Robust control of nonlinear systems with parametric uncertainty

Probabilistic robustness analysis and synthesis for nonlinear systems with uncertain parameters are presented. Monte Carlo simulation is used to estimate the likelihood of system instability and violation of performance requirements subject to variations of the probabilistic system parameters. Stochastic robust control synthesis searches the controller design parameter space to minimize a cost that is a function of the probabilities that design criteria will not be satisfied. The robust control design approach is illustrated by a simple nonlinear example. A modified feedback linearization control is chosen as controller structure, and the design parameters are searched by a genetic algorithm to achieve the tradeoff between stability and performance robustness.     

Decision support systems based on the Life Cycle Inventory for Municipal Solid Waste management under uncertainty

Life Cycle Inventory (LCI) – part of a Life Cycle Assessment (LCA) method – was used to evaluate two scenarios for waste to energy gasification plants based on the American (design at 200 T/D) and Australian (design at 240 T/D) gasification technologies including a 15‐year income statement projection. The paper uses stochastic modeling based on the internal rate of return (IRR) and net present value (NPV) values of the new and actual equipment. The Monte Carlo simulation with the Excel spreadsheet and Crystal Ball^® software was used to develop scenarios for uncertainty inputs. The sensitivity analysis and frequency charts represent the Crystal Ball^® output and simulation results.     

基于贝叶斯和蒙特卡罗的多信号模型扩展研究

传统多信号模型基于确定性测试假设条件,忽略了系统存在不确定性的真实情况,在传统多信号模型基础上引入贝叶斯条件概率来表示不确定性问题,并通过蒙特卡罗方法进行仿真模拟,将不确定性问题转化为单次试验确定性问题,进而使用相关矩阵进行测试性分析,通过程序实现和算例验证了该方法的有效性,并可以根据反馈数据进行参数学习,修正初始条件概率。     

蒙特卡洛法在发动机推力测量不确定度评估中的应用

现行对发动机试验推力测量不确定度的评估一直采用GUM法,存在输入量和输出量概率分布假设以及非线性模型近似等问题,有一定的局限性;以发动机推力矢量测量为例,文中简述了压电式推力矢量测量的数学模型,运用GUM法对推力矢量参数的不确定度评估,同时分析了蒙特卡洛法的原理、具体评估过程和适用性,编制了软件,并将不确定度评估结果与GUM法评估结果进行对比;对比结果表明,在发动机试验推力矢量参数的不确定度评估过程中,蒙特卡洛法相比GUM法更为适用.     

Methods for uncertainty propagation in life cycle assessment

Life cycle assessment (LCA) calculates the environmental impact of a product over its entire life cycle. Uncertainty analysis is an important aspect in LCA, and is usually performed using Monte Carlo sampling. In this study, Monte Carlo sampling, Latin hypercube sampling, quasi Monte Carlo sampling, analytical uncertainty propagation and fuzzy interval arithmetic were compared based on e.g. convergence rate and output statistics. Each method was tested on three LCA case studies, which differed in size and behaviour. Uncertainty propagation in LCA using a sampling method leads to more (directly) usable information compared to fuzzy interval arithmetic or analytical uncertainty propagation. Latin hypercube and quasi Monte Carlo sampling provide more accuracy in determining the sample mean than Monte Carlo sampling and can even converge faster than Monte Carlo sampling for some of the case studies discussed in this paper.     

Sequential monte carlo techniques for the solution of linear systems

Given alinear system Ax=b, wherex is anm-vector,direct numerical methods, such as Gaussian elimination, take timeO(m ³) to findx. Iterative numerical methods, such as the Gauss-Seidel method or SOR, reduce the system to the formx=a+Hx, whence and then apply the iterationsx ₀=a,x _s+1=a+Hx _s , until sufficient accuracy is achieved; this takes timeO(m ²) per iteration. They generate the truncated sums The usualplain Monte Carlo approach uses independent random walks, to give an approximation to the truncated sumx _s , taking timeO(m) per random step. Unfortunately, millions of random steps are typically needed to achieve reasonable accuracy (say, 1% r.m.s. error). Nevertheless, this is what has had to be done, ifm is itself of the order of a million or more.The alternative presented here, is to apply a sequential Monte Carlo method, in which the sampling scheme is iteratively improved. Simply put, ifx=y+z, wherey is a current estimate ofx, then its correction,z, satisfiesz=d+Hz, whered=a+Hy–y. At each stage, one uses plain Monte Carlo to estimatez, and so, the new estimatey. If the sequential computation ofd is itself approximated, numerically or stochastically, then the expected time for this process to reach a given accuracy is againO(m) per random step; but the number of steps is dramatically reduced [improvement factors of about 5,000, 26,000, 550, and 1,500 have been obtained in preliminary tests].     

Computation of the effects of uncertainty in volatility on option pricing and hedging

We quantify the effect of uncertainty in the volatility parameter σ on the Black–Scholes price of the European and American put. We apply probabilistic uncertainty analysis to the Black–Scholes model and compare the results with those of the Uncertain Volatility model. From historical data, we calibrate a probability distribution for the volatility. We then use Monte Carlo (MC) and a surrogate Polynomial Chaos (PC)/MC method to compute uncertainty bounds. The calibrated probability distribution is not one related to a standard orthogonal basis, so a basis is constructed numerically for the PC approximation. We show how to construct one stably from the probability distribution. We show that both methods give the same results, and quantify the relative speedup of the surrogate method. Finally, we investigate the effect of the parametric uncertainty, and show, for example, that the presence of uncertainty smoothes out the optimal exercise boundary of the American put.     

