Operational methods in problems of identification of experimental trend functions
The systems of technical diagnosis of industrial and power plants are intended both for monitoring their current state and identifying the trend functions that are necessary to forecast slowly developing failures. As usual, by trend function is meant the time \((t)\) profile of a diagnostic attribute \(x.\) In the one-dimensional case under consideration, the experimental trend functions are presented through pairs \(x_i\), and \(t_i\), the points corresponding to them being usually widely scattered over the plane \((x,t).\) Smoothing of the set \(x_i,\) \(t_i\) by the well-known operations of integration or averaging enables to obtain more concentrated points in the corresponding planes such as (integral, time), (integral, function), etc., which can facilitate the identification of smoothed relationships from which the required trend functions \(x(t)\) are established. The present paper proposes some generalizations of the well-known smoothing operations and new methods of identification of the trend \(x(t)\) which are based on some integral transformation. These operations can also be used to solve problems of technical diagnosis.
scientific article; zbMATH DE number 1283822