An industrial fault detection method based on structured augmented dictionary learning

Abstract

The application discloses an industrial fault detection method based on structured augmented dictionary learning, which firstly processes the fault-free component through a basic dictionary, and simultaneously introduces an additional low-dimensional sparse dictionary for accurately reconstructing the fault-related part, thereby avoiding the dispersion of fault information. Secondly, in order to ensure that the fault-free part is in a statistical control state, the steady-state statistical characteristics and manifold structure constraints are embedded in the basic dictionary coefficients, and the feature variables related to faults are accurately selected through a hard sparse constraint, thereby effectively ensuring that the fault-free signal in the industrial process is not disturbed, so that the accurate separation of the fault and normal components of the signal is realized in sparse decoding, and the fault mode is accurately revealed. In addition, the application adopts an aggregation method based on a moving window, which significantly improves the sensitivity and detection efficiency of the initial fault of the industrial process, and provides an efficient and reliable fault diagnosis solution for industrial applications.

Description

Technical Field

[0001] This invention belongs to the field of fault detection technology, specifically relating to an industrial fault detection method based on structured augmented dictionary learning. Background Technology

[0002] The increasing complexity and automation of modern industrial processes place higher demands on real-time monitoring technologies to ensure system stability and operational efficiency. Most fault monitoring methods are based on data-driven models, such as principal component analysis, partial least squares regression, and canonical correlation analysis. These methods project data into a low-dimensional space to extract key features for monitoring process status. However, low-dimensional spaces often fail to fully represent the diversity and potential characteristics of process data and are prone to losing crucial information. This is particularly evident when dealing with high-dimensional, multimodal data in complex industrial processes.

[0003] To address this deficiency, projecting data into a high-dimensional space allows for more efficient decoupling of complex relationships between variables, capturing subtle data changes, and extracting deep-level features. This approach has driven the widespread application of high-dimensional modeling techniques such as kernel methods, deep learning, and dictionary learning in industrial fault detection. Among these, dictionary learning, as a powerful signal processing tool, is widely used due to its concise model structure and excellent monitoring performance. In practical applications, dictionary learning provides appropriate high-dimensional sparse representations of the original data through matrix theory and sparsity-induced techniques. By linearly combining the coefficient matrices, the atoms of a complete dictionary can not only accurately reconstruct normal data but also produce significant reconstruction errors for abnormal data, thereby achieving effective fault detection and demonstrating great potential in the field of process monitoring.

[0004] Despite significant progress in dictionary-based fault monitoring techniques, the following limitations remain:

[0005] 1) Sparse coding techniques (such as...) or Regularization may suppress key, subtle anomalies in the coefficients, which are important indicators of early / initial failures.

[0006] 2) Improving detection sensitivity by enhancing the significance of reconstruction error may weaken the ability of dictionary coefficients to distinguish initial faults, and vice versa.

[0007] 3) Ignoring the interaction between variables when fixing the fault direction or performing iterative reconstruction may damage the internal structure and attributes of the data, resulting in inaccurate isolation results.

[0008] For time-varying industrial processes, existing methods have certain limitations in real-time monitoring and cannot fully meet the fault detection needs in complex dynamic environments. Summary of the Invention

[0009] The purpose of this invention is to provide an industrial fault detection method based on structured augmented dictionary learning.

[0010] This invention provides an industrial fault detection method based on structured augmented dictionary learning, which includes the following steps:

[0011] Step 1: Collect the operating conditions under normal operation in the industrial process through multi-dimensional sensors and construct a training sample dataset. Based on the training sample dataset, build a basic dictionary model and obtain the basic dictionary.

[0012] Step 2: Collect real-time monitoring operating condition signals and build a structured augmented dictionary learning model based on the collected real-time operating condition signals to obtain a low-dimensional sparse dictionary and extended sparse coding.

[0013] Step 3: Obtain monitoring statistics based on the low-dimensional sparse dictionary and extended sparse coding, and use the monitoring statistics to determine whether there is an industrial fault; if there is an industrial fault, proceed to step 4.

