Construction of passport static characteristics of the system using the interval approach

Abstract

An approach to constructing direct and inverse static characteristics of the system is considered proceeding from the experimental data obtained using a traditional «black box» concept, whereby the results of the experiment containing measured input and output values are used which, in practice, are determined with errors. The presence of various sources and trigger interference factors leads to a significant distortion of the error estimates and the formation of an inadequate conversion response. A crucially different character of the impact on the measurement results can be observed taking into account the type and sources of errors upon formation of the static characteristics and developing a model of noise arising upon measurements in actual operation conditions and during the experiment. However, analysis of the existing method based on a statistical approach and used for determining the error of the object model revealed a number of shortcomings: focusing mainly on the random components of errors and complexity of taking into account non-statistical information, including a priori information about the systematic errors, round-off and sampling errors, and the errors of the measurement system used in upon developing a model of the system. The statistical approach does not provide theoretical substantiation of the solution of the problem of the inverse static characteristic of the system which is relevant for many applications. Moreover, the fact that the interference models under experimental and real operation conditions have different sources and are generated by different factors is ignored in the framework of the statistical approach, which can lead to a significant distortion of the error estimates of the system model and to the formation of an inadequate direct and inverse transformation characteristics. We propose to eliminate the aforementioned shortcomings using the interval approach. The problem of developing a new method for constructing the passport characteristic of the inverse static function of a system is solved on the basis of a two-stage procedure of the experimental design. A new method based on the interval approach has been developed in which the problem of constructing the inverse static characteristic of the system and the problem of determining the error of the measurement system are solved separately using different types of active experiment. The boundaries of the uncertainty interval of the measurement system are defined in the general case by spline-functions. A concept of the operating range of the system, which does not coincide with the range of changes of the measured value in an active experiment, is introduced. It is shown that outside the operating range the system error sharply increases and becomes asymmetric with respect to the inverse static characteristic.