Reliability-based design optimization for problems with interval distribution parameters

Traditional reliability-based design optimization (RBDO) generally describes uncertain variables using random distributions, while some crucial distribution parameters in practical engineering problems can only be given intervals rather than precise values due to the limited information. Then, an important probability-interval hybrid reliability problem emerged. For uncertain problems in which interval variables are included in probability distribution functions of the random parameters, this paper establishes a hybrid reliability optimization design model and the corresponding efficient decoupling algorithm, which aims to provide an effective computational tool for reliability design of many complex structures. The reliability of an inner constraint is an interval since the interval distribution parameters are involved; this paper thus establishes the probability constraint using the lower bound of the reliability degree which ensures a safety design of the structure. An approximate reliability analysis method is given to avoid the time-consuming multivariable optimization of the inner hybrid reliability analysis. By using an incremental shifting vector (ISV) technique, the nested optimization problem involved in RBDO is converted into an efficient sequential iterative process of the deterministic design optimization and the hybrid reliability analysis. Three numerical examples are presented to verify the proposed method, which include one simple problem with explicit expression and two complex practical applications.     

Formulating and solving parametric design problems involving non-interference constraints

Improvements in computer-aided design (CAD) tools can significantly increase designer productivity, since the ability to explore a variety of possible designs quickly and effectively is essential for a designer. Using an optimization tool, systematic exploration of design spaces can be achieved readily. The general goal of the work presented here is to aid design by combining the strengths of optimization techniques with those of CAD systems. The specific objective of this paper is to introduce goal directed geometry (GDG) as a computational framework for parametric design, aiding the formulation of engineering problems with geometric considerations and their solution with a multi-objective optimization package. Using GDG, What if questions can be posed and answered in a systematic fashion. Specific issues to be addressed include the development of a general parametric design problem formulation, development of static and dynamic geometric non-interference constraints for use in this formulation, and investigation of the efficacy of the adaptive linear programming (ALP) multiobjective optimization algorithm in solving such problems. Two examples are presented, one each to illustrate the use of the static and dynamic non-interference constraints. Results demonstrate that the GDG formulation can be applied readily to a wide variety of parametric design problems. Additionally, the ALP algorithm successfully navigates around geometric constraints, although care must be taken when linearizing highly non-linear design spaces.     

Estimation of distribution algorithms on non-separable problems

The evolutionary algorithms discussed in this paper do not use crossover, nor mutation. Instead, they estimate and evolve a marginal probability distribution, the only distribution responsible for generating new populations of chromosomes. So far, the analysis of this class of algorithms was confined to proportional selection and additive decomposable functions. Dropping both assumptions, we consider here truncation selection and non-separable problems with polynomial number of distinct fitness values. The emergent modelling is half theoretical – with respect to selection, completely characterized by stochastic calculus – and half empirical – concerning the generation of new individuals. For the latter operator, we sample the chromosomes arbitrarily, one for each selected level of fitness. That is the break-symmetry point, making the difference between the finite and infinite population cases, and ensuring the convergence of the model.     

Verification of backtracking and branch and bound design templates

The design and analysis of computer algorithms is a requirement of computer curricula. It covers many topics, including data structures, complexity theory, and algorithmic design patterns. This course is about the greedy method, divide and conquer, dynamic programming, backtracking, and branch and bound. Naturally, all the listed design patterns are taught, learned, and comprehended using examples. However, they can be semiformalized as design templates, specified by correctness conditions, and manually verified by means of the Floyd method. Moreover, this approach can lead to new insights and better comprehension of the design patterns, specifications, and verification methods. In this paper, we demonstrate the utility of the approach using the study of the backtracking and branch-and-bound design patterns. In particular, we prove the correctness of the suggested templates when the boundary condition is monotone, but the decision condition is antimonotone on sets of “visited” vertices.     

集合划分问题的分布估计求解

集合划分问题对日常生活中的仓库装填问题,生产线排程问题有很大意义,但是无论采用精确算法还是启发式算法都不能很好求解。提出一种改进的分布估计算法,采用实数编码和基于矩阵的概率向量存储方式,并且引入权值的概念,改进了概率向量的更新方式。将它与标准DM（the Differencing Method）算法进行了比较,实验结果证明,它可以有效解决DM算法在25维以下得不到正解的问题。另外,算法还延伸到高维和多分类问题上,这里给出了实验结果。     

Estimation of soil water distribution: Identifiability and observation design

Identifiability and observation design problems for the Burgers equation, a model for the nonhysteretic infiltration in nonswelling soil, are considered. In estimating initial water distribution from a finite set of measurements, the identifiability under approximation is proved. In predicting the water distributions, an algorithm for observation design problems is provided and analyzed with the maximum error bound. Also, numerical simulations are performed.     

