随机分布系统可靠保性能控制算法的研究

针对随机分布系统采用数值优化算法设计的控制器不稳定的问题, 研究了可靠保性能控制算法。该控制算法可实现将随机分布系统的值优化算法转换为线性矩阵不等式的可行解问题, 并通过线性矩阵不等式的方法给出可靠保性能控制算法的充分条件, 采用凸优化技术进行优化。通过实例仿真, 证明该算法能够实现输出概率密度函数渐进追踪目标概率密度函数, 并使随机分布系统的鲁棒性和稳定性有较好的改善。     

基于LMI的参数随机变化系统的概率密度函数控制

针对模型参数在有界区域内随机变化的系统, 基于平方根 B 样条模型, 提出了输出概率密度函数 (Probability density function, PDF) 跟踪控制策略. 目标是控制系统输出的概率密度函数跟踪给定的概率密度函数. 通过 B 样条逼近建立了输出 PDF 和权值之间的对应关系, 把 PDF 的跟踪转化为权值的跟踪, 同时系统转化为 MIMO 系统,从而权值向量的跟踪就转化为 MIMO 系统的跟踪问题, 接着给出了系统输出概率密度函数跟踪给定概率密度函数的控制器存在的充分条件, 通过求解线性矩阵不等式完成状态反馈和输出反馈跟踪控制器的设计, 得到了系统具有 Hinfinity 范数界 Gamma 鲁棒镇定的结果. 仿真结果表明本文提出的控制算法是有效的.     

采用随机Petri网的嵌入式机载软件可靠性检测

针对嵌入式机载软件设计中存在的典型缺陷问题，结合嵌入式机载软件任务调度特性，提出采用随机Petri网对嵌入式机载软件设计进行仿真验证的可靠性检测方法，以提高嵌入式机载软件设计的可靠性。该方法采用随机Petri网对嵌入式机载软件系统行为建模，并给出典型缺陷的检测策略和判定准则，然后通过对Petri网模型进行仿真验证，检测系统是否存在此类设计缺陷；并给出了软件设计的运行流程的仿真验证算法，以支持对相应设计的可靠性检测。通过与其他可靠性检测方法的比较，表明了该方法的有效性。     

随机系统输出分布的建模、控制与应用

介绍近年来新发展的随机分布控制的基本思想、建模、控制和应用。讨论了线性、平方根和有理3种B样条模型表示形式，将概率密度函数模型转化为权向量模型。以线性B样条模型为例介绍了控制器设计的一般原理。对离散线性动态系统，输出概率密度函数和输入之间存在一个简单的回归模型，采用二次型瞬间性能指标，可以得到控制量的最优闭环结构。结合造纸、化工、粮食加工和燃烧过程，讨论了方法的应用前景及如何获取概率密度函数这一关键问题。     

基于有理平方根逼近的非高斯随机分布系统的故障诊断和容错控制

随机分布系统指的是输入为常规向量而输出为系统输出的概率密度函数所描述的一类随机系统．该类系统控制算法的目标是选择一个控制输入使得系统的实际输出概率密度函数尽可能跟踪一个事先给定的概率密度函数．本文对采用有理平方根B样条逼近其输出概率密度函数的非高斯动态随机分布系统,提出了一种基于非线性自适应观测器的故障诊断方法．该方法可快速有效地诊断出非高斯随机分布系统故障．通过对故障系统的重组,使故障后系统的输出概率密度函数仍能跟踪给定的分布,实现了该随机系统的容错控制,提高了随机系统的可靠性．     

非线性随机系统的概率密度追踪控制

针对目前非线性随机系统控制方法的设计复杂、 计算成本高以及缺乏稳定性或收敛性证明等缺点, 提出了一种全新的基于等效非线性系统法求近似稳态解的思想设计的非线性随机系统的反馈控制, 使受控系统输出的稳态概率密度函数逼近事先给定的目标概率密度函数. 利用 Lyapunov 函数法证明了受控系统的收敛性. 数学仿真结果证明了这种方法的可行性和正确性.     

