A Sequential Algorithm for Possibility-Based Design Optimization

2007 ◽  
Vol 130 (1) ◽  
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.

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.

A Sequential Algorithm for Reliability-Based Robust Design Optimization Under Epistemic Uncertainty

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Yuanfu Tang ◽  
Jianqiao Chen ◽  
Junhong Wei
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Epistemic Uncertainty ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Sequential Algorithm ◽  
Practical Applications ◽  
Reliability Based Design ◽  
Design Variables ◽  
Novel Concept

In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some probabilistic constraints in a reliability based design optimization (RBDO) problem. It is important to ensure that the probabilistic constraints at the optimum in a RBDO problem are insensitive to the variations of design variables. In this paper, we propose a novel concept and procedure for reliability based robust design in the context of random uncertainty and epistemic uncertainty. The epistemic uncertainty of design variables is first described by an info gap model, and then the reliability-based robust design optimization (RBRDO) is formulated. To reduce the computational burden in solving RBRDO problems, a sequential algorithm using shifting factors is developed. The algorithm consists of a sequence of cycles and each cycle contains a deterministic optimization followed by an inverse robustness and reliability evaluation. The optimal result based on the proposed model satisfies certain reliability requirement and has the feasible robustness to the epistemic uncertainty of design variables. Two examples are presented to demonstrate the feasibility and efficiency of the proposed method.

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.

Barrier Function Method in Reliability Based Design Optimization

2005 ◽  
Vol 297-300 ◽  
pp. 1882-1887
Author(s):  
Tae Hee Lee ◽  
Jung Hun Yoo
Keyword(s):  
Design Optimization ◽  
Barrier Function ◽  
Reliability Index ◽  
Feasible Solution ◽  
Reliability Based Design Optimization ◽  
User Requirement ◽  
Mean Values ◽  
Reliability Based Design ◽  
Design Variables ◽  
Reliability Method

In practical design applications, most design variables such as thickness, diameter and material properties are not deterministic but stochastic numbers that can be represented by their mean values with variances because of various uncertainties. When the uncertainties related with design variables and manufacturing process are considered in engineering design, the specified reliability of the design can be achieved by using the so-called reliability based design optimization. Reliability based design optimization takes into account the uncertainties in the design in order to meet the user requirement of the specified reliability while seeking optimal solution. Reliability based design optimization of a real system becomes now an emerging technique to achieve reliability, robustness and safety of the design. It is, however, well known that reliability based design optimization can often have so multiple local optima that it cannot converge into the specified reliability. To overcome this difficulty, barrier function approach in reliability based design optimization is proposed in this research and feasible solution with specified reliability index is always provided if a feasible solution is available. To illustrate the proposed formulation, reliability based design optimization of a bracket design is performed. Advanced mean value method and first order reliability method are employed for reliability analysis and their optimization results are compared with reliability index approach based on the accuracy and efficiency.

Reliability-based design optimization of electromagnetic shielding structure using neural networks and real-coded genetic algorithm

2014 ◽  
Vol 228 (18) ◽  
pp. 3471-3481 ◽  
Author(s):  
Heeralal Gargama ◽  
Sanjay K Chaturvedi ◽  
Awalendra K Thakur
Keyword(s):  
Genetic Algorithm ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Design Optimization ◽  
Electromagnetic Shielding ◽  
Optimization Approach ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Design Variables ◽  
Real Coded Genetic Algorithm

The conventional approaches for electromagnetic shielding structures’ design, lack the incorporation of uncertainty in the design variables/parameters. In this paper, a reliability-based design optimization approach for designing electromagnetic shielding structure is proposed. The uncertainties/variability in the design variables/parameters are dealt with using the probabilistic sufficiency factor, which is a factor of safety relative to a target probability of failure. Estimation of probabilistic sufficiency factor requires performance function evaluation at every design point, which is extremely computationally intensive. The computational burden is reduced greatly by evaluating design responses only at the selected design points from the whole design space and employing artificial neural networks to approximate probabilistic sufficiency factor as a function of design variables. Subsequently, the trained artificial neural networks are used for the probabilistic sufficiency factor evaluation in the reliability-based design optimization, where optimization part is processed with the real-coded genetic algorithm. The proposed reliability-based design optimization approach is applied to design a three-layered shielding structure for a shielding effectiveness requirement of ∼40 dB, used in many industrial/commercial applications, and for ∼80 dB used in the military applications.

