Fault Detection Index Research Articles

Maximizing Fault Detectability with Closed-Loop Control

This paper addresses the fault detectability problem for PCA-based process monitoring methods under closed-loop control. Unlike previous research assuming the same process variation for both modeling and monitoring periods, the impact of controller on data variation is considered. The effective fault direction is given in order to describe the effect of process variation on fault detection index under different controllers. The minimum variance along the effective fault direction is developed by introducing the concept of block-lower-triangular interactor matrix and conditional minimum variance control. The sufficient condition for a fault to be detectable under any controllers is provided. The proposed method is demonstrated with the simulation examples.

Model‐Based Analysis of Spur Gears’ Dynamic Behavior in the Presence of Multiple Cracks

Early detection of tooth cracks is crucial for effective condition‐based monitoring and decision making. The scope of this work was to bring more insight into the vibration behavior of spur gears in the presence of single and multiple simultaneous tooth cracks. The investigation was conducted in both time and frequency domains. A finite element analysis was performed to determine the variation in stiffness with respect to the angular position for different combinations of crack lengths. A simplified nonlinear lumped parameter model of a one‐stage gearbox with six degrees of freedom was then developed to simulate the vibration response of faulty external spur gears. Four different multiple‐crack scenarios were proposed and studied. The performances of various statistical fault detection indicators were considered and investigated. The simulation results obtained via MATLAB indicated that, as the severity of a single crack increases, the values of the time domain statistical indicators increase also, but at different rates. Moreover, the number of cracks was found to have a negative effect on the values of all the performance indicators, except for the RMS. The number and amplitude of the sidebands in the frequency spectrum were also considered, while assessing the severity of the faults in each scenario. It was observed that, in the case of consecutive tooth cracks, the number of spectrum peaks and the number of cracks were consistent in the frequency range of 4‐5 kHz. The main finding of this study was that the peak spectral amplitude was the most sensitive indicator of the number and severity of cracks.

A Kalman Filter Based Technique for Stator Turn-Fault Detection of the Induction Motors

AbstractMonitoring of the Induction Motors (IMs) through stator current for different faults diagnosis has considerable economic and technical advantages in comparison with the other techniques in this content. Among different faults of an IM, stator and bearing faults are more probable types, which can be detected by analyzing signatures of the stator currents. One of the most reliable indicators for fault detection of IMs is lower sidebands of power frequency in the stator currents. This paper deals with a novel simple technique for detecting stator turn-fault of the IMs. Frequencies of the lower sidebands are determined using the motor specifications and their amplitudes are estimated by a Kalman Filter (KF). Instantaneous Total Harmonic Distortion (ITHD) of these harmonics is calculated. Since variation of the ITHD for the three-phase currents is considerable in case of stator turn-fault, the fault can be detected using this criterion, confidently. Different simulation results verify high performance of the proposed method. The performance of the method is also confirmed using some experiments.

Sensor fault detection based on principal component analysis for interval-valued data

ABSTRACTPrincipal component analysis (PCA)-based fault detection and isolation (FDI) is a well-established data-driven diagnosis strategy that has long been praised for its performances. However, it is still not optimal for uncertain systems, mainly since the model uncertainties usually have a significant effect on the reliability of the method. As an alternative solution, modeling with PCA for interval-valued data ensures a better monitoring by apprehending the sensor uncertainties and including them in the modeling phase. This article presents an extension of data-driven PCA fault detection to the case of interval-valued data. The PCA model is built based on the complete information principal component analysis (CIPCA) for interval-valued data, and different fault detection indices are generated based on the squared prediction error (SPE) statistic. A fault detection scheme is proposed based on squared interval norm of residuals vector. The performances of the proposed fault detection scheme are illustrated using a simulation example and a milling machine process, along with a Monte Carlo experiment for validation.