[0014] Step 4: Construct an optimized model for the fault indication matrix based on monitoring statistics to obtain the fault indication matrix; indicate unqualified operating conditions based on the fault indication matrix to complete the accurate detection of industrial faults.

[0015] Preferably, the structured augmented dictionary learning model constructed in step two is as follows:

[0016]

[0017] in, This is a data matrix consisting of L samples collected through a moving window; Let L be the data matrix at time t; L is the size of the sliding window. To expand the dictionary, ; A low-dimensional sparse dictionary; Basic dictionary; For use with extended dictionaries The corresponding extended sparse coding, ; For dictionary The corresponding main code, ; This is the main code at time t; For low-dimensional sparse dictionaries The corresponding extended encoding, ; This is the extended code at time t; For low-dimensional sparse dictionaries The kth atom; For atoms The index that is zero; For atoms The set of indices that are zero; , and These are model parameters; ; This represents the square of the Frobenius norm.

[0018] Preferably, the basic dictionary model constructed in step one is:

[0019]

[0020] in, It is a K-dimensional sparse coefficient vector; Representing the basic dictionary The kth atom; N is the number of samples; and They represent Sum of squares of norm Norm.

[0021] Preferably, in step three, the monitoring statistic is the Hotelling statistic. Sum of squared prediction errors .

[0022] Preferably, in step three, the Hotling statistic is used. Sum of squared prediction errors The method to obtain it is as follows:

[0023]

[0024] in, Reconstruction error The mean, ; A precision matrix constructed from data collected from the normal operation of an industrial process.

[0025] Preferably, in step three, the criterion for determining whether an industrial fault exists is: if the Hotelling statistic... Greater than the preset Hotelling statistic threshold or squared prediction error If the error exceeds the preset squared prediction error threshold, an industrial fault exists; otherwise, no industrial fault exists.

[0026] Preferably, in step four, the fault indication matrix is ​​constructed. The optimization model is as follows:

[0027]

[0028] in, Used to indicate faults that affect monitoring statistics; and These are the model parameters.

[0029] Preferably, in step four, after obtaining the fault indication matrix... Then, based on the fault indication matrix Calculate fault score To assess the severity of the fault, a fault score is used. The expression is:

[0030]

[0031] in, This represents the value in the i-th row and j-th column of the fault indication matrix; ; For control limits; b represents the hyperparameter of a specific process; b represents the monitoring statistic.

[0032] Preferably, in step four, the basis for indicating unqualified operating conditions is: obtaining the fault score for each operating condition according to the fault scoring formula. If the fault score corresponding to a working condition is greater than the preset fault score threshold, then the working condition is unqualified.

[0033] Preferably, in step two, the acquired operating condition signals are segmented and processed using a sliding window to construct a structured augmented dictionary learning model.

[0034] The beneficial effects of this invention are:

[0035] 1. This invention expands the basic dictionary with a sequential low-dimensional sparse dictionary, decomposing sensor signals in industrial processes into fault-free and fault-related dictionary components, thus avoiding the dispersion of fault information. At the same time, it adopts a moving window-based aggregation method to solve the problems of untimely detection, high false alarm rate, and high false alarm rate of existing methods, significantly improving the sensitivity and detection efficiency of faults in the early stage of industrial processes, and providing an efficient and reliable fault diagnosis solution for industrial applications.

[0036] 2. This invention effectively ensures that fault-free signals in industrial processes are not disturbed by applying statistical and geometric constraints to the coefficients of the basic dictionary, thereby achieving accurate separation of faulty and normal components of the signal in sparse decoding. Simultaneously, applying hard sparsity constraints to the extended dictionary can uncover potential patterns in fault-related signals, significantly improving the accuracy and robustness of fault isolation. Attached Figure Description

[0037] Figure 1 This is an overall flowchart of the method of the present invention.

[0038] Figure 2 This is a schematic diagram of the key variable collection in Embodiment 1 of the present invention.

[0039] Figure 3 This is a schematic diagram of the rough fault detection results in Embodiment 1 of the present invention; wherein, (a) is a schematic diagram of the Hotling statistic; and (b) is a schematic diagram of the Hotling statistic.