基于深度强化学习的动基座双自由度系统动力学控制方法

本文研究了在FOPID控制器控制下的广义Van Der Pol随机系统瞬态概率密度函数和可靠性函数变化情况.首先,引入广义谐和函数,将快变变量转换为慢变变量,并利用分数阶微积分的性质,获得了FOPID控制器在慢变变量形式下的新表达式.在此基础上,由于径向基神经网络具有准确性高,易于求解高维问题,求解速度快等优势,所以我们应用径向基神经网络分别对该随机系统所满足的前向和后向柯尔莫哥洛夫方程进行求解,得到随机系统的瞬态概率密度函数和可靠性函数.最后,通过分析控制器中分数阶导数和分数阶积分对Van Der Pol随机系统响应和可靠性的影响,我们得到结论,分数阶控制器一定程度上会增强系统的响应,并导致分岔.     

随机系统输出概率密度函数的有限时间镇定

针对一类含有限能量未知扰动的随机动态系统,研究基于随机分布函数的有限时间控制问题.通过B样条逼近建立了输出概率密度函数(PDF)与权值之间的对应关系,利用线性矩阵不等式,给出了基于观测器的PDF有限时间控制器的参数化设计方法.采用该方法设计的控制器,可使系统对所有满足条件的未知扰动是随机有限时间有界和随机有限时间镇定的.仿真实例验证了所提出方法的有效性.     

一种基于吉布斯抽样的MUSIC多维参数联合估计算法

将马尔可夫蒙特卡罗(MCMC)方法与多重子空间分类(MUSIC)方法估计相结合,提出一种用于联合估计多个目标的频率、方位和俯仰,基于吉布斯抽样的MUSIC多维参数联合估计新方法。该方法将MUSIC方法的谱函数作为频率、方位和俯仰的联合概率密度函数,采用MCMC吉布斯抽样方法对该联合概率密度函数进行采样。理论分析和仿真实验表明:在目标个数较少时,该方法不仅保持了常规MUSIC方法的高分辨能力,而且减少了计算量和存储量     

随机不确定网络控制系统的L_2-L_∞输出跟踪控制

本文研究了一类具有时延和凸多面体不确定性的随机网络控制系统的模型参考输出跟踪问题。基于线性矩阵不等式方法推出了该随机网络控制系统的稳定性和控制器设计的充分条件,并将控制器的设计转化为一个凸优化的求解问题。所设计的控制器能够保证相对于所有能量有界的外界扰动信号,随机网络控制系统的L2-L∞性能指标小于一定值γ。仿真实例证实了该设计方法的有效性。     

An efficient method of solving design optimization problems with arbitrary random distributions in gradient-based design spaces

Reliability-Based Design Optimization (RBDO) algorithms, such as Reliability Index Approach (RIA) and Performance Measure Approach (PMA), have been developed to solve engineering optimization problems under design uncertainties. In some existing methods, the random design space is transformed to standard normal design space and the reliability assessment, such as reliability index from RIA or performance measure from PMA, is estimated in order to evaluate the failure probability. When the random variable is arbitrarily distributed and cannot be properly fitted to any known form of probability density function, the existing RBDO methods cannot perform reliability analysis in the original design space. This paper proposes a novel Ensemble of Gradient-based Transformed Reliability Analyses (EGTRA) to evaluate the failure probability of any arbitrarily distributed random variables in the original design space. The arbitrary distribution of the random variable is approximated by a merger of multiple Gaussian kernel functions in a single-variate coordinate that is directed toward the gradient of the constraint function. The failure probability is then estimated using the ensemble of each kernel reliability analysis. This paper further derives a linearly approximated probabilistic constraint at the design point with allowable reliability level in the original design space using the aforementioned fundamentals and techniques. Numerical examples with generated random distributions show that existing RBDO algorithms can improperly approximate the uncertainties as Gaussian distributions and provide solutions with poor assessments of reliabilities. On the other hand, the numerical results show EGTRA is capable of efficiently solving the RBDO problems with arbitrarily distributed uncertainties.     

