Fault detection and identification using fuzzy wavelets

A new intelligent methodology for the Fault Detection and Identification (FDI) in complex systems is proposed by combining Fuzzy Logic tools and Wavelet Transform Techniques. This arrangement is called Fuzzy Wavelet Analysis (FWA) and provides the ability to analyze the fault signatures in time (or space)/frequency localized manner with the ability to accommodate uncertainty. Development of FWA as an intelligent paradigm provides on-line adaptability and FDI process improvement through learning. Both on-line and off-line learning aim at maximizing the performance. The off-line learning is achieved by maximizing the detectability and identifiability measures. These measures can be calculated from analytic formulas and are the primary constraints for designing knowledge-based systems. The on-line learning process involves parametric adjustment of the fuzzification process so as to minimize the sensitivity to noise. A new similarity measure is therefore defined which has a nonlinear adjustment of the input sensitivity.; The FWA can be applied in principle to only a 1-D data stream. However, it can be applied to 2-D images with a specialized scanning technique known as fractal scanning. This scanning technique scans the 2-D image and transforms it into a 1-D data stream, but unlike conventional scanning techniques, it retains the neighborhood relationship of the 2-D data. This is achieved by scanning a small region of the image completely before moving to the next region. This technique uses self similar fractal shaped scanning patterns which can be scaled down to the size of the smallest fault feature.; This research provides a new perspective to view the problem of FDI by introducing new processing and analytic tools like fractal scanning and fuzzy wavelet analysis. It also introduces measures of self assessment like detectability and identifiability indices. A new method of training an expert system is also developed.; Feasibility of FWA is demonstrated by applying these tools to such application examples as failures analysis of a jet engine and inspection of woven textile fabrics. The test results in both of these applications have shown that FWA provides a robust and efficient means of FDI.