[0040] Figure 4 The diagrams show rough fault detection results obtained based on traditional methods; (a) is a schematic diagram of the PCA detection method; (b) is a schematic diagram of the Basic detection method; (c) is a schematic diagram of the MWRBC detection method; (d) is a schematic diagram of the MCC detection method; and (e) is a schematic diagram of the KL detection method.

[0041] Figure 5 This is a schematic diagram of the accurate fault detection results in Embodiment 1 of the present invention; wherein, (a) is a schematic diagram of the Hotelling statistic; and (b) is a schematic diagram of the Hotelling statistic.

[0042] Figure 6 The diagrams show the accurate fault detection results obtained based on traditional methods; (a) is a schematic diagram of the MWRBC-SPE detection method; (b) is a schematic diagram of the SpCP detection method; (c) is a schematic diagram of the DL-RBC detection method; and (d) is a schematic diagram of the DL-IRBC detection method. Detailed Implementation

[0043] The present invention will be further described below with reference to the accompanying drawings.

[0044] like Figure 1 As shown, an industrial fault detection method based on structured augmented dictionary learning includes the following steps:

[0045] Step 1: Building the basic dictionary

[0046] The system collects data on the normal operating conditions of industrial processes using multi-dimensional sensors and constructs a training sample dataset. The samples in the training sample dataset are continuous n-dimensional signals under multiple operating conditions. And solve the basic dictionary based on the following basic dictionary model. :

[0047] (1)

[0048] in, It is a K-dimensional sparse coefficient vector (K > 10n); Dictionary The kth atom; N is the number of samples; and They represent Sum of squares of norm Norm; and These are the model parameters.

[0049] Step 2: Acquire multi-dimensional sensor process signals from online monitoring, and process the signals in segments using a sliding window; construct the structured augmented dictionary learning model as follows:

[0050] (2)

[0051] in, This is a data matrix consisting of L samples collected through a moving window; Let L be the data matrix at time t; L is the size of the sliding window. To expand the dictionary, ; A low-dimensional sparse dictionary; For use with extended dictionaries The corresponding extended sparse coding, ; For dictionary The corresponding main code, ; This is the main code at time t; For low-dimensional sparse dictionaries The corresponding extended encoding, ; This is the extended code at time t; For low-dimensional sparse dictionaries The kth atom; For atoms The index that is zero; For atoms The set of indices that are zero; These are model parameters; ; This represents the square of the Frobenius norm.

[0052] Calculate atoms The cumulative variance contribution rate of each element is used to determine the index set. Based on the structured augmented dictionary learning model, a low-dimensional sparse dictionary is obtained. and extended sparse coding .

[0053] and For data fidelity, the former analyzes the signal decomposition of the process, while the latter aims to eliminate potential zero-coefficient problems during decoding and avoid information loss; to enhance the reliability of the fault-free part, a manifold geometric constraint term is introduced. This constraint optimizes the local geometric relationships of fault-free signals based on the properties of k-nearest neighbors. To ensure that the atoms of the sparse dictionary can robustly match fault modes, constraint terms are introduced. Adjusting the difference between the sparse dictionary and its mean matrix. The model solution process involves the master encoder. and extended encoding This corresponds to the sub-problem in the structured augmented dictionary learning model, and can be solved as a LASSO problem. The main encoding... A column-by-column update approach is used to improve computational efficiency. Low-dimensional sparse dictionary. The update involves two main steps: unconstrained optimization and convex projection.

[0054] Step 3: Rough Fault Detection

[0055] To determine whether an industrial fault exists based on monitoring statistics, this embodiment selects the Hotelling statistic. Sum of squared prediction errors As the basis for judgment, its expression is:

[0056] (3)

[0057] in, Reconstruction error The mean, ; A precision matrix constructed from data collected from the normal operation of an industrial process.

[0058] If Hotling statistic Greater than the preset Hotelling statistic threshold or squared prediction error If the error exceeds the preset squared prediction error threshold, an industrial fault is considered to exist, and step four is executed; otherwise, no industrial fault is considered to exist. The presence of an industrial fault is determined through a rough fault detection process.

