Study On Several Stochastic Problems In The Diversion And Closure Construction

Taking the randomness as the main research background and the main research topic, three kinds of problems induced by randomness were studied after analyzing the characteristics of each kind of problem. To study these problems, three different methods of stochastic analysis were respectively used due to the characteristics of them. By using these methods, the knowledge of each problem had been deepened from an angle differ from the past, and each problem was somehow resolved. Specifically, the three kinds of problems concerned in this paper are:A. The diversion risk analysis problem when considering the effects of both hydrologic randomness as well as hydraulic randomness; B. The stochastic start problem of the closure block which is synthetically affected by the randomness of the flow fluctuation and the randomness of the river bed location where the block lies; C. The random vibration problem of the sluice gate which is vibrated by fluctuating pressure of flow. Researches on these kinds of problems respectively constitute the chapter3, the chapter4and the chapter5in this paper.1) For the A-kind of problem, a probability density evolution (PDF) method was used so that the research goal of "analyzing the changing process of the diversion risk while obtaining the final risk ratio when considering multiple randomness" can be achieved.In view of that the cofferdam’s upstream level (CUL) can synthetically reflect the effects of both hydrologic and hydraulic randomness, the CUL was taken as the diversion risk carrier, and the probability distribution of CUL at each moment was to be acquired by using the probability density evolution method hoping that the changing process of the diversion risk can be analyzed according to it. Therefore, in chapter3, in accordance with the ideas of PDF method, a state equation about the CUL was offered in the first step based on the rule of reservoir’s storage balance. And then, after analyzing the uncertainties of both hydrology and hydraulic, the random factors were imported by assuming that each stochastic parameter follow Gaussian distributions. According to the state equation, a generalized density evolution equation about CUL as well as the computation procedure of it had then been built and introduced. Meanwhile, by adding absorbing boundary condition, a method to calculate the diversion risk ratio was put forward. At the end of this chapter, certain water-power engineering was taken as a case. By numerically solving the generalized density evolution equation about CUL which contains7random variables, the probability density of CUL under3typical flow levels as well as each diversion risk ratio was successfully acquired. For validation, the ratio was compared with the ratio obtained by using Monte-Carlo method.Through case analysis above, it is found that the probability density of CUL’s distribution as well as its evolution pattern, which is hard to acquire by traditional methods, can be obtained easily by using PDF method. Therefore, by using this method, abundant probabilistic information can be acquired intuitively and in real time, so that the diversion risk analysis based on it can be made. Besides, the validity of calculating the diversion risk ratio by this method was approved by comparing with the result got from Monte-Carlo method.2) For the B-kind of problem, according to a description of blocks’random start phenomenon, the starting probability of a block in many conditions was calculated by using the Monte-Carlo (MC) method.Specifically, the starting probability of a block in a non-obstruct and non-cover circumstance was calculated by applying the MC method at the beginning of chapter4. The only random variable in this case is the instantaneous velocity. In this case, the starting probability calculated by using the MC method was compared with the analytical solution, therefore, the validity of calculating the starting probability by using MC method was approved. And then, the MC method was applied to many other cases in which there were more random variables, and which therefore were more complicated. The cases calculated in this paper included:"obstruct and non-cover" caseN "obstruct and cover" case. Besides, in order to reflect the real circumstance of block’s start, the starting probability was first calculated by using MC method when putting a block in a three-dimensional space, and some characteristics under this computational circumstance were also concluded.Through the calculating above, it can be found that the starting probability of a block which is affected by multiple randomness can be easily and effectively obtained by using Monte-Carlo method. Therefore, the stability of a closure block can be analyzed and judged from the aspect of starting probability, which is to provide basis for related risk analysis.3) For the C-kind of problem, an orthogonal expansion method was used for the stochastic process of water-flow’s fluctuating pressure, by which the stochastic process in frequency domain was transformed into the time domain, and therefore established an excitation model for the research of gate vibration. The validity of the model is tested from the aspect of second order statistics such as sampling ensemble power spectrum and sample mean square error. Furthermore, taking a simple flat plate construction as the force body of gate,252fluctuating load samples generated by the excitation model were loaded on the construction, and its dynamic responses were analyzed by the method of PDF. By using the PDF method, the probability density of displacement at any position of the structure at any time was acquired, and thus a kind of research model named"excitation modeling from time domain to frequency domain-response anlyzing by PDF method"was given.