Sensor fault detection, isolation and reconstruction using nonlinear principal component analysis

The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover nonlinear relationships between variables. Also, nonlinear PCA can deal with variables at their appropriate measurement level; for example, it can treat Likert-type scales ordinally instead of numerically. Every observed value of a variable can be referred to as a category. While performing PCA, nonlinear PCA converts every category to a numeric value, in accordance with the variable's analysis level, using optimal quantification. The authors discuss how optimal quantification is carried out, what analysis levels are, which decisions have to be made when applying nonlinear PCA, and how the results can be interpreted. The strengths and limitations of the method are discussed. An example applying nonlinear PCA to empirical data using the program CATPCA (J. J. Meulman, W. J. Heiser, & SPSS, 2004) is provided.

ABSTRACTQuick and timely fault detection is of great importance in control systems reliability. Undetected faulty sensors could result in irreparable damages. Although fault detection and isolation (FDI) methods in control systems have received much attention in the last decade, these techniques have not been applied for some classes of nonlinear systems yet. This paper deals with the issues of sensor fault detection and isolation for a class of Lipschitz uncertain nonlinear system. By introducing a coordinate transformation matrix for states and output, the original system is first divided into two subsystems. The first subsystem is affected by uncertainty and disturbance. The second subsystem just has sensor faults. The nonlinear term is separated to linear and pure nonlinear parts. For fault detection, two sliding mode observers (SMO) are designed for the two subsystems. The stability condition is obtained based on the Lyapunov approach. The necessary matrices and parameters are obtained by solving the linear matrix inequality (LMI) problem. Furthermore, two sliding mode observers are designed for fault isolation. Finally, the effectiveness of the proposed approach is illustrated by simulation examples.

Sensor fault identification based on time-lagged PCA in dynamic processes

Detection, isolation and identification of multiple actuator and sensor faults in nonlinear dynamic systems: Application to a waste water treatment process

An approach for model-based fault detection and isolation (FDI) of sensor and process faults for nonlinear processes is presented. The process is decomposed into several sub-processes and for each process a nonlinear model is identified. This model bank consisting of fuzzy models (Takagi-Sugeno type) is used to generate several different estimates for process outputs and states. Comparing these estimates with the actual measured ones leads to residuals which indicate the state of the system and provide information about the source of possible faults. The two ways to implement a model, as a parallel or as a series-parallel model lead to different FDI results. Hence, this different sensitivity is also investigated in this contribution. The practical applicability is illustrated on an industrial scale thermal plant. Here, seven different process faults and eight different sensor faults can be detected.

This paper presents the design and analysis of a methodology for detecting and isolating multiple sensor faults in large-scale interconnected nonlinear systems. The backbone of the proposed decentralized methodology is the design of a local sensor fault diagnosis agent dedicated to each interconnected subsystem, without the need to communicate with neighboring agents. Each local sensor fault diagnosis agent is responsible for detecting and isolating multiple faults in the local set of sensors. The local sensor fault diagnosis agent consists of a bank of modules that monitor smaller groups of sensors in the corresponding local sensor set. The detection of faults in each of the sensor groups is conducted using robust analytical redundancy relations, formulated by structured residuals and adaptive thresholds. The multiple sensor fault isolation in each local sensor fault diagnosis agent is realized by aggregating the decisions of the modules and applying a diagnostic reasoning-based decision logic. The performance of the proposed diagnostic scheme is analyzed with respect to sensor fault detectability and multiple sensor fault isolability. A simulation example of two interconnected robot manipulators is used to illustrate the application of the multiple sensor fault detection and isolation methodology.

Complex-valued neural networks for nonlinear complex principal component analysis

Principal Component Analysis (PCA) is a commonly employed technique in industrial systems for process monitoring and fault diagnosis, owing to its capability to efficiently process large datasets. Traditionally, it is applied to single-valued variables, where critical information can be lost in real scenarios with data uncertainties. Interval-valued PCA methods like Symbolic Covariance PCA (SCPCA) and Complete Information PCA (CIPCA) have been developed to enhance fault detection by incorporating data uncertainties in the PCA model. This paper presents a novel adaptation of SCPCA for detecting incertain sensor faults, marking the first correct implementation of SCPCA for fault detection and isolation (FDI). It aims to compare the performance of the new SCPCA with that of CIPCA, evaluating its reliability and accuracy in detecting sensor faults in a greenhouse prototype system.

