Stochastic Newmark scheme

In this paper, we are concerned with numerical resolution of the dynamical equation of linear oscillators. An answer is given to the following question: can one use widely implemented Newmark's algorithm when the acceleration is a white noise instead of a regular deterministic one? After showing drawbacks of such a practice, a modification of the usual Newmark schemes is introduced, to be used for the numerical resolution of such a stochastic dynamical equation. The modification is only in the stochastic part, so that already implemented softwares can be used, the input only having to be carefully adapted. After that, mathematical analysis of this new scheme is fulfilled. First and second moments, as well as the power spectral density resulting from the use of this scheme are compared with the corresponding quantities resulting from the theoretical process, and also from usual Newmark scheme and Euler schemes. Almost sure convergence of this new scheme is proved.     

Stochastic quasi-gradient based optimization algorithms for dynamic reliability applications

On one hand, PSA results are increasingly used in decision making, system management and optimization of system design. On the other hand, when severe accidental transients are considered, dynamic reliability appears appropriate to account for the complex interaction between the transitions between hardware configurations, the operator behavior and the dynamic evolution of the system. This paper presents an exploratory work in which the estimation of the system unreliability in a dynamic context is coupled with an optimization algorithm to determine the “best” safety policy. Because some reliability parameters are likely to be distributed, the cost function to be minimized turns out to be a random variable. Stochastic programming techniques are therefore envisioned to determine an optimal strategy. Monte Carlo simulation is used at all stages of the computations, from the estimation of the system unreliability to that of the stochastic quasi-gradient. The optimization algorithm is illustrated on a HNO₃ supply system.     

A critical appraisal of reliability estimation procedures for high dimensions

A critical appraisal of reliability procedures for high dimensions is presented. Available approximate methods and methods based on Monte Carlo simulation are discussed. It is shown that procedures which perform well in low dimensions may become impractical if the dimension increases considerably or tends to infinity. It is observed that some types of Monte Carlo based simulation procedures in fact are capable of treating high dimensional problems.     

随机综合生产计划模型及其求解研究

制订一个有效、可行的综合生产计划,必须考虑各种随机因素的影响。本文在前人工作的基础上,提出了一种改进的随机综合生产计划模型,并探讨了采用数学分析和蒙特卡罗模拟相结合的模型求解方法。     

Stochastic modeling of ecosystem with two competing species

A nonlinear stochastic model describing two competing species of grass and woody vegetation is proposed. The nonlinear behaviors are caused by the interspecies and intraspecies competitions, and the stochastic variation describes the uncertainty in the cattle stocking rate. Two types of stochastic processes are proposed to model the variation part of the stocking rate. One is Gaussian white-noise process, and another is randomized sinusoidal process. The system nonlinear behaviors are investigated for the deterministic case and the cases with two different stochastic variations. Some key characteristics of the system dynamics are found to be different for cases with and without stochastic variations. With the stochastic variation, a single stable state in the deterministic system is diffused into a region of stable states, and a separatrix dividing the two attraction zones no longer exists. The system may follow different trajectories and lead to different outcomes, beginning from the same initial state. It is also found that the stationary probability of the system response depends on the initial conditions, a special phenomenon for the investigated nonlinear system. Although the white-noise process and the randomized sinusoidal process are quite different in nature, the qualitative behaviors of the system are similar. Furthermore, effects of the initial state and the intensity of the stochastic variations on the system behaviors are investigated.     

Efficient estimation of first passage probability of high-dimensional nonlinear systems

An efficient method for estimating low first passage probabilities of high-dimensional nonlinear systems based on asymptotic estimation of low probabilities is presented. The method does not require any a priori knowledge of the system, i.e. it is a black-box method, and has very low requirements on the system memory. Consequently, high-dimensional problems can be handled, and nonlinearities in the model neither bring any difficulty in applying it nor lead to considerable reduction of its efficiency. These characteristics suggest that the method is a powerful candidate for complicated problems. First, the failure probabilities of three well-known nonlinear systems are estimated. Next, a reduced degree-of-freedom model of a wind turbine is developed and is exposed to a turbulent wind field. The model incorporates very high dimensions and strong nonlinearities simultaneously. The failure probability of the wind turbine model is estimated down to very low values; this demonstrates the efficiency and power of the method on a realistic high-dimensional highly nonlinear system.     

An Efficient Sampling Technique for Bayesian Inference With Computationally Demanding Models

In the environmental sciences, a large knowledge base is typically available on an investigated system or at least on similar systems. This makes the application of Bayesian inference techniques in environmental modeling very promising. However, environmental systems are often described by complex, computationally demanding simulation models. This strongly limits the application of Bayesian inference techniques, because numerical implementation of these techniques requires a very large number of simulation runs. The development of efficient sampling techniques that attempt to approximate the posterior distribution with a relatively small parameter sample can extend the range of applicability of Bayesian inference techniques to such models. In this article a sampling technique is presented that tries to achieve this goal. The proposed technique combines numerical techniques typically applied in Bayesian inference, including posterior maximization, local normal approximation, and importance sampling, with copula techniques for the construction of a multivariate distribution with given marginals and correlation structure and with low-discrepancy sampling. This combination improves the approximation of the posterior distribution by the sampling distribution and improves the accuracy of results for small sample sizes. The usefulness of the proposed technique is demonstrated for a simple model that contains the major elements of models used in the environmental sciences. The results indicate that the proposed technique outperforms conventional techniques (random sampling from simpler distributions or Markov chain Monte Carlo techniques) in cases in which the analysis can be limited to a relatively small number of parameters.     