指数威布尔分布参数的模糊最小二乘估计

讨论了当寿命数据含有异常数据时指数威布尔分布参数的估计问题。当寿命数据含有异常数据时,利用基于模糊聚类的最小二乘方法对参数进行估计,这种方法能削弱异常数据的影响。并获得了在完全样本情形下参数的最小二乘估计和加权最小二乘估计。最后给出数值模拟,结果显示模糊最小二乘估计是正确有效的。     

BIM 正向设计存在的问题和思考

BIM 正向设计能够减少部分建模环节、降低劳动和信息交换成本,其优点得到业 界的广泛认同。随着国内BIM 技术的不断推广,现有的BIM 咨询模式已不能满足快速发展的 应用需求,正向设计在实际应用过程中也遇到了很多困难。通过工程经验和文献调研总结了正 向设计存在的问题,如：①缺乏与之适应的标准;②国内环境的制约;③技术链和产业链不够 成熟等,并对上述问题进行了思考与分析,得出以下结论：以出图为导向的正向设计是BIM 技 术应用的过渡性策略,需补充相适应的标准体系、加大国内BIM 软件和云平台体系的开发力度、 促进设计与施工管理一体化。正向设计的推广不仅需要有力的技术支持,更需要管理模式的不 断创新,为BIM 技术的应用和发展提供保障。     

Evaluation of a supermarket twin-checkout involving forward and backward operation

Cashier workplaces recently put into service in self-service shops of a retail company provide a face-to-face position of two cashiers. These twin-checkouts involve both traditional goods handling from the front to the rear as well as a reverse technique - i e, forward operation from behind. By means of different methods they have been analysed from an ergonomics point of view and evaluated in respect of operators' workload resulting from the specific layout. The results support the conclusion that the new 'backward' system and twin-checkouts are not inferior to traditional single checkouts. On the contrary, a working technique where the arm moves from behind to the front involves a better approach to accounting for physiological characteristics and obviously allows a better fitting of the task of operators.     

Estimation of parameters of the Makeham distribution using the least squares method

The Makeham distribution has been used to describe human mortality and establish actuarial tables. The hazard function is defined by μ(t)=A+BC^t$\mu (t)=A+B{C}^t$, we use the least squares type estimation to estimate the parameters of Makeham distribution in this paper. Seven cases are considered, when A, B, C are known or unknown, respectively. Also, we evaluated the mean square errors of these estimators.     

Robust design of a cellular-line production system with unreliable facilities

A cellular-line production system consists of multiple flow shops which are individual sets composed of functionally different facilities. The cellular-line production system is carefully designed and controlled so as to group facilities that perform similar operations and balance the workload among facilities considering the planned product mix and its variations. Thus, a drastic reduction in production lead time is possible as long as all of the facilities composing cellular-lines in the system are reliable. The present paper deals with a design problem of the cellular-line production system which includes unreliable facilities. We assume that the times to failure and times to repair are exponentially distributed and that the latter is not lengthy, that is, that the times to repair are at most several times the cycle time, which is the input interval for the cellular-lines. A methodology for designing the system in a machine-failure environment is presented and the results of numerical experiments and simulation are shown to verify the usefulness of the proposed methodology. Finally, the practical significance of quantitative analysis and evaluation in the stochastic design problem is discussed.     

Estimation of distribution algorithms with Kikuchi approximations

The question of finding feasible ways for estimating probability distributions is one of the main challenges for Estimation of Distribution Algorithms (EDAs). To estimate the distribution of the selected solutions, EDAs use factorizations constructed according to graphical models. The class of factorizations that can be obtained from these probability models is highly constrained. Expanding the class of factorizations that could be employed for probability approximation is a necessary step for the conception of more robust EDAs. In this paper we introduce a method for learning a more general class of probability factorizations. The method combines a reformulation of a probability approximation procedure known in statistical physics as the Kikuchi approximation of energy, with a novel approach for finding graph decompositions. We present the Markov Network Estimation of Distribution Algorithm (MN-EDA), an EDA that uses Kikuchi approximations to estimate the distribution, and Gibbs Sampling (GS) to generate new points. A systematic empirical evaluation of MN-EDA is done in comparison with different Bayesian network based EDAs. From our experiments we conclude that the algorithm can outperform other EDAs that use traditional methods of probability approximation in the optimization of functions with strong interactions among their variables.     

