Design Optimization With Discrete and Continuous Variables of Aleatory and Epistemic Uncertainties

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Hong-Zhong Huang ◽  
Xudong Zhang
Keyword(s):  
Design Optimization ◽  
Engineering Design ◽  
Epistemic Uncertainty ◽  
Reliability Assessment ◽  
Structure Design ◽  
Sequential Optimization ◽  
Continuous Variables ◽  
Reliability Based Design ◽  
Design Variables ◽  
Discrete Design Variables

Reliability based design optimization has received increasing attention for satisfying high requirements on reliability and safety in structure design. However, in practical engineering design, there are both continuous and discrete design variables. Moreover, both aleatory uncertainty and epistemic uncertainty may associate with design variables. This paper proposes the formulation of random/fuzzy continuous/discrete variables design optimization (RFCDV-DO) and two different approaches for uncertainty analysis (probability/possibility analysis). A method named random/fuzzy sequential optimization and reliability assessment is proposed based on the idea of sequential optimization and reliability assessment to improve efficiency in solving RFCDV-DO problems. An engineering design problem is utilized to demonstrate the approaches and the efficiency of the proposed method.

Possibility-Based Multidisciplinary Design Optimization in the Framework of Sequential Optimization and Reliability Assessment

2009 ◽  
Author(s):  
Xudong Zhang ◽  
Hong-Zhong Huang ◽  
Shengkui Zeng ◽  
Zhili Wang
Keyword(s):  
Design Optimization ◽  
Engineering Design ◽  
Multidisciplinary Design Optimization ◽  
High Reliability ◽  
Reliability Assessment ◽  
Coupled Systems ◽  
Multidisciplinary Design ◽  
Sequential Optimization ◽  
Sufficient Information ◽  
Early Design

Reliability Based Multidisciplinary Design Optimization (RBMDO) has received increasing attention to reach high reliability and safety in complex and coupled systems. In early design of such systems, however, information is often not sufficient to construct the precise probabilistic distributions required by the RBMDO and consequently RBMDO can not be carried out effectively. The present work proposes a method of Possibility Based Multidisciplinary Design Optimization (PBMDO) within the framework of the Sequential Optimization and Reliability Assessment (PBMDO-SORA). The proposed method enables designers to solve MDO problems without sufficient information on the uncertainties associated with variables, and also to efficiently decrease the computational demand. The efficiency of the proposed method is illustrated with an engineering design.

An Efficient Approach for Reliability-Based Design Optimization Combined Sequential Optimization with Approximate Models

2018 ◽  
Vol 15 (04) ◽  
pp. 1850018 ◽  
Author(s):  
Bao Quoc Doan ◽  
Guiping Liu ◽  
Can Xu ◽  
Minh Quang Chau
Keyword(s):  
Design Optimization ◽  
Reliability Assessment ◽  
Latin Hypercube Sampling ◽  
Assessment Method ◽  
Probabilistic Constraints ◽  
Sequential Optimization ◽  
Reliability Based Design Optimization ◽  
Efficient Approach ◽  
Reliability Based Design ◽  
Approximate Models

Reliability-based design optimization (RBDO) involves evaluation of probabilistic constraints which can be time-consuming in engineering structural design problems. In this paper, an efficient approach combined sequential optimization with approximate models is suggested for RBDO. The radial basis functions and Latin hypercube sampling are used to construct approximate models of the probabilistic constraints. Then, a sequential optimization with approximate models is carried out by the sequential optimization and reliability assessment method which includes a serial of cycles of deterministic optimization and reliability assessment. Three numerical examples are presented to demonstrate the efficiency of the proposed approach.

A Sequential Algorithm for Possibility-Based Design Optimization

2006 ◽  
Author(s):  
Jun Zhou ◽  
Zissimos P. Mourelatos
Keyword(s):  
Design Optimization ◽  
Optimization Algorithm ◽  
Computational Cost ◽  
Possibility Theory ◽  
Sequential Optimization ◽  
Sequential Algorithm ◽  
Computationally Efficient ◽  
Worst Case ◽  
Reliability Based Design ◽  
Design Variables

Deterministic optimal designs that are obtained without taking into account uncertainty/variation are usually unreliable. Although reliability-based design optimization accounts for variation, it assumes that statistical information is available in the form of fully defined probabilistic distributions. This is not true for a variety of engineering problems where uncertainty is usually given in terms of interval ranges. In this case, interval analysis or possibility theory can be used instead of probability theory. This paper shows how possibility theory can be used in design and presents a computationally efficient sequential optimization algorithm. After, the fundamentals of possibility theory and fuzzy measures are described, a double-loop, possibility-based design optimization algorithm is presented where all design constraints are expressed possibilistically. The algorithm handles problems with only uncertain or a combination of random and uncertain design variables and parameters. In order to reduce the high computational cost, a sequential algorithm for possibility-based design optimization is presented. It consists of a sequence of cycles composed of a deterministic design optimization followed by a set of worst-case reliability evaluation loops. Two examples demonstrate the accuracy and efficiency of the proposed sequential algorithm.

Sequential Particle Swarm Optimization and Reliability Assessment of Planar-Type Voice Coil Motor

2013 ◽  
Author(s):  
Haikun Wang ◽  
Hong-Zhong Huang ◽  
Huanwei Xu ◽  
Zhonglai Wang ◽  
Xiaoling Zhang
Keyword(s):  
Particle Swarm Optimization ◽  
Design Optimization ◽  
Force Constant ◽  
Reliability Assessment ◽  
Particle Swarm ◽  
Voice Coil Motor ◽  
Sequential Optimization ◽  
Reliability Based Design Optimization ◽  
Swarm Optimization ◽  
Reliability Based Design

Planar-type voice coil motor (VCM) is a key component in ultra-precision motion of fine stage of lithography machine. The reliability-based design optimization (RBDO) method given in this work provides a novel criterion to ensure performance of Lorentz motors by evaluating the reliability of force constant. To solve the reliability based design optimization problem in discrete space with the speed of decoupled loop in sequential optimization and reliability assessment (SORA) for global solution, a Sequential Particle Swarm Optimization and Reliability Assessment method is proposed. The reliability boundary shift is put into penalty function for constrained optimization in fitness evaluation of particle swarm optimization (PSO). The presented optimization design model, the geometric parameters of the studied Planar-type VCM in finite element model are treated as design variables whereas the thrust force constant is an output quantity of interests. By using electromagnetic analysis, the desired requirements of Lorentz motors are verified.

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