Fault diagnosis is very important for modern production technology and has received increasing theoretical and practical attention during the last few years. This paper presents a model‐based diagnostic method for industrial systems. An online, real‐time, deep knowledge based fault detection system has been developed by combining different development environments and tools. The system diagnoses, predicts and compensates faults by coupling symbolic and numerical data in a new environment suitable for the interaction of different sources of knowledge and has been successfully implemented and tested on a real hydraulic system.

A method is given for obtaining series expansions for the coefficients in the double series for the autocorrelation function of the output of a nonlinearity with a signal plus noise as input. Two series are obtained, one in powers and the other in inverse powers of the signal-to-noise ratio. The terms in the series are products of two functions. In these series one function depends on the moments of the signal (or noise) and the other on characteristics of the nonlinearity and the noise (or signal). Differential recursion relationships that simplify evaluation of the nonlinearity-dependent functions are given.