Selection of the number of digits of histograms for random characteristics of the dynamics of the transport system

Abstract

Abstract The article deals with the experimental studies of the machines, characterized by many random dynamic effects, both from the working bodies, and from the microrelief of the fields where the technological process is carried out, and the roads when the car is moving. The histogram of a dynamic random process, as the main means of systematization, requires optimal selection of the number of discharges to obtain the effects of factors distribution patterns. The selection of the number of discharges for the histogram distributions of experimental data sets is the key to the theoretical compile statistics. The method is illustrated using a histogram comparing a stepped histogram of an empirical distribution and a theoretical law similar to a normal one. The methods of selecting a rational choice for the number of digits is presented, that allows with the required confidence probability, to obtain correspondence of empirical histograms to the theoretical laws of distribution of random variables, for which it is proposed to use the criteria of agreement of Student, Fisher, Cochren and others. Formulas are proposed for determining the number of digits in cases of similarity of the histograms to the theoretical laws of distribution of random Gauss (normal), Rayleigh, exponential, gamma distribution, log-normal, beta distribution and other laws. Numerical testing of the method for the dynamic support reactions of the car during its movement along the microrelief is given.