In this paper, a sensor fault detection and isolation scheme for nonlinear systems is considered. A nonlinear diffeomorphism is introduced to explore the system structure and a simple filter is presented to ‘transform’ the sensor fault into a pseudo‐actuator fault scenario. A sliding mode observer is designed to reconstruct the sensor fault precisely if the system does not experience any uncertainty, and to estimate the sensor fault when uncertainty exists. The reconstruction and estimation signals are based only on available information and thus can be implemented online. Finally, a mass–spring system is used to illustrate the approach. Copyright © 2007 John Wiley & Sons, Ltd.

Sensor fault detection and isolation of an industrial gas turbine using partial adaptive KPCA

In this paper the problem of fault diagnosis in an aircraft jet engine is investigated by using an intelligent-based methodology. The proposed fault detection and isolation (FDI) scheme is based on the multiple model approach and utilizes autoassociative neural networks (AANNs). This methodology consists of a bank of AANNs and provides a novel integrated solution to the problem of both sensor and component fault detection and isolation even though possibly both engine and sensor faults may occur concurrently. Moreover, the proposed algorithm can be used for sensor data validation and correction as the first step for health monitoring of jet engines. We have also presented a comparison between our proposed approach and another commonly used neural network scheme known as dynamic neural networks to demonstrate the advantages and capabilities of our approach. Various simulations are carried out to demonstrate the performance capabilities of our proposed fault detection and isolation scheme.

This paper addresses the Fault Detection and Isolation (FDI) of the problem of multiple non-concurrent faults on actuator and sensor of quadrotors, which is described by a nonlinear model. To the best of authors' knowledge, this paper provides, for the first time, a solution to the FDI problem for quadrotors affected by both actuator and sensor faults. The literature proposes FDI schemes dedicated only to actuators or only to sensors, indeed. The Non Linear Geometric Approach is based on the mathematical model of the system and allows to determine detection filters sensitive to a selected set of fault and structurally decoupled from the other faults (out of the selected set) thus providing the base for the fault isolation. Several simulation trials have been performed and the analysis of the results proves that the developed diagnostic system represents an effective solution to the problem of multiple actuator and sensor fault detection and isolation for quadrotors.

This paper focuses on Kernel Principal Component Analysis (KPCA) in order to solve the problem of sensor fault detection and identification without linear relationship between sensors. After samples are projected into high-dimensional space, new Principal Component Analysis (PCA) model is established in the kernel principal component eigenvector space. By the contrast with SPE, Hotelling T2 is an appropriate parameter to detect sensor fault because it is more sensitive to sensor failure. The contribution of different sensor to Hotelling T2 is utilized to identify sensor fault for the faulty sensor’s contribution is large than others significantly. Finally, the proposed method is illustrated by the sensors of oil-providing system in the process of aero-engine ground testing. Experiment results show the applicability and effectiveness of the proposed method.

In this paper an approach to design controllers based on principal components analysis (PCA) models is presented. Closed-loop control can be formulated and implemented within the reduced space defined by a PCA model. This PCA controller, results in an integral controller, which can be used as an inferential controller when a measurement of a primary variable is not available. The main contributions of the paper are: a) the incorporation of an adjustable gain on the classical PCA controller; b) the proposal of a set of tuning rules; c) the performance evaluation of this new controller, in nominal operation conditions and in faulty situations. Some experimental results, obtained with the three tank benchmark (European COSY project), are presented.

Nonlinear principal component analysis (NLPCA) is known as a nonlinear generalization of the standard principal component analysis (PCA). Since nonlinear PCA is a non-unique concept, it is discussed, how nonlinear PCA can be defined as a nonlinear feature extraction technique most similar to linear PCA. The nonlinear reduction of a data set from its original dimension to the intrinsic dimension of the data is one aspect, but we also request that the nonlinear features spanning this intrinsic data space are hierarchically arranged similar to the linear features of PCA. Thus, such nonlinear PCA is a powerful pre-processing step. It can be used as nonlinear sphering (whitening) or it can be considered as a smoothing method which removes nonlinear correlations between variables. Nonlinear PCA can be performed by minimizing a hierarchical error function. This error function is applied to the autoencoder which is a multi-layer perceptron used in auto-associative mode to perform the identity mapping.