Reliability-Based Design Optimization of Complex Problems With Multiple Design Points via Narrowed Search Region

2019 ◽  
Vol 142 (6) ◽  
Author(s):  
Yutian Wang ◽  
Peng Hao ◽  
Zhendong Guo ◽  
Dachuan Liu ◽  
Qiang Gao
Keyword(s):  
Design Optimization ◽  
Risk Function ◽  
Computational Cost ◽  
Reliability Based Design Optimization ◽  
Search Region ◽  
Complex Problems ◽  
Reliability Based Design ◽  
Training Samples ◽  
Gradient Based ◽  
Similar Accuracy

Abstract The expensive computational cost is always a major concern for reliability-based design optimization (RBDO) of complex problems. The performance of RBDO can be lowered by the inaccuracy of reliability analysis (RA) which is caused by multiple local optimums and multiple design points in highly non-linear space. In order to reduce the computational burden and guarantee the accuracy of RA (and thus to improve the RBDO performance), a global RBDO algorithm by adopting an improved constraint boundary sampling (GRBDO-ICBS) method is proposed. Specifically, the GRBDO-ICBS method first narrows the concerned search region by using a Kriging-based global search. The accuracies of the design points are verified by the expected risk function (ERF), and the corresponding inaccurate design points are added into training samples to update Kriging. Then a multi-start gradient-based sequential RBDO is carried out, which tries to find out all multiple design points in the concerned search region. The performance of GRBDO-ICBS is demonstrated by four examples. All results have shown that the proposed method can achieve similar accuracy as Monte Carlo simulation (MCS)-based RBDO but with a much lower computational cost.

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.

Development of a Multistage Reliability-Based Design Optimization Method

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Eric J. Paulson ◽  
Ryan P. Starkey
Keyword(s):  
Objective Function ◽  
Design Optimization ◽  
Technology Development ◽  
Computational Cost ◽  
Optimization Method ◽  
Comparison Method ◽  
Reliability Based Design Optimization ◽  
Numerical Example ◽  
Reliability Based Design ◽  
System Acquisition

Complex system acquisition and its associated technology development have a troubled recent history. The modern acquisition timeline consists of conceptual, preliminary, and detailed design followed by system test and production. The evolving nature of the estimates of system performance, cost, and schedule during this extended process may be a significant contribution to recent issues. The recently proposed multistage reliability-based design optimization (MSRBDO) method promises improvements over reliability-based design optimization (RBDO) in achieved objective function value. In addition, its problem formulation more closely resembles the evolutionary nature of epistemic design uncertainties inherent in system design during early system acquisition. Our goal is to establish the modeling basis necessary for applying this new method to the engineering of early conceptual/preliminary design. We present corrections in the derivation and solutions to the single numerical example problem published by the original authors, Nam and Mavris, and examine the error introduced under the reduced-order reliability sampling used in the original publication. MSRBDO improvements over the RBDO solution of 10–36% for the objective function after first-stage optimization are shown for the original second-stage example problem. A larger 26–40% improvement over the RBDO solution is shown when an alternative comparison method is used than in the original. The specific implications of extending the method to arbitrary m-stage problems are presented, together with a solution for a three-stage numerical example. Several approaches are demonstrated to mitigate the computational cost increase of MSRBDO over RBDO, resulting in a net decrease in calculation time of 94% from an initial MSRBDO baseline algorithm.

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