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This paper presents some approaches on the new applications in fault estimation, detection and diagnosis emerged from three powerful concepts: theory of distributed parameter systems, applied to large and complex physical processes, artificial intelligence, with its tool adaptive-network-based fuzzy inference and the intelligent wireless ad-hoc sensor networks. Sensor networks have large and successful applications in the real world. They may be placed in the areas of distributed parameter systems, to be seen as a "distributed measuring sensor" for the physical variables. Using sensor networks multivariable estimation techniques may be applied in distributed parameter systems. Fault detection and diagnosis in distributed parameter systems become more easily and more performing using these concepts. The paper presents some applications in fault detection and diagnosis based on the adaptive-network-based fuzzy inference, allows treatment of large and complex systems with many variables by learning and extrapolation.