[0059] Compared with traditional monitoring statistics, the statistics of this invention have the following characteristics:

[0060] (1) The separability of sparse coding allows statistical constructions to be independent of each other;

[0061] (2) Combining the correlation between sparse atoms and precision matrices, we can comprehensively integrate the important factors of process changes.

[0062] Step 4: Precise Fault Detection

[0063] Because structured augmented dictionary learning models explicitly contain fault information, they can be easily improved by examining low-dimensional sparse dictionaries. Non-zero elements in or by comparing reconstruction errors To achieve accurate fault detection, this invention uses a method based on […]. To suppress abnormal disturbances during the process, […]. A regularized feature selection model eliminates fault-free features while robustly preserving relevant features of potential fault variables. Simultaneously, it considers the similarity of fault modes between adjacent windows to construct a fault indication matrix. The optimization model is as follows:

[0064] (4)

[0065] in, Used to indicate faults that affect monitoring statistics; and These are the model parameters.

[0066] Obtain the Hotelling statistic separately Sum of squared prediction errors Corresponding fault indication matrix ( or To facilitate the assessment of fault severity, fault scores for each operating condition at different time points are obtained. Its expression is:

[0067]

[0068] in, This represents the value in the i-th row and j-th column of the fault indication matrix; ; For control limits; b represents the hyperparameter of a specific process; b represents the monitoring statistic.

[0069] Fault scores for each operating condition at different time points were obtained based on the fault scoring formula. If the fault score corresponding to a certain operating condition exceeds a preset fault score threshold, the operating condition is considered unqualified, thus achieving accurate fault detection in the industrial process. Accurate fault detection helps determine the cause of industrial faults.

[0070] Example 1

[0071] This embodiment is applied to a multi-dimensional sensor network in an industrial field. Multiple sensors can collect multi-dimensional signals of key variables during the industrial glass melting process in real time. Its fault detection method includes the following steps:

[0072] Step 1, such as Figure 2As shown, to monitor the process status, multiple sensors were deployed inside the vessel to collect data on 14 process variables, including furnace temperatures (T1~T8) and coil power (P1~P4) at multiple locations, as well as glass viscosity μ and coil voltage v. Under normal operating conditions of industrial glass melting, data was recorded every 5 minutes, thus constructing a continuous training sample dataset X. i And based on the basic learning dictionary model of Equation (1), the basic dictionary is solved. .

[0073] Step 2: Collect process signals from multiple sensors monitored online, and process the signals in segments, each segment generated by a sliding window. Obtain a low-dimensional sparse dictionary based on the structured augmented dictionary learning model of Equation (2). and the extended encoding of the corresponding extended dictionary .

[0074] Step 3: Based on the Hotelling statistic Sum of squared prediction errors Determine if an industrial fault exists; if the Hotelling statistic... Greater than the preset Hotelling statistic threshold or squared prediction error If the error exceeds the preset squared prediction error threshold, an industrial fault is considered to exist, and step four is executed; otherwise, no industrial fault is considered to exist. The fault detection results based on these two monitoring statistics are as follows: Figure 3 As shown, the fault detection rates are as high as 73.48% and 95.65%, respectively; compared with the results obtained by traditional fault detection methods, such as... Figure 4 The fault detection results shown demonstrate that the fault detection rate of this invention has been significantly improved. This comparison fully highlights the outstanding potential and advantages of this invention in dealing with gradually developing or early-stage faults.

[0075] Step 4: Solve for the fault indication matrix using the optimization model based on the constructed fault indication matrix. And calculate the fault score for each variable. This enables accurate fault detection; the fault scoring formula is used to obtain... score vector The result is as follows Figure 5 As shown. From Figure 5 As can be seen, this invention precisely focuses on key problem variables in the initial stage: , and Further analysis revealed that the initial cracks in the furnace vessel were clearly reflected in the readings of the 7th temperature sensor and the 1st and 4th coil sensors. The intensity of the color visually indicated the degree of the fault, with darker colors signifying more severe damage. Compared to traditional fault detection methods, this method yielded significantly better results. Figure 6The score vectors shown fail to accurately detect the variables where faults have occurred, and exhibit a high false alarm rate. This result demonstrates that the present invention exhibits excellent accuracy and reliability in the detection and isolation of early faults.

