# Robust Correlation Monitoring of a Defect at its Origin

When using traditional technologies of signal analysis in solving a monitoring task, getting more or less acceptable results is possible only if the error has a salient character, the analyzed signals are stationary and are subjected to the normal distribution law, the correlation between the noise and the useful signal is equal to zero, and the noise represents white noise. However, even in this case, the errors from the obtained estimates depend on the change of the noise variance, the change of the correlation between the noise and the legitimate signal, or the change of their distribution law. Due to this, the adequacy of the description of many analyzed processes by means of probabilistic-statistical methods is not satisfied and we end up with wrong results in determining the origin of a defect. For these reasons, in the framework of classical theories, many problems of great importance are practically not solved nowadays. Thus, great possibilities are not realized, but if they were, we would solve a great number of problems having tremendous economical and social importance.

For example, eliminating the disadvantages of traditional technologies would allow us to increase the reliability of forecasting earthquakes and other natural disasters, improve disease diagnostics, increase the efficiency of prospecting mineral resources, increase the reliability of forecasting failures at heat and nuclear power stations, forecast failures in drilling, diagnose a technical plane state, allow us to realize adequate mathematical models, and so on. In this connection, among real applications of great potential of considered theories lies the necessity to revise traditional algorithms and create new technologies that provide the robustness of the obtained estimates in fulfilling classical conditions and in case there is a lack of obedience to classical conditions.

In this chapter, on the basis of the technology of noise analysis is a robust technology of correlation analysis. Due to this, the opportunity appears to eliminate serious obstacles by using the enormous potential of this technology for solving the most important tasks of monitoring an error at its origin.

## Keywords

Correlation Function Autocorrelation Function Time Shift Positive Product Stationary Random Process
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