An improved plant‐wide fault detection scheme based on PCA and adaptive threshold for reliable process monitoring: Application on the new revised model of Tennessee Eastman process

AbstractAn improved process monitoring scheme is presented in this paper, it is based on the integration of multivariate and univariate statistical analysis methods. Instead of conventional fixed control limits, adaptive thresholds are developed for common fault detection indices used with principal component analysis, including the Hotelling T2 statistic and the sum of squared prediction error known as the Q statistic. The thresholds are updated based on a modified exponentially weighted moving average chart with a limited window length. The primary goal of this strategy is to enhance the performance of principal component analysis–based process monitoring method and overcome its shortcomings, by increasing fault detection rate to improve monitoring sensitivity and eliminating false alarms to ensure higher robustness and reliability. Fault detection in the revised model of Tennessee Eastman process benchmark is also investigated. The developed monitoring scheme is tested and compared with conventional fixed threshold technique, and its performance is evaluated across various types of process faults. The obtained results demonstrate the promising capabilities of the developed scheme.

Monitoring Batch Processes Using Sparse Parallel Factor Decomposition

Traditional multivariate statistical analysis methods used for batch process monitoring fail to build high-performance monitoring models partly because of the inability to extract sparse and interpretable latent variables from the batch data. To overcome this deficiency, we propose sparse parallel factor (SPARAFAC) decomposition for the sparse modeling of three-way data arrays of batch processes. The SPARAFAC extracts sparse factor matrices from the three-way data array. Sparse factor matrices have the potential advantage of being easier to interpret because they eliminate redundant data information and reveal significant variable correlations. A SPARAFAC-based batch process monitoring method is proposed. Because of the sparsity and interpretability, the SPARAFAC monitoring model is well suitable for fault detection, analysis, and diagnosis. Two fault detection indices are defined based on the SPARAFAC model, and they are capable of detecting the occurrence of process faults. Multilevel contribution plots...

Parallel projection to latent structures for quality-relevant process monitoring

Abstract Projection to latent structures(PLS) is widely applied in quality-related process monitoring. Since it is a data-based method, the noise in data will affect PLS model parameter, which may lead to inappropriate space division. In this paper, an approach called parallel projection to latent structures (P-PLS) is proposed. To remove negative effect of the noise, P-PLS firstly updates original correlation matrix obtained by PLS through l0 minimization. Then process input (i.e., process variables) are divided into two orthogonal subspaces – the output-relevant and the input-relevant subspace by singular value decomposition (SVD) on updated correlation matrix. With respect to process output (i.e., quality variables), the unpredictable part is further decomposed by principal component analysis (PCA). Thus, P-PLS decomposes the whole input and output data space into only 4 subspaces, in which correlation subspace, unpredictable output principal subspace and unpredictable output residual subspace are output-relevant and input-residual subspace is input-relevant. Four fault detection indices are designed for complete monitoring the faults in respective subspaces. Furthermore, the relationships among P-PLS and concurrent PLS models are analyzed in detail. Numerical examples and Tennessee Eastman Process (TEP) are utilized to verify the effectiveness and superiority of proposed P-PLS algorithm.

A novel dynamic PCA algorithm for dynamic data modeling and process monitoring

Principal component analysis (PCA) has been widely applied for data modeling and process monitoring. However, it is not appropriate to directly apply PCA to data from a dynamic process, since PCA focuses on variance maximization only and pays no attention to whether the components contain dynamics or not. In this paper, a novel dynamic PCA (DiPCA) algorithm is proposed to extract explicitly a set of dynamic latent variables with which to capture the most dynamic variations in the data. After the dynamic variations are extracted, the residuals are essentially uncorrelated in time and static PCA can be applied. The new models generate a subspace of principal time series that are most predictable from their past data. Geometric properties are explored to give insight into the new dynamic model structure. For the purpose of process monitoring, fault detection indices based on DiPCA are developed based on the proposed model. Case studies on simulation data, data from an industrial boiler process, and the Tennessee Eastman process are presented to illustrate the effectiveness of the proposed dynamic models and fault detection methods.

