非平稳地震动的广义演变谱模型及在水工抗震中的应用

在平稳地震动过程的功率谱密度函数基础上,发展了一类时-频全非平稳地震动过程的广义演变谱模型。广义演变谱模型可以全面地反映地震动的时域特性和频域特性,如强度非平稳性、持续时间、地震动峰值加速度以及频率非平稳性、场地特性和反应谱。结合我国现行的水工建筑物抗震设计规范,确立了广义演变谱模型的参数取值。同时,应用非平稳随机过程模拟的谱表示-随机函数方法,建立了4类场地条件下的水工建筑物抗震设计所用地震动的代表性时程。最后,通过代表性时程的二阶统计值与目标值的比较,以及代表性时程的平均反应谱与规范反应谱的拟合误差,验证了广义演变谱模型的合理性和优越性。     

地震动过程的概率模型及在重力坝抗震可靠度分析中的应用

在随机过程的正交展开式中,通过构造标准正交随机变量的随机函数形式,建立了非平稳地震动过程的概率模型。在此模型中,利用基本随机变量的离散代表点集,可以直接获取具有给定赋得概率的非平稳地震动过程的代表性样本集合。应用所生成的252条非平稳地震动代表性时程,并考虑地震动峰值加速度均值为0.2 g、0.4 g和0.5 g三种情况,分别对Koyna重力坝进行了地震动力有限元分析。同时,结合概率密度演化方法,给出了坝体结构薄弱部位处的地震反应概率信息和抗震可靠度。     

基于反应谱的土与结构体系均匀调制过程随机响应分析

 利用功率谱与反应谱的转换关系，建立了均匀调制过程输入功率谱密度函数表达式，提出了分析土与结构相互作用体系均匀调制过程的反应谱分析方法。该方法利用新规范中的加速度反应谱作为目标谱，计算与之相对的功率谱并按该功率谱作为地震输入谱进行土与结构相互作用体系随机地震反应分析，研究表明该方法反映了地震动和相互作用体系的动力特性，是进行土与结构相互作用体系随机地震反应分析的一种有效方法。     

多向聚焦波浪作用下直立圆柱受力的实验研究

利用波能聚焦的方法在水池中模拟产生多向聚焦波浪,研究了多向极限大波作用在垂直圆柱上引起的波浪力的特点。实验中研究了不同的波浪参数,如聚焦波幅、谱峰频率、频率宽度和方向分布等多向聚焦波浪对圆柱作用的影响,并将实验结果与二维实验结果进行了比较。结果表明聚焦波浪参数对圆柱作用力具有明显的影响,并且实验结果与二维规则波结果相当,但比二维聚焦波浪实验结果要小。     

随机波浪作用于三桩桩列上的横向力的水动力特征及群桩效应

本文试验研究了随机波浪作用于串列及并列三桩桩列上的横向力的水动力特征及组成桩间的群桩效应，给出了横向力系数与ＫＣ、ＬＤ两参数的相关曲线。在频域内建议了一个新参数一横向力比频率，它能从一个方面较好地概括横向力谱的特征。以孤立桩柱的横向力为基准考查了桩间相互干扰产生的横向力变化，并以群桩横向力系数描述了这一变化规律。针对随机波浪的特点，文中给出了计算各组成桩上横向力及合力的实用化方法。     

随机地震动输入模型研究及渡槽抗震分析

在平稳地震动过程的Kanai-Tajimi模型和Clough-Penzien模型的基础上,分别建立了2种全非平稳地震动加速度过程的广义演变谱模型。根据我国现行的《水工建筑物抗震设计规范》(DL 5073—2000),确定了2种广义演变谱模型的参数值。应用非平稳随机过程模拟的谱表示-随机函数方法,分别生成了基于2种广义演变谱的全非平稳地震动代表性时程集合,并进行了二阶数值统计值的对比分析。同时,通过代表性时程集合的平均反应谱与规范反应谱的拟合比较,发现K-T(Kanai-Tajimi)广义演变谱模型更适用于水工建筑物抗震设计。最后,将K-T广义演变谱模型与概率密度演化理论相结合,对渡槽结构进行了随机地震反应和抗震可靠度分析。     

随机波浪作用于三桩桩列上的横向力的水动力特征及群…

本文试验研究了随机波浪作用于串列及并列三桩桩列上的横向力的水动力特征及桩间的群桩效应，给出了横向力系数与ＫＣ、ＬＤ两参数的相关曲线。在频域内建议了一个新参数一横向力比频率，它能从一个较好地概括横向力谱的特征。     

