Formation of the Convergence Functions of Errors of Input Data of Measurement Systems Computing Components on the Basis of the Finite Automatics Theory

Abstract

This paper presents the results of an investigation into the behavior of the functions of transforming the input data errors for different types of measurement systems’ computing components in order to use their generalized models developed on the basis of the finite automata theory. It is shown that, depending on the kind and value of an input data error transformation function (metrological condition of computing components), the errors of measurement results obtained with the systems’ measuring channels have a determinate character of changes in both static and dynamic regimes of computing components. Determined are the basic dependences of the errors of measurement results upon the input data errors, and upon the types of input data transformation functions; given are the results of their calculation. The investigation results demonstrate a linear character of the dependence of measurement result errors upon the input data errors ΔХ{(tn). In addition, the transformation function calculation f = ΔY{(tn)/ΔХ{(tn) gives its steady state value f = 1,0, i.e. a computing component does not transform the input data error, and does not reverse its sign. For the iterative procedures, the input data errors do not affect the final measurement result, and its accuracy. The measurement error values Δуn depend on the iteration number, and decrease with the increasing number. Of particular interest is the behavior of the function of transforming the input data errors: first, its values are dependent upon the number of iterations; second, f < 1, which clearly shows that the input data errors decrease with the increa­sing number of iterations; and third, the availability of values f = 0 indicates that the function of transforming the input data errors is able to «swallow up» the input data error at the end of the computational procedure. For the linear-chain structures, data have been obtained for a predominantly linear dependence of the measurement error Δs on the input data error Δх, and for the absence of the chain’s transformation function f dependence on the input data errors Δх. For the computing components having a cyclic structure, typi­cal is the same dependence of measurement errors Δt on the input data errors and on the behavior of transformation function ft/x which are specific to the above mentioned computing components that rea­lize iterative procedures. The difference is that the computing components having a cyclic structure realize the so-called (sub)space iteration as opposed to the time iteration specific to the computing components considered. The computing components having a complicated structure (e.g. serial-cyclic, serial-parallel, etc.) demonstrate the dependence of measurement errors on the input data errors which is specific to the linear link that, with such a structure, is determinative for eva­luating the measurement error. Also the function of transforming the input data errors behaves similarly.