Abstract
When performing calculations to assess reliability of hydraulic structures of cascades of hydroschemes on the basis of probabilistic methods, the necessity to simulate random natural-climatic phenomena producing loads and effects on hydraulic structures arises. In particular, statistical series of random quantities of such important natural-climatic phenomena are considered: annual lowest average monthly temperatures, annual maximal amplitudes of average monthly temperatures. Each of the enumerated natural-climatic phenomena is characterized by presence of close correlation connections between random quantities when passing from one hydroscheme of the cascade to another. The necessity to consider correlation connections requires construction (simulation) of joint distribution law of random quantities system. The purpose of the work is simulation of joint distribution law of system of random variables that do not satisfy the normal distributions, taking into account correlation connections between random variables when passing from one hydroscheme of the cascade to another. Methods of the theory of correlation and methods of mathematical statistics with the use of software package MathCad were used in the course of the investigation. Simulation of joint law of distribution of system of random variables that do not satisfy normal distributions, taking into account correlation connections between random variables when passing from one hydroscheme of the cascade to another, and also assessment of accuracy of results, that were performed, have shown advantages of this approach from the viewpoint of accuracy of results obtained by different procedures. The results can be used in probabilistic calculations of reliability of hydraulic structures and cascades of hydroschemes.
Highlights
Assessment of safety and reliability of hydraulic structures on the basis of probabilistic methods is regulated by normative documents [1,2,3,4,5,6,7,8,9]
During performing calculations on assessment of reliability of hydraulic structures of hydroscheme cascades, necessity to simulate distribution laws of random natural-climatic phenomena that create loads and effects on hydraulic structures arises. In this investigation the approaches that allow simulating a joint law of distribution of system of random quantities that do not satisfy the normal distributions in the closed form, and obtaining the conditional distribution laws of random quantities of natural-climatic phenomena taking into account correlation connections, are realized
Statistic series of random quantities of such important natural-climatic phenomena, obtained by direct measurements in dam sites of hydroschemes of the Dnieper cascade of hydroelectric stations: annual maximal flood discharges Qmax,i, annual maximal ice thickness hmax,i, annual lowest average monthly temperatures tmin,i, annual maximal amplitudes of average monthly temperatures 'tmin,i were investigated by methods of probability theory and mathematical statistics with substantiation of the proposed distribution laws in investigations [10,11,12]
Summary
Assessment of safety and reliability of hydraulic structures on the basis of probabilistic methods is regulated by normative documents [1,2,3,4,5,6,7,8,9]. During performing calculations on assessment of reliability of hydraulic structures of hydroscheme cascades, necessity to simulate distribution laws of random natural-climatic phenomena that create loads and effects on hydraulic structures arises. In this investigation the approaches that allow simulating a joint law of distribution of system of random quantities that do not satisfy the normal distributions in the closed form, and obtaining the conditional distribution laws of random quantities of natural-climatic phenomena taking into account correlation connections, are realized. The necessity to take into account correlation connections between natural-climatic phenomena requires construction (simulation) of joint distribution law of random quantities system, which is realized in investigation [11]. Multidimensional distribution laws of random variables simulated with the use of the copula theory are presented in investigations [29, 32,33,34,35,36,37,38,39], in particular, hydrologic mode of hydrosystem in flood period is simulated in investigation [32]
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