Solving the problem of analytical description of static characteristics in conditions of interval uncertainty

Abstract

It is shown that the description of the error corridor of the model, obtained under the assumption that the inaccuracy of the source data is specified in the interval form, in contrast to the statistical approach, is given by four functions instead of two and can be represented by linear spline functions, where the first pair of functions describes the error corridor inside the range of change of the input variable in the experiment, and the second pair — outside this range. The problem of analyzing and developing of the methods for approximation of the static characteristics represented as linear splines by smooth functions of the second order is solved. It is also shown that second-order polynomials and implicit functions in the form of conic sections can be successfully used for approximation of linear splines which define the error corridor. A computational experiment was designed within which the criteria determining the accuracy of the solution of the approximation problem were formulated and the areas for placing experimental points on the boundaries of the interval corridor (on the basis of which the coefficients of the approximating functions were calculated) were determined. The developed experiment minimizes the number of calculation points when the specified accuracy of the solution of the approximation problem is ensured. It is shown that when a quadratic function is used for approximation of the boundaries of the interval corridor, the calculations can be carried out for only one of the boundaries with subsequent simplest calculation of the parameters of the other boundary which almost halves the computations. Approximation of the linear splines that define the uncertainty corridor requires the use of no more than 30 experimental points. Comparison of the results showed a slight difference in the criterion values when polynomial or implicit function are used for approximation with a slight advantage of the approximation by a polynomial function.