Structured Dictionary Learning for Fault Detection and Isolation

Analysis of smearing-out in contribution plot based fault isolation for Statistical Process Control

Sparse representation and dictionary learning have been successfully applied to encode dense data and facilitate image classification. Though existing dictionary learning methods achieve better performance than their counterparts, the class discriminative ability of learned dictionary is still limited. This paper proposes a novel supervised dictionary learning method based on the prior of the block diagonal phenomenon, i.e., each sample should be well reconstructed by the samples in the same class while poorly reconstructed by the samples in other class. Specifically, a block diagonal regularizer is imposed on the affinity matrix to enforce the sparse representation matrix to have an approximately block diagonal structure, which makes the learned dictionary more discriminative and suitable for classification tasks. Furthermore, we present an effective optimization strategy by combining the alternating minimization with the alternating direction method of multipliers (ADMM) for the proposed framework. Experimental results on six real-world datasets show that the proposed method is more effective than state-of-the-art dictionary learning methods.

This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing the separable dictionary learning model. Two different approaches for learning mixture of separable dictionaries are explored and sufficient conditions for local identifiability of the underlying dictionary are derived in each case. Moreover, computational algorithms are developed to solve the problem of learning mixture of separable dictionaries in both batch and online settings. Numerical experiments are used to show the usefulness of the proposed model and the efficacy of the developed algorithms.

Breakthrough results in compressive sensing (CS) have shown that high dimensional signals (vectors) can often be accurately recovered from a relatively small number of non-adaptive linear projection observations, provided that they possess a sparse representation in some basis. Subsequent efforts have established that the reconstruction performance of CS can be improved by employing additional prior signal knowledge, such as dependency in the location of the non-zero signal coefficients (structured sparsity) or by collecting measurements sequentially and adaptively, in order to focus measurements into the proper subspace where the unknown signal resides. In this paper, we examine a powerful hybrid of adaptivity and structure. We identify a particular form of structured sparsity that is amenable to adaptive sensing, and using concepts from sparse hierarchical dictionary learning we demonstrate that sparsifying dictionaries exhibiting the appropriate form of structured sparsity can be learned from a collection of training data. The combination of these techniques (structured dictionary learning and adaptive sensing) results in an effective and efficient adaptive compressive acquisition approach which we refer to as LASeR (Learning Adaptive Sensing Representations).

Isolation of plant-wide faults using causality detection methods

Linguistic OWA and two time-windows based fault identification in wide plants

Adaptive sparse principal component analysis for enhanced process monitoring and fault isolation

Dictionary learning (DL) technique has received a great interest recently, due to its significant role in feature extraction. Although many DL‐based methods have been presented, some of them still suffer from the lack of discriminative features, especially for the local manifold features. To mitigate this problem, the authors propose a novel DL method named low‐rank representation based on twin tensor kernel (LRR‐TTK) DL for face recognition in this study. Specifically, the training samples are projected to a high‐dimensional space with TTK. Then, they extract the local manifold features and spatial features (representation coefficients) hidden in the facial images by TT locality preserving projection. In addition, powered by LRR reconstruction and DL theory, much more discriminative features are obtained, which can improve the recognition rate greatly. Comprehensive experimental results at AR, extended Yale‐B and FERET face databases demonstrate the superiority of their proposed method.

In industrial process monitoring, it is always a challenging and practical problem to analyze the causes of the system fault by isolating true fault variables from vast amounts of process data. However, the phenomenon of smearing effect occurs by using the traditional contribution analysis-based isolation methods since the defined isolation indices of different variables affect each other. In this paper, a new fault isolation method is proposed based on local outlier factor and improved k-nearest neighbor rule aiming to improve the isolation accuracy. Firstly, the nearest neighbors of each sample are obtained along the direction of a specific variable. Based on the nearest neighbors, the outlier-degree value of the variable is calculated and regarded as the contribution of the variable. Then, the contribution of the variable in all samples are obtained in the same way, among which the maximum one is selected as the isolation threshold value of this variable. During the online monitoring, the contribution of the variable in the newly collected sample is calculated in real time. Once the contribution is greater than the threshold, the variable is judged to be the dominant factor causing the system fault. Two cases on numerical example and Tennessee Eastman process are conducted to evaluate the effectiveness of the proposed method.