Claims

1. An industrial fault detection method based on structured augmented dictionary learning, characterized in that: Includes the following steps: Step 1: Collect the operating conditions under normal operation in the industrial process through multi-dimensional sensors and construct a training sample dataset. Based on the training sample dataset, build a basic dictionary model and obtain the basic dictionary. Step 2: Collect real-time monitoring operating condition signals and build a structured augmented dictionary learning model based on the collected real-time operating condition signals to obtain a low-dimensional sparse dictionary and extended sparse coding. In step two, the structured augmented dictionary learning model is constructed as follows: in, This is a data matrix consisting of L samples collected through a moving window; Let L be the data matrix at time t; L is the size of the sliding window. To expand the dictionary, ; A low-dimensional sparse dictionary; Basic dictionary; For use with extended dictionaries The corresponding extended sparse coding, ; For dictionary The corresponding main code, ; This is the main code at time t; For low-dimensional sparse dictionaries The corresponding extended encoding, ; This is the extended code at time t; For low-dimensional sparse dictionaries The kth atom; For atoms The index that is zero; For atoms The set of indices that are zero; , and These are model parameters; ; Represents the square of the Frobenius norm; Step 3: Obtain monitoring statistics based on the low-dimensional sparse dictionary and extended sparse coding, and use the monitoring statistics to determine whether there is an industrial fault; if there is an industrial fault, proceed to step 4. Step 4: Construct an optimized model for the fault indication matrix based on monitoring statistics to obtain the fault indication matrix; indicate unqualified operating conditions based on the fault indication matrix to complete the accurate detection of industrial faults.

2. The industrial fault detection method based on structured augmented dictionary learning according to claim 1, characterized in that: In step one, the basic dictionary model constructed is as follows: in, It is a K-dimensional sparse coefficient vector; Representing the basic dictionary The kth atom; N is the number of samples; and They represent Sum of squares of norm Norm.

3. The industrial fault detection method based on structured augmented dictionary learning according to claim 1, characterized in that: In step three, the monitoring statistics used are the Hotelling statistics. Sum of squared prediction errors .

4. The industrial fault detection method based on structured augmented dictionary learning according to claim 3, characterized in that: In step three, the Hotelling statistic... Sum of squared prediction errors The method to obtain it is as follows: in, Reconstruction error The mean, ; A precision matrix constructed from data collected from the normal operation of an industrial process.

5. The industrial fault detection method based on structured augmented dictionary learning according to claim 4, characterized in that: In step three, the criterion for determining whether an industrial fault exists is: if the Hotelling statistic... Greater than the preset Hotelling statistic threshold or squared prediction error If the error exceeds the preset squared prediction error threshold, an industrial fault exists. Conversely, there are no industrial failures.

6. The industrial fault detection method based on structured augmented dictionary learning according to claim 1, characterized in that: In step four, the fault indication matrix is ​​constructed. The optimization model is as follows: in, Used to indicate faults that affect monitoring statistics; and These are the model parameters.

7. The industrial fault detection method based on structured augmented dictionary learning according to claim 1, characterized in that: In step four, the fault indication matrix is ​​obtained. Then, based on the fault indication matrix Calculate fault score To assess the severity of the fault, a fault score is used. The expression is: in, This represents the value in the i-th row and j-th column of the fault indication matrix; ; For control limits; 'b' represents the hyperparameter of a specific process; 'b' represents the monitoring statistic.

8. The industrial fault detection method based on structured augmented dictionary learning according to claim 7, characterized in that: In step four, the basis for indicating unqualified operating conditions is: obtaining the fault score for each operating condition according to the fault scoring formula. If the fault score corresponding to a working condition is greater than the preset fault score threshold, then the working condition is unqualified.

9. The industrial fault detection method based on structured augmented dictionary learning according to claim 1, characterized in that: In step two, the acquired operating condition signals are segmented and processed using a sliding window to construct a structured augmented dictionary learning model.

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