A comparative study of probability estimation methods for reliability analysis

In this paper we investigate the performance of probability estimation methods for reliability analysis. The probability estimation methods typically construct the probability density function (PDF) of a system response using estimated statistical moments, and then perform reliability analysis based on the approximate PDF. In recent years, a number of probability estimation methods have been proposed, such as the Pearson system, saddlepoint approximation, Maximum Entropy Principle (MEP), and Johnson system. However, no general guideline to suggest a most appropriate probability estimation method has yet been proposed. In this study, we carry out a comparative study of the four probability estimation methods so as to derive the general guidelines. Several comparison metrics are proposed to quantify the accuracy in the PDF approximation, cumulative density function (CDF) approximation and tail probability estimations (or reliability analysis). This comparative study gives an insightful guidance for selecting the most appropriate probability estimation method for reliability analysis. The four probability estimation methods are extensively tested with one mathematical and two engineering examples, each of which considers eight different combinations of the system response characteristics in terms of response boundness, skewness, and kurtosis.     

Random field modeling with insufficient field data for probability analysis and design

Often engineered systems entail randomness as a function of spatial (or temporal) variables. The random field can be found in the form of geometry, material property, and/or loading in engineering products and processes. In some applications, consideration of the random field is a key to accurately predict variability in system performances. However, existing methods for random field modeling are limited for practical use because they require sufficient field data. This paper thus proposes a new random field modeling method using a Bayesian Copula that facilitates the random field modeling with insufficient field data and applies this method for engineering probability analysis and robust design optimization. The proposed method is composed of three key ideas: (i) determining the marginal distribution of random field realizations at each measurement location, (ii) determining optimal Copulas to model statistical dependence of the field realizations at different measurement locations, and (iii) modeling a joint probability density function of the random field. A mathematical problem was first employed for the purpose of demonstrating the accuracy of the random field modeling with insufficient field data. The second case study deals with the assembly process of a two-door refrigerator that challenges predicting the door assembly tolerance and minimizing the tolerance by designing the random field and parameter variables in the assembly process with insufficient random field data. It is concluded that the proposed random field modeling can be used to successfully conduct the probability analysis and robust design optimization with insufficient random field data.     

A novel general approach to evaluating the PCBA for components with different membership function

The logistic support of high tech industry all emphasize that reliability design start, one must fully considers its life cycle. The reliability analysis and prediction are the main work objectives. The purpose is to ensure that the system (product) can achieve its designed functions under specific operating conditions. However, the incomplete failure data and different fault probability density function of the system elementary event also increase the difficulty of reliability design and calculation. It cannot be fully solved by traditional probability reliability. Therefore, a more general and efficient algorithm to assess the system reliability is needed. This paper proposed speculation by experts’ opinions according to incomplete information condition. It reasonably gives different fault membership function of possibility of failure distribution under different bottom event. It also applies fault-tree analysis, α-cut of vague set, and interval arithmetic operations of vague set to obtain fault interval and reliability interval of the system. Moreover, this paper also modifies Tanaka et al.’s fuzzy fault-tree definition and extended the new usage to fit different membership function of vague fault-tree. Then, find out the critical elementary event that affects the reliability of the system, which could be used for managerial decision-making, and as the bases to future system maintenance strategy. In numerical verification, a malfunction of printed circuit board assembly (PCBA) is presented as a numerical example. The result of the proposed method is compared with the listing approaches of reliability analysis methods.     