Both process monitoring and fault isolation are important and challenging tasks for quality control and improvement in high-dimensional processes. Under a practical assumption that not all variables would shift simultaneously, this paper proposes a variable-selection-based multivariate statistical process control (SPC) procedure for process monitoring and fault diagnosis. A forward-selection algorithm is first utilized to screen out potential out-of-control variables; a multivariate control chart is then set up to monitor suspicious variables. Therefore, detection of faulty conditions and isolation of faulty variables can be achieved in one step. Both simulation studies and a real example have shown the effectiveness of the proposed procedure.

A Conjugated and Augmented Dictionaries (CAD) learning method based on Sparse Auto-Encoder (SAE) is proposed for hyperspectral image classification. The CAD originates from the intention to combine the synthesis model and analysis model. These two models are used to obtain the sparse representation or feature of the pixels. In this paper, CAD has a three-step strategy to learn the dictionaries and classify the pixels of Hyperspectral image. Firstly, we adopt the Sparse Auto-Encoder model to complete the learning process of the suggested dictionaries. Secondly, test samples are reconstructed using the learned dictionaries. Finally, we embed the reconstructed pixels into a linear SVM for classification. Indiana Pine subset is used for the classification experiment, and the classification results show that the reconstructed pixels have the high discrimination characteristics, which makes our method outperforms other hyperspectral image classification algorithms as contrast.

Dictionary learning (DL) techniques aim to find sparse signal representations that capture prominent characteristics in a given data. Such methods operate on a data matrix $Y\in \mathbb {R}^{N\times M}$ , where each of its columns $y_i\in \mathbb {R}^N$ constitutes a training sample, and these columns together represent a sampling from the data manifold. For signals $y\in \mathbb {R}^N$ residing on weighted graphs, an additional challenge is incorporating the underlying geometric structure of the data domain into the learning process. In such cases, the topological graph structure may provide a crucial interpretation for the columns, while the data manifold itself may also possess a low-dimensional intrinsic structure that should be taken into account. In this work, we propose a novel dictionary learning algorithm for graph signals that simultaneously takes into account the underlying structure in both the signal and the manifold domains. Specifically, we require that the dictionary atoms are smooth with respect to the graph topology, as encapsulated by the graph Laplacian matrix. Furthermore, we propose to learn this graph Laplacian within the dictionary learning process, adapting it to promote the desired smoothness. Utilizing the manifold structure, we propose to encourage the smoothness of the sparse representations on the data manifold in a similar manner. Both these smoothness forces implicitly enhance the learned dictionary. The efficiency of the proposed approach is demonstrated on synthetic examples as well as on real data, showing that it outperforms other dictionary learning methods in typical problems such as resistance to noise and data completion.

The paper presents a new approach to the selection of tests used in service diagnosis of dynamical systems. It proposes a method to select input signals that steer the system into a particular operating region and to find the corresponding local residuals for evaluating the system's I/O behavior. The tests allow the isolation of faults that are generally not distinguishable, but become isolable under specific operation conditions. The method is based on the analysis of the structure graph, which represents the couplings among external and internal signals of the system and the possible faults. This graph changes if the system variables are restricted to different operating regions. Accordingly, the local structure of the system distinguishes from the global structure that holds for the unrestricted variables. By utilizing this difference, it is possible to determine tests that are sensitive to specific faults. The method is illustrated by its application to a throttle valve.

Unsupervised feature selection (UFS) aims to reduce the time complexity and storage burden, as well as improve the generalization performance. Most existing methods convert UFS to supervised learning problem by generating labels with specific techniques (e.g., spectral analysis, matrix factorization and linear predictor). Instead, we proposed a novel coupled analysis-synthesis dictionary learning method, which is free of generating labels. The representation coefficients are used to model the cluster structure and data distribution. Specifically, the synthesis dictionary is used to reconstruct samples, while the analysis dictionary analytically codes the samples and assigns probabilities to the samples. Afterwards, the analysis dictionary is used to select features that can well preserve the data distribution. The effective L2p-norm (0 < p <1) regularization is imposed on the analysis dictionary to get much sparse solution and is more effective in feature selection.We proposed an iterative reweighted least squares algorithm to solve the L2p-norm optimization problem and proved it can converge to a fixed point. Experiments on benchmark datasets validated the effectiveness of the proposed method

An extensible quality-related fault isolation framework based on dual broad partial least squares with application to the hot rolling process