Fault Detection Statistics Research Articles

Improved diffusion mapping combined with procrustes analysis for capturing local-global data structures in industrial process monitoring

BackgroundProcess monitoring, by providing early warnings of abnormal operating states resulting from process faults, facilitates the maintenance of normal production and ensures process safety. In the domain of industrial process monitoring, capturing the local-global structural features of data and acquiring an explicit mapping relationship for dimensionality reduction projection holds significant importance for online fault detection in industrial processes. MethodsThis study introduces an Improved Diffusion Mapping and Procrustes analysis (IDM-P) method for this purpose. Initially, considering the multiscale and correlation among industrial data features, the Mahalanobis distance is incorporated to improve the diffusion mapping algorithm. Utilizing this method allows for the concurrent capture of both local and global data structures, leading to a more efficient extraction of data-representative features, which enhances the accuracy of fault detection. Procrustes analysis is then used to obtain an explicit mapping matrix between high-dimensional data and low-dimensional manifolds, improving the efficiency of the key feature extraction of the new samples. Finally, this matrix is utilized to construct process monitoring statistics for fault detection. Significant FindingsThe method's effectiveness was validated through experiments on the TEP dataset and actual industrial data, demonstrating that IDM-P maintains higher accuracy and achieves optimal fault detection compared to other methods.

Variable contribution analysis in multivariate process monitoring using permutation entropy

Multivariate statistical process monitoring is widely used in industrial processes for performance monitoring and fault detection. Once a fault has been detected, fault diagnoses must be performed to identify the variables that are responsible for the fault or the deviation from normal operation. In this paper, we present a new data-driven method for variable contribution analysis to a fault or abnormal behaviour in a process. The method is based on permutation entropy (PE), which measures the order of fluctuations within a time series. The PE method for variable contribution analysis is independent of fault detection statistics, and is used to evaluate which variables experienced the greatest change in their expected behaviour over time, immediately after the fault has been identified. We show how PE can be used to identify and interpret the variables responsible for, or affected by faults in an industrial process. The well-known Tennessee Eastman Process (TEP) is used to illustrate the application of PE for variable contribution analysis. The results show that PE is an efficient analysis tool for specifying variable contributions to faults.

Fault Detection Statistics in the Presence of Additive Measurement Errors

In the study, the noncentral Wishart matrix trace-based fault detection statistics is proposed for sensor/actuator fault detection in the presence of measurement bias. As the difference from the most of existing innovation-based fault detection methods, this approach allows to detect sensor/actuator faults in the presence of additive measurement errors. The trace of the noncentral Wishart matrix is used in this method for the fault detection statistics. The proposed innovation approach-based sensor/actuator fault detection using trace of the noncentral Wishart matrix is applied to a dynamic model of an unmanned aerial vehicle (UAV). The sensor bias and actuator loss of control effectiveness type faults are considered. The proposed and traditional methods for detecting faults in the presence of slowly developing gyroscope drift are considered and compared.

A state-domain robust autonomous integrity monitoring with an extrapolation method for single receiver positioning in the presence of slowly growing fault

Single receiver positioning has been widely used as a standard and standalone positioning technique for about 25 years. To detect the slowly growing faults caused by satellite and receiver clocks in single receiver positioning, the Autonomous Integrity Monitoring with an Extrapolation method (AIME) was proposed based on the Kalman filter measurement domain. However, AIME was designed with the assumption of there is the same number of visible satellites at each epoch, which limits its application. To address this issue, this paper proposes a state-domain Robust Autonomous Integrity Monitoring with the Extrapolation Method (SRAIME). The slowly growing fault detection statistics is established based on the difference between the estimates of the state propagator and the posterior state estimation in Kalman filtering. Meanwhile, singular value decomposition is adopted to factor the covariance matrix of the difference to increase computational robustness. Besides, the relevant formulas of the proposed method are theoretically derived, and it is proven that the proposed method is suitable for any positioning model based on the Kalman filter. Additionally, the results of two experiments indicate that SRAIME can detect slowly growing faults in single receiver positioning earlier than AIME.

