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1. Introduction
Sensors play an important role in monitoring and controlling systems. They are the devices from which the majority of information about a system is acquired. Once sensor performance degradation, fault or failure occurs, the abnormal phenomenon will appear sensor data. Such faults have the potential to generate untrustworthy data and, therefore, can have serious financial implications. Soft faults are those which are usually hard to detect and diagnose when compared to mutational faults. Consequently, soft faults are more likely to lead to financial loss. Therefore, to ensure that sensors operate as efficiently as possible, soft fault diagnosis for sensors is very important.
Taking advantage of redundant information from sensors to undertake fault diagnosis forms is the basic principle of fault diagnosis of sensors. A method based on mechanism model or data-driven model could be used to obtain the redundant outputs of sensor. The method based on the mechanism model is mainly applied to the linear system and the linear model of non-linear system linearised at the operating point; however, the accurate mechanism models can hardly be established by this method for these non-linear systems with relatively stronger complexity (Wei et al. , 2010; Mid, 2011). The method based on the data-driven model has a more extensive application for its better applicability to the modelling of complicated non-linear system and the fault diagnosis of sensor. The prediction model can be established by using the latter method. The redundant outputs of sensor obtained through the prediction model would be contrasted with the actual sensor exports to diagnose the faults (Sourander et al. , 2009; Yu, 2011).
The methods to diagnose fault in sensors include hardware redundancy, software redundancy and hybrid redundancy (Zhang and Yang, 2001; Zhang et al. , 2009). Hybrid redundancy integrates hardware redundancy and software redundancy and, therefore, has specific advantages. Many papers have examined in this [hybrid redundancy] area in detail, such as dual hardware redundancy with double observers (Stuckenberg, 1985), dual hardware redundancy with double Kalman filters (Cunningham and Poyneer, 1977) and a group of sensors with Kalman filters (Clark, 1979; Chen and Zhang, 1990).
Tracking differentiators have been shown to use an input signal to determine accurately a filtered signal and an approximate differential of the input signal (between specific...