Pseudorandom number generation for computer modeling of actual shapes of spatial bar structures

Abstract

Spatial bar structures consist of a large number of individual elements. During the assembly process these bars are consecutively connected to each other through structural joints. The actual dimensions of the bars differ from the nominal values and vary from one bar to another due to random inaccuracies in their manufacturing. These inaccuracies are regulated by a special system of tolerances, but, anyway, their accumulation during assembly leads to errors in the geometric shape of the bar structure. The errors that arise in the spatial bar structures make it difficult to connect the elements among themselves, and reduce the load-carrying capacity of structures due to the appearance of additional internal forces. Therefore, studies of possible errors in spatial bar structures help to improve their reliability.Studies of possible errors are performed on a computer by simulating the assembly of spatial bar structures using the Monte Carlo method. This method requires the introduction of random variability in the lengths of the bars when assembled into a single spatial structure. In addition, it involves statistical analysis of the results obtained, which is why it is called the statistical computer simulation method. The reliability of computer simulation of the actual shape of the spatial bar structures can be achieved only in the case of using normally distributed random deviations in bar lengths.To obtain normally distributed random deviations in bar lengths, special algorithmic calculators for uniformly distributed random numbers in the interval from 0 to 1 are used. One of these algorithms is investigated in this paper. It should be noted, that the numbers obtained by these algorithms are not strictly random, and therefore they are called pseudorandom. However, their sequence has the properties of randomly obtained numbers. The author also recommends an algorithm for obtaining normally distributed pseudo-random numbers from uniformly distributed pseudo-random numbers.The process of statistical computer simulation of actual geometric shapes of spatial bar structures requires the use of a very large number of pseudo-random numbers, since multiple numerical simulation of structures is being performed. Consequently, the random nature of the pseudo-random numbers used in the simulation must be flawless. To achieve reliable results of computer simulation of the actual geometric shape of spatial bar structures, the author recommends algorithms for obtaining pseudo-random numbers both uniformly distributed from 0 to 1, and normally distributed with statistical mean μ = 0 and standard deviation σ = 1. In order to confirm the quality of the pseudo-random numbers obtained by this algorithm, their sequence was subjected to statistical testing at different regions.From different regions of the large sequence of pseudo-random numbers samples were formed with the aid of the author's computer program, which were then subjected to statistical testing. Based on the test results, histograms of the distribution were plotted, according to which the chi-square criterion was determined. The results of testing allow us to conclude that the presented algorithms for obtaining pseudo-random numbers can be recommended for computer simulation of actual geometric shapes of spatial bar structures. With the aid of these algorithms, reliable results of such studies can be obtained.