Shape shift refers to the phenomenon where by amplitude and scaling of samples of the same fault vary with the environment. How to incrementally diagnose industrial faults under shape shift samples with directly interpretability is a challenging problem. Therefore, a new convertible shapelet learning with incremental learning capability method is proposed in this study. First, incrementally learning under shape shift samples is formulated as how to learn new scaling shift and amplitude shift samples in industrial process. A shape shift detection method is proposed to detect new shape domain. Second, a new parameter initialization method for shapelet learning is proposed, which employs pretraining technology to obtain better initial shapelets. Third, the convertible shapelet-transformed representation is proposed to enhance informativeness of shapelets. An incremental convertible shapelet learning loss is proposed to alleviate catastrophic forgetting in incrementally training new shape time series. By comparing with other state-of-the-art methods, experiments on the Tennessee Eastman Process and real-world aluminum electrolysis process demonstrate the superior performance of the proposed method in accuracy, alleviating catastrophic forgetting and interpretability.

Unknown abnormal working condition discovery is the key of refinement industrial production. Clustering industrial time series is an effective way to discover unknown working condition types. However, it is challenge for existing time series cluster methods to discover unknown abnormal working condition from industrial time series. In this study, a novel prior knowledge-augmented unsupervised shapelet learning method is proposed to discover abnormal and meaningful working condition through interpretable subsequences. A prior feature extracting module is proposed to change prior knowledge into a recognizable form for the data model. The prior knowledge contains abnormal working condition information. The knowledge-augmented clustering module can learn informative shapelets which stand for abnormal working condition by combining prior features with data features. Furthermore, the preference of prior knowledge and data are self-adjusted in the learning phase. Numerical test results on the real-world aluminum electrolysis process, simulated Tennessee Eastman process, and continuous stirred tank heater process verify the superior performances of the proposed method. The proposed method provides a new perspective for the fusion of prior knowledge and data model. It also provides a new way to solve the problem of abnormal unknown working condition discovery in industrial process.

Failure Mode and Effect Analysis (FMEA) is a prospective and systematic analytical tool widely used to improve the reliability and safety of various industries. However, the existing FMEA methods have received criticism for their inherent deficiencies that limit their flexibility and effectiveness. To address these issues, we propose a novel FMEA model that combines Probabilistic Free Double Hierarchy Hesitant Linguistic Term Set (PFDHHLTS), Extended Grey Relation Analysis (EGRA), and ORESTE to determine the priorities of Failure Modes (FMs). Firstly, the PFDHHLTSs are proposed to represent experts’ assessments, improving the flexibility and accuracy of experts’ expressions. Secondly, the PFDHHLTS-EGRA is proposed to determine the evaluation matrix and the weights of risk factors in a large group environment. Furthermore, the ORESTE method is extended to the PFDHHLTS environment. Lastly, we verify the effectiveness of our method through a case study on the aluminum electrolysis process. The results demonstrate the effectiveness and flexibility of our method in expressing experts’ assessments and obtaining more accurate and reliable risk priorities.

Early classification predicts the class of the incoming sequences before it is completely observed. How to quickly classify streaming time series without losing interpretability through early classification method is a challenging problem. A novel memory shapelet learning framework for early classification is proposed in this article. First, a memory distance matrix is introduced to store the historical characteristics of streaming time series, which can alleviate repetitive calculations caused by the growing length of time series. Second, early interpretable shapelets are extracted in the proposed method by optimizing both accuracy objective and earliness objective simultaneously. The proposed method employs end-to-end learning, which allows the model to directly learn early shapelets without the necessity of searching for numerous candidate shapelets. Third, an objective function of memory shapelet learning is proposed by overall considering accuracy and earliness, which can be optimized by gradient descent algorithm. Finally, experiments are conducted on benchmark dataset UCR, Tennessee Eastman process, and real-world aluminum electrolysis process in China. Comparable results with other state-of-the-art methods demonstrate the superior performance of the proposed method in interpretability, accuracy, earliness, and time complexity.

In the aluminum electrolysis process, the accurate identification of anode effect (AE) can improve production efficiency. However, the existing methods fail to effectively capture the features of the anode current signal (ACS) due to its complex dynamic characteristics and temporal–spatial dependence. To address this issue, we propose a Process Knowledge-guided Deep Temporal–spatial Feature Learning Network (PKG-DTSFLN). We believe that knowledge and production data are complementary. Knowledge has potential to deduce beyond observational conditions. Data can be used to detect unexpected patterns. The combination of data and knowledge is potential to improve the performance. Specifically, knowledge is utilized to construct the adjacency matrix to represent the spatial structure of ACS. Then, a deep learning model is constructed by integrating the 1D-CNN and GAT, which is used to capture the temporal–spatial features of ACS. The experimental results on ACS dataset show that the accuracy is more than 99% with low computational cost.