Incipient fault detection with smoothing techniques in statistical process monitoring

In modern industry, detecting incipient faults timely is of vital importance to prevent serious system performance deterioration and ensure optimal process operation. Recently, multivariate statistical process monitoring (MSPM) techniques have been extensively studied and widely applied to modern industrial systems. However, conventional fault detection indices utilized in statistical process monitoring are not sensitive to incipient faults with small magnitude. In this paper, by introducing two representative smoothing techniques, novel incipient fault detection strategies based on a generic fault detection index in MSPM are proposed. Fault detectability for each proposed strategy is analyzed. In addition, the effects of the smoothing parameters on fault detection, including advantages and disadvantages, are also investigated. Finally, case studies on a numerical example and two practical industrial processes are carried out to demonstrate the effectiveness of the proposed incipient fault detection strategies.

Double-layer ensemble monitoring of non-gaussian processes using modified independent component analysis

The modified independent component analysis (MICA) was proposed mainly to obtain a consistent solution that cannot be ensured in the original ICA algorithm and has been widely investigated in multivariate statistical process monitoring (MSPM). Within the MICA-based non-Gaussian process monitoring circle, there are two main problems, i.e., the selection of a proper non-quadratic function for measuring non-Gaussianity and the determination of dominant ICs for constructing latent subspace, have not been well attempted so far. Given that the MICA method as well as other MSPM approaches are usually implemented in an unsupervised manner, the two problems are always solved by some empirical criteria without respect to enhancing fault detectability. The current work aims to address the challenging issues involved in the MICA-based approach and propose a double-layer ensemble monitoring method based on MICA (abbreviated as DEMICA) for non-Gaussian processes. Instead of proposing an approach for selecting a proper non-quadratic function and determining the dominant ICs, the DEMICA method combines all possible base MICA models developed with different non-quadratic functions and different sets of dominant ICs into an ensemble, and a double-layer Bayesian inference is formulated as a decision fusion method to form a unique monitoring index for online fault detection. The effectiveness of the proposed approach is then validated on two systems, and the achieved results clearly demonstrate its superior proficiency.

Demagnetisation fault detection in PMSM using zero sequence current components

A demagnetisation fault detection method for a delta-connected permanent magnet synchronous machine (PMSM) based on zero sequence current components (ZSCC) is proposed. The model of the delta-connected PMSM with the demagnetisation fault is first established. Then the expression of the ZSCC is presented for the delta-connected PMSM, and an equivalent fault severity index which can quantify the demagnetisation degree is obtained, being not limited by the partial or uniform demagnetisation. Finally, the simulation results show that the potential of the proposed fault severity index for the demagnetisation fault detection.

A new adaptive PCA based thresholding scheme for fault detection in complex systems

For large scale and complex processes, data-driven analysis methods are receiving increasing attention for fault detection and diagnosis to improve process operation by detecting when abnormal process operations exist and diagnosing the sources of the abnormalities. Common methods based on multivariate statistical analysis are widely used and particularly principal component analysis (PCA), fault detection indices used along with PCA including the Hotelling T² statistic and the sum of squared prediction error (SPE) known as the Q statistic can be used to identify faults. This paper develops a new adaptive thresholding scheme based on a modified exponentially weighted moving average (EWMA) control chart statistic, which is effective in detecting small changes and abrupt shifts in the process operation. The aim is to enhance the performance of PCA methods for process monitoring, while maintaining a low false alarm rate with good sensitivity of anomalies. The performance of the developed scheme is compared to a conventional fixed thresholding technique by evaluating the detection performance across various types of faults that occurred in the Tennessee Eastman Process, The results demonstrate the promising capabilities of our proposed scheme.

