Neural Network Algorithm for Parametric Identification of Distribution Laws for Measurement Samples Using the Kolmogorov Goodness-of-Fit Criterion

The purpose of the study is to monitor the technical condition of ships and water transport facilities during operation and repair, as well as to manage product quality under the digital transformation of production and services. For this purpose, an algorithm has been synthesized for automating the parametric identification of distribution laws for samples of measured time-to-failure data of components and instruments of ship systems using the Kolmogorov goodness-of-fit criterion, numerical methods of computer simulation and differentiation, and neural-network regression of the obtained probability density. The algorithm is applicable in automated control systems and softwareand- measurement complexes on ships and at water transport facilities when processing the results of observations, measurements, inspection, and product testing. In addition, the proposed algorithm can be used in cases where the processing of experimental data requires solving problems related to the analysis of the statistical properties of distributions that do not always fit within the theory of normal processes, for which parametric statistical tests, such as Student’s and Fisher’s tests, and nonparametric tests, such as the Kolmogorov, Cramér–von Mises–Smirnov, Anderson–Darling, Cooper, and other tests, have been developed. Unlike parametric tests, which are based on the assumption that the statistic follows a normal (Gaussian) distribution, nonparametric tests do not require the assumption of a known sample distribution law and are designed to compare an empirical distribution with a theoretical distribution, for example, a normal distribution, or with another empirical distribution. To implement these tests, null and alternative hypotheses are formulated; to verify them, probabilistic models of empirical and hypothetical distribution functions are constructed using analytical and numerical methods of statistical analysis, and the discrepancy between them is determined. Taking into account the high accuracy requirements that analytical methods cannot satisfy, an algorithm has been developed and implemented as a software program for identifying, by a confidence indicator, whether the tested distribution conforms to the normal distribution according to the Kolmogorov goodness-of-fit criterion, with estimation of its parameters, namely the mean and standard deviation, using a feedforward neural network with feedback connections, which provides fast training and acceptable accuracy. The results of computer and numerical simulation of the neural-network algorithm for parametric identification confirm the adequacy of the tested probabilistic model to the specified normal distribution.

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