Few-shot new faults are constantly emerging due to the dynamic environments and operations in the industrial process. It is a challenge for existing fault diagnosis methods to diagnose few-shot new faults without forgetting old faults by fine tuning the base model. This article defines this challenge as few-shot fault incremental learning problem, and proposes a multiview shapelet prototypical network to solve this problem. First, a multiview metalearning framework that simulates true incremental tasks and combines multiview information is proposed in this article to build a generalizable feature space for unseen classes. Second, a multiview shapelet prototypical classifier is proposed to enhance the generalization ability of shapelets in adapting new faults with few samples. Third, multiview metacalibration modules based on transformers are proposed to fuse multiview information and calibrate prototypes and embedded features into a distinguishable space. Finally, experiments are conducted on the benchmark Tennessee Eastman process and the real-world aluminum electrolysis process. Experimental results illustrate that the proposed method is better than the existing methods in terms of interpretability, alleviating catastrophic forgetting, and reducing time complexity.

Anode effect (AE) is influenced by adaptive spatial and temporal factors in the aluminum electrolysis process. Anode current signals (ACS) are the only online distributed signals which provide spatial temporal characteristics of AE. How to extract interpretability adaptive spatial and temporal characteristics of ACS for AE prediction is a challenging problem. In this paper, a multi -generator adversarial dynamic spatial-temporal shapelet network is proposed to capture the explainable spatial-temporal characteristics. Multi -generator adversarial training added into shapelet learning is used to reinforce the interpretability of shapelets. A dynamic distance calculation strategy is proposed to extract dynamic shapelets of multi -variable time series whose dynamic discriminative subsequence is not restricted to dimension. Based on the proposed self -regulative spatial network and diversity regularization, the extracted shapelets will have adaptive spatial networked correlations and diversity. Moreover, the proposed method can guide the domain technicians to locate the abnormal conditions. The results of experiment using real -world aluminum electrolysis plant data show that the proposed method is feasible and quite effective to detect anode effect earlier and enhance the interpretability of shapelets.

Superheat degree identification of aluminum electrolysis cell is a typical knowledge-intensive work which is the precondition of efficient production. However, existing methods have application limitations, and the large cognitive differences among experts are ignored in the existing methods. To address these issues, we propose the consensus-based probabilistic hesitant intuitionistic linguistic Petri nets (CPHILPNs). The truth values of places in CPHILPNs are represented by probabilistic hesitant intuitionistic linguistic term sets (PHILTSs), which can enrich the experts’ expression and improve the efficiency of dealing with uncertainties. The proposed probabilistic hesitant intuitionistic linguistic consensus optimization model can reduce the deviation of individual preferences to reach a consensus. Then the obtained experts’ weights and decision assessments will be more accurate and comprehensive with objective evaluations. The order weighted averaging PHILTSs concurrent reasoning algorithm is proposed to enhance the inference efficiency. Finally, the usefulness and validity of the proposed CPHILPNs are verified by conducting comparisons and actual experiments in a real-world plant.

Anode effect in aluminum electrolysis cells occurs quickly and is very harmful. The existing cell condition identification methods are difficult to identify anode effect in a timely, accurate, and interpretable manner. By combining shapelet learning and early classification methods, we propose a new interpretable cell condition identification method for real-time voltage signals. A novel loss function that comprehensively consider accuracy and earliness is proposed in this paper. At the same time, early shapelets can be optimized in this loss function. The experiment in the aluminum electrolysis process illustrate the superiority performance of the proposed methodology.

Root cause analysis (RCA) is a powerful tool utilized to identify the underlying causes of an event or problem. However, due to the specificity of production requirements in the process industry, existing methods still face challenges such as insufficient or unreliable data, and intrinsic complexities. Therefore, RCA relies on decision making in the process industry which is actually a typical knowledge-intensive work. To address these challenges, we propose a new causal knowledge maps-based RCA method that combines a newly developed grey reasoning dynamic uncertain causality graph (GRDUCG) with an improved grey relation analysis (IGRA) technique. The proposed method utilizes GRDUCG to construct a causal knowledge map to represent the complex knowledge. Under the large group environment, the IGRA method is employed to integrate causal knowledge provided by domain experts, thus determining the parameters' values which take the form of interval grey numbers. Due to the importance of distinguishing coefficient in IGRA, a new decision method is proposed to improve GRA instead of subjective decision based on the maximum information entropy. Root causes are identified using the maximum posterior probability on the causal knowledge map. Finally, we demonstrate the effectiveness and practicality of our proposed approach by utilizing GRDUCG-IGRA to analyze abnormal conditions in a real-world aluminum electrolysis plant.