Application of variance reduction techniques in Monte Carlo simulation of clinical electron linear accelerator

Computation time constitutes an important and a problematic parameter in Monte Carlo simulations, which is inversely proportional to the statistical errors so there comes the idea to use the variance reduction techniques. These techniques play an important role in reducing uncertainties and improving the statistical results. Several variance reduction techniques have been developed. The most known are Transport cutoffs, Interaction forcing, Bremsstrahlung splitting and Russian roulette. Also, the use of a phase space seems to be appropriate to reduce enormously the computing time. In this work, we applied these techniques on a linear accelerator (LINAC) using the MCNPX computer Monte Carlo code. This code gives a rich palette of variance reduction techniques. In this study we investigated various cards related to the variance reduction techniques provided by MCNPX. The parameters found in this study are warranted to be used efficiently in MCNPX code. Final calculations are performed in two steps that are related by a phase space. Results show that, comparatively to direct simulations (without neither variance-reduction nor phase space), the adopted method allows an improvement in the simulation efficiency by a factor greater than 700.     

Monte Carlo and variance reduction methods for structural reliability analysis: A comprehensive review

Monte Carlo methods have attracted constant and even increasing attention in structural reliability analysis with a wide variety of developments seamlessly presented over decades. Along the way, a number of specialized reviews and benchmark studies have been provided from time to time, aiming at summarizing and comparing selected few approaches in detail, mainly from an implementation point of view. In contrast, the aim of the present survey is to play a comprehensive role as a methodological guidebook on Monte Carlo simulation and its related, especially variance reduction, techniques through a covering of 444 references in the relevant literature. To achieve this goal, we present an extensive review of formulations and techniques along with insightful summaries of developments of existing numerical methods, ranging from the general formulation, sub-categories and variants, to their combined uses with other simulation techniques and surrogate models, as well as the key advantages and assumptions.     

Bayesian Computations for a Class of Reliability Growth Models

In this article, we consider the development and analysis of both attribute- and variable-data reliability growth models from a Bayesian perspective. We begin with an overview of a Bayesian attribute-data reliability growth model and illustrate how this model can be extended to cover the variable-data growth models as well. Bayesian analysis of these models requires inference over ordered regions, and even though closed-form results for posterior quantities can be obtained in the attribute-data case, variable-data models prove difficult. In general, when the number of test stages gets large, computations become burdensome and, more importantly, the results may become inaccurate due to computational difficulties. We illustrate how the difficulties in the posterior and predictive analyses can be overcome using Markov-chain Monte Carlo methods. We illustrate the implementation of the proposed models by using examples from both attribute and variable reliability growth data.     

工业钼靶X射线光机能谱的蒙特卡罗模拟

利用蒙特卡罗模拟程序EGSnrc,构建出工业钼靶X射线光机模型,进行了28 keV的电子束经过钼靶产生的光子在光机各组件中的传输模拟,得到距源焦点50 cm处, 射野半径为5 cm平面上的粒子相空间文件,通过对相空间文件分析得到粒子注量、能谱分布、角分布、平均能量等信息,模拟计算了过滤材料和管电压对钼靶X射线谱分布的影响。钼过滤下钼靶X射线的平均能量小于铑过滤,但对较高能量部分的影响要大于铑过滤;随着管电压的升高,钼靶光机的光子产生效率呈上升趋势,平均能量增加。25,28,30,35 kV 4组辐射质条件下,钼靶X射线能谱的平均能量分别为16.0,16.6,17.0,17.8 keV,与实验测量值接近,相对误差在1%以内。     

Identification of missing scenarios in ESDs using probabilistic dynamics

The event sequence diagram (ESD) framework can be used to qualitatively represent dynamic scenarios. The solution of ESDs can be performed in an analytical manner. Since the construction of ESDs has some inherent analyst dependence, there is scope for omitting scenarios due to certain simplifying assumptions. This is one of the prime drawbacks of the ESD framework. This paper presents an approach for identifying missing scenarios by combining ESDs with probabilistic dynamics. The approach also helps in reducing the variance of a Monte Carlo simulation procedures.     