A Novel Fault Detection Model Based on Vector Quantization Sparse Autoencoder for Nonlinear Complex Systems

To solve the problem of nonlinear factors in the fault detection process of complex systems, this article proposes a fault detection model based on vector quantization sparse autoencoder. First, a feature extraction model, which consists of a self-normalizing convolutional autoencoder module, a vector quantization module, a gradient module, and a loss module, is developed. The first module employs self-normalizing convolutional layers with good stability and generalization ability to extract the nonlinear structural features of complex systems. A nearest neighbor search strategy is implemented in the vector quantization module to further mine the nonlinear information. The gradient module adopts a straight-through estimation technique to improve the training efficiency. Sparse constraints are introduced into the loss module to obtain the essential features and enhance interpretability. Thereafter, a construction rule based on local Mahalanobis distance and K nearest neighbors is designed to calculate K Mahalanobis neighbor metrics that depend on the sparse features obtained by the feature extraction model. A comprehensive statistic for fault detection is constructed to accurately track the operating status of complex systems by combining the loss metric and the K Mahalanobis neighbor metric. Finally, the threshold of the fault detection statistics is determined by modeling the generalized extreme value distribution. Three case studies, a numerical simulation, the Tennessee Eastman benchmark process, and a typical circuit system, are adopted to demonstrate the effectiveness and merits of the proposed fault detection model.

Sequential advanced receiver autonomous integrity monitoring method considering the optimal sample size

The integrity monitoring performance of Receiver Autonomous Integrity Monitoring (RAIM) degrades when insufficient satellites are visible, which may cause RAIM to fail to support the approach procedure with vertical guidance service. We propose a sequential advanced receiver autonomous integrity monitoring (S-ARAIM) method to improve the integrity monitoring capability and availability. We first introduce a sample size to a dominant snapshot technique, advanced RAIM (ARAIM), to formulate cumulative test statistics for fault detection. The sample size is then determined to maximize the fault detection capability, including the response speed and sensitivity to minor faults. Meanwhile, the optimal sample size minimizes the undetected fault magnitude bound when no fault is declared. In this manner, S-ARAIM combines the advantage of snapshot RAIM and sequential RAIM in detecting severe pulse and small persistent faults. Additionally, we derive a protection level to envelop the estimate error under the constraints of continuity and integrity requirements. Experiments validate the fault detection performance under single-satellite-fault and dual-satellite-fault scenarios. Compared with least square residual RAIM and ARAIM, S-ARAIM improves the integrity availability by 45.91% and 5.64%, respectively.

Code phase tracking error based autonomous integrity monitoring for GNSS/INS ultra-tightly integrated system

The ultra-tight integration of GNSS (Global Navigation Satellite System) and INS (Inertial Navigation System) may suffer from faults in GNSS, INS and integration filter. Both the faults occurred at the current epoch and at previous epochs affect the position solution deviation of ultra-tight integration at the current epoch, and the effect is reflected in GNSS code phase tracking errors. In this paper, a new autonomous integrity monitoring algorithm is proposed for the federated GNSS/INS ultra-tight integrations in which the code phases of local GNSS signal replicas for GNSS signal tracking are completely derived from the integrated navigation solution. In the proposed algorithm, GNSS code phase tracking errors are employed to construct the test statistics for fault detection through a MHSS (Multiple Hypothesis Solution Separation) method improved from the classical MHSS used in ARAIM (Advanced Receiver Autonomous Integrity Monitoring). With the improved MHSS, the proposed algorithm can account for GNSS nominal biases, multiple GNSS faults and the faults in INS and integration filter. The protection levels under multiple hypothesis are also derived. A semi-physical simulation of the federated ultra-tight integration of GPS (Global Positioning System) and INS in airplane approaching case and a vehicle-based field test of the federated ultra-tight integration of GPS, Galileo and INS are conducted to validate the proposed algorithm. The experiments show that the designed fault detection can effectively detect the occurred faults and the derived protection levels can correctly bound the caused position solution error.

