导截流工程中的几个随机性问题的研究
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摘要
本文以随机性为大的研究背景和研究主题,针对施工导截流过程中的三个由随机性所引发的工程问题,在分析了各问题自身特点的基础上,分别应用了三种不同的随机性分析方法,使各问题从与以往不同的角度得到了新的认识和一定程度上的解决。具体地,本文所分析的三个随机性问题分别为：A.受水文和水力随机性共同影响时的导流风险分析问题；B.由水流脉动随机性以及块体在床面所处位置随机性所产生的,截流块体的随机性起动问题；C.在脉动水压作用下的闸门的随机振动问题。对以上三个问题的研究,分别构成了本论文的第三、四、五章。
1)对于随机性问题A,本文应用了一种概率密度演化的方法,以达到“既能对受多重随机因素影响时的风险演化过程进行分析,又能获取最终的导流风险率”的研究目的。
鉴于上游围堰的堰前水位能综合地体现出水文和水力随机性的共同影响,因此,本文以堰前水位作为导流风险的载体,试图采用概率密度演化方法对堰前水位分布在各时刻的概率密度进行求解,以期能据此对导流风险的演化过程进行分析。为此,在第三章中,基于概率密度演化方法的研究思路,首先根据水库蓄量平衡关系,为该方法的应用提供了一个关于堰前水位的状态方程。然后,在分析了水文和水力不确定性的基础上,通过对各随机参数进行以设计值为均值的正态分布假设,向状态方程中引入了水文和水力随机性。根据此状态方程,本章随后建立了针对堰前水位的广义概率密度演化方程,并介绍了基于此方程的对堰前水位分布的概率密度进行求解的计算流程。同时,通过在该计算流程中添加吸收壁边界条件,提出了导流风险率的计算方法。本章最后,以某水电工程为例,通过数值求解带有7个随机变量的广义概率密度演化方程,成功地获取了3个典型流量水平下的堰前水位分布在计算时段内各时刻的概率密度,并对各流量水平下的导流风险率进行了计算,为了对比验证,该风险率还与由Monte-Carlo法所得到的风险率进行了比较。
通过以上对实例的分析,可以发现,应用概率密度演化方法能够方便地获取由传统方法所不易得到的堰前水位分布的概率密度及其随时间的变化情况,可以直观、实时地从蕴含有丰富概率信息的该变化过程中,对导流风险进行分析与判断。另外,通过与Monte-Carlo法的计算结果进行对比,说明了基于概率密度演化方法还可以对导流风险率进行有效的求取。
2)对于随机性问题B,本文根据对块体随机性起动现象的一种描述,应用Monte-Carlo法,对处于多种情况下的截流块体的起动概率进行了计算。
具体地,在第四章中,首先仅以瞬时流速作为随机参数,对处于无阻挡无遮掩这一简单情况下的截流块体的起动概率用Monte-Carlo法进行了计算,并通过与该情况下的理论解进行对比,说明了Monte-Carlo法在计算块体起动概率方面的可行性。然后,对块体处于更复杂、受更多随机性因素影响下的情况,仍用Monte-Carlo法计算了其起动概率。此处,这些情况包括：有阻挡无遮掩以及有阻挡有遮掩的情况。另外,为能更加合理地反映出截流块体的实际起动情况,本章还首次应用Monte-Carlo法对块体在三维空间内的起动概率进行了计算,得到了块体在该情况下的一些起动规律,并与在二维情况下的相同计算进行了比较。
通过以上的一系列计算,显示了Monte-Carlo法可以方便且有效地求取受多重随机性因素影响的截流块体的起动概率,使截流块体在动水作用下的起动难度(或稳定性)可以从概率的层面上进行量化,为截流块体的选取及其带来的相关的风险估计提供了依据。
3)对于随机性问题C,本文应用正交展开的方法,使脉动水压从频域内的随机过程转化为时域内的随机过程,从而为由脉动水压所引起的闸门振动问题建立了激励模型。通过与目标随机过程在均值、方差以及功率谱层面的比较,验证了该激励模型的准确性。进一步地,本章以一个简单的平板结构作为闸门受力体,将由激励模型所生成的252条激励样本作用于该结构,并通过概率密度演化方法对该结构进行了动力响应分析,得到了结构任意位置处的振动位移量在计算时段内任意时刻的概率分布情况,为闸门振动研究提供了一种“频域到时域的激励建模——概率密度演化方法的响应分析”的研究模式。
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.
