Yvon Tharrault

Fault detection and isolation with robust principal component analysis

Principal component analysis (PCA) is a powerful fault detection and isolation method. However, the classical PCA which is based on the estimation of the sample mean and covariance matrix of the data is very sensitive to outliers in the training data set. Usually robust principal component analysis was applied to remove the effect of outliers on the PCA model. In this paper, a fast two-step algorithm is proposed. First, the objective was to find a robust PCA model that could be used for outliers detection and isolation. Hence a scale-M estimator (R.A. Maronna, 2005) is used to determine a robust model. This estimator is computed using an iterative re-weighted least squares (IRWLS) procedure. This algorithm is initialized from a very simple estimate derived from a one-step weighted variance-covariance estimate (A. Ruiz-Gazen, 1996). Second, structured residuals are used for multiple fault detection and isolation. These structured residuals are based on the reconstruction principle and the existence condition of such residuals is used to determine the detectable faults and the isolable faults. The proposed scheme avoids the combinatorial explosion of faulty scenarios related to multiple faults to consider. Then, this procedure for outliers detection and isolation is successfully applied to an example with multiple faults.

WWTP diagnosis based on robust principal component analysis

Principal component analysis (PCA) is a powerful fault detection and isolation method. However, the classical PCA which is based on the estimation of the sample mean and variance-covariance matrix of the data is very sensitive to outliers in the training data set. Usually robust principal component analysis was applied to remove the effect of outliers on the PCA model. In this paper, a fast two-step algorithm is proposed. First, the objective was to find a robust PCA. Hence a scale-M estimator is computed using an iterative re-weighted least squares (IRWLS) procedure. This algorithm is initialized from a nearly robust variance-covariance estimate which tends to emphasize the contribution of close observations in comparison with distant observations (outliers). Second, structured residuals are used for multiple fault detection and isolation. These structured residuals are based on the reconstruction principle and the existence condition of such residuals is used to determine the detectable faults and the isolable faults. The proposed scheme avoids the combinatorial explosion of faulty scenarios related to multiple faults to consider. Then, this procedure is successfully applied for sensor fault detection and isolation of the hydraulic part of an activated sludge wastewater treatment plant (WWTP).

Sensor Fault Detection and Isolation by Robust Principal Component Analysis

Sensors are essential components of modern control systems. Any faults in sensors will affect the overall performance of a system because their effects can easily propagate to manipulative variables through feedback control loops and also disturb other process variables. The task for sensor validation is to detect and isolate faulty sensors and estimate fault magnitudes afterwards to provide fault-free values. Model-based methods constitute an important approach to sensor fault detection and isolation (FDI). A model-based approach consists in generating residuals as the difference between the measurements and the estimates provided by the relationships existing between the various variables of the process. The analysis of these residuals may lead to detect and isolate the faulty sensors. Almost all conventional model-based methods presume the knowledge of an accurate model of the system, e.g. transfer function or system matrices in the state space representation. Principal component Analysis (PCA) is a data-driven method which is particularly well adapted to reveal linear relationships among the plant variables without formulating them explicitly and has also been employed for system identification. PCA has some other nice features. It can handle high dimensional and correlated process variables, provides a natural solution to the errors-in-variables problem and includes disturbance decoupling (Li & Qin, 2001). Moreover in the FDI field, Gertler & McAvoy (1997) have shown a close link between PCA and parity space method. Principal component analysis (PCA) has then been applied successfully in the monitoring of complex systems (Chiang & Colegrove, 2007; Harkat et al., 2006; Kano & Nakagawa, 2008). 17

New hierarchical approach for multiple sensor fault detection and isolation. Application to an air quality monitoring network

Our work is devoted to the problem of multiple sensor fault detection and isolation using principal component analysis. Structured residuals are used for multiple fault isolation. These structured residuals are based on the principle of variable reconstruction. However, multiple fault isolation based on reconstruction approach leads to an explosion of the reconstruction combinations. Therefore instead of considering all the subsets of faulty variables, we determine the isolable multiple faults by removing the subsets of variables that have too high minimum fault amplitudes to ensure fault isolation. Unfortunately, in the case of a large number of variables, this scheme yet leads to an explosion of faulty scenarios to consider. An effective approach is to use multi-block reconstruction approach where the process variables are partitioned into several blocks. In the first step of this hierarchical approach, the goal is to isolate faulty blocks and then in the second step, from the faulty blocks, faulty variables have to be isolated. The proposed approach is successfully applied to multiple sensor fault detection and isolation of an air quality monitoring network.

Multiple sensor fault detection and isolation of an air quality monitoring network using RBF-NLPCA model

This paper presents a data-driven method based on non-linear principal component analysis to detect and isolate multiple sensor faults. The RBF-NLPCA model is obtained by combining a principal curve algorithm and two three-layer radial basis function (RBF) networks. The reconstruction approach for multiple sensors is proposed in the non-linear case and successfully applied for multiple sensor fault detection and isolation of an air quality monitoring network. The proposed approach reduces considerably the number of reconstruction combinations and allows to determine replacement values for the faulty sensors.