The empirical construction of mathematical models of measuring and optimal computing transducers

Abstract

It follows from the theory of measuring-computing systems [1] that the requirements for a measuring transducer (MT) that converts an external influence into an electric signal in order to obtain the maximal interpretation accuracy are significantly different depending on how it is going to function: by itself or as a part of a measuring-computing transducer (MCT) as its component. In the first case, the maximal accuracy has to be provided by the MT and it is bounded by physical laws. In the second case, it has to be provided by the MCT, which is considered to be a measuring device for the same or a different purpose, in particular, that of the “perfect” device for a researcher. The accuracy of an MCT is determined by both the mathematical properties of its model and the “quality” of the algorithm that converts MT output into a form determined by the measurement objective that is achieved by a computing transducer (CT) as a component of the MCT. For any specific mathematical model of the MCT this algorithm has to provide the maximal quality of the MCT. An MT that is optimal for that purpose can often be different from an MT that is optimal by itself. As a rule, the exact mathematical model of the MT and, hence, the algorithm of the CT that is optimal for it, are not known to the researcher, but he can perform test measurements of known input signals that simulate the interaction of the MT and the measured object using the MT. The aim of this article is to use test measurements to synthesize both the response of an MT with an unknown model and the optimal interpretation of the measurement result, i.е., the output signal of the MCT. It is shown that even without knowing the exact MT model, but with the ability to perform test measurements on the same MT a researcher is able to synthesize both the MT response and the results of the interpretation of measurement results, both in an optimal way.