1)对于随机性问题A,本文应用了一种概率密度演化的方法,以达到“既能对受多重随机因素影响时的风险演化过程进行分析,又能获取最终的导流风险率”的研究目的。
鉴于上游围堰的堰前水位能综合地体现出水文和水力随机性的共同影响,因此,本文以堰前水位作为导流风险的载体,试图采用概率密度演化方法对堰前水位分布在各时刻的概率密度进行求解,以期能据此对导流风险的演化过程进行分析。为此,在第三章中,基于概率密度演化方法的研究思路,首先根据水库蓄量平衡关系,为该方法的应用提供了一个关于堰前水位的状态方程。然后,在分析了水文和水力不确定性的基础上,通过对各随机参数进行以设计值为均值的正态分布假设,向状态方程中引入了水文和水力随机性。根据此状态方程,本章随后建立了针对堰前水位的广义概率密度演化方程,并介绍了基于此方程的对堰前水位分布的概率密度进行求解的计算流程。同时,通过在该计算流程中添加吸收壁边界条件,提出了导流风险率的计算方法。本章最后,以某水电工程为例,通过数值求解带有7个随机变量的广义概率密度演化方程,成功地获取了3个典型流量水平下的堰前水位分布在计算时段内各时刻的概率密度,并对各流量水平下的导流风险率进行了计算,为了对比验证,该风险率还与由Monte-Carlo法所得到的风险率进行了比较。
通过以上对实例的分析,可以发现,应用概率密度演化方法能够方便地获取由传统方法所不易得到的堰前水位分布的概率密度及其随时间的变化情况,可以直观、实时地从蕴含有丰富概率信息的该变化过程中,对导流风险进行分析与判断。另外,通过与Monte-Carlo法的计算结果进行对比,说明了基于概率密度演化方法还可以对导流风险率进行有效的求取。
2)对于随机性问题B,本文根据对块体随机性起动现象的一种描述,应用Monte-Carlo法,对处于多种情况下的截流块体的起动概率进行了计算。
具体地,在第四章中,首先仅以瞬时流速作为随机参数,对处于无阻挡无遮掩这一简单情况下的截流块体的起动概率用Monte-Carlo法进行了计算,并通过与该情况下的理论解进行对比,说明了Monte-Carlo法在计算块体起动概率方面的可行性。然后,对块体处于更复杂、受更多随机性因素影响下的情况,仍用Monte-Carlo法计算了其起动概率。此处,这些情况包括：有阻挡无遮掩以及有阻挡有遮掩的情况。另外,为能更加合理地反映出截流块体的实际起动情况,本章还首次应用Monte-Carlo法对块体在三维空间内的起动概率进行了计算,得到了块体在该情况下的一些起动规律,并与在二维情况下的相同计算进行了比较。
通过以上的一系列计算,显示了Monte-Carlo法可以方便且有效地求取受多重随机性因素影响的截流块体的起动概率,使截流块体在动水作用下的起动难度(或稳定性)可以从概率的层面上进行量化,为截流块体的选取及其带来的相关的风险估计提供了依据。
3)对于随机性问题C,本文应用正交展开的方法,使脉动水压从频域内的随机过程转化为时域内的随机过程,从而为由脉动水压所引起的闸门振动问题建立了激励模型。通过与目标随机过程在均值、方差以及功率谱层面的比较,验证了该激励模型的准确性。进一步地,本章以一个简单的平板结构作为闸门受力体,将由激励模型所生成的252条激励样本作用于该结构,并通过概率密度演化方法对该结构进行了动力响应分析,得到了结构任意位置处的振动位移量在计算时段内任意时刻的概率分布情况,为闸门振动研究提供了一种“频域到时域的激励建模——概率密度演化方法的响应分析”的研究模式。
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.
引文
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