Sparsity and manifold regularized convolutional auto-encoders-based feature learning for fault detection of multivariate processes

Deep neural networks (DNNs) are popular in process monitoring for its remarkable feature extraction from data. However, the increased dimension and correlation of the process variables degrade performance of these DNNs in feature extraction of data. This paper proposes a sparsity and manifold regularized convolutional auto-encoders (SMRCAE) for fault detection of complex multivariate processes. SMRCAE can learn high-level features from the data in an unsupervised way. A sparsity-and-manifold-regularization term is integrated into the learning procedure of SMRCAE, which allows SMRCAE to perform feature selection and capture intrinsic data information. Moreover, a depthwise separable convolution (dsConv) block is used to reduce the computational cost. Two typical fault detection statistics, namely Hotelling’s T-squared (T2) and the squared prediction error (SPE), are developed on the feature space and residual space of SMRCAE, respectively. The performance of SMRCAE is evaluated on an industrial benchmark, i.e., Tennessee Eastman process (TEP) and a real process of industrial conveyor belts. The experimental results show the feasibility of SMRCAE in extracting representative features for process fault detection. The average fault detection rate of SMRCAE is 92.03% and 100% on the two cases, respectively.

A sensor fault diagnosis method based on KPCA and contribution graph

In this paper, a sensor fault diagnosis method based on KPCA and contribution graph are proposed to adapt to the nonlinear and non-Gaussian characteristics of the system. Based on the kernel function theory, this method uses SPE and T2 statistics for fault detection and contribution graph for fault location, thus completing fault diagnosis. The numerical simulation results verify that the proposed method is more effective than the traditional PCA method in detecting nonlinear faults. At the same time, the KPCA contribution map can be used to accurately locate the fault sensor, which can provide a reference value for the sensor fault diagnosis of nonlinear systems in the future.

Data-driven fault diagnosis for dynamic traction systems in high-speed trains

Traction systems are an important aspect of high-speed trains, and their reliable operation is crucial. With data available from trains, this paper proposes an optimal fault detection and diagnosis (FDD) strategy for dynamic traction systems. Based on the established dynamic model, using sensor measurements, a correlation-aided subspace identification technique is proposed to formulate residual signals and corresponding test statistics for fault detection. Then, a modified support vector machine (SVM) is designed for optimally solving the diagnosis bias caused by the difference in the apparent probabilities of multiple fault scenarios. The feasibility and effectiveness of the proposed optical FDD performance are illustrated in the CRRC experimental platforms.

Deep neural network based recursive feature learning for nonlinear dynamic process monitoring

AbstractThe data collected from modern industrial processes always have nonlinear and dynamic characteristics. The recently developed deep neural network method, stacked denoising auto‐encoder (SDAE), can extract robust nonlinear latent variables from data against noise. However, it leaves the dynamic relationship unconsidered. To solve this problem, a novel algorithm named the recursive stacked denoising auto‐encoder (RSDAE) is proposed. To learn the dynamic relationship, the RSDAE focuses on the predictability of the latent variables in the recurrence to contain the most dynamic variations. After the dynamic variations are extracted by the RSDAE, there is little autocorrelation left in the residuals. Then, the residuals can be monitored by principal component analysis (PCA). For the purpose of process monitoring, corresponding fault detection statistics are developed based on the RSDAE. Finally, a numerical case and the Tennessee Eastman process benchmark are used to demonstrate the effectiveness of the proposed algorithm.