Estimation of sensitivity coefficients of nonlinear model input parameters which have a multinormal distribution

This paper considers the estimation of sensitivity coefficients based on sequential random sampling when the input parameters of a nonlinear model are correlated and have a multinormal distribution. Due to the difficulties in generating sequential random samples for correlated model inputs and the properties of response surface models, sampling-based (simulation- and experiment-based) methods could not be used to estimate sensitivity coefficients of correlated model inputs. For this reason, an algorithm based on multi-expressions of multinormal distribution has been developed and used to generate sequential random samples for estimation of sensitivity coefficients. The multi-expression approach has very high accuracy in generating multinormal random samples. The estimated sensitivity coefficients based on sequential random samples changed when sample size changed. Most estimates converged with a sample size of 5000. Model structure mainly determined the speed of convergence. Both correlation among input parameters and model structure influenced the estimates of sensitivity coefficients. The sensitivity coefficients were compared to global partial derivatives that were computed using numerical integration.     

Greedy algorithms for eigenvalue optimization problems in shape design of two-density inhomogeneous materials

This paper studies the eigenvalue optimization problems in the shape design of the two-density inhomogeneous materials. Two types of greedy algorithms are proposed to solve three optimization problems in finite element discretization. In the first type, the whole domain is initialized by one density. For each problem of the eigenvalue optimizations, we define a measurement of the element, which is the criterion to determine the ‘best’ element. We change the density of the ‘best’ element to the other density. Then the algorithm repeats the procedure until the area constraint is satisfied. In the second type, the algorithm begins with the density distribution satisfying the area constraint. Also, according to the measurement of the element, the algorithm finds a pair of the ‘best’ elements and exchanges their densities between each other. Furthermore, the accelerating greedy algorithms are proposed to speed up both two types. Three numerical examples are provided to illustrate the results.     

Estimation of parameters of failure distributions with fuzzy data

In this paper a simple procedure of estimation of parameters of two widely used failure distributions (the normal and Weibull distributions) and a method of finding confidence intervals for the parameters is developed. The computational burden of estimation with fuzzy data as observed by Kruse and Meyer (1988) is easily overcome by using special properties of the estimators. It is also demonstrated that the order statistics procedure of estimation can easily be modified to tackle fuzzy data.     

Optimum design of structures with random parameters

A general formulation of the minimum-weight optimization problem for indeterminate structures with random parameters is presented. The formulation enables the designer to specify maximum allowable probability of system failure and maximum allowable probabilities of occurrence of individual failure modes. All random parameters are characterized by their mean values and coefficients of variation, with the latter assumed to be amenable to realistic estimation at the outset. The standard deviations of response quantities are then obtained in a straightforward manner for use in the constraint equations, which generally resemble those for deterministic optimization problems. Several examples of truss and frame designs illustrate applications of the formulation.     

On thickness and orientational design with orthotropic materials

Recent results from sensitivity analysis for strain energy with anisotropic elasticity are applied to thickness and orientational design of laminated membranes. The first order gradients of the total elastic energy are primarily used in an optimality criteria based method. This traditional method is shown to give slow convergence with respect to design parameters, although the convergence of strain energy is very good. To gain a deeper insight into this rather general characteristic, second order derivatives are included and it is shown how they can be obtained by first order sensitivity analysis. Examples of thickness design only, orientational design only and combined thickness-orientational design are presented.     

峰值电流控制模式有源箝位正激变换器的小信号模型与设计

电流控制模式的补偿网络比电压控制模式的补偿网络容易调整,但是前者的建模要比后者的建模复杂得多。采用状态空间平均法为峰值电流控制有源箝位正激变换器建立了小信号模型,分析了箝位电路对变换器动态性能的影响,并给出了补偿网络的设计方法。     

Combined computer-aided approach for the facilities design problem and estimation of the distribution parameter in the case of multigoal optimization

The multigoal facilities design problem, a case of quadratic assignment problem, deals with the problem of optimum assignment of n facilities to n locations, optimizing multigoal cost objectives. These objectives are classified into two categories, conflicting and congruent. Conflicting objectives aim at minimization of total flow cost and maximization of total closeness rating, whereas congruent objectives aim at maximization of distance weighted cost of several attributes, vis. flow, closeness rating, etc. The technique available for dealing with the congruent objective optimization does not consider the weightage to these attributes. The optimality of a suboptimal solution should also be checked at all levels of weightages in order to arrive at a correct solution, with the help of estimation of the distribution parameter, in the case of the multigoal facilities design problem.

This paper presents a combined computer-aided approach which determines the solution of the multigoal facilities design problem at different weightages to attributes, finds the parameter of distribution viz. mean, median, mode, standard deviation, checks the optimality of solution, plots the histogram and gives the nature of distribution.