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The paper presents new approaches to determination and validation of critical measurements and critical sets. These approaches are based on the use of test equations for the problems of state estimation. The concept of test equations is outlined, the methods for a priori data analysis using test equations are presented, the possible application of dynamic algorithms and artificial neural network (ANN) to search for bad data is considered. The idea of neural network validation is based on the capability of the learned ANN to restore an ideal image by its distorted copy. The efficiency of the suggested approaches has been confirmed by the results of experimental studies.