Superheat degree is a core technical parameter and management index of aluminum electrolysis cell. However, the existing methods have limited abilities when applied to superheat degree recognition of aluminum electrolysis cell (SDRAEC). In addition, the important hesitant degree is ignored in the unbalance double hierarchy linguistic term set (DHLTS). To address these issues, an unbalance double hierarchy hesitant linguistic Petri net (UDHHLPN) model and extended TOPSIS is proposed for SDRAEC. In this model, the coupling relationships among variables is made to be explicit knowledge, and the unbalance double hierarchy hesitant linguistic term set (UDHHLTS) is proposed to represent the value of knowledge parameter. The relative entropy is introduced to enhance the performance of extended TOPSIS. Moreover, hybrid averaging UDHHLTS concurrent reasoning algorithm is proposed to improve the reasoning efficiency. Finally, thermal analysis experiments conducted in a real-world aluminum electrolysis plant are used to demonstrate the effectiveness of the proposed method. Compared with other methods, the accuracy of SDRAEC has been increased to 89.00%.

As an important modeling tool for knowledge representation and reasoning (KRR), fuzzy Petri nets (FPNs) have been applied in kinds of fields. However, there exist some deficiencies for existing FPNs, resulting in application limitations. (1) The sum of membership and non-membership is less than 1, which is hard to model various types of uncertain knowledge by existing FPNs; (2) The reasonable and nonidentical experiential knowledge for electrolysis operation among domain experts should be fused; (3) The existing knowledge reasoning algorithm min, max, and product operators may not work well in many practical applications. In an effort to overcome the shortcomings of existing FPNs, a new type of FPNs is proposed, called simplified neutrosophic Petri nets (SNPNs). First, the simplified neutrosophic sets (SNSs) are introduced into SNPNs, characterized by three independent degrees of truth-membership, indeterminacy-membership and falsity-membership, to depict the experiential cognition of domain experts. Second, the extended TOPSIS (ETOPSIS) is proposed for knowledge fusion. Third, hybrid averaging SNNs concurrent reasoning algorithm (HASCRA) is also proposed to improve the knowledge reasoning efficiency. Finally, a novel model for the identification of superheat degree of aluminum electrolysis cell (ISDAEC) is proposed based on SNPNs. Comparative experimental results show that the SNPNs provide a feasible and practical decision-making method. Moreover, this fact denotes that the proposed method has potential applications in intelligent ISDAEC.

Anode current signals (ACS) play an important role in aluminum reduction production. Owing to the complexity dynamic and temporal-spatial dependency characteristics, classification of ACS is a challenging problem and the existing classification methods are failed to capture these characteristics. To address this issue, a multiple temporal-spatial convolution network (MTSCN) combining graph convolutional network (GCN) and one-dimension convolutional neural network (1-D-CNN) is proposed in this paper. Firstly, a adjacency matrix is first introduced to characterize spatial structure of ACS. Secondly, based on the spatial structure, a novel machine learning framework which combines GCN and 1-D-CNN is proposed. Specifically, multi-layer of 1-D-CNN and multi-layer of GCN are used to capture temporal and spatial dependencies of ACS, respectively. The obtained data-dirved model is able to identify abnormalities of ACS. Finally, results carried out in real-world ACS data set are given to verify the effectiveness of the proposed method.

Classification of multi-dimension time series (MTS) plays an important role in knowledge discovery of time series. Many methods for MTS classification have been presented. However, most of these methods did not consider the kind of MTS whose discriminative subsequence was not restricted to one dimension and dynamic. In order to solve the above problem, a method to extract new features with extended shapelet transformation is proposed in this study. First, key features is extracted to replace k shapelets to calculate distance, which are extracted from candidate shapelets with one class for all dimensions. Second, feature of similarity numbers as a new feature is proposed to enhance the reliability of classification. Third, because of the time-consuming searching and clustering of shapelets, distance matrix is used to reduce the computing complexity. Experiments are carried out on public dataset and the results illustrate the effectiveness of the proposed method. Moreover, anode current signals (ACS) in the aluminum reduction cell are the aforementioned MTS, and the proposed method is successfully applied to the classification of ACS.