An improved PCA scheme for sensor FDI: Application to an air quality monitoring network

Abstract

In this paper a sensor fault detection and isolation procedure based on principal component analysis (PCA) is proposed to monitor an air quality monitoring network. The PCA model of the network is optimal with respect to a reconstruction error criterion. The sensor fault detection is carried out in various residual subspaces using a new detection index. For our application, this index improves the performance compared to classical detection index SPE. The reconstruction approach allows, on one hand, to isolate the faulty sensors and, on the other hand, to estimate the fault amplitudes.

Introduction

Many human activities produce primary pollutants like nitrogen oxides (NO₂ and NO) and volatile organic compounds (VOC) which formed in the lower atmosphere, by chemical or photochemical reactions, secondary pollutants like ozone. The acceptable concentrations of these pollutants, harmful for human health and the environment, are defined by European standards. Air quality monitoring networks have the following main missions: the measurement network management (recording of pollutant concentrations and a range of meteorological parameters related to pollution events) and the diffusion of data for permanent information of population and public authorities in reference to norms. To ensure these missions, the validity of the delivered information is essential before any use of measurements, mainly those of pollutants. Moreover, the geographical area monitored by a network being large, fault diagnosis procedure also enables to optimize the maintenance actions. Therefore sensor validation is an issue of great importance for the development of reliable environmental monitoring and management systems. In collaboration with AIRLOR, an air quality monitoring network (France), the aim of this work is to develop a method to perform sensor validation, mainly sensors measuring the concentrations of ozone and nitrogen oxides.

The task for sensor validation is to detect, isolate, and identify faulty sensors by examining the sensor measurements. The sensor validation is usually performed either using “outlier” detection methods which only enable to identify extreme values out of measurement range or manually by an operator. Unfortunately, this latter approach is too subjective and often impractical in real-time due to high process dimensionality which produces a large amount of collected data.

However, the availability of many sensors in the network provides valuable redundancy for fault detection and isolation because some sensor measurements are highly correlated under normal conditions. The analytical redundancy approach consists of checking the consistency between the measurements and the estimates provided by the relationships existing between the various variables of the process [3]. This analysis may lead to detect and isolate the faulty sensors. In most practical situations, fault diagnosis needs to be performed in the presence of disturbances, noise and modelling errors. These mathematical relations between the plant variables generally take two forms [4]. Analytical redundancy methods used explicit input–output model usually derived from system identification. However, in the considered sensor network, this explicit formulation of the redundancy relationships may be difficult to obtain (owing to complexity of the process and high process dimensionality) because it must be guided mainly by performance criteria of the diagnosis system. As an alternative, implicit modelling approaches, which are data-driven techniques (like principal component analysis), are particularly well adapted to reveal linear relationships among the plant variables without formulating them explicitly. Moreover the number of these relations could be determined by minimizing a criterion based on the best reconstruction of the variables with respect to the number of principal components in the PCA model [12]. 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 [4].

The widely used detection index SPE (squared prediction error) indicates how much each sample deviates from the PCA model. Indeed SPE performs fault detection in the the residual space. However, Harkat et al. [6] have shown experimentally on real data that the SPE is sensitive to the modelling errors. Indeed modelling errors could be projected into the residual space which results in residuals with higher variance than the others. Then the SPE will be heavily biased in favour of those equations with the largest residual variance whereas the residuals with the smallest residual variances are most useful for sensor fault diagnosis because they are associated with linear relationships.

After a fault has been detected, it is important to isolate faulty sensor. In the PCA framework, the well known isolation approaches are residual enhancement, contribution plots and variable reconstruction methods [13]. The residual enhancement technique generates structured residuals that selectively respond to subsets of faults [5]. Such residuals may be obtained by algebraic transformation, or by a direct technique that involves a bank of partial PCA models [4]. However, for high dimensionality process, it is not always possible to find the algebraic transformation that enables to obtain the desired isolation properties because these properties are only defined according to the occurrence of the faults in the residuals without taking into account the sensitivities of the residuals to the faults. These comments are also true for the direct method. For fault isolation contribution plots show the contribution of each process variable to the detection statistic [8]. It is assumed that the process variable with the highest contribution is likely the faulty one. However, the contribution plots may not explicitly identify the cause of an abnormal condition [9], and sometimes lead to incorrect conclusions [13]. An alternative approach for fault isolation is the variable reconstruction method proposed by Dunia et al. [2]. It is based on the idea that the influence of fault on the detection index is eliminated when the faulty variable is reconstructed using the PCA model from the variables without defect.

In this paper, a sensor fault detection and isolation procedure based on principal component analysis is proposed to monitor an air quality monitoring network. Taking into account the high redundancy among the process variables, this procedure is based on the variable reconstruction approach in order to design the PCA model of the network, to isolate the faulty sensors and to estimate the fault amplitudes. To improve fault detection, a new fault detection index is proposed which monitors the last principal components (which have smallest variances) in different residual subspaces, starting with a single direction (the last principal direction) and gradually increasing the dimension of the residual to the full residual space. Mathematically, it is difficult to prove that the new index has better fault sensitivity than the SPE because they perform fault detection in different residual spaces where the sensitivities of the residuals to the faults may be different. Therefore experimental data set was used to evaluate the performance of the proposed index. For our application, this index improves the fault detection compared to classical detection index SPE.

First, we present the principle of PCA modelling based on the variable reconstruction approach. Then, after having summarized the principle of sensor fault detection in the PCA framework, we propose our new detection index. For isolation of the faulty sensors, we combine the proposed index and the variable reconstruction principle. In Section 4, we present the application of the proposed method to sensor fault detection and isolation of an air quality monitoring network in Lorraine. Conclusions and future works are finally presented in the last section.