Probability of random events of inspection and repair and maintaining reliability of structures

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The curious events leading to the theory of shock waves

We review the history of the development of the modern theory of shock waves. Several attempts at an early-theory quickly collapsed for lack of foundations in mathematics and thermodynamics. It is not until the works of Rankine and later Hugoniot that a full theory is established. Rankine is the first to show that within the shock a non-adiabatic process must occur. Hugoniot showed that in the absence of viscosity and heat conduction conservation of energy implies conservation of entropy in smooth regions and a jump in entropy across a shock. Even after the theory is fully developed, old notions continue to pervade the literature well into the early part of the twentieth century. Natura non facit saltus. Lucretius Caro (98 BC-55 BC). I will tell you these stories, not in the fashion of those textbook writers who manufacture historical notices so as to bear out their own views of how science ought have developed, but instead as they really did occur. Clifford Truesdell (1919-2000). This paper is based on the invited lecture that was presented at the 17th International Shock Interaction Symposium (ISIS17), Rome, Italy, 4–8 September 2006.     

Calendar of events

Experimental Techniques -     

Calendar of events

Experimental Techniques -     

Calendar of events

Experimental Techniques -     

Reliability Index and Failure Probability

Abstract

Numerical algorithms for the solution of nonlinear algebraic equation systems are discussed. Special application to the mechanism and multibody system kinematic analysis, as well as to the problems of constraint stabilization during dynamics simulation is regarded. Special attention is paid to the approaches of a separate solution of the differential equations and constraint stabilization. Numerical procedures that are effective additions to the well-known algorithms based on the Newton-Raphson method are presented. The problems of loss of precision and achievement of large unreal increments of the varying parameters are discussed. The traditional Newton-Raphson method is modified by applying a step reduction procedure that is developed numerically for the symbolic form of kinematic and dynamic equations. An optimization method for stabilization of constraints using the mass matrix of dynamic equations is suggested. According to the objective function defined the stabilization procedure provides minimal deviations of the parameters and their velocities with respect to the solution of the differential equations. No generalized coordinate partitioning is required either for solution of the dynamic equations or for stabilization of the constraints. Several examples of kinematic analysis of single and four contour plane mechanisms and constraint stabilization are solved, and the results are compared. The advantages of the algorithms developed are tested with a high-degree of initial deviation from the real solution. It is also shown that the step correction algorithm could provide admissible solution even when, in many cases, the classical approaches are not reliable. An example of the direct and inverse kinematic problem solutions of the four-degrees-of-freedom spatial platform is presented.     

随机过程的概率密度函数估计

从概率密度演化理论的基本思想出发,发展了随机过程一维概率密度函数估计的新方法。以独立获取的各随机过程样本作为随机过程的代表性时程,通过求解广义密度演化方程,获得了随机过程的一维概率密度函数及其均值与标准差过程。以脉动风速随机过程的统计为例,进行了风速时程的概率密度函数估计,为认识随机过程的概率结构提供了新的可能。     

PROBABILITY DISTRIBUTION FUNCTION OF NEAR-WALL TURBULENT VELOCITY FLUCTUATIONS

IntroductionNear-wall turbulence plays an important role in environmental engineering due to itsgreat impact on the transport of pollutants,nutrients,sediments,etc.Therefore,peoplehave long been studying the wall-bounded turbulence[1,2],in which the proba…     

冲击载荷作用下加筋板架破坏概率分析

取导弹战斗部初始撞击速度、战斗部质量、加筋板架材料的弹性模量和极限强度作为随机变量;采用对较小的样本数量进行拟合的方法,用产生随机数程序得到50组随机变量的初始值,利用ANSYS/LS-DYNA有限元程序进行仿真计算,得到导弹战斗部击穿加筋板架后的末速度值;验证击穿板架后战斗部的末速度是否服从正态分布,若不服从正态分布则采用最大熵法拟合击穿板架后的末速度的分布函数;考虑战斗部撞击点和板架加强筋的相对位置关系,采用速度准则,利用蒙特卡罗方法模拟得到当战斗部入射角度分别为0°、30°、45°时,击穿单层和双层加筋板架的概率。     

非线性随机动力系统的概率密度演化分析

阐述了基于概率密度演化理论进行多自由度结构非线性随机动力反应分析的基本思想.采用随机过程的正交分解或物理系统建模的思想,实现随机激励的随机函数表述.对由此获得的随机状态方程采用概率密度演化理论求解,可以获得随机动力系统反应的概率密度函数及其演化.以某剪切型框架结构的非线性随机地震反应分析为例,说明了所发展方法的可行性和有效性.     

Probability distribution functions for small scale turbulence

The exact expression for the probability distribution function (pdf),P(Δu_r), of a velocity difference Δu_r, over a distancer, in incompressible fluid turbulence, obtained from the Navier-Stokes equations, is used as a basis for deriving approximate profiles forP(Δu_r). These approximate forms are deduced from an approximate factorisation of the underlying functional probability distribution of the flow field, in which the individual factors capture different physical effects.P(Δu_r) is represented as the integral, with respect to the spatially averaged dissipation rateε _r, of the product of the conditionalpdf of Δu_r givenε _r, and thepdf ofε _r. The approximation yields the latter as a log-Poissonpdf, while the conditionalpdf is found to be a Gaussian for a transverse increment, and the product of a Gaussian and a cubic polynomial for a longitudinal increment. This approximation is equivalent to the refined similarity hypothesis coupled with the log-Poisson distribution, and it possesses the characteristic features ofP(Δu_r), including symmetric profiles for transverse increments, asymmetric profiles for longitudinal increments, and the development of pronounced non-Gaussian features at small separations. The associated scaling exponents for longitudinal and transverse structure functions are shown to be identical, in this approximation, and to assume the log-Poisson form.     

Probability analysis of random plane waves in gas dynamics

A statistical analysis is made of random nonlinear plane waves in a gas with polytropic exponent = 3 by reduction of the original problem to an auxiliary Cauchy boundary-value problem for a system of stochastic ordinary differential equations. The probability distribution is found for the velocity and density of the gas in the case when at the initial time the gas density is constant and the velocity field Gaussian and statistically homogeneous. It is noted that there exists a finite time of statistical nonlinear interaction of colliding waves during which the probability distribution of the velocity and density of the gas can be essentially non-Gaussian.Translated from Izvesitya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–104, September–October, 1982.I thank A. N. Malakhov and S. N. Gurbatov for helpful discussions.     

重要性抽样法在计算球罐断裂失效概率中的应用

本文结合实例,在探讨了原分布函数平移一定距离后作为重要性函数的基础上,提出采用优化理论中的直接搜索法,以原分布函数与重要性函数相似比的变异系数最小为优化目标求得最佳平移量。同时提出迭代计算程序,即依据前次迭代计算得到的失效点分布确定计算时原分布函数的平移量,经多次迭代也能求出最佳平移量。多次迭代后诸失效点的中值与一阶二次矩法的设计点值接近。在本文算例中,由这二种方法求得的重要性函数减少了模拟计算总次数和提高了计算精度。     

Probability Inequalities for Sums of Independent Unbounded Random Variables

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