基于ANSYS的静力问题结构可靠性分析方法

分别使用ANSYS中的拉丁超立方样本蒙特卡罗法、中心复合设计样本响应面法以及Box—Behnken矩阵样本响应面法进行结构可靠性分析和计算．比较分析结果证明,对于静力问题结构可靠性分析,响应面分析结果仅在输出参数的均值、最大值以及最小值上逼近蒙特卡罗法结果,确定目标的可靠度以及输出参数标准差结果偏差较大;对于灵敏度分析结果,仅有高灵敏度变量结果可信．     

基于 MCM 噪声参数测量不确定度评定的方法研究磁

开展了基于蒙特卡洛法（MCM ）的噪声参数测量不确定度评定工作,以等效噪声参数方程作为不确定度评定的测量模型,利用从测量系统获得的物理量求解函数方程,得到反映等效噪声参数分布情况的数据,并从等效噪声参数导出噪声参数及其概率分布,最后得到噪声参数测量的不确定度。该方法有效地结合了数学随机仿真、物理测量边界判据,实现了噪声参数测量结果的不确定度评定,该方法符合国际标准,可应用的测量系统种类多,普适性高。最后通过实验数据验证,证明了评定方法的有效性,不确定度评定数据的真实性和可靠性。     

激光半主动寻的导引头目标捕获概率仿真研究

该文针对某型激光制导航空炸弹系统,在加入各种干扰因素的基础上进行了全弹道计算机数学仿真,采用蒙特卡洛法估算了该激光制导航空炸弹在各种干扰下对目标的捕获概率,分析了风场、投弹篮框和初始离轴发射角三种扰动因素对目标的捕获概率的影响,并在此基础上提出了两种提高捕获概率的方法。仿真结果表明,所述方法对提高导引头对目标的捕获概率效果明显,可以应用到激光制导航空炸弹的制导与控制系统中。     

Modeling temporal processes via belief networks and Petri nets,with application to expert systems

We show how Bayesian belief networks (BNs) can be used to model common temporal knowledge. Two approaches to their structuring are proposed. The first leads to BNs with nodes representing states of a process and times spent in such states, and with a graphical structure reflecting the conditional independence assumptions of a Markovian process. A second approach leads to BNs whose topology represents a conditional independence structure between event-times. Once required distributional specifications are stored within the nodes of a BN, this becomes a powerful inference machine capable, for example, of reasoning backwards in time. We discuss computational difficulties associated with propagation algorithms necessary to perform these inferences, and the reasons why we chose to adopt Monte Carlo-based propagation algorithms. Two improvements to existing Monte Carlo algorithms are proposed; an enhancement based on the principle of importance sampling, and a combined technique that exploits both forward and Markov sampling. Finally, we consider Petri nets, a very interesting and general representation of temporal knowledge. A combined approach is proposed, in which the user structures temporal knowledge in Petri net formalism. The obtained Petri net is then automatically translated into an equivalent BN for probability propagation. Inferred conclusions may finally be explained with the aid of Petri nets again.     

非线性奇摄动系统的小增益增长条件

给出小增益增长条件使得在此条件下快慢子系统的渐近稳定性能够保证其原奇摄动系统的相应稳定性,并给出估计摄动参数的稳定界的解析表示及其应用例子.     

Identification of systems containing linear dynamic and static nonlinear elements

Identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered. Previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems. It is shown that systems composed of cascade, feedforward, feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only.     

A lattice model of fashion propagation with correlation analysis

Spatial and temporal changes in fashion are very complicated in an information-oriented society. In this article, we introduce a lattice model of fashion which is composed of two competing trends. Simulation is carried out by two methods: local and global interactions. In the former case interaction occurs between adjacent lattice sites, while in the latter it occurs between any pair of lattice sites. Computer simulations reveal that the fashion is more prevalent for global interaction than for local interaction. Various spatial patterns in fashion are analysed by both auto- and cross-correlations. We find universally a power law which leads to collective behaviours of fashion: if the number of people with a trend is extremely decreased, they are localised in scattered very small areas. For the producer/maker of fashion, global transmission is far more important than local dispersal.     

Simultaneous estimation of the input and output frequencies of nonlinear systems

In this paper, the simultaneous estimation of the input and output frequencies of nonlinear systems is considered. As the output frequencies are generated from the input frequencies, and are integer combinations of these frequencies, it is shown in this paper that the simultaneous estimation of both the input and output frequencies can therefore be formulated as a constrained estimation problem. First, the constrained Cramér-Rao lower bound, an important general property of any unbiased estimator, is derived. The procedure and algorithm for estimating the input and output frequencies are devised based on the periodogram method. Numerical examples are presented to illustrate the performance and implementation of the proposed estimation procedure and algorithm.     

一种新的组网雷达优化布站方法

为了在给定的自然环境和现有组网雷达资源下形成最大的探测区域,以提高组网雷达的探测能力、反隐身、抗综合电子干扰、抗低空突防和抗反辐射导弹能力,提出了一种基于探测概率的组网雷达优化布站方法.在分析了三种典型的组网雷达布站方式的基础上,推导单部雷达探测概率计算方法和组网雷达联合探测概率模型,并运用蒙特卡罗方法进行建模仿真,仿真结果得出了各雷达的最佳部署位置坐标和给定高度下的最大探测面积.给出了组网雷达最优部署的原则及性能评估方法,并为实际阵地环境下组网雷达的优化部署提供参考.     

反跑道集束战斗部毁伤概率研究

该文采用蒙特卡洛方法,建立反跑道集束战斗部毁伤概率的数学模型,给出了计算毁伤概率的仿真算法,开发相应仿真软件,并给出具体的仿真算例和仿真分析,最后,对影响毁伤概率的诸因素进行了讨论。