A Comparison of Different Statistics for Detecting Multiplicative Faults in Multivariate Statistics-Based Fault Detection Approaches

The explosion of different fault detection (FD) statistics in multivariate statistics-based FD approaches has meant that the practitioner is faced with the unenviable job of determining which to use in a given circumstance. Moreover, compared to extensive investigations on additive faults, the performance of commonly used FD statistics for detecting multiplicative faults has not been holistically evaluated. Therefore, this paper seeks to investigate the different statistics that can be applied to detect multiplicative faults in order to provide users and practitioners in the FD field with guidance to select an appropriate method. The considered statistics are broadly classified into three groups: traditional methods ( e.g. $T^{2}$ -statistic) and their extensions; the Wishart distribution-based methods; and those methods created in the information and communication fields to describe the measurement variance and covariance ( e.g. Kullback-Leibler divergence). These three groups are compared by considering the required probability distributions, interconnections, and detection performance for multiplicative faults. Using simulated data from numerical examples and the Tennessee Eastman benchmark process, the theoretical results are validated, and the applicability of multivariate statistics-based FD methods incorporating all considered statistics for detecting multiplicative faults is examined at the end of this paper.

Comparison of Two Basic Statistics for Fault Detection and Process Monitoring

In this paper, two common statistics, the T2 and the Q statistics, for fault detection and process monitoring are compared. Specifically, the geometric relationship between the T2 statistic and 3 common forms of the Q statistics is analysed. Furthermore, using the false alarm rate (FAR) and the fault detection rate (FDR), the fault detection performance of both statistics is quantified and compared. The results show that, for a given significance level, the T2 statistic has the best overall FDR.

Quality-Relevant Batch Process Fault Detection Using a Multiway Multi-Subspace CVA Method

For batch process fault detection, regular data-driven methods cannot distinguish quality-irrelevant faults from quality-relevant faults. To solve such problem, we propose a multiway multi-subspace canonical variate analysis (MMCVA) method for the batch processes. First, the combination of batch-wise unfolding and variable-wise unfolding is adopted to unfold the three-way process and quality data in to two-way data. Then, we use CVA to project the process and quality data spaces to three subspaces, a process-quality correlated subspace, a quality-uncorrelated process subspace, and a process-uncorrelated quality subspace. Fault detection statistics are developed based on the three subspaces. The proposed MMCVA method is capable of indicating the normality or abnormality of the quality variables, while detecting a process fault. The simulation results of a fed-batch penicillin fermentation process illustrate the effectiveness of the proposed method.

Canonical correlation analysis based fault diagnosis method for structural monitoring sensor networks

The health conditions of in-service civil infrastructures can be evaluated by employing structural health monitoring technology. A reliable health evaluation result depends heavily on the quality of the data collected from the structural monitoring sensor network. Hence, the problem of sensor fault diagnosis has gained considerable attention in recent years. In this paper, an innovative sensor fault diagnosis method that focuses on fault detection and isolation stages has been proposed. The dynamic or auto-regressive characteristic is firstly utilized to build a multivariable statistical model that measures the correlations of the currently collected structural responses and the future possible ones in combination with the canonical correlation analysis. Two different fault detection statistics are then defined based on the above multivariable statistical model for deciding whether a fault or failure occurred in the sensor network. After that, two corresponding fault isolation indices are deduced through the contribution analysis methodology to identify the faulty sensor. Case studies, using a benchmark structure developed for bridge health monitoring, are considered in the research and demonstrate the superiority of the new proposed sensor fault diagnosis method over the traditional principal component analysis-based and the dynamic principal component analysis-based methods.