A new fault detection index based on Mahalanobis distance and kernel method

This paper suggests an extension of the PCMD index proposed for sensor fault diagnosis in linear systems to the nonlinear case. The proposed index is entitled KPCMD, and it is based on Mahalanobis distance and moving window kernel principal component analysis (MWKPCA) technique. The principle of this index is to detect dissimilarity between a reference KPCA model that represents normal operation of the system and a current KPCA model that represents current system behavior. The proposed KPCMD index compute Mahalanobis distance between principal components corresponding to the reference KPCA model and those corresponding to the current KPCA model which are obtained online using MWKPCA. The proposed KPCMD indices have been applied successfully for monitoring of numerical example as well a continuous stirred tank reactor (CSTR).

Fault propagation path estimation in NGL fractionation process using principal component analysis

Multivariate statistical methods for process monitoring are attaining a lot of attention in chemical and process industries to enhance both the process performance and safety. The fault in one process variable readily affects the other variables which makes it difficult to identify the fault variable precisely. In this study, principal component analysis (PCA) model has been developed and applied to monitor the NGL (natural gas liquid) fractionation process. Normal and fault case scenarios are developed and compared statistically to identify the fault variable and to estimate the fault propagation path in the system. The simulated NGL plant is first validated against the design data and then the developed methodology is applied to predict the fault direction by projecting the samples on the residual subspace (RS). The RS of fault data is usually superimposed by normal variations which must be eliminated to amplify the fault magnitude. The RS is further transformed into co-variance matrix followed by Singular Value Decomposition (SVD) analysis to generate the fault direction matrix corresponding to the highest eigenvalue. The process variables are further analyzed according to their magnitude of contribution towards a particular fault that in turn can be used for the determination of fault propagation path in the system. Furthermore, the applied methodology can quickly detect the fault variable irrespective of using the fault detection indices where the variable showing highest variation is most likely to be the fault variable.

Ensemble modified independent component analysis for enhanced non-Gaussian process monitoring

As a multivariate statistical tool, the modified independent component analysis (MICA) has drawn considerable attention within the non-Gaussian process monitoring circle since it can solve two main problems in the original ICA method. Despite the diversity in applications, the determination logic for non-quadratic functions involved in the iterative procedures of MICA algorithm has always been empirical. Given that the MICA is an unsupervised modeling method, a direct rational study that can conclusively demonstrate which non-quadratic function is optimal for the general purpose of fault detection is inaccessible. The selection of non-quadratic functions is still a challenge that has rarely been attempted. Recognition of this issue and motivated by the superiority of ensemble learning strategy, a novel ensemble MICA (EMICA) modeling approach is presented for enhancing non-Gaussian process monitoring performance. Instead of focusing on a single non-quadratic function, the proposed method combines multiple base MICA models derived from different non-quadratic functions into an ensemble one, and the Bayesian inference is employed as a decision fusion method to form a unique monitoring index for fault detection. The enhanced fault detectability of the EMICA method is also illustrated on two industrial processes.

A data-based technique for monitoring of wound rotor induction machines: A simulation study

Detecting faults induction machines is crucial for a safe operation of these machines. The aim of this paper is to present a statistical fault detection methodology for the detection of faults in three-phase wound rotor induction machines (WRIM). The proposed fault detection approach is based on the use of principal components analysis (PCA). However, conventional PCA-based detection indices, such as the T2 and the Q statistics, are not well suited to detect small faults because these indices only use information from the most recent available samples. Detection of small faults is one of the most crucial and challenging tasks in the area of fault detection and diagnosis. In this paper, a new statistical system monitoring strategy is proposed for detecting changes resulting from small shifts in several variables associated with WRIM. The proposed approach combines modeling using PCA modeling with the exponentially weighted moving average (EWMA) control scheme. In the proposed approach, EWMA control scheme is applied on the ignored principal components to detect the presence of faults. The performance of the proposed method is compared with those of the traditional PCA-based fault detection indices. The simulation results clearly show the effectiveness of the proposed method over the conventional ones, especially in the presence of faults with small magnitudes.