New method for efficient Monte Carlo–Neumann solution of linear stochastic systems

The Neumann series is a well-known technique to aid the solution of uncertainty propagation problems. However, convergence of the Neumann series can be very slow, often turning its use highly inefficient. In this article, a λ convergence parameter is introduced, which yields accurate and efficient Monte Carlo–Neumann solutions of linear stochastic systems using first order Neumann expansions. The λ convergence parameter is found as solution to a distance minimization problem, for an approximation of the inverse of the system matrix using the Neumann series. The method presented herein is called Monte Carlo–Neumann with λ convergence, or simply MC–N λ method. The accuracy and efficiency of the MC–N λ method is demonstrated in application to stochastic beam bending problems.     

Evaluation of Measurement Uncertainty Based on the Propagation of Distributions Using Monte Carlo Simulation

The uncertainty associated with a value of some quantity is widely recognized throughout scientific disciplines as a quantitative measure of the reliability of that value. In addition, measurement uncertainty is increasingly seen as essential in quality assurance for industry. The Guide to the Expression of Uncertainty in Measurement (GUM) provides internationally agreed recommendations for the evaluation of uncertainties. This paper outlines the current situation of uncertainty evaluation in the context of international norms and arrangements. It describes the basic ideas and concepts that underlie the GUM and serves as a brief tutorial on methods for evaluating measurement uncertainty in a manner consistent with the GUM. It recommends an approach to evaluating measurement uncertainty based on the propagation of distributions using Monte Carlo simulation. An example is presented to illustrate Monte Carlo simulation.     

Stochastic finite element analysis of a cable-stayed bridge system with varying material properties

Stochastic seismic finite element analysis of a cable-stayed bridge whose material properties are described by random fields is presented in this paper. The stochastic perturbation technique and Monte Carlo simulation (MCS) method are used in the analyses. A summary of MCS and perturbation based stochastic finite element dynamic analysis formulation of structural system is given. The Jindo Bridge, constructed in South Korea, is chosen as a numerical example. The Kocaeli earthquake in 1999 is considered as a ground motion. During the stochastic analysis, displacements and internal forces of the considered bridge are obtained from perturbation based stochastic finite element method (SFEM) and MCS method by changing elastic modulus and mass density as random variable. The efficiency and accuracy of the proposed SFEM algorithm are evaluated by comparison with results of MCS method. The results imply that perturbation based SFEM method gives close results to MCS method and it can be used instead of MCS method, especially, if computational cost is taken into consideration.     

微小封闭空间气体取样过程瞬态模拟

为研究0.001 cc微小封闭空间内部气氛瞬态检测过程中的气体压力变化与质量歧视现象,本文使用直接模拟蒙特卡罗方法结合简化伯努利碰撞对选择格式,针对由取样腔、毛细管、进样通道、离化室与质谱仪组成的典型检测系统,对不同分压比下的氮气与氢气二元混合气体瞬态检测过程进行了研究。结果显示研究中取样腔压力的降低对于毛细管流导的影响可忽略,但毛细管对于混合气体中各组分流导会随质量较轻气体的占比增加而增加。离化室中气体压力在快速上升至最大值后在模拟时间内近似指数下降,同时气体分压比在检测过程中存在剧烈变化,为准确获取样品内气体分压比带来挑战。文章提出了利用混合气体流导值与离化室压力下降曲线对气体质量歧视现象进行修正的方法,气体分压修正偏差小于6%,分压比修正偏差小于1%。研究结果为微气量瞬态检测分析与气体质量歧视的修正提供了理论参考。     

基于Bayes小子样二项分布单元可靠性评定的仿真方法

对于小子样二项分布单元可靠度下限评定，经典方法有很大局限性，文中介绍了Bayes方法。并在其基础上提出基于Bayes方法的Monte Carlo仿真方法，示例证明，该方法有很好的应用前途。     

Stochastic and chaotic sub- and superharmonic response of shallow cables due to chord elongations

The paper deals with the non-linear response of shallow cables driven by stochastically varying chord elongations caused by random vibrations of the supported structure. The chord elongation introduces parametric excitation in the linear stiffness terms of the modal coordinate equations, which are responsible for significant internal subharmonic and superharmonic resonances. Under harmonically varying support motions coupled ordered or chaotic in-plane and out-of-plane subharmonic and superharmonic periodic motions may take place. If the harmonically varying chord elongation is replaced by a zero-mean, stationary narrow-band random excitation with the same standard deviation and center frequency, qualitatively and quantitatively completely different modes of vibration are registered no matter how small the bandwidth of the excitation process is. Additionally, the stochastic excitation process tends to enhance chaotic behavior. Based on Monte Carlo simulation on a reduced non-linear two-degree-of freedom system the indicated effects have been investigated for stochastic subharmonic resonance of order 2:1, and stochastic superharmonic resonances of orders 1:2 and 2:3. By analyzing the responses for two chord elongation processes with almost identical auto-spectral density function, but completely different amplitudes, it is shown that the indicated qualitative and quantitative changes of the subharmonic resonance primarily are caused by the slowly varying phase of the stochastic excitation. The superharmonic stochastic responses are dominated by random jumps between a single mode in-plane and a coupled mode attractor, which are caused by the variation of the amplitude of the random excitation. Such jumps do not occur in the subharmonic response, because the single mode in-plane attractor is unstable.