地震动和结构参数双重随机的重力坝抗滑稳定可靠度分析

地震动和坝体结构参数的随机性均对重力坝抗滑稳定可靠度有重要影响。首先建立了重力坝建基面抗滑稳定极限状态方程,将坝体水平和竖向惯性力随机过程的最大值作为随机变量,根据随机过程参数获得此随机变量的均值和方差,实现了将地震荷载和结构参数双重随机性问题统一到随机变量模式下;然后采用JC法分析了某实际工程重力坝建基面抗滑稳定可靠度,并结合地震发生的概率分析了该重力坝抗滑稳定的失效概率;最后采用正交试验法分析了各结构随机参数对可靠度和失效概率的敏感性。结果表明：本文提出将随机过程最大值作为随机变量的方法可以用于地震动和结构参数双重随机情况下的重力坝抗滑稳定可靠度分析;实例工程混凝土重力坝沿建基面抗滑稳定可靠指标为4.23,失效概率为0.001 17%;坝体材料密度、地基泊松比以及建基面黏聚力系数和摩擦系数对可靠度计算结果影响较为显著。     

自动编码解码器和本征正交分解在倾斜圆盘绕流尾流场中的应用

本征正交分解(Proper Orthogonal Decomposition, POD）是一种传统降维模型，在流体力学中广泛应用。在流场分析中，POD把高维流场数据降维，映射到低维的正交基模态空间，从而分析出流场的主要特征及其对应的基模态系数。随着深度学习的发展，运用卷积神经网络(convolutional neural network, CNN）自动编码解码器在数据降维方面具有的固有优势，可以作为一种降维方法应用在流场降维与数据处理方面。该文以三维倾斜圆盘绕流尾流场中的典型二维截面为例，将圆盘后速度场作为研究对象，分别使用POD和自动编码解码器对流场进行特征提取，并比较了两种方法的优缺点。     

空化荷载功率谱的估计

本文建议了用随机脉冲过程模拟空泡溃灭时作用在某一固体壁上的冲击压力;给出了估计该数学模型中各参数的方法;得到了当频率不是很高时,空化荷载的功率谱接近于白谱的结论;还讨论了通气对荷载谱的影响.     

随机质点瞬时加速度谱的构建方法探讨

基于随机过程理论、应用统计学、随机信号分析理论,通过试验实时量测了5种不同流量条件下,顶冲角度分别为83.87°、54.82°、21.71°、2.24°时,不同断面水深对应的60余组瞬时流速信号,构建了随机质点瞬时流速概率模型,并以此推出了随机质点瞬时加速度谱概率模型及随机波列模拟方法。结果表明:基于赖斯白噪声理论的波动模拟新方法构建随机质点瞬时流速概率模型精准可靠,推求的随机质点瞬时加速度谱真实有效。     

Stochastic simulation of fluid flow in porous media by the complex variable expression method

A stochastic simulation of fluid flow in porous media using a complex variable expression method (SFCM) is presented in this paper. Hydraulic conductivity is considered as a random variable and is then expressed in complex variable form, the real part of which is a deterministic value and the imaginary part is a variable value. The stochastic seepage flow is simulated with the SFCM and is compared with the results calculated with the Monte Carlo stochastic finite element method. In using the Monte Carlo method to simulate the stochastic seepage flow field, the hydraulic conductivity is assumed in three different probability distributions using random sampling method. The obtained seepage flow field is examined through skewness analysis, and the skewed distribution probability density function is given. The head mode value and the head comprehensive standard deviation are used to represent the statistics of calculation results obtained by the Monte Carlo method. The stochastic seepage flow field simulated by the SFCM is confirmed to be similar to that given by the Monte Carlo method from numerical aspects. The range of coefficient of variation of hydraulic conductivity in SFCM is larger than used previously in stochastic seepage flow field simulations, and the computation time is short. The results proved that the SFCM is a convenient calculating method for solving the complex problems.     

STOCHASTIC ANALYSIS OF WATER FLOW IN HETEROGENEOUS MEDIA

A stochastic model for saturated-unsaturated flow is developed based on the combination of the KarhunenLoeve expansion of the input random soil properties with a perturbation method. The saturated hydraulic conductivity ks(x) is assumed to be log-normal random functions, expressed by f(x). f(x) is decomposed as infinite series in a set of orthogonal normal random variables by the Karhunen-Loeve (KL) expansion and the pressure head is expand as polynomial chaos with the same set of orthogonal random variables. With these expansions, the stochastic saturated-unsaturated flow equation and the corresponding initial and boundary conditions are represented by a series of deterministic partial differential equations which can be solved subsequently by a suitable numerical method. Some examples are given to show the reliability and efficiency of the proposed method.     

A Novel Solution for Stochastic Dynamic Game of Water Allocation from a Reservoir Using Collocation Method

In this study, a continuous model of stochastic dynamic game for water allocation from a reservoir system was developed. The continuous random variable of inflow in the state transition function was replaced with a discrete approximant rather than using the mean of the random variable as is done in a continuous model of deterministic dynamic game. As a result, a new solution method was used to solve the stochastic model of game based on collocation method. The collocation method was introduced as an alternative to linear-quadratic (LQ) approximation methods to resolve a dynamic model of game. The collocation method is not limited to the first and second degree approximations, compared to LQ approximation, i.e. Ricatti equations. Furthermore, in spite of LQ related problems, consideration of the stochastic nature of game on the action variables in the collocation method would be possible. The proposed solution method was applied to the real case of reservoir operation, which typically requires considering the effect of uncertainty on decision variables. The results of the solution of the stochastic model of game are compared with the results of a deterministic solution of game, a classical stochastic dynamic programming model (e.g. Bayesian Stochastic Dynamic Programming model, BSDP), and a discrete stochastic dynamic game model (PSDNG). By comparing the results of alternative methods, it is shown that the proposed solution method of stochastic dynamic game is quite capable of providing appropriate reservoir operating policies.     

