Optimal uncertainty reduction for multi-disciplinary multi-output systems using sensitivity analysis

Li, M.; Hamel, Joshua M.; Azarm, Shapour

doi:10.1007/s00158-009-0372-6

Cited by 17 publications

(7 citation statements)

References 26 publications

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“…Deterministic approaches, on the other hand, incorporate non-statistical index such as gradient information (Taguchi, 1978; Renaud, 1997; Lee and Park, 2001; Kim et al , 2010; Papadimitriou and Giannakoglou, 2013) or sensitivity region information (Gunawan and Azarm, 2004; Gunawan and Azarm, 2005; Li et al , 2009; Li et al , 2010; Li et al , 2011; Zhou et al , 2012; Mortazavi et al , 2013; Cheng et al , 2015) into the original optimization problem to obtain a robust optimum. The interval number programming method is also used as a deterministic approach to obtain a robust optimum under interval uncertainty (Li et al , 2013; Wu et al , 2015a; Wu et al , 2015b).…”

Section: Introductionmentioning

confidence: 99%

A multi-objective robust optimization approach for engineering design under interval uncertainty

Zhou

Shao

Jiang

et al. 2018

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Purpose Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty. Design/methodology/approach In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process. Findings Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost. Practical implications The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties. Originality/value A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

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Section: Introductionmentioning

confidence: 99%

A multi-objective robust optimization approach for engineering design under interval uncertainty

Zhou

Shao

Jiang

et al. 2018

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“…RO methods can be classified into two types: Probabilistic approaches perform the RO by using the probability distribution of variable variations, usually mean and variance of uncertain variables (Du et al , 2008; Li et al , 2015; Carpinelli et al , 2015; Pedersen et al , 2016). Deterministic approaches , on the other hand, incorporate non-statistical index such as gradient information (Taguchi, 1978; Renaud, 1997; Lee and Park, 2001; Kim et al , 2010; Papadimitriou and Giannakoglou, 2013) or sensitivity region information (SRI) (Gunawan and Azarm, 2004; Gunawan and Azarm, 2005; Li et al , 2009; Li et al , 2010; Li et al , 2011; Zhou et al , 2012; Mortazavi et al , 2013; Cheng et al , 2015) into the original optimization problem to obtain a robust optimum. …”

Section: Introductionmentioning

confidence: 99%

“…Deterministic approaches , on the other hand, incorporate non-statistical index such as gradient information (Taguchi, 1978; Renaud, 1997; Lee and Park, 2001; Kim et al , 2010; Papadimitriou and Giannakoglou, 2013) or sensitivity region information (SRI) (Gunawan and Azarm, 2004; Gunawan and Azarm, 2005; Li et al , 2009; Li et al , 2010; Li et al , 2011; Zhou et al , 2012; Mortazavi et al , 2013; Cheng et al , 2015) into the original optimization problem to obtain a robust optimum.…”

Section: Introductionmentioning

confidence: 99%

An on-line Kriging metamodel assisted robust optimization approach under interval uncertainty

Zhou

Jiang

Shao

et al. 2017

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Purpose Uncertainty is inevitable in real-world engineering optimization. With an outer-inner optimization structure, most previous robust optimization (RO) approaches under interval uncertainty can become computationally intractable because the inner level must perform robust evaluation for each design alternative delivered from the outer level. This paper aims to propose an on-line Kriging metamodel-assisted variable adjustment robust optimization (OLK-VARO) to ease the computational burden of previous VARO approach. Design/methodology/approach In OLK-VARO, Kriging metamodels are constructed for replacing robust evaluations of the design alternative delivered from the outer level, reducing the nested optimization structure of previous VARO approach into a single loop optimization structure. An on-line updating mechanism is introduced in OLK-VARO to exploit the obtained data from previous iterations. Findings One nonlinear numerical example and two engineering cases have been used to demonstrate the applicability and efficiency of the proposed OLK-VARO approach. Results illustrate that OLK-VARO is able to obtain comparable robust optimums as to that obtained by previous VARO, while at the same time significantly reducing computational cost. Practical implications The proposed approach exhibits great capability for practical engineering design optimization problems under interval uncertainty. Originality/value The main contribution of this paper lies in the following: an OLK-VARO approach under interval uncertainty is proposed, which can significantly ease the computational burden of previous VARO approach.

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“…This method however did not address the interaction between design parameters, and only the main effect was analyzed. A hybrid approach [26,27] was developed to analyze the sensitivity of parameterized interval variables via multi-objective optimization problems, where the variation of an output with a given interval input was estimated by optimization. The searching procedure for optimization can be computationally expensive for highly nonlinear and coupled systems.…”

Section: Introductionmentioning

confidence: 99%

“…Different from other interval based SA approaches [25][26][27], our approach considers both the main and interaction effects for feasible design problems with continuous design parameters. Our SA approach for interval-valued variables is global.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Analysis in Quantified Interval Constraint Satisfaction Problems

Wang

Cheng

et al. 2015

Journal of Mechanical Design

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Interval is an alternative to probability distribution in quantifying uncertainty for sensitivity analysis (SA) when there is a lack of data to fit a distribution with good confidence. It only requires the information of lower and upper bounds. Analytical relations among design parameters, design variables, and target performances under uncertainty can be modeled as interval-valued constraints. By incorporating logic quantifiers, quantified constraint satisfaction problems (QCSPs) can integrate semantics and engineering intent in mathematical relations for engineering design. In this paper, a global sensitivity analysis (GSA) method is developed for feasible design space searching problems that are formulated as QCSPs, where the effects of value variations and quantifier changes for design parameters on target performances are analyzed based on several proposed metrics, including the indeterminacy of target performances, information gain of parameter variations, and infeasibility of constraints. Three examples are used to demonstrate the proposed approach.

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Optimal uncertainty reduction for multi-disciplinary multi-output systems using sensitivity analysis

Cited by 17 publications

References 26 publications

A multi-objective robust optimization approach for engineering design under interval uncertainty

A multi-objective robust optimization approach for engineering design under interval uncertainty

An on-line Kriging metamodel assisted robust optimization approach under interval uncertainty

Sensitivity Analysis in Quantified Interval Constraint Satisfaction Problems

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