10000, and the step length value is 500 to 1000.
The specific process of the step (3) is as follows:
(3-1) taking a value from the lower limit to the upper limit of the search range at intervals of one step length from the value of the penalty coefficient;
(3-2) calculating the normalized arrangement entropy and the summation arrangement entropy of each mode obtained by VMD decomposition corresponding to each penalty coefficient, wherein the calculation formula is as follows:
NPEk＝PEk/ln(N-d+1)
Wherein, NPE kIs the normalized permutation entropy value of the kth mode, PE kIs the original permutation entropy value for the k-th mode, N is the loop output signal length, d takes the value of 5, and SPE is the summed permutation entropy.
In the step (5), the selection rule of the effective modes is as follows: the normalized correlation coefficient is greater than 0.2 and the normalized permutation entropy is less than 0.4. The normalized correlation coefficient calculation formula is as follows:
Cov stands for covariance, u k(t) represents the mode obtained by decomposition, x (t) represents the loop output signal, σ x(t)Representing the standard deviation of the loop output signal, 
Represents the standard deviation, ρ, of the k-th mode kRepresenting the correlation coefficient between the loop output signal x (t) and the kth mode shape, max representing the maximum value, λ kRepresenting the normalized correlation coefficient of the kth mode.
In the step (6), the specific manner of judging whether the nonlinear oscillation exists is as follows:
If the center frequency between two or more active modes satisfies ω j/ωiIf k, i is not equal to j, and | round (k) -k |, is less than or equal to 0.2, then there is a multiple relation, so that the effective modes belong to the same nonlinear oscillation; where round represents the nearest integer to k, ω iAnd ω jTwo effective modes to be judged;
If a single active mode does not have a multiple relationship with the center frequency of any other mode, then that mode is considered a single linear oscillation.
Compared with the prior art, the invention has the following beneficial effects:
1. According to the invention, external additional signal excitation is not needed when the signal is collected, additional disturbance is not introduced to the control system, and non-invasive detection and diagnosis can be realized.
2. The phase correction signal mean value (PRSA) processing adopted by the invention can effectively improve the signal-to-noise ratio of the frequency spectrum and can obtain a clearer peak value under a strong noise background.
3. The method for detecting the nonlinear oscillation in the industrial process based on the improved variational modal decomposition can directly obtain more accurate oscillation frequency instead of only one frequency range, so that the idea of detecting the nonlinear oscillation by utilizing harmonic waves is simpler and more accurate to implement.
4. When the detection method is used for decomposing the oscillation signal, the generated redundant component and the error component are much less than those of methods such as EMD and MEMD, and the misjudgment rate for eliminating the redundant component and the error component is reduced.
5. The invention completely adopts a data driving type method, does not need prior process knowledge and does not need manual intervention.
Drawings
FIG. 1 is a schematic flow chart of an industrial process nonlinear oscillation detection method based on improved variational modal decomposition according to the present invention;
FIG. 2 is a diagram of process output signals of a control loop to be detected collected according to an embodiment of the present invention;
FIG. 3 is a graph of a spectrum of a process output signal according to an embodiment of the present invention;
FIG. 4 is a frequency spectrum of a process output signal after being averaged with a phase correction signal in an embodiment of the present invention;
FIG. 5 is a diagram illustrating the summed permutation entropy obtained by VMD decomposition corresponding to different penalty coefficients in an embodiment of the present invention;
FIG. 6 shows the decomposition result of the final VMD in the embodiment of the present invention.
Detailed Description
for this loop, it is known a priori that the system has nonlinear oscillation caused by valve sticking, and the data is derived from "Jelali M, Huang B.Detection and diagnostics of simulation in Control L oops: State of the Art and Advanced Methods [ M ]. Springer L on, 2009", the first chemical loop in the book, namely, chemical. lop 1. PV.
As shown in fig. 1, a method for detecting nonlinear oscillation of an industrial process based on improved variational modal decomposition includes:
Step 1, collecting a process output signal of a control loop to be detected.
The method for acquiring the process output signal comprises the following steps: the process data in the control loop to be detected is recorded in each preset sampling interval, and the process data collected in each sampling interval is added to the tail end of the process data collected previously.
The sampling interval refers to the sampling interval of the performance evaluation system. The process data is continuously updated over time, with new process data added to the end of the previously acquired process data for each length of time that a sampling interval has elapsed. The sampling interval of the performance evaluation system is generally the same as the control period in the industrial control system, and can also be selected as an integral multiple of the control period, and is specifically determined according to the real-time requirements and data storage capacity limitations of performance monitoring and industrial sites.
The raw data of the process output signal collected in this embodiment is shown in fig. 2, where the abscissa in fig. 2 is time, the unit is second, and the ordinate is flow rate.
And 2, calculating the frequency spectrum of the loop and the frequency spectrum after the phase correction signal mean value processing, and determining the modal number and the central frequency initialization value.
The frequency spectrum of the loop and the frequency spectrum after the phase correction signal averaging process are calculated, and it is found that the frequency spectrum of the loop has two peaks as shown in fig. 3, while the frequency spectrum after the phase correction signal averaging process has only one peak as shown in fig. 4.
The number of modes K is determined according to the following formula:
K＝max{Kfft,KPRSA}+1
The number of modes K is 3, and the corresponding initialization values of the center frequency are 0.01, 0.03, and 0.05.
In this example, the phase-corrected signal averaging algorithm (PRSA) is implemented according to "Bauer A, Kantelhardt J W, Bunde A, et al. phase-corrected averaging detectors silicon-periodicities in non-stationary data [ J ]. physical statistical mechanical & Its Applications,2006,364:423-434 ].
And step 3, determining the search range and step length of the penalty coefficient.