Reliability analysis of structures with complex limit state functions using probability density evolution method

In reliability-based structural analysis and design optimization, there exist some limit state functions exhibiting disjoint failure domains, multiple design points and discontinuous responses. This study addresses this type of challenging problem of reliability assessment of structures with complex limit state functions based on the probability density evolution method (PDEM). Probability density function (PDF) of stochastic structures under static and dynamic loads can be acquired, which is independent of the specific form of limit state functions. Numerical results of several typical examples illustrate that, the time-invariant and instantaneous PDF curves and failure probabilities of stochastic structures with disjoint failure domains, multiple design points and discontinuous responses are calculated effectively and accurately. Moreover, the PDEM is validated to be more efficient than the Monte Carlo simulation and the subset simulation, and is a feasible and general approach to tackle the reliability analysis of complicated problems. In addition, the influence of random design parameters of structures on uncertainty propagation is also scrutinized.     

Maximising profits for an EPQ model with unreliable machine and rework of random defective items

This article deals with an economic production quantity (EPQ) model in an imperfect production system. The production system may undergo in ‘out-of-control’ state from ‘in-control’ state, after a certain time that follows a probability density function. The density function varies with reliability of the machinery system that may be controlled by new technologies, investing more costs. The defective items produced in ‘out-of-control’ state are reworked at a cost just after the regular production time. Occurrence of the ‘out-of-control’ state during or after regular production-run time is analysed and also graphically illustrated separately. Finally, an expected profit function regarding the inventory cost, unit production cost and selling price is maximised analytically. Sensitivity analysis of the model with respect to key parameters of the system is carried out. Two numerical examples are considered to test the model and one of them is illustrated graphically.     

A fast approximate method for parameter sensitivity estimation in Monte Carlo structural reliability

In estimating the effect of a change in a random variable parameter on the (time-invariant) probability of structural failure estimated through Monte Carlo methods the usual approach is to carry out a duplicate simulation run for each parameter being varied. The associated computational cost may become prohibitive when many random variables are involved. Herein a procedure is proposed in which the numerical results from a Monte Carlo reliability estimation procedure are converted to a form that will allow the basic ideas of the first order reliability method to be employed. Using these allows sensitivity estimates of low computational cost to be made. Illustrative examples with sensitivities computed both by conventional Monte Carlo and the proposed procedure show good agreement over a range of probability distributions for the input random variables and for various complexities of the limit state function.     

An efficient reliability-based optimization scheme for uncertain linear systems subject to general Gaussian excitation

A very efficient methodology to carry out reliability-based optimization of linear systems with random structural parameters and random excitation is presented. The reliability-based optimization problem is formulated as the minimization of an objective function for a specified reliability. The probability that design conditions are satisfied within a given time interval is used as a measure of the system reliability. Approximation concepts are used to construct high quality approximations of dynamic responses in terms of the design variables and uncertain structural parameters during the design process. The approximations are combined with an efficient simulation technique to generate explicit approximations of the reliability measures with respect to the design variables. In particular, an efficient importance sampling technique is used to estimate the failure probabilities. The number of dynamic analyses as well as reliability estimations required during the optimization process are reduced dramatically. Several example problems are presented to illustrate the effectiveness and feasibility of the suggested approach.     

An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals

The reliability analysis approach based on combined probability and evidence theory is studied in this paper to address the reliability analysis problem involving both aleatory uncertainties and epistemic uncertainties with flexible intervals (the interval bounds are either fixed or variable as functions of other independent variables). In the standard mathematical formulation of reliability analysis under mixed uncertainties with combined probability and evidence theory, the key is to calculate the failure probability of the upper and lower limits of the system response function as the epistemic uncertainties vary in each focal element. Based on measure theory, in this paper it is proved that the aforementioned upper and lower limits of the system response function are measurable under certain circumstances (the system response function is continuous and the flexible interval bounds satisfy certain conditions), which accordingly can be treated as random variables. Thus the reliability analysis of the system response under mixed uncertainties can be directly treated as probability calculation problems and solved by existing well-developed and efficient probabilistic methods. In this paper the popular probabilistic reliability analysis method FORM (First Order Reliability Method) is taken as an example to illustrate how to extend it to solve the reliability analysis problem in the mixed uncertainty situation. The efficacy of the proposed method is demonstrated with two numerical examples and one practical satellite conceptual design problem.