Database Reconciliation in Applied Interval Analysis

Abstract

The article deals with the problem of the reconciliation of observation results, which arises when solving problems of interval analysis of a database. It is found that the values of the set of input variables and the output variable are consistent if the graph of the desired dependence is located at the inner points of the interval hyper-rectangle in each observation. In this case, it is proposed to use special solutions of interval systems of linear algebraic equations (ISLAU) to analyze the data of linear processes. However, in real and model conditions, the specified property of the database is not always fulfilled a priori. In these cases, it is proposed to use the principle of robust estimation: inconsistent observations should either be excluded from the sample or adjusted. This paper presents the results of the study of these methods of matching the used experimental database on model linear processes under conditions when the basic assumptions of interval estimation of dependencies are fulfilled. In addition, variant computational experiments have been investigated to reveal the possibility of increasing the accuracy of interval analysis due to preliminary correction of observations, including the possibility of guaranteed estimation of the sought dependences.