Operational methods in problems of identification of experimental trend functions
type: Item
instance of: scholarly article
title: Operational methods in problems of identification of experimental trend functions
zbMATH Open document ID: 0922.93048
author: L. G. Sobolev
published in: Automation and Remote Control
publication date: 1999-09-13T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 93E14
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 44A35
Mathematics Subject Classification ID: 44A45
zbMATH DE Number: 1283822
zbMATH Keywords: system identification
zbMATH Keywords: operational calculus
zbMATH Keywords: integral transforms
zbMATH Keywords: experimental trend function
zbMATH Keywords: smoothing operations
zbMATH Keywords: technical diagnosis
reviewed by: Anatoliy Swishchuk
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1283822