Comparison of fault detection techniques

Haar Wave-Net (HWN) and Projection Pursuit Regression (PPR) are two useful modeling tools for pattern classification. In this study, the two methodologies are compared with respect to the problem of misclassification close to class boundaries with sparse training data. A variety of examples were specifically tailored to elucidate their respective properties. It is observed that PPR locates the class boundaries at the midline of two classes of training data, which is a logical choice for the class boundary location, in the absence of sufficient information. For HWN, both the initial positioning of receptive fields and the density of training data near the class boundary may have great impact on the definition of the class boundary. Additionally, PPR and HWN are also compared to the Backpropagation Network (BPN), a standard technique for fault detection, with respect to their sensitivity to noise. The orthonormal and localized properties of the Haar basis functions enable a HWN to limit the noise effect within its local receptive fields. BPN propagates the noise effect throughout the input space. PPR provides a good tradeoff between reasonable generalization and noise localization. The fault diagnosis problem is investigated in a CSTR process, at both steady state and dynamic conditions. It is found that, for the dynamic case, the misclassification close to the class boundary is often due to lack of system observability.