Oscillation detection and diagnosis method, device and storage medium for device cascade process system based on multivariate nonlinear frequency modulation modal decomposition

Abstract

The present invention discloses a method for detecting and diagnosing oscillations in a cascaded device process system based on multivariate nonlinear frequency modulation modal decomposition. The method comprises the following steps: Step S1: Data preparation and preprocessing; Step S2: Oscillation detection phase: Advanced multivariate signal decomposition of process data using multivariate nonlinear frequency modulation modal decomposition technology is performed to effectively extract modal signals with time-varying and time-invariant characteristics, and oscillation detection is performed using correlation coefficients and autocovariance function zero-crossing regularity indicators; Step S3: Oscillation diagnosis phase: After confirming the existence of oscillations, grouped multivariate Granger causality analysis and phase correlation analysis are combined. The multivariate nonlinear frequency modulation modal decomposition method of the present invention can effectively extract time-invariant and time-varying oscillation modes in the cascaded device process and achieve inter-modal alignment, making it particularly suitable for diagnosing oscillations in complex multiple systems in industrial processes.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial process data analysis, and in particular to a method for detecting and diagnosing oscillation of a device cascade process system based on multivariate nonlinear frequency modulation modal decomposition. Background Art

[0002] In the increasingly complex modern process industry, a typical production process often consists of thousands of units and control loops. Due to the tight coupling between process equipment, an oscillation in a single local loop can quickly propagate throughout the entire system, leading to widespread instability in the control system and, in turn, system oscillation. System oscillation is not only a primary manifestation of deteriorating controller performance but also a key threat to the safe operation of industrial processes. Therefore, as an early warning signal of potential system failure, the detection and diagnosis of system oscillation is crucial for preventive maintenance and fault prediction.

[0003] System oscillations are common during device cascades due to factors such as fluctuating external input conditions and valve sticking. Cascades involve multiple equipment units and control loops, making them susceptible to variations in equipment characteristics or external interference. This can lead to single-loop oscillations or even system-wide oscillations, further increasing control system instability. Oscillations often occur when system control performance degrades or potential faults emerge.

[0004] However, traditional oscillation diagnosis methods usually focus on the detection and diagnosis of single-loop oscillations, and are difficult to adapt to time-varying, nonlinear and non-stationary oscillation phenomena, resulting in efficiency and effectiveness challenges in system-level oscillation detection and diagnosis. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention proposes a method for detecting and diagnosing oscillations in a device cascade process system based on multivariate nonlinear frequency modulation modal decomposition, so as to effectively improve the accuracy and practicality of system oscillation diagnosis.

[0006] Based on this, the present invention proposes a method for detecting and diagnosing oscillation of a device cascade process system based on multivariate nonlinear frequency modulation mode decomposition, which includes the following steps:

[0007] Step S1, data preparation and preprocessing:

[0008] Collect the online data x of the device cascade process and use Min-Max normalization preprocessing;

[0009] Step S2, oscillation detection:

[0010] Apply the multivariate nonlinear frequency modulation mode decomposition method to decompose the normalized online data x, extract the time-invariant and time-varying oscillation modes, and calculate the correlation coefficient θ between each mode and the original signal.q,m , remove false modes with low correlation, and calculate the zero-crossing regularity index r of the autocovariance function q,m , identify the true oscillation mode;

[0011] Step S3, oscillation diagnosis:

[0012] After identifying the oscillation modes, the oscillation modes with similar frequencies are grouped. For each oscillation mode group G q , performs oscillation diagnosis based on multivariate Granger causality analysis, based on phase correlation information The results of multivariate Granger causality analysis are optimized to eliminate irrelevant causal relationships and accurately locate the oscillation source.

[0013] In one possible design, the signal decomposition in step S2 to extract the time-invariant and time-varying oscillation modes is as follows:

[0014] A multivariate AM / FM signal with M channels can be expressed as follows:

[0015]

[0016] Among them, a m (t), f m and φ m represent the instantaneous amplitude, instantaneous frequency and initial phase of the mth component respectively;

[0017] The simplified analytical expression of the signal g(t), that is, the analytical form of the multivariate nonlinear frequency modulation mode, can be expressed as:

[0018]

[0019] Among them, f(t) and a(t) are the instantaneous frequency and instantaneous amplitude of the current multivariate nonlinear frequency modulation mode, j represents the imaginary unit in complex algebra, and the core of the multivariate nonlinear frequency modulation mode decomposition is to find a smooth function To estimate the instantaneous frequency of the multivariate nonlinear frequency modulation mode and ensure the bandwidth of the baseband signal is the narrowest;

[0020] According to the properties of trigonometric functions, the multivariate nonlinear frequency modulation mode can be reconstructed using the following formula:

[0021]

[0022] Among them, u(t) and v(t) are two demodulated signals, which can be expressed as:

[0023]

[0024] Assuming the number of modes is Q and the number of channels is M, the multivariate nonlinear frequency modulation mode decomposition aims to extract the Decompose the combination of Q multivariate nonlinear frequency modulation modes so that the sum of their bandwidths is minimized. The objective function of multivariate nonlinear frequency modulation mode decomposition can be expressed as:

[0025]

[0026] Where q and m represent the modality index and channel index respectively, q = 1, 2, ..., Q, m = 1, 2, ..., M; To reconstruct the input signal x of the mth channel m The signal of the qth mode of the multivariate nonlinear frequency modulation mode combination; where u' q ' ,m (t),v' q ' ,m (t) are two demodulated signals, smoothing function Used to estimate the instantaneous frequency of multivariate nonlinear frequency modulation modes. m is a pre-set minimum value.

