Approximation-evaluation tests for a stress-strain state of deformable solids

Quasi-Deterministic Processes with Monotonic Trajectories and Unsupervised Machine Learning

“…. , y k , holds δ lq (k 0 ) > 0, then we can say that near the point y k the character of the increase y t changed from linear to parabolic [24,25], i.e., under the condition δ lq (k 0 ) > 0 the null hypothesis H 0 is rejected, the alternative hypothesis H 1 is accepted, and the Markov stopping time for the parabolic approximation-estimation test will be…”

“…To test the statistical hypotheses H 0 and H 1 , we use the approximation-estimation tests [24,25]. We will construct quadratic forms of approximation-estimation tests as the difference between the quadratic error of the linear approximation of the numerical sequence y t and the quadratic error of the nonlinear approximation of y t in various classes of nonlinear functions.…”

“…Ordered pairs (i, y i ) are the knots of approximation for the numerical sequence y t where i is a natural argument, y i is the corresponding value of the sequence y t . We will be called (i, y i ) the natural knot of approximation [24,25].…”

“…Thus, for three different sets of knots y 0 , y 1 , y 2 and the critical value at the point y 3 , were received different the ratio of the first order finite differences. Consequently, the comparison of finite differences of elements of the sequence y t cannot be used to obtain a criterion determining the point of change of character of increase for the y t [25].…”

“…Table 1 (adapted from [25]) shows the results of the tangential test for the approximation-estimation tests by three, four, five, six, and seven approximation knots ; the values of the δ 2 were calculated by Formulas ( 30)- (38). It is important to note that the character of an increase in any variable does not depend on the scale.…”