基于Neumann展开随机有限元的混凝土重力坝结构可靠度分析

针对混凝土重力坝等大体积混凝土结构中,受原材料、混凝土拌合过程以及浇筑施工影响而产生的材料特性空间分布的随机性问题,采用平稳随机场局部平均法离散理论,推导了基于Neumann展开随机有限元的重力坝结构随机响应计算公式,提出了重力坝可靠度计算方法,并开发了相应Matlab计算程序。通过悬臂梁算例对该方法进行验证,并运用该方法研究了随机场离散单元尺寸及相关偏度对结构可靠度的影响,进而计算了典型重力坝坝踵抗拉可靠度。结果表明,相关偏度取值对大坝的可靠度影响显著,可靠度随相关偏度的减小而增大,仅将坝体弹性模量视为单一随机变量时所得可靠度较实际值低;随机场离散单元尺寸应依据相关偏度确定且不宜过大,建议取值不大于相关偏度的1/10～1/8。     

APPLICATION OF MAXIMUM ENTROPY PRINCIPLE METHOD TO THE STUDY OF WAVE CLIMATE STATISTICAL CHARACTERISTICS

The Maximum Entropy Principle (MEP) method is elaborated, and the corresponding probability density evaluation method for the random fluctuation system is introduced, the goal of the article is to find the best fitting method for the wave climate statistical distribution. For the first time, a kind of new maximum entropy probability distribution (MEP distribution) expression is deduced in accordance with the second order moment of a random process. Different from all the fitting methods in the past, the MEP distribution can describe the probability distribution of any random fluctuation system conveniently and reasonably. If the moments of the random signal is limited to the second order, that is, the ratio of the root-mean-square value to the mean value of the random variable is obtained from the random sample, the corresponding MEP distribution can be computed according to the deduced expression in this essay. The concept of the wave climate is introduced here, and the MEP distribution is applied to fit the probability density distributions of the significant wave height and spectral peak period. Take the Mexico Gulf as an example, three stations at different locations, depths and wind wave strengths are chosen in the half-closed gulf,the significant wave height and spectral peak period distributions at each station are fitted with the MEP distribution, the Weibull distribution and the Log-normal distribution respectively, the fitted results are compared with the field observations, the results show that the MEP distribution is the best fitting method, and the Weibull distribution is the worst one when applied to the significant wave height and spectral peak period distributions at different locations, water depths and wind wave strengths in the Gulf. The conclusion shows the feasibility and reasonability of fitting wave climate statistical distributions with the deduced MEP distributions in this essay, and furthermore proves the great potential of MEP method to the study of wave statistical properties.     

考虑介质随机性的结构-地基系统地震反应分析

本文结合近场波动数值模拟的解耦方法和随机有限元方法，提出了一种可考虑介质随机性的时域土-结构体系地震反应分析的解耦方法，此方法的给出为在场地及结构地震反应分析中考虑场地介质及结构参数的随机性的影响提供了较高精度且便于应用的理论方法。本文还以小湾拱坝为例分析了考虑介质随机性时结构的地震反应。     

广义Bayes法在裂隙岩体渗透系数随机反演中的应用

工程中由于存在各种随机因素,采用确定性的渗流分析方法进行渗透系数的反演必然会导致结果的不确定性.本文基于渗流场的随机有限元分析方法,结合变尺度优化算法和广义Bayes法,建立了一种渗透系数的随机反演方法,推导了详细的计算公式.该方法不仅考虑量测水头、渗透系数的随机性,还考虑了边界水头的随机性,不仅可以获得渗透系数的均值反演结果,还可以得到标准差的反演结果.最后将该法应用于重力坝坝基渗流算例分析中,以渗流有限元正分析计算结果作为"假想"的实测点水头值,通过随机反演,同时获得渗透系数均值与标准差的反演结果,将输入信息与反演结果对比分析,验证了渗透系数和标准差反演结果的正确性.     

Random atmospheric pressure at the free surface and microseisms in deep ocean

A general stochastic model of the atmospheric pressure at the ocean surface was proposed, in which the pressure variation was represented by a spectral decomposition through a random process of orthogonal increments. From the basic equations of ideal and incompressible fluid a set of perturbation equations up to second order had been derived and solved. The pressure variation in the flow field had been calculated using the explicit solutions obtained, and which demonstrated a clear relation between the atmospheric pressure and the one at the bottom of deep ocean. It can be seen that there is a part of the pressure variation which is not attenuating with the depth. The result had been compared with those of Longuet-Higgins and Kadota et al. and all previous results are contained in the solution given in this artice. The restriction on the previous works with regard to the probability law has been removed, and all conclusions are deduced without specific assumptions. The flexibility of the proposed model allows for further generalization and extension in the physical aspects and statistical treatment.