[0027] In a possible design, the correlation coefficient θ between each mode and the original signal is calculated as described in step S2. q,m , remove the false modes with low correlation, specifically: remove the false modes that may be generated by multivariate nonlinear frequency modulation mode decomposition, the false modes g q,m With the original signal x m The correlation between them is usually low, and the correlation between them is evaluated by calculating the correlation coefficient between them. The correlation coefficient can be calculated as follows:

[0028]

[0029] Where cov(·,·) and std(·) represent the covariance and standard deviation, respectively. The normalized correlation coefficient can be calculated using the following formula:

[0030]

[0031] max q (·) represents the maximum; let the threshold of the normalized correlation coefficient be T θ , that is, to determine θ q,m ≤T θ g q,m False mode.

[0032] In one possible design, the calculation of the autocovariance function zero-crossing regularity index r in step S2 is q,m, identify the true oscillation mode, specifically: the zero-crossing regularity index of the autocovariance function can be used to identify time-invariant and time-varying oscillation modes. For mode g q,m Zero-crossing sequence If the standard deviation σ of the sequence t,q,m Less than its average value μ t,q,m One third of , it can be determined that the mode has oscillation characteristics. Based on this criterion, the zero-crossing regularity index of the autocovariance function can be defined as:

[0033]

[0034] This indicator reveals the variability of the zero-crossing sequence relative to its mean, and the threshold is set to T r , when r is satisfied q,m >T r When the mode g q,m Has an oscillating nature.

[0035] In one possible design, in step S2, the threshold value T of the normalized correlation coefficient is θ is 0.4; the threshold T in the zero-crossing regularity index of the autocovariance function r is 1.

[0036] In one possible design, the oscillation diagnosis in step S3 includes the following steps:

[0037] In step S3.1, the oscillation detection result can be expressed by the following oscillation matrix:

[0038]

[0039] Among them, q,m If and only if the event ((θ q,m >T θ )&(r q,m >T r )) takes the value 1 when it is true, which means g q,m Neither is it a spurious mode nor does it actually exhibit oscillatory behavior;

[0040] Step S3.2: Group the oscillation modes with similar frequencies. The specific process is as follows:

[0041] G q ={g q,m}(o q,m =1)

[0042] For each oscillation mode group G with similar frequency q Perform independent oscillation diagnosis based on multivariate Granger causality analysis to accurately obtain the root cause analysis results of multiple oscillation phenomena. Assume that p q,i,j Represents the oscillation signal gq,i and g q,j The p-value obtained by the Granger causality F test is considered to be g if the following conditions are met. q,j For g q,i There is Granger causality:

[0043] p q,i,j <1-α

[0044] Here, α represents the confidence level.

[0045] Step S3.3, by evaluating the phase correlation between different modes in the same modal group, the relative time delay between the signals is identified to optimize the diagnosis result; given two oscillating signals g q,i and g q,j , transform these two signals through Fourier transform FFT to obtain their spectrum representation:

[0046] X q,i (f) = FFT(g q,i )

[0047] X q,j (f) = FFT(g q,j )

[0048] The phase correlation between these two signals is calculated using the following formula:

[0049]

[0050] in, Represents g q,j The conjugate of the FFT result of ; IFFT(·) stands for inverse Fourier transform. Finally, by finding the maximum value in the phase correlation result, the signal g can be determined q,i Relative to g q,j The time delay is expressed as follows:

[0051]

[0052] in, Indicates the index where the maximum phase correlation is located, which can be used to estimate the time delay between the two signals, and thus indirectly estimate the phase difference; set the threshold to When satisfied When g q,j Prior to g in time q,i , that is, g q,i For g q,j There is no temporal causal action;

[0053] For two oscillating signals g q,i and g q,j,event If it is true, then g q,j For g q,i There is a causal effect, that is, g q,i The oscillation of g q,j cause.

[0054] In one possible design, the threshold is set in step S3 is 5.

[0055] A device, characterized in that it includes a memory, a control processor and a computer program stored in the memory and executable on the control processor, wherein the control processor executes the program to implement the device cascade process system oscillation detection and diagnosis method based on multivariate nonlinear frequency modulation modal decomposition as described in any one of claims 1 to 7.

[0056] The present invention also provides a computer-readable storage medium storing computer-executable instructions for implementing the aforementioned method for detecting and diagnosing oscillations in a cascaded process system of a device based on multivariate nonlinear frequency modulation modal decomposition.

[0057] In summary, this invention uses multivariate nonlinear frequency modulation modal decomposition (MNFMDM) to perform advanced multivariate signal decomposition on process data, effectively extracting modal signals with both time-varying and time-invariant characteristics. Oscillation detection is performed using correlation coefficients and the zero-crossing regularity of the autocovariance function. Once oscillation is confirmed, grouped multivariate Granger causality analysis and phase correlation analysis are combined to effectively improve the accuracy and practicality of system oscillation diagnosis.

[0058] The present invention has the following advantages:

[0059] (1) The multivariate nonlinear frequency modulation modal decomposition method of the present invention can effectively extract the time-invariant and time-varying oscillation modes in the device cascade process and achieve alignment between the modes. It is particularly suitable for diagnosing complex multi-system oscillations in industrial processes.

[0060] (2) The present invention effectively eliminates misleading modes that may be generated by the multivariate nonlinear frequency modulation modal decomposition method by calculating the correlation coefficient between the false mode and the original signal and the zero-crossing regularity index of the autocovariance function of each mode, thereby ensuring the accuracy and reliability of the oscillation analysis;

[0061] (3) The present invention optimizes the traditional multivariate Granger causality analysis results by introducing an adjustment method based on trigonometric function phase information, fully utilizes the modal features extracted by the multivariate nonlinear frequency modulation modal decomposition method, and improves the accuracy of system oscillation diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] The features and advantages of the present invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the present invention in any way. In the accompanying drawings:

[0063] Figure 1 This is a schematic diagram of the cascading process of the device according to an embodiment of the present invention;

[0064] Figure 2 Schematic diagram of the flow of the oscillation detection and diagnosis method of the device cascade process system based on multivariate nonlinear frequency modulation modal decomposition according to the present invention;

[0065] Figure 3 This is a graph showing the decomposition results of the multivariate nonlinear frequency modulation mode decomposition of variables No. 30, No. 31, and No. 32 in sub-block 4 of an embodiment of the present invention;

[0066] Figure 4 This is a graph showing the decomposition results of the multivariate nonlinear frequency modulation modal decomposition of variables No. 33, No. 34, and No. 35 in sub-block 4 of an embodiment of the present invention;

[0067] Figure 5 This is a graph showing the decomposition results of the multivariate nonlinear frequency modulation mode decomposition of variables No. 36, No. 37, and No. 38 in sub-block 4 of an embodiment of the present invention;

[0068] Figure 6 This is a visualization diagram of the oscillation detection results of sub-block 4 of an embodiment of the present invention;

[0069] Figure 7 This is a comparison diagram of the causal analysis of sub-block 4 of the embodiment of the present invention, where (a) is multivariate Granger causal analysis, and (b) is multivariate Granger causal analysis + phase correlation analysis;

[0070] Figure 8 This is the oscillation diagnosis directed graph of sub-block 4 in the embodiment of the present invention. DETAILED DESCRIPTION

[0071] The following embodiments of the present invention are described in further detail with reference to the accompanying drawings and examples. The following examples are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0072] To further illustrate each embodiment, the present invention provides drawings, which are part of the disclosure of the present invention. They are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. By referring to these contents, ordinary technicians in this field should be able to understand other possible implementation methods and advantages of the present invention. The components in the figures are not drawn to scale, and similar component symbols are generally used to represent similar components.

[0073] Currently, data-driven system oscillation diagnosis methods are mainly divided into two categories: frequency domain analysis methods and time-frequency analysis methods. Frequency domain analysis methods mainly include spectral principal component analysis (SPCA), spectral independent component analysis (SICA), spectral non-negative matrix factorization (SNMF), and spectral genetic algorithm (SGA). SPCA-based system oscillation diagnosis methods suffer from modal aliasing. To address this issue, a SICA-based system oscillation diagnosis method was proposed. However, this method lacks robustness in the face of interference and is difficult to adapt to practical industrial environments. SNMF-based system oscillation diagnosis methods offer improved computational speed and strong noise handling capabilities compared to the previous two methods, making them more suitable for system oscillation diagnosis in complex noise environments. Subsequently, several researchers proposed SGA-based system oscillation diagnosis methods. Due to SGA's advantage in its ability to globally search the solution space, it minimizes the error when reconstructing the original power spectrum matrix, demonstrating superior diagnostic performance compared to SICA and SNMF.

[0074] System oscillation diagnosis based on time-frequency analysis methods mainly includes multivariate empirical mode decomposition (MEMD), multivariate intrinsic timescale decomposition (MITD), multivariate variational mode decomposition (MVMD), and multivariate nonlinear modal decomposition (MNCMD). Multivariate time-frequency analysis methods, with their significant advantages in processing and analyzing nonlinear and nonstationary signals, are gradually gaining wider application and recognition in the field of system oscillation diagnosis. The introduction of MEMD into the field and its combination with correlation coefficient matrices and sparsity metrics can achieve system oscillation diagnosis. Subsequently, a system oscillation diagnosis method based on auxiliary noise MEMD effectively avoids the modal aliasing problem of MEMD. The MITD-based system oscillation diagnosis method can reduce the time complexity of multivariate signal decomposition. Unlike previous empirical signal decomposition methods, MVMD is based on a sound mathematical theory. Although MVMD performs well in decomposing narrowband signals, its ability to process broadband or time-varying signals is relatively limited. A system oscillation diagnosis algorithm based on multivariate nonlinear modal decomposition overcomes this limitation. Furthermore, by combining grouped multivariate Granger causality tests, it achieves even more effective oscillation diagnosis.

[0075] Frequency-domain analysis methods have been widely used in numerous fields due to their long history and significant effectiveness. However, time-frequency analysis methods, by comprehensively considering the time and frequency characteristics of a signal, provide new perspectives and tools for analyzing and resolving nonlinear, nonstationary signals and signals with multiple frequency components, demonstrating their significant potential and role in addressing practical industrial challenges.

[0076] To address the challenges of oscillation detection and diagnosis in cascaded process systems, this paper proposes a method for oscillation detection and diagnosis in cascaded process systems based on multivariate nonlinear frequency modulation modal decomposition (MNFMDM). MNFMDM employs advanced multivariate signal decomposition of process data to effectively extract modal signals with both time-varying and time-invariant characteristics. Oscillation detection is performed using correlation coefficients and the zero-crossing regularity index of the autocovariance function. Once oscillation is confirmed, grouped multivariate Granger causality analysis and phase correlation analysis are combined to effectively improve the accuracy and practicality of system oscillation diagnosis.

[0077] In order to solve the above-mentioned problems in the oscillation detection and diagnosis of the device cascade process system, the present invention proposes a device cascade process system oscillation detection and diagnosis method based on multivariate nonlinear frequency modulation mode decomposition, comprising the following steps:

[0078] S1. Data preparation and preprocessing: Collect online data of the device cascade process and use Min-Max normalization preprocessing;

[0079] S2, Oscillation detection stage: Apply multivariate nonlinear frequency modulation mode decomposition technology to decompose the normalized online data x to extract time-invariant and time-varying oscillation modes, and calculate the correlation coefficient θ between each mode and the original signal q,m , remove false modes with low correlation to ensure the accuracy of analysis, and calculate the zero-crossing regularity index r of the autocovariance function q,m , identify the true oscillation mode and lay the foundation for further diagnosis;

[0080] S3, oscillation diagnosis stage: After identifying the oscillation mode, the oscillation modes with similar frequencies are grouped. For each oscillation mode group G q , performs oscillation diagnosis based on multivariate Granger causality analysis, based on phase correlation information The results of multivariate Granger causality analysis are optimized (pruned) to remove irrelevant causal relationships and accurately locate the oscillation source.

[0081] Furthermore, step S2 includes the following steps:

[0082] S2.1. First, a multi-channel AM / FM signal can be expressed as follows:

[0083] The formula is:

[0084]

[0085] Among them, a m (t), f m and φ mrepresent the instantaneous amplitude, instantaneous frequency and initial phase of the mth component respectively.

[0086] S2.2. The simplified analytical expression of the signal g(t), that is, the analytical form of the multivariate nonlinear frequency modulation mode (multivariate nonlinear frequency modulation mode), can be expressed as:

[0087]

[0088] Among them, f(t) is the instantaneous frequency of the current multivariate nonlinear FM mode, a(t) is the instantaneous amplitude of the current multivariate nonlinear FM mode, and j represents the imaginary unit in complex algebra. The core of multivariate nonlinear FM mode decomposition is to find a smooth function To estimate the instantaneous frequency of the multivariate nonlinear frequency modulation mode and ensure that the bandwidth of the baseband signal is the narrowest.

[0089] S2.3 According to the properties of trigonometric functions, the multivariate nonlinear frequency modulation mode can be expressed as follows:

[0090] Reconstruct the formula to obtain:

[0091]

[0092] Among them, u(t) and v(t) are two demodulated signals, which can be expressed as:

[0093]

[0094] S2.4, set the number of modes to Q, the number of channels to M, and the multivariate nonlinear frequency modulation mode decomposition to obtain the input signal Decompose the combination of Q multivariate nonlinear frequency modulation modes so that the sum of their bandwidths is minimized. To achieve this goal, the objective function of multivariate nonlinear frequency modulation mode decomposition can be expressed as:

[0095]

[0096] Wherein, q and m represent the modality index and channel index respectively, q = 1, 2, ..., Q, m = 1, 2, ..., M. To reconstruct the input signal x of the mth channel m The signal of the qth mode multivariate nonlinear frequency modulation mode combination. q ' ,m (t),v' q ' ,m (t) are two demodulated signals, smoothing function Used to estimate the instantaneous frequency of multivariate nonlinear frequency modulation modes. m is a pre-set minimum value.

[0097] S2.5. In order to ensure the accuracy and reliability of oscillation analysis, it is necessary to eliminate the false modes that may be generated by multivariate nonlinear frequency modulation mode decomposition. q,m With the original signal x m The correlation between them is usually low, so calculating the correlation coefficient between them is an effective method to evaluate the correlation between them. The correlation coefficient can be calculated as follows:

[0098]

[0099] Where cov(·,·) and std(·) represent the covariance and standard deviation respectively. Accordingly, the normalized correlation coefficient can be calculated by the following formula:

[0100]

[0101] max q (·) represents the maximum value. The threshold value T of the normalized correlation coefficient is θ Set to 0.4, that is, to determine θ q,m ≤T θ g q,m This threshold setting is designed to effectively retain key oscillation modes while preventing the erroneous removal of key components in control loop signals with multiple oscillation characteristics.

[0102] S2.6, the zero-crossing regularity index of the autocovariance function can be used to identify time-invariant and time-varying oscillation modes. q,m Zero-crossing sequence If the standard deviation σ of the sequence t,q,m Less than its average value μ t,q,m If the value is one third of , then the mode can be determined to have oscillation characteristics. Based on this criterion, the zero crossing regularity index of the autocovariance function can be defined as:

[0103]

[0104] This indicator reveals the variability of the zero-crossing sequence relative to its mean. Set the threshold T r is 1, when r q,m >T r When the mode g q,m Has an oscillating nature.

[0105] Furthermore, step S3 includes the following steps:

[0106] S3.1. The oscillation detection result can be expressed by the following oscillation matrix:

[0107]

[0108] Among them,q,m If and only if the event ((θ q,m >T θ )&(r q,m >T r )) takes the value 1 when it is true, which means g q,m Neither is it a spurious mode nor does it exhibit oscillatory behavior.

[0109] S3.2. To facilitate subsequent root cause diagnosis, oscillation modes with similar frequencies need to be grouped. The specific process is as follows:

[0110] G q ={g q,m}(o q,m =1)

[0111] S3.3, for each oscillation mode group G with similar frequency q Perform independent oscillation diagnosis based on multivariate Granger causality analysis to accurately obtain the root cause analysis results of multiple oscillation phenomena. Assume that p q,i,j Represents the oscillation signal g q,i and g q,j The p-value obtained by the Granger causality F test is: q,j For g q,i There is Granger causality:

[0112] p q,i,j <1-α

[0113] Here, α represents the confidence level.

[0114] S3.4. By evaluating the phase correlation between different modes in the same modal group, the relative time delay between the signals can be identified to optimize the diagnosis results. q,i and g q,j ,First, transform the two signals by Fourier transform (FFT) to obtain their spectral representation:

[0115] X q,i (f) = FFT(g q,i )

[0116] X q,j (f) = FFT(g q,j )

[0117] The phase correlation between these two signals is calculated using the following formula:

[0118]

[0119] in, Represents gq,j The conjugate of the FFT result of ; IFFT(·) stands for inverse Fourier transform. Finally, by finding the maximum value in the phase correlation result, the signal g can be determined q,i Relative to g q,j The time delay is expressed as follows:

[0120]

[0121] in, Indicates the index where the maximum phase correlation is located, which can be used to estimate the time delay between two signals and thus indirectly estimate the phase difference. Set the threshold is 5, when When g q,j Prior to g in time q,i , that is, g q,i For g q,j There is no temporal causality. The entire process utilizes the spectral information of the signals to estimate the phase difference between them. By calculating the Fourier transforms of the two signals, then multiplying the FFT of one signal by the conjugate FFT of the other, and finally performing an inverse Fourier transform to obtain the phase correlation, the relative delay between the signals is determined from its maximum value. By considering the time-dependent phase difference information, multivariate Granger causality analysis can be effectively "pruned," thereby improving the accuracy of oscillation diagnosis.

[0122] S3.5. For two oscillating signals g q,i and g q,j ,event If it is true, then g q,j For g q,i There is a causal effect, that is, g q,i The oscillation of g q,j cause.

[0123] (3) Beneficial effects

[0124] The above-mentioned device cascade process system oscillation detection and diagnosis method of the present invention has the following advantages:

[0125] (1) Multivariate nonlinear frequency modulation modal decomposition can effectively extract the time-invariant and time-varying oscillation modes in the device cascade process and achieve inter-modal alignment, which is particularly suitable for diagnosing complex multi-system oscillations in industrial processes;

[0126] (2) By calculating the correlation coefficient between the false modes and the original signal and the zero-crossing regularity index of the autocovariance function of each mode, the misleading modes that may be generated by the multivariate nonlinear frequency modulation mode decomposition are effectively eliminated, ensuring the accuracy and reliability of the oscillation analysis;

[0127] (3) By introducing an adjustment method based on trigonometric function phase information, the traditional multivariate Granger causality analysis results are optimized, and the modal features extracted by multivariate nonlinear frequency modulation modal decomposition are fully utilized to improve the accuracy of system oscillation diagnosis.

[0128] In at least one embodiment, Figure 1 The aluminum oxide evaporation process shown is a typical device cascade process. Figure 1 The process flow diagram depicted utilizes a two-stage, seven-effect, five-flash evaporation method. This evaporation process consists of seven evaporators, seven preheaters, six flash evaporators (including one raw liquid flash evaporator), and several condensate tanks. Steam is supplied to the outside of the evaporator's heating tubes, indirectly heating the mother liquor inside to boiling, thereby concentrating it. The concentrated mother liquor is discharged through a discharge port at the bottom of the evaporation chamber, while the separated secondary steam is released through a steam outlet to provide heat for the next-stage evaporator. Based on the direction of material flow, the evaporation process can be subdivided into the material flow, steam flow, and water flow. The following focuses on the first two: ① Material flow: A portion of the evaporated raw liquid first enters the five-effect evaporator via a feed pump, then passes through the fourth- to first-effect evaporators and the first- to fifth-stage flash evaporators. The final portion of the highly concentrated mother liquor is discharged directly, while the remaining portion flows into a blending tank. Another portion of the evaporated raw liquid first enters the raw liquid flash evaporator, then passes through the seventh- to sixth-effect evaporators, and finally flows into a blending tank, where it is blended with a portion of the raw liquid and alkali solution to form a qualified mother liquor. ② Steam process: New steam enters the heating chamber of the first-effect evaporator to heat the material and promote its evaporation, and the secondary steam generated by the first-effect evaporator is then transported to the heating chamber of the second-effect evaporator to further heat the material and achieve evaporation; similarly, the secondary steam generated by the second-effect evaporator is introduced into the third-effect heating chamber; the secondary steam generated by the third-effect evaporator is introduced into the fourth-effect heating chamber; the secondary steam generated by the fourth-effect evaporator is introduced into the fifth-effect heating chamber; the secondary steam generated by the fifth-effect evaporator is introduced into the sixth-effect heating chamber; the secondary steam generated by the sixth-effect evaporator is introduced into the seventh-effect heating chamber; the secondary steam generated by the seventh-effect evaporator enters the water cooler for condensation; the secondary steam generated by the first to fifth-stage flash evaporators enter the third to seventh-effect heating chambers respectively for final exhaust steam utilization.

[0129] For the aluminum oxide evaporation process, a device cascade process system oscillation detection and diagnosis method based on multivariate nonlinear frequency modulation mode decomposition is proposed, specifically Figure 2 As shown, the following steps are included:

[0130] S1. Data Preparation and Preprocessing: Online data from the alumina evaporation process was collected and preprocessed using Min-Max normalization. Considering the effectiveness and practicality of fault diagnosis, process variables were initially divided into three categories: output variables, input variables, and intermediate variables. Specifically, the first sub-block output variables included variables 1, 2, 3, 4, 13, 44, and 45; the second sub-block input variables included variables 5, 6, 7, 8, 9, 10, 11, 12, and 29. After determining the output and input variables, the remaining 29 intermediate variables were further subdivided into three sub-blocks using the mutual information K-means clustering method. The third sub-block included variables 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, and 28; the fourth sub-block included variables 30, 31, 32, 33, 34, 35, 36, 37, and 38; and the fifth sub-block included variables 39, 40, 41, 42, and 43. The fourth sub-block was selected for the system oscillation diagnosis method based on multivariate nonlinear frequency modulation mode decomposition. The sub-block 4 dataset contained 400 samples and 9 variables, with a sampling interval of 2 minutes.

[0131] S2, oscillation detection stage: The result of performing multivariate signal decomposition on sub-block 4 by multivariate nonlinear frequency modulation mode decomposition method is as follows Figure 3 、 Figure 4 and Figure 5 Then, the correlation coefficient and the autocovariance function zero-crossing regularity index are used to detect oscillation. The oscillation mode is Figure 6 The data is marked with black squares. The analysis shows that there is an obvious oscillation mode g2 in the data. However, mode g1 reflects the trend of the original variable, and mode g3 is a false mode or noise mode, which are not oscillation modes. In addition, the variable x representing the steam chamber pressure of the six-effect and seven-effect evaporators is 31 and x 38 No oscillation phenomenon is shown, indicating that these pressure variables relatively close to the new steam input maintain a relatively stable state;

[0132] S3, Oscillation diagnosis stage: Figure 7 As shown in the figure, based on the grouping, a single multivariate Granger causality analysis results in numerous false causal relationships because it does not consider time-related information. Based on the background knowledge of the material flow of the alumina evaporation process, a portion of the evaporation raw liquid first enters the raw liquid flash evaporator, then passes through the seventh-effect evaporator to the sixth-effect evaporator, and finally flows to the blending tank. Based on this, the relevant variable x of the sixth-effect evaporator is 30 and x 32 The influence on other variables is extremely limited. However, the simple multivariate Granger causality analysis misjudges the temperature x before the heat exchange of the six-effect raw liquid. 32 Will affect the raw liquid flash evaporator feed flow x33 、The discharge temperature of the raw liquid flash evaporator x 34 And the raw liquid flash evaporator steam pressure x 35 , which contradicts the actual material flow. Such misjudgments are primarily due to the fact that multivariate Granger causality analysis considers only the prediction error perspective, ignoring the critical time-correlated phase difference information. Introducing phase correlation analysis effectively eliminates these unreasonable causal relationships, significantly reducing erroneous causal inferences and significantly improving the accuracy of oscillation diagnosis.

[0133] The final oscillation diagnosis result is as follows Figure 8 As shown, the feed flow rate of the raw liquid flash evaporator x 33 、The temperature of the seven-effect raw liquid before heat exchange x 36 And the steam temperature of the seven-effect evaporator x 37 It is the root cause of system oscillation. In addition, the steam temperature of the six-effect evaporator x 30 、6-effect stock solution temperature before heat exchange x 32 Variables such as oscillations due to these root causes fluctuate, a finding consistent with the actual material and energy flow characteristics of the alumina evaporation process. By pinpointing the oscillation source to specific process steps and equipment, we not only accurately capture the oscillation's origin, but also understand its propagation path and impact throughout the evaporation system, providing a powerful basis for further operational optimization and fault prevention.

[0134] In summary, the above-mentioned oscillation detection and diagnosis method for the device cascade process system based on multivariate nonlinear frequency modulation mode decomposition has the following advantages:

[0135] (1) Multivariate nonlinear frequency modulation modal decomposition can effectively extract the time-invariant and time-varying oscillation modes in the device cascade process and achieve inter-modal alignment, which is particularly suitable for diagnosing complex multi-system oscillations in industrial processes;

[0136] (2) By calculating the correlation coefficient between the false modes and the original signal and the zero-crossing regularity index of the autocovariance function of each mode, the misleading modes that may be generated by the multivariate nonlinear frequency modulation mode decomposition are effectively eliminated, ensuring the accuracy and reliability of the oscillation analysis;

[0137] (3) By introducing an adjustment method based on trigonometric function phase information, the traditional multivariate Granger causality analysis results are optimized, and the modal features extracted by multivariate nonlinear frequency modulation modal decomposition are fully utilized to improve the accuracy of system oscillation diagnosis.

[0138] The present invention also provides a device comprising a memory, a control processor, and a computer program stored in the memory and executable on the control processor, wherein the control processor executes the program to implement the aforementioned device cascade process system oscillation detection and diagnosis method based on multivariate nonlinear frequency modulation modal decomposition.

[0139] The present invention also provides a computer-readable storage medium, which stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to implement the aforementioned device cascade process system oscillation detection and diagnosis method based on multivariate nonlinear frequency modulation modal decomposition.

[0140] Although the above methods are illustrated and described as a series of actions for simplicity of explanation, it should be understood and appreciated that these methods are not limited by the order of the actions, because according to one or more embodiments, some actions may occur in different orders and / or concurrently with other actions from the diagrams and descriptions herein or not illustrated and described herein but understood by those skilled in the art. Those skilled in the art will further appreciate that the various illustrative logic blocks, modules, circuits, and algorithm steps described in conjunction with the embodiments disclosed herein can be implemented as electronic hardware, computer software, or a combination of the two. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps are generally described above in terms of their functionality. Whether such functionality is implemented as hardware or software depends on the specific application and the design constraints imposed on the overall system. Technicians can implement the described functionality in different ways for each specific application, but such implementation decisions should not be interpreted as resulting in a departure from the scope of the present invention. The various illustrative logic blocks, modules, and circuits described in conjunction with the embodiments disclosed herein may be implemented or executed using a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, a battery compartment control board, a micro-battery compartment control board, or a state machine. A processor may also be implemented as a combination of computing devices, such as a combination of a DSP and a microprocessor, multiple microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. The software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read and write information from / to the storage medium. In an alternative, the storage medium may be integrated into the processor. The processor and storage medium may reside in an ASIC. The ASIC may reside in a user terminal. In an alternative, the processor and storage medium may reside in the user terminal as discrete components. In one or more exemplary embodiments, the functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software as a computer program product, the functions may be stored or transmitted as one or more instructions or codes on a computer-readable medium.Computer-readable media include both computer storage media and communication media, including any media that facilitates the transfer of a computer program from one place to another. Storage media can be any available media that can be accessed by a computer. As an example and not limitation, such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, disk storage or other magnetic storage device, or any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer. Any connection is also properly referred to as a computer-readable medium. For example, if the software is transmitted from a website, a central control computer, or other remote source using a coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwaves, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwaves are included in the definition of medium. As used herein, disk and disc include compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and Blu-ray disc, where disks typically reproduce data magnetically, while discs reproduce data optically with lasers. Combinations of the above should also be included within the scope of computer-readable media.

[0141] Although the above methods are illustrated and described as a series of acts for simplicity of explanation, it is to be understood and appreciated that these methods are not limited by the order of the acts, as some acts may occur in a different order and / or concurrently with other acts from those illustrated and described herein or not illustrated and described herein but understandable to those skilled in the art according to one or more embodiments.

[0142] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

[0143] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations shall fall within the scope defined by the appended claims.

Claims

1. A method for detecting and diagnosing oscillations in a cascaded process system based on multivariate nonlinear frequency modulation modal decomposition, characterized in that: The following steps are involved: Step S1, data preparation and preprocessing: Collect the online data x of the device cascade process and use Min-Max normalization preprocessing; Step S2, oscillation detection: Apply the multivariate nonlinear frequency modulation mode decomposition method to decompose the normalized online data x, extract the time-invariant and time-varying oscillation modes, and calculate the correlation coefficient θ between each mode and the original signal. q,m , remove false modes with low correlation, and calculate the zero-crossing regularity index r of the autocovariance function q,m , identify the true oscillation mode; Step S3, oscillation diagnosis: After identifying the oscillation modes, the oscillation modes with similar frequencies are grouped. For each oscillation mode group G q , performs oscillation diagnosis based on multivariate Granger causality analysis, based on phase correlation information The results of multivariate Granger causality analysis are optimized to eliminate irrelevant causal relationships and accurately locate the oscillation source.

2. The method for detecting and diagnosing oscillation of a cascaded process system based on multivariate nonlinear frequency modulation mode decomposition according to claim 1, characterized in that: The signal decomposition described in step S2 extracts the time-invariant and time-varying oscillation modes, specifically: A multivariate AM / FM signal with M channels can be expressed as follows: Among them, a m (t), f m and φ m represent the instantaneous amplitude, instantaneous frequency and initial phase of the mth component respectively; The simplified analytical expression of the signal g(t), that is, the analytical form of the multivariate nonlinear frequency modulation mode, can be expressed as: Among them, f(t) and a(t) are the instantaneous frequency and instantaneous amplitude of the current multivariate nonlinear frequency modulation mode, j represents the imaginary unit in complex algebra, and the core of the multivariate nonlinear frequency modulation mode decomposition is to find a smooth function To estimate the instantaneous frequency of the multivariate nonlinear frequency modulation mode and ensure the bandwidth of the baseband signal is the narrowest; According to the properties of trigonometric functions, the multivariate nonlinear frequency modulation mode can be reconstructed using the following formula: Among them, u(t) and v(t) are two demodulated signals, which can be expressed as: Assuming the number of modes is Q and the number of channels is M, the multivariate nonlinear frequency modulation mode decomposition aims to extract the Decompose the combination of Q multivariate nonlinear frequency modulation modes so that the sum of their bandwidths is minimized. The objective function of multivariate nonlinear frequency modulation mode decomposition can be expressed as: Where q and m represent the modality index and channel index respectively, q = 1, 2, ..., Q, m = 1, 2, ..., M; u" q,m (t),v” q,m (t), To reconstruct the input signal x of the mth channel m The signal of the qth mode multivariate nonlinear frequency modulation mode combination; where u” q,m (t),v” q,m (t) are two demodulated signals, smoothing function Used to estimate the instantaneous frequency of multivariate nonlinear frequency modulation modes; ε m is a pre-set minimum value.

3. The method for detecting and diagnosing oscillation of a cascaded process system based on multivariate nonlinear frequency modulation mode decomposition according to claim 2, characterized in that: The correlation coefficient θ between each mode and the original signal is calculated as described in step S2 q,m , remove the false modes with low correlation, specifically: remove the false modes that may be generated by multivariate nonlinear frequency modulation mode decomposition, the false modes g q,m With the original signal x m The correlation between them is usually low, and the correlation between them is evaluated by calculating the correlation coefficient between them. The correlation coefficient can be calculated as follows: Where cov(·,·) and std(·) represent covariance and standard deviation respectively; normalized correlation coefficient θ q,m It can be calculated by the following formula: max q (·) represents the maximum value; let the threshold of the normalized correlation coefficient be T θ , that is, to determine θ q,m ≤T θ g q,m False mode.

4. The method for detecting and diagnosing oscillation of a cascaded process system based on multivariate nonlinear frequency modulation mode decomposition according to claim 3, characterized in that: The calculation of the autocovariance function zero crossing regularity index r described in step S2 q,m , identify the true oscillation mode, specifically: the zero-crossing regularity index of the autocovariance function can be used to identify time-invariant and time-varying oscillation modes. For mode g q,m Zero-crossing sequence If the standard deviation σ of the sequence t,q,m Less than its average value μ t,q,m One third of , it can be determined that the mode has oscillation characteristics. Based on this criterion, the zero-crossing regularity index of the autocovariance function can be defined as: This indicator reveals the variability of the zero-crossing sequence relative to its mean, and the threshold is set to T r , when r is satisfied q,m >T r When the mode g q,m Has an oscillating nature.

5. The method for detecting and diagnosing oscillation of a cascaded process system based on multivariate nonlinear frequency modulation mode decomposition according to claim 4, characterized in that: In step S2, the threshold value T of the normalized correlation coefficient is θ is 0.4; the threshold T in the zero-crossing regularity index of the autocovariance function r is 1.

6. The method for detecting and diagnosing oscillation of a cascaded process system based on multivariate nonlinear frequency modulation mode decomposition according to claim 4 or 5, characterized in that: The oscillation diagnosis described in step S3 includes the following steps: In step S3.1, the oscillation detection result can be expressed by the following oscillation matrix: Among them, q,m If and only if the event ((θ q,m >T θ )&(r q,m >T r )) takes the value 1 when it is true, which means g q,m Neither is it a spurious mode nor does it actually exhibit oscillatory behavior; Step S3.2: Group the oscillation modes with similar frequencies. The specific process is as follows: G q ={g q,m }(o q,m =1) For each oscillation mode group G with similar frequency q Perform independent oscillation diagnosis based on multivariate Granger causality analysis to accurately obtain the root cause analysis results of multiple oscillation phenomena. Assume that p q,i,j Represents the oscillation signal g q,i and g q,j The p-value obtained by the Granger causality F test is considered to be g if the following conditions are met. q,j For g q,i There is Granger causality: p q,i,j ＜1-α Among them, α represents the confidence level; Step S3.3, by evaluating the phase correlation between different modes in the same modal group, the relative time delay between the signals is identified to optimize the diagnosis result; given two oscillating signals g q,i and g q,j , transform these two signals through Fourier transform FFT to obtain their spectrum representation: X q,i (f)=FFT(g q,i ) X q,j (f)=FFT(g q,j ) The phase correlation between these two signals is calculated using the following formula: in, Represents g q,j The conjugate of the FFT result of ; IFFT(·) stands for inverse Fourier transform. Finally, by finding the maximum value in the phase correlation result, the signal g can be determined q,i Relative to g q,j The time delay is expressed as follows: in, Indicates the index where the maximum phase correlation is located, which can be used to estimate the time delay between the two signals, and thus indirectly estimate the phase difference; set the threshold to When satisfied When g q,j Prior to g in time q,i , that is, g q,i For g q,j There is no temporal causal action; For two oscillating signals g q,i and g q,j ,event If it is true, then g q,j For g q,i There is a causal effect, that is, g q,i The oscillation of g q,j cause.

7. The method for detecting and diagnosing oscillation of a cascaded process system based on multivariate nonlinear frequency modulation mode decomposition according to claim 6, characterized in that: In step S3, the threshold is set is 5.

8. A device, characterized in that: The method comprises a memory, a control processor, and a computer program stored in the memory and executable on the control processor, wherein the control processor executes the program to implement the device cascade process system oscillation detection and diagnosis method based on multivariate nonlinear frequency modulation modal decomposition as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to implement the device cascade process system oscillation detection and diagnosis method based on multivariate nonlinear frequency modulation modal decomposition as described in any one of claims 1 to 7.

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