On the use of reconstruction-based contribution for fault diagnosis

In the multivariate statistical process monitoring (MSPM) area, principal component analysis (PCA) and reconstruction-based contribution (RBC) are two commonly used techniques for fault detection and fault diagnosis problems, respectively. This paper starts with a review of the two methods. It is then pointed out that, when the dimensionality of the principal component subspace or the residual subspace in the PCA model is equal to 1, several fault detection indices based RBC will be invalid for fault diagnosis. Corresponding geometric interpretations of the invalidation cases are illustrated intuitively according to the definition of RBC. In order to perform effective fault diagnosis in such invalidation cases, three methods including the available combined index based RBC, the derived Mahalanobis distance based RBC, and the proposed chi-square contribution (CSC) are introduced. The CSC is constructed by employing a moving window and the effect of the window width on its diagnosis performance is investigated. The failure cases of the RBC, the effectiveness of the proposed CSC, as well as the comparison of these three methods for fault diagnosis are demonstrated by case studies on two numerical examples and a simulated three-tank system.

Variable Elimination-Based Contribution for Accurate Fault Identification

We propose a new fault identification method, which can describe the contribution of each process variable to a detected fault and identify a faulty variable more accurately than conventional methods. In the proposed method, in addition to a fault detection model that describes normal operating condition (NOC), multiple fault identification models that describe the same NOC are also constructed by eliminating one variable from all monitored variables at a time. After a fault is detected with the fault detection model, the fault detection index, e.g. a combined index of the T2 and Q statistics, is calculated by using each of the fault identification models. When the faulty variable is eliminated, the index does not change before and after the fault occurs. On the other hand, when the normal variable is eliminated, the index is affected by the fault and increases after the fault occurs. Thus, the eliminated variable corresponding to the index that does not increase after the occurrence of the fault is identified as a faulty variable. In the proposed method, the ratio of the average index in NOC to the current index is used as a fault identification index or a contribution. To validate the proposed method, VEC was compared with the reconstruction-based contribution (RBC) through numerical examples. The results have demonstrated that VEC outperformed RBC in fault identification performance both in the linear case and in the nonlinear case.

Research on the meshing stiffness and vibration response of cracked gears based on the universal equation of gear profile

To achieve the expected purpose monitoring the gearbox condition and preventing the occurrence of dangerous situations, it is important to improve the accuracy of the vibration response, which is primarily caused by the time-varying mesh stiffness. Thus, a universal gear profile equation that references the actual manufacturing process was applied to calculate the meshing stiffness. Based on the universal gear profile equation, two methods of calculating tooth thickness decrements (method 1: straight-affecting line; method 2: parabolic-affecting line) in cracked gears were compared, and their different effects on the vibration response were investigated with fault detection indicators, including RMS and kurtosis. The results revealed that the fault detection indicators of two affecting lines intersect when the crack size reaches a special point at which the two affecting lines overlap, and this result contrasts with those of previous research. The double pulse observed in the residual signals was analyzed, and the results revealed that the double pulse was generated by the two step-points of the residual stiffness. The behaviors of the fault detection indicators of the two affecting lines were investigated, and the results revealed that the parabolic-affecting method was appropriate for the calculating the decrement in tooth thickness.

Data density-based fault detection and diagnosis with nonlinearities between variables and multimodal data distributions

Multivariate statistical process control (MSPC) is an important means of monitoring multiple process variables and their interrelationships while controlling chemical and industrial plants efficiently and stably. To consider nonlinearities between process variables and multimodal data distributions, the data density can be used as an index for fault detection. Data domains with a low data density are considered abnormal states. However, after fault detection, faulty process variables cannot be diagnosed with an MSPC model based on the data density. Therefore, we have developed a new index to diagnose the process variables that contribute to process faults using a data density-based MSPC model. The proposed index uses the partial derivative of an MSPC model with respect to each process variable. We demonstrate the effectiveness of the proposed method using numerical simulation data, Tennessee Eastman process data, and real plant data analyses.