And determining that the search range of the penalty coefficient is approximately 100 to 10000, and the step length is 500 or 1000.
And 4, calculating summation arrangement entropy obtained by VMD decomposition corresponding to different penalty coefficients.
The sum arrangement entropy obtained by VMD decomposition corresponding to different penalty coefficients is shown in fig. 5 and table 1, and it can be seen that the penalty coefficient corresponding to the minimum sum arrangement entropy is 8100.
TABLE 1
| Penalty factor | 100 | 1100 | 2100 | 3100 | 4100 |
| Sum permutation entropy | 0.8084 | 0.5907 | 0.5553 | 0.5466 | 0.5361 |
| Penalty factor | 5100 | 6100 | 7100 | 8100 | 9100 |
| Sum permutation entropy | 0.5331 | 0.5272 | 0.5255 | 0.5254 | 0.5257 |
And 5, performing VMD decomposition to obtain the central frequency corresponding to the effective mode.
Under the conditions that the number of modes determined in the step 2 and the step 4 is 3, the initial center frequency is 0.01, 0.03 and 0.05 and the penalty coefficient is 8100, the arrangement entropy value, the correlation coefficient and the center frequency of the effective mode obtained by decomposition are shown in table 2.
TABLE 2
The decomposition result obtained by performing VMD decomposition in this step is shown in fig. 6, which includes, from top to bottom, the original signal, the reconstructed signal (the sum of the effective modes obtained by decomposition), the effective mode u1, and the effective mode u 2. It can be seen that the curves of the effective mode u1 and the effective mode u2 exhibit the form of a frequency and amplitude modulated signal, the reconstructed signal is approximately the same as the original signal, and the decomposition effect is satisfactory.
And 6, calculating whether the center frequencies of the effective modes have a multiple relation or not, and further judging whether nonlinear oscillation exists or not.
Since the ratio of the center frequencies of the effective mode u2 and the effective mode u1 is 3.1826, it is clear that | round (3.1816) -3.1816| -0.1816 ≦ 0.2, the output signal of this control loop contains a fundamental component and a third harmonic component, i.e., there is nonlinear oscillation, and the conclusion is consistent with the prior knowledge.
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 (4)
1. An industrial process nonlinear oscillation detection method based on improved variational modal decomposition is characterized by comprising the following steps:
(1) Collecting a group of loop output signals of the industrial process to be detected;
(2) Calculating the frequency spectrum of the loop output signal and the mean frequency spectrum of the phase correction signal, and determining the number of modes and the initial value of the central frequency; the specific process is as follows:
(2-1) calculating a Fourier spectrum of an output signal x (t) in the process and a spectrum subjected to phase correction signal mean value processing;
(2-2) determining the number of modes K according to the following formula
K＝max{Kfft,KPRSA}+1
Wherein, K fftRepresenting the number of peaks, K, in the Fourier spectrum PRSAThe number of peaks of the frequency spectrum after the mean value processing of the phase correction signal is represented;
(2-3) taking the frequency values of all the peak values as the initialization value omega of the center frequency init；
(3) Setting a search range and a step length of the penalty coefficient, calculating VMD decomposition corresponding to different penalty coefficients to obtain the sum of normalized arrangement entropies of each mode, and obtaining a summation arrangement entropy;
(4) Selecting a penalty coefficient corresponding to the minimum summation arrangement entropy as an optimal penalty coefficient;
(5) Performing VMD decomposition by using the mode number, the initial value of the central frequency and the selected penalty coefficient as parameters, and obtaining an effective mode according to the normalized permutation entropy and the correlation coefficient; the selection rules of the effective modes are as follows: the normalized correlation coefficient is greater than 0.2 and the normalized permutation entropy is less than 0.4; the normalized correlation coefficient calculation formula is as follows:
Cov stands for covariance, u k(t) represents the mode obtained by decomposition, x (t) represents the loop output signal, σ x(t)Representing the standard deviation of the loop output signal, 
Represents the standard deviation, ρ, of the k-th mode kRepresenting the correlation coefficient between the loop output signal x (t) and the kth mode shape, max representing the maximum value, λ kA normalized correlation coefficient representing a kth mode;
(6) And calculating whether the center frequencies of the effective modes have a multiple relation or not, and further judging whether nonlinear oscillation exists or not.
2. The method for detecting the nonlinear oscillation of the industrial process based on the improved variational modal decomposition according to claim 1, wherein in the step (3), the search range of the penalty coefficient is 100 to 10000, and the step size is 500 to 1000.
3. The method for detecting the nonlinear oscillation of the industrial process based on the improved variational modal decomposition according to claim 1, wherein the specific process of the step (3) is as follows:
(3-1) taking a value from the lower limit to the upper limit of the search range at intervals of one step length from the value of the penalty coefficient;
(3-2) calculating the normalized arrangement entropy and the summation arrangement entropy of each mode obtained by VMD decomposition corresponding to each penalty coefficient, wherein the calculation formula is as follows:
NPEk＝PEk/ln(N-d+1)
Wherein, NPE kIs the normalized permutation entropy value of the kth mode, PE kIs the original permutation entropy value for the k-th mode, N is the loop output signal length, d takes the value of 5, and SPE is the summed permutation entropy.
4. The method for detecting nonlinear oscillation in industrial process based on improved variational modal decomposition according to claim 1, wherein in the step (6), the specific manner for determining whether nonlinear oscillation exists is as follows:
If the center frequency between two or more active modes satisfies ω j/ωiK, i ≠ j, and | round (k) -k ≦ 0.2, which is equivalent to a multiple relationship, then the several valid modes belong to the same nonlinear oscillation, where round represents the nearest integer to k;
If a single active mode does not have a multiple relationship with the center frequency of any other mode, then that mode is considered a single linear oscillation.
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