Response Surface Methods and Pareto Optimization in Crashworthiness Design

2003 ◽  
Author(s):  
Johan Andersson ◽  
Marcus Redhe
Keyword(s):  
Response Surface ◽  
Optimization Technique ◽  
Engineering Problem ◽  
Multi Objective Optimization ◽  
Maximum Acceleration ◽  
Response Surface Methods ◽  
Multi Objective ◽  
Engineering Design Problems ◽  
Conflicting Objectives ◽  
Crashworthiness Design

This paper presents a method where a multi objective optimization technique is used together with response surface methods in order to support crashworthiness design. As in most engineering design problems there are several conflicting objectives that have to be considered when formulating a design problem as an optimization problem. Here this is exemplified by the desire to minimize the intrusion into the passenger compartment area and simultaneously obtain low maximum acceleration during vehicle impact. These two objectives are naturally conflicting, since low maximum acceleration implies large intrusion. The contribution of this paper is to show a successful application of a set of existing methods to solve a real world engineering problem. The paper also presents methods of illustrating the results obtained from the multi-objective optimization.

Reducible Uncertain Interval Design by Kriging Metamodel Assisted Multi-Objective Optimization

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Joshua M. Hamel ◽  
Shapour Azarm
Keyword(s):  
Probability Distributions ◽  
Optimization Technique ◽  
Upper And Lower Bounds ◽  
Design Under Uncertainty ◽  
Multi Objective Optimization ◽  
Input Uncertainty ◽  
Multi Objective ◽  
Engineering Design Problems ◽  
Kriging Metamodel ◽  
Input Parameters

Sources of reducible uncertainty present a particular challenge to engineering design problems by forcing designers to make decisions about how much uncertainty to consider as acceptable in final design solutions. Many of the existing approaches for design under uncertainty require potentially unavailable or unknown information about the uncertainty in a system’s input parameters, such as probability distributions, nominal values, and/or uncertain intervals. These requirements may force designers into arbitrary or even erroneous assumptions about a system’s input uncertainty. In an effort to address these challenges, a new approach for design under uncertainty is presented that can produce optimal solutions in the form of upper and lower bounds (which specify uncertain intervals) for all input parameters to a system that possess reducible uncertainty. These solutions provide minimal variation in system objectives for a maximum allowed level of input uncertainty in a multi-objective sense and furthermore guarantee as close to deterministic Pareto optimal performance as possible with respect to the uncertain parameters. The function calls required by this approach are kept to a minimum through the use of a kriging metamodel assisted multi-objective optimization technique performed in two stages. The capabilities of this approach are demonstrated through three example problems of varying complexity.

Efficient Computation of Probabilistic Dominance in Multi-objective Optimization

2021 ◽  
Vol 1 (4) ◽  
pp. 1-26
Author(s):  
Faramarz Khosravi ◽  
Alexander Rass ◽  
Jürgen Teich
Keyword(s):  
Optimization Problems ◽  
Statistical Tests ◽  
Optimization Techniques ◽  
Simultaneous Optimization ◽  
Sampled Data ◽  
Efficient Computation ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Comparison Operator

Real-world problems typically require the simultaneous optimization of multiple, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables or objective functions. To cope with such uncertainties, stochastic and robust optimization techniques are widely studied aiming to distinguish candidate solutions with uncertain objectives specified by confidence intervals, probability distributions, sampled data, or uncertainty sets. In this scope, this article first introduces a novel empirical approach for the comparison of candidate solutions with uncertain objectives that can follow arbitrary distributions. The comparison is performed through accurate and efficient calculations of the probