An early fault detection method based on time-space hybrid model of wavelet transform

Abstract

The present invention provides a method for early fault detection based on a time-space hybrid model of wavelet transform, which belongs to the technical field of statistical analysis and machine learning. The method solves the problem that small faults in complex dynamic systems are difficult to detect in real time. The technical scheme is as follows: it includes the following steps: 1) performing multi-level decomposition and denoising processing; 2) establishing the principal component subspace of the training data set and the test data set; 3) calculating the neighbor sample set of the time dimension and the space dimension in each time window; 4) using the cumulative sum algorithm CUSUM and the Mahalanobis distance MD to calculate the statistics of the time dimension and the space dimension respectively; 5) obtaining the basic weights of the time and space sequences; 6) using the kernel density estimation KDE method to estimate the upper threshold limit of the hybrid statistic to determine whether a fault occurs. The beneficial effects of the present invention are: the present invention is used for real-time detection and analysis of small faults in highly dynamic and complex systems.

Description

Technical Field

[0001] The present invention relates to the technical field, and in particular to an early fault detection method of a space-time hybrid model based on wavelet transform. Background Art

[0002] In the highly automated and intelligent contemporary industrial environment, the stable operation of equipment and systems plays a vital role in ensuring production safety, improving efficiency and reducing costs. With the development of technology, systems have become more and more complex, which makes fault detection and diagnosis more difficult, especially the increasing need to accurately identify minor faults in the early stages. Minor faults, if not discovered and handled in a timely manner, may lead to system performance degradation or even major accidents. Specifically, existing monitoring systems often have difficulty effectively handling the data dynamics generated by high-frequency operational changes in the system and the intricate spatial associations between production links. In addition, these systems are often particularly inadequate in identifying and responding to early minor changes or anomalies due to the lack of advanced data processing methods that can integrate and synchronously analyze these complex dynamics. Therefore, effective fault detection of complex industrial processes is an effective means to ensure the safe production of industrial processes. New technologies to improve the accuracy and response speed of early fault detection have become an important research direction in this field.

[0003] The paper "Fault detection and isolation for output feedback system based on space geometry method" (HOU Y, HUANG R, CHENG Q, et al., Cluster Computing-the Journal of Networks Software Tools and Applications, 2019, 22: S9313-S21) introduces spatial data processing technology and performs fault detection and isolation on the output feedback system based on the spatial geometry method. By establishing a mathematical model based on spatial geometric characteristics, complex data is converted into points in geometric space, and geometric characteristics are used for fault detection and isolation, which effectively improves the efficiency and accuracy of fault detection. However, this method still has some shortcomings in practical applications, such as high computational complexity when processing high-dimensional data, and the robustness to noisy data needs to be further improved.

[0004] The paper "Wind turbine fault detection based on spatial-temporal featureand neighbor operation state" (QIAN X, SUN T, ZHANG Y, et al., Renewable Energy, 2023, 219) proposed a wind turbine fault detection method based on spatiotemporal features and neighbor operation status. By combining time series analysis and spatial analysis, the ability to predict the development trend of faults is improved. Specifically, the study proposed a new fault detection model through the analysis of time series data and combined with the operating status of the neighboring areas of wind turbines, which improved the accuracy and timeliness of fault prediction. Although some progress has been made, there are still many challenges, including how to effectively integrate spatiotemporal features and how to process and analyze large-scale industrial data. Solving these problems will be the key to further improving fault detection technology. Summary of the invention

[0005] The object of the present invention is to provide a time-space hybrid model early fault detection method based on wavelet transform, which is used for real-time detection and analysis of small faults in highly dynamic and complex systems.

[0006] The inventive concept of the present invention is as follows: the method first reduces the impact of environmental noise by denoising with wavelet transform WT. The principal component subspace of the training data set and the test data set is established by principal component analysis PCA. Given a sliding window W, the neighbor sample sets of the time dimension and the space dimension in each time window are calculated, and the statistics of the time dimension and the space dimension are calculated by the cumulative sum algorithm CUSUM and the Mahalanobis distance MD respectively. The present invention uses absolute deviation to calculate the basic weights of the time and space sequences, and obtains the final mixed statistic S according to the weight distribution. ts , effectively enhancing the correlation between high-frequency time dynamics and space, and improving the accuracy of fault detection. Finally, the kernel density estimation KDE method is used to estimate the upper threshold limit of the mixed statistic. The proposed spatiotemporal mixed model fault detection method is applied to the Tennessee-Eastman process TE for fault detection experiments. The performance of the STHM method is compared with that of principal component analysis PCA and spatiotemporal neighbor STN using representative fault detection performance indicators FDR and FAR. The results show that the proposed method has a higher fault detection rate and a lower false alarm rate in multi-group fault detection, which can better ensure the safety of the production process and the high quality of the product. The present invention provides a novel, accurate and efficient detection technology solution for minor faults in dynamic complex systems, which has broad application prospects.

[0007] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is specifically: a time-space hybrid model early fault detection method based on wavelet transform, comprising the following steps:

[0008] Step 1: wavelet transform. The wavelet transform uses the Mallat algorithm to perform multi-level decomposition on the data signal to effectively separate the different frequency components of the signal. First, the acquired original signal is decomposed by the wavelet function to obtain the frequency structure of the decomposed signal. Further, a threshold is set to filter and quantize the high-frequency signal with noise. Finally, wavelet reconstruction is performed according to the signal characteristics of the lowest and highest frequencies to achieve the purpose of denoising.

[0009] By performing wavelet transform on the signal, wavelet coefficients at all levels are obtained. These coefficients reflect the energy distribution of the signal at different scales. The frequency band range of wavelet decomposition is related to the sampling frequency. If N layers of decomposition are performed, the range of each frequency band is:

[0010]

[0011] In the above relationship, F s is the sampling frequency, f max is the maximum sampling frequency of the signal, F s =2f max It is obtained according to the Nyquist sampling theorem.

[0012] In order to distinguish noise from useful signals, a soft threshold function is set. The wavelet coefficients below this threshold are regarded as noise and filtered out, while those above the threshold are retained as effective components of the signal. The soft threshold function is:

[0013]

[0014] By setting the threshold function, the key features of the signal are retained, avoiding the problem of signal feature loss that may be caused by traditional filtering technology.

[0015] Through this wavelet denoising method of comprehensive feature extraction and low-pass filtering, the noise in the TE data set can be effectively removed without losing the essential information of the signal, thereby providing more accurate and clearer data support for subsequent fault detection.

[0016] A noisy model can be expressed as follows:

[0017] S(k)=f(k)+ε*e(k) k=1,2...,n (3)

[0018] Among them, f(k) is the real signal we need, S(k) is the original signal with noise added, e(k) is the noise, and ε is the variable coefficient of the noise.

[0019] Step 2, feature extraction, the feature extraction includes constructing a principal component subspace based on PCA. The m-dimensional original data is projected into a k-dimensional space by projection. Its principal component is a mutually orthogonal feature. The data set consisting of n sampling points and m features is standardized into an n×m dimensional matrix, and the covariance formula is used to observe the correlation between two features. The original data set is projected into the space formed by k feature vectors to obtain a principal component model.

[0020] For m features, in order to obtain the correlation between every two features, an m×m dimensional covariance matrix is ​​constructed.

[0021]

[0022] C mm Solve for the eigenvalue λ m and the eigenvector p m , eigenvalue λ m The corresponding eigenvector p can be obtained m The importance of m The values ​​of the eigenvalues ​​are arranged in order to obtain the corresponding eigenvector p m Generate load matrix P m . C mm Eigenvalues ​​λ sorted by numerical value m , its corresponding eigenvector p m , is an important basis for PCA to select the m×m-dimensional principal component. mm is a symmetric matrix, so C mm The eigenvectors of are mutually orthogonal, so there is no connection between the principal components of PCA. Suppose we want to reduce the dimension of the m-dimensional vector to k-dimensional, we only need to take P m The first k columns of compose the matrix. The n×k dimensional matrix T after dimensionality reduction, that is, the original data set is projected into the space formed by k eigenvectors, and the principal component model is obtained:

[0023] X=TP T +E (6)

[0024] Among them, TP T is the principal element subspace, and E is the residual space.

[0025] Step 3: Fault detection model, which includes a spatiotemporal hybrid model. By combining principal component analysis (PCA) and cumulative sum algorithm (CUSUM), the processed data is deeply analyzed to extract key spatiotemporal features. In addition, the model also introduces kernel density estimation (KDE) to determine the threshold of the statistic to further optimize the fault detection process. Through this series of technical innovations, the STHM model can not only effectively handle high-frequency temporal dynamics and complex spatial correlations, but also significantly improve the precision and accuracy of fault detection.

[0026] For a single direction CUSUM, the calculation formula can be expressed as:

[0027] CUSUM i =max(0,CUSUM i-1 +(x i -μ-K) (7)

[0028] Among them, x i is the observed value of the ith sample, μ is the expected mean of the process, CUSUM i is the cumulative sum of the i-th sample.

[0029] Based on the above formula, for a given time window W, we get the sample x i Statistics S in the time dimension time (x i )for:

[0030]

[0031] Calculate the mean of the spatial dimension sample set And the covariance matrix ∑, get the sample x i Statistics S in the spatial dimension space (x i )for:

[0032]

[0033] The basic weights of the time and space series are calculated based on the absolute deviation of the time and space statistics, and the final mixed statistics are obtained according to the weight distribution. The absolute deviation is defined as follows:

[0034]

[0035] Among them, M i is the absolute deviation of the time dimension and space dimension statistics of the i-th sample. Based on the above formula, the basic weight based on the time dimension is obtained as

[0036]

[0037] The statistical proportions of different dimensions based on the spatiotemporal hybrid model with the maximum fault degree are obtained by scaling, and the final hybrid statistic S ts The expression takes the form

[0038] S ts (x i )=ω(x i )·S time (x i )+(1-ω(x i ))·S space (x i ) (12)

[0039] Step 4: Fault detection implementation includes early identification of minor faults: early identification and early warning of minor faults are achieved through the high sensitivity of the model to minor changes. The fault detection implementation also includes real-time monitoring and diagnosis: the trained model is deployed in the real-time monitoring system to continuously monitor and diagnose faults in the industrial system. When the statistic is greater than the threshold, the system determines that it is a fault warning, and when the statistic is less than the threshold, the system determines that no fault has occurred.

[0040] The kernel density estimation (KDE) method is used to estimate the upper threshold of the mixture statistic to determine whether a failure has occurred. Given a significance level of α = 0.05, the KDE method is used to measure S ts Upper limit of statistics

[0041]

[0042] Where p(z) is the probability density function of the random variable z. In practice, the following fault detection logic is used:

[0043]

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] 1. The present invention uses wavelet transform to denoise the original data, effectively reducing the impact of environmental noise on signal analysis, thereby improving data quality. In addition, combined with principal component analysis, this technology can extract key spatiotemporal features from the denoised data. This method of comprehensive use of wavelet transform and principal component analysis has significant advantages in improving the sensitivity and accuracy of early fault detection.

[0046] 2. The present invention innovatively introduces the cumulative sum algorithm (CUSUM) and Mahalanobis distance to calculate the time dimension and space dimension statistics of the processed data. This method can sensitively capture subtle changes in the process through accurate calculation of statistics, thereby achieving efficient identification of early faults and significantly improving the real-time and accuracy of fault detection.

[0047] 3. The present invention proposes a spatiotemporal hybrid model (STHM), which establishes an analysis framework that integrates the time dimension and the space dimension by integrating the data denoised by wavelet transform and the results of principal component analysis. The model uses a sliding window method to find the nearest neighbor sample set in time and space, and uses a method combining the cumulative sum algorithm (CUSUM) with the Mahalanobis distance statistic, which not only improves the model's sensitivity to faults, but also enhances the ability to identify fault types and their development trends. In addition, by optimizing the weight distribution through the calculation of absolute deviation, this model can effectively improve the accuracy of fault detection and reduce false alarms, making it have significant application advantages in changeable and complex industrial environments. The present invention aims to effectively and synchronously process high-frequency temporal dynamics and spatial correlations, and is suitable for the detection of minor faults. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0049] Figure 1 The present invention is a flowchart of an early fault detection method of a space-time hybrid model based on wavelet transform.

[0050] Figure 2 The figure is a wavelet transform schematic diagram of an early fault detection method of a space-time hybrid model based on wavelet transform according to the present invention.

[0051] Figure 3 This is a comparison diagram of the FDR effects of different detection methods of an early fault detection method of a space-time hybrid model based on wavelet transform of the present invention.

[0052] Figure 4 This is a test result diagram of the statistics of different detection methods of the early fault detection method of the space-time mixed model based on wavelet transform of the present invention; among them, (a) is the statistics of the STHM method in the detection of small faults 15; (b) is the statistics of the STN method in the detection of small faults 15; (c) and (d) are the statistics of the PCA method in the detection of small faults 15. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

[0054] Example 1

[0055] See also Figures 1 to 4The present invention provides a technical solution, which is a time-space hybrid model early fault detection method based on wavelet transform, which is applied to the Tennessee-Eastman process (TE) for fault detection, such as Figure 1 As shown, according to the fault detection workflow diagram, it can be seen that the following steps are included:

[0056] S1. Perform wavelet transform on the data set to reduce the impact of environmental noise and obtain a new data set X(i).

[0057] S2. Divide the data set into normal training data sets and test sample set And standardized into n×m dimensional matrices and

[0058] S3. Use PCA to build a model with a normal training data set to obtain the loading matrix P mk , and further calculate the principal component subspace N(x) of the test data set.

[0059] S4. Given a sliding window W, find sample x i The nearest neighbor sample set in the time direction And the first K nearest neighbor sample set in the spatial direction Calculate the sample x separately i Time dimension statistics S time (x i ) and spatial dimension statistics S space (x i ).

[0060] S5. Repeat the previous step using a sliding window to finally obtain n time dimension statistics S time and the statistics S of the spatial dimension space S6. Assign weight M according to absolute deviation i , in step 4, the corresponding weights are assigned to the samples x i Time dimension statistics S time and the statistics S of the spatial dimension space , obtain the mixed statistic S of STHM ts .

[0061] S7. Given a confidence level, estimate the control limits using the KDE method

[0062] S8, based on the mixed statistic S of the test data set ts and control limits Make a comparison to determine whether a fault has occurred.

[0063] like Figure 2As shown in the figure, in wavelet analysis, the signal is decomposed into approximate components and detail components. The approximate component captures the low-frequency part of the signal and represents the main trend of the signal, while the detail component contains the high-frequency part and is usually related to noise. In practical applications, the noise of the signal is often manifested as high-frequency fluctuations, while the useful signal features are reflected in the low-frequency fluctuations. The basic implementation process of wavelet denoising can be divided into the following steps: first, the acquired original signal is decomposed by the wavelet function to obtain the frequency structure of the decomposed signal; further, the threshold is set to filter and quantize the high-frequency signal with noise; finally, wavelet reconstruction is performed according to the signal characteristics of the lowest and highest frequencies to achieve the purpose of denoising. By performing wavelet transform on the signal, the wavelet coefficients of each level are obtained, which reflect the energy distribution of the signal at different scales. Through this wavelet denoising method of comprehensive feature extraction and low-pass filtering, the noise in the TE data set can be effectively removed without losing the essential information of the signal, thereby providing more accurate and clearer data support for subsequent fault detection.

[0064] like Figure 3 As shown in the figure, the fault detection rate effect comparison of each detection method under different fault types is further demonstrated. In the TE process, different fault detection methods - spatiotemporal hybrid model STHM, STN method and PCA method all show their unique advantages and limitations. Specifically, the STHM method shows significant advantages in most fault types, and both the fault detection rate and product false alarm rate have obvious advantages, which shows its high sensitivity to early fault characteristics and accurate recognition ability.

[0065] The entire system uses efficient data processing capabilities and advanced algorithm models to achieve real-time monitoring, rapid diagnosis and automated processing of minor faults in industrial machines, greatly improving the stability and safety of industrial production. This system can not only reduce downtime caused by faults, but also continuously optimize performance in long-term operation and adapt to various complex and changing working environments.

[0066] Working principle: The specific implementation of the present invention provides a time-space hybrid model early fault detection method based on wavelet transform. The method is specially designed for highly complex and dynamically changing industrial environments, aiming to improve the detection sensitivity and diagnostic accuracy of minor faults.

[0067] First, by performing wavelet transform on the signal, wavelet coefficients at each level are obtained. These coefficients reflect the energy distribution of the signal at different scales. In this process, the signal energy is mainly concentrated in a limited number of coefficients, while the noise energy is distributed in the entire coefficient array, and the signal wavelet coefficients are generally larger than the noise wavelet coefficients. These coefficients describe the energy distribution of the signal at different scales. A noisy model can be expressed as follows:

[0068] Z(i)=X(i)+ε*e(i) i=1,2...,n (1)

[0069] Among them, X(i) is the required real signal, Z(i) is the original signal containing noise, e(i) is the noise, and ε is the variable coefficient of the noise.

[0070] In order to effectively distinguish noise from real signals, the corresponding threshold is set and the wavelet coefficients smaller than the threshold are discarded. This study uses a soft threshold function. In this method, all wavelet coefficients below the set threshold are regarded as noise and filtered out, while coefficients above the threshold are retained as important components of the signal. The soft threshold function is:

[0071]

[0072] Among them, w j,k It represents the j-th layer and k-th wavelet coefficient in the wavelet transform, thr represents the threshold value. The reasonable selection of the threshold value can make the noise reduction effect obvious and the key features will not be lost. The threshold calculation formula is as follows:

[0073]

[0074] Among them, σ represents the standard deviation of the noise after the j-th layer decomposition, which is estimated as follows:

[0075]

[0076] The real signal X(i) is obtained through wavelet transform, which provides more accurate and clearer data support for subsequent fault detection and enhances the reliability and accuracy of the fault diagnosis process.

[0077] Furthermore, based on PCA to construct the principal component subspace, this study assumes that an industrial process has m observed variables, which are obtained by sampling data n times. The wavelet denoising method is used for preprocessing to obtain a new data set X(i), which is divided into a normal training data set And the test dataset The normal training set X tr And the test dataset X te Normalize into n×m dimensional matrices and The matrix is ​​normalized to eliminate the adverse effects of the dominant variables in the dimensionality reduction process. In order to observe the dispersion of m columns of data, the covariance formula is used to observe the correlation between two features. For m features, in order to obtain the correlation between each two features, an m×m dimensional covariance matrix is ​​constructed. Covariance matrix C mm for:

[0078]

[0079] C mm Solving for the eigenvalue λ m and the eigenvector p m According to the eigenvalue λ m The values ​​of are arranged in order to obtain the corresponding eigenvector p m Generator Matrix P m Assume that the m-dimensional vector is reduced to k-dimensional, and select the load matrix P m The first k columns of the load matrix P mk Then, X nm Reconstruct the score matrix, that is, project the original data set into the space formed by k eigenvectors, and finally obtain the principal component model:

[0080] X=TP T +E (6)

[0081] In the formula, X nm P mk is the principal element subspace, and E is the residual space.

[0082] The number of principal components is selected using the cumulative variance contribution rate (CPV). First, an expected CPV percentage must be given, and the value cannot be less than 85%. mm The resulting eigenvalue λ m , select the first k eigenvalues, and the ratio of the sum of the first k eigenvalues ​​to the sum of the total m eigenvalues ​​of the sample is called the contribution rate. When the cumulative contribution rate is greater than the threshold for the first time, the required k value can be determined. The formula is as follows:

[0083]

[0084] In this study, principal component analysis (PCA) was used to process the normal training data set. The load matrix P calculated by formulas (5)-(7) is mk , effectively extracting the most important variation direction in the data. Through these principal components, the test data set Reconstruct and finally get the principal element subspace N(x)∈R n×k This approach optimizes the data processing pipeline and can more effectively identify and analyze key features in complex data.

[0085] Given a sliding window W, find the neighboring sample set T(x) = {x1, x2, ..., x W}∈R W×k , based on the distance, find the first K nearest neighbor sample set S(x)={x1,x2,...,x K}∈R K×k .

[0086] In data analysis, especially in monitoring industrial processes or system state changes, CUSUM is a common algorithm for detecting subtle changes. It is a sequential detection technique that accumulates incremental changes in data through a recursive method to form a continuous cumulative sum, updates and detects statistical deviations in real time in the data stream, and more effectively captures small changes in the process or behaviors that deviate from the normal range. For each variable, the calculation formula of its CUSUM can be expressed as:

[0087] CUSUM ij =max(0,CUSUM i-1,j +(x ij -μ j -c) (8)

[0088] Where CUSUM ij is the CUSUM value of the jth variable in the ith sample, x ij is the observed value of the jth variable in the ith sample, μ j is the expected shift value of the jth variable, and c is the decision interval.

[0089] In the CUSUM algorithm, the decision interval c has a significant impact on the sensitivity and false alarm rate of the algorithm. In order to optimize this balance, first, the standard deviation σ of the neighboring sample set process in the time dimension is estimated. A coefficient r is selected to observe the sensitivity of CUSUM changes. The setting of the decision interval depends on the following formula to determine the threshold of the change of the statistic:

[0090] c=r×σ (9)

[0091] According to formulas (14)-(15), for a given time window W, we can obtain the statistics S of sample x in the time dimension: t for:

[0092]

[0093] For the neighboring sample set S(x) of sample x in the spatial dimension, calculate the mean of the sample set and the covariance matrix ∑.

[0094] First, the data points are rotated, and the dimensions are linearly independent, then

[0095] F=S(x)=U T X (11)

[0096] Since the dimensions are linearly independent after the transformation and the variance of each dimension is its own eigenvalue, it satisfies:

[0097] (F-μ)(F-μ)T =U T ∑U (12)

[0098] By scaling the Euclidean distance rotation transformation, the Mahalanobis distance calculation formula is obtained as follows:

[0099]

[0100] According to formulas (17)-(19), we can obtain the statistics S of sample x in the spatial dimension: s for:

[0101]

[0102] Absolute deviation can increase the sensitivity of the model to changes in the temporal and spatial dimensions of the data, especially when there is temporal correlation between the statistics. It is defined as follows:

[0103]

[0104] Where M i is the absolute deviation of the time dimension and space dimension statistics of the i-th sample. Based on the above formula, the basic weight based on the time dimension is obtained as

[0105]

[0106] The statistical proportions of different dimensions based on the spatiotemporal hybrid model with the maximum fault degree are obtained by scaling, and the final hybrid statistic S ts Expressions take the following form:

[0107] S ts (x i )=ω i ·S t (x i )+(1-ω i )·S s (x i ) (17)

[0108] The kernel density estimation method can flexibly and accurately estimate the density of complex data distribution and improve the accuracy and reliability of the fault detection process. Given a significance level of α = 0.05, the KDE method is used to measure S ts Upper limit of statistics

[0109]

[0110] Where p(z) is the probability density function of the random variable z. In practice, the following fault detection logic is used:

[0111]

[0112] Each test set of the TE process contains 960 samples. Data is collected every three minutes. Fault data is introduced from the eighth hour. An alarm is issued when the statistic exceeds the threshold.

[0113] Table 1 is a table of FDR and FAR data of different fault types of an early fault detection method of a space-time hybrid model based on wavelet transform of the present invention.

[0114] Table 1

[0115]

[0116] From the data analysis in Table 1, it can be seen that the STHM method has significant advantages in most fault types, and the effects of fault detection rate and product false alarm rate are both significantly superior, which shows its high sensitivity to early fault characteristics and accurate recognition ability. The small faults 15 with sticking characteristics in the TE process are extracted for comparative analysis. The detection results of the STHM method, STN method, and PCA method on the statistical quantities are as follows: Figure 4 As shown. The dotted line in the figure is the threshold line. For faults 3 and 15 with slight changes, it can be seen that the PCA method and the STN method cannot effectively detect them. In contrast, the STHM method has a higher fault detection rate in the principal component space, demonstrating the advantage of the STHM method in identifying minor faults. Through the comprehensive analysis of temporal and spatial data, STHM improves the sensitivity to subtle changes, can accurately detect fault signs early, and significantly enhances the system's early warning capability. The false alarm rate of the STHM method for products is slightly higher than that of PCA. 2 Detection,This situation may be because the STHM method enhances the sensitivity to faults through cumulative summation in the time dimension and correlation calculation in the space dimension, thereby responding to normal fluctuations or non-fault variations in the system. Simulation results show that this method improves the detection performance of early faults in complex industrial processes.

[0117] 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 principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A time-space hybrid model early fault detection method based on wavelet transform, characterized in that: The following steps are involved: 1) Use wavelet transform to perform multi-level decomposition and denoising on the input industrial process data, distinguish noise from useful signals, set a soft threshold function, and the part of the wavelet coefficient below this threshold is regarded as noise and filtered out, while the part above the threshold is retained as the effective component of the signal. The soft threshold function is: Among them, thr is the threshold value, w is the wavelet coefficient; 2) Apply principal component analysis (PCA) to extract features from the denoised data and establish the principal component subspace of the training and test data sets; 3) Set a sliding window and calculate the neighbor sample set in the time dimension and space dimension within each time window; 4) The cumulative sum algorithm CUSUM and the Mahalanobis distance MD are used to calculate the statistics of the time dimension and the space dimension respectively; for the CUSUM in a single direction, the calculation formula can be expressed as: CUSUM i =max(0,CUSUM i-1 +(x i -μ-K) (2) Among them, x i is the observed value of the ith sample, μ is the expected mean of the process, CUSUM i is the cumulative sum of the i-th sample; Based on formula (2), for a given time window W, we get sample x i Statistics S in the time dimension time (x i )for: Calculate the mean of the spatial dimension sample set And the covariance matrix ∑, get the sample x i Statistics S in the spatial dimension space (x i )for: 5) The basic weights of the time and space series are calculated based on the absolute deviation of the time and space statistics, and the final mixed statistics are obtained according to the weight distribution. The absolute deviation is defined as follows: Among them, M i is the absolute deviation of the time dimension and space dimension statistics of the i-th sample. Based on the above formula, the basic weight based on the time dimension is obtained as: The statistical proportions of different dimensions based on the spatiotemporal hybrid model with the maximum fault degree are obtained by scaling, and the final hybrid statistic S ts Expressions take the following form: S ts (x i )=ω(x i )·S time (x i )+(1-ω(x i ))·S space (x i ) (7) 6) Use the kernel density estimation (KDE) method to estimate the upper threshold of the mixed statistic to determine whether a fault has occurred; Given a significance level of α = 0.05, the KDE method was used to measure S ts Statistical upper limit: Where p(z) is the probability density function of the random variable z. In practice, the following fault detection logic is used:

2. The method for early fault detection based on the time-space hybrid model of wavelet transform according to claim 1 is characterized in that: In the step 1), the wavelet transform uses the Mallat algorithm to decompose the data signal and separate different frequency components of the signal.

3. The early fault detection method based on the time-space hybrid model of wavelet transform according to claim 1 is characterized by: In the step 2), the principal component analysis PCA includes selecting the number of principal components using the cumulative variance contribution rate CPV to ensure that the retained components contain enough information for fault detection.

4. The method for early fault detection based on the time-space hybrid model of wavelet transform according to claim 1 is characterized in that: In step 4), the cumulative sum algorithm CUSUM is used to detect and amplify subtle changes in time series data, and the Mahalanobis distance is used to measure the relative distance between each sample point in the sample set and the center.

5. The method for early fault detection based on the time-space hybrid model of wavelet transform according to claim 1 is characterized by: In the step 5), the calculation of the absolute deviation is based on the standard deviation of the time dimension statistics and the space dimension statistics.

6. The method for early fault detection based on the time-space hybrid model of wavelet transform according to claim 1 is characterized by: In step 6), the kernel density estimation (KDE) method is used to dynamically adjust the fault detection threshold and determine the optimal threshold according to the distribution characteristics of the statistical data.

7. The method for early fault detection based on the time-space hybrid model of wavelet transform according to claim 1 is characterized by: Includes a user interface that displays real-time data processing results, fault alarms and statistical analysis, allowing users to customize threshold settings and alarm parameters.

8. The method for early fault detection based on the time-space hybrid model of wavelet transform according to claim 2 is characterized by: The wavelet transform parameters are automatically optimized based on the operating conditions and historical performance data of the industrial process, including wavelet type, decomposition level and threshold selection.

9. The method for early fault detection based on the time-space hybrid model of wavelet transform according to claim 8 is characterized by: The method continuously receives real-time industrial process data, applies wavelet transform to denoise the data in real time, and immediately calculates temporal and spatial statistics to monitor the status of industrial systems in real time and respond quickly to potential failures.

10. The early fault detection method based on the time-space hybrid model of wavelet transform according to claim 1 is characterized by: The system comprises one or more processors and a memory, wherein the instructions stored in the memory enable the processor to execute a data anomaly detection algorithm, which is based on the comparison between the mixed statistics calculated in real time and the historical statistical model to identify abnormal patterns in the data and prevent potential failures from occurring.

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