Multiple Component Analysis and Its Application in Process Monitoring With Prior Fault Data

Traditional principal component analysis (PCA) based process monitoring method is unsupervised learning method, which builds a statistical model only based on the normal operating dataset. However, in industrial process database, there are also some faulty operating datasets available which are omitted by PCA but may be helpful for fault detection performance improvement. To better utilize both normal operating data and prior faulty data, a modified PCA method, called multiple component analysis (MCA) is presented for monitoring process faults. MCA statistical modelling involves two kinds of data feature extractions. Firstly, based on normal operating data, MCA applies conventional PCA transformation to obtain the principal component features, which describe normal data distribution directions. Then, for the known fault data, non-local preservation projection technique is used to compute fault discriminant features, which describe the fault data distribution directions. Lastly these features are integrated to construct monitoring statistics for fault detection. Simulations on Tennessee Eastman benchmark process show that the proposed method outperforms traditional PCA method in terms of fault detection performance.

New kernel independent and principal components analysis‐based process monitoring approach with application to hot strip mill process

In this article, a new kernel independent and principal components analysis (kernel ICA–PCA) based process monitoring approach is proposed for hot strip mill process (HSMP). HSMP appears widely in iron and steel industry, which runs in an environment with significant nonlinearity, non-Gaussianity and some other uncertainties. The present method, namely kernel ICA–PCA, firstly addresses the nonlinearity via the popular kernel trick, then applies kernel ICA model to isolate the non-Gaussian independent information, finally, utilises kernel PCA model to account for the uncertain part and extract the principal components. To avoid the disadvantage of the original fault detection statistics, a k nearest neighbour data description-based technique is employed into the kernel ICA–PCA for monitoring the variations occurring in the independent and principal components, whereas traditional Q statistic is employed to reflect the disturbance in the residuals. All of their thresholds will be determined by a new emerging bootstrap-based technique. The applicability of the new scheme is represented via hot strip mill process dataset recorded in the iron and steel company.

Correlation Analysis for Fault Detection Statistics in Integrated GNSS/INS Systems

Global Satellite Navigation Systems (GNSS) have been widely used for positioning, navigation and timing (PNT). Therefore, the integrity of the satellite based navigation systems has been a major concern for many liability critical applications, such as civil aviation, and location-based services (LBS). Over the past two decades, GNSS Receiver Autonomous Integrity Monitoring (RAIM) procedures have been developed, but the efficiency of such procedures is highly dependent on measurement redundancy and geometric strength within the GNSS positioning solutions. Reliability of a PNT system can be measured by, not only the wellknown Minimal Detectable Biases (MDBs), but also the recently derived Minimal Separable Biases (MSBs) for the measurements. While the previous research has shown that the MSBs are directly related to the correlations between the faulty measurement detection statistics, a comprehensive analysis for such correlations between fault (or outlier) detection statistics is still lacking, even for commonly used GNSS/INS integration scenarios. In this research, we have demonstrated that with the aid of inertial sensors, even with low-cost MEMS sensors, the MDBs and correlation coefficients between the measurement fault detection statistics can be significantly reduced, thus improving the separability of faults in GNSS measurements.

Improved principal component monitoring using the local approach

This paper shows that current multivariate statistical monitoring technology may not detect incipient changes in the variable covariance structure nor changes in the geometry of the underlying variable decomposition. To overcome these deficiencies, the local approach is incorporated into the multivariate statistical monitoring framework to define two new univariate statistics for fault detection. Fault isolation is achieved by constructing a fault diagnosis chart which reveals changes in the covariance structure resulting from the presence of a fault. A theoretical analysis is presented and the proposed monitoring approach is exemplified using application studies involving recorded data from two complex industrial processes.

Optimization of correlated multiple quality characteristics robust design using principal component analysis

This paper shows that current multivariate statistical monitoring technology may not detect incipient changes in the variable covariance structure nor changes in the geometry of the underlying variable decomposition. To overcome these deficiencies, the local approach is incorporated into the multivariate statistical monitoring framework to define two new univariate statistics for fault detection. Fault isolation is achieved by constructing a fault diagnosis chart which reveals changes in the covariance structure resulting from the presence of a fault. A theoretical analysis is presented and the proposed monitoring approach is exemplified using application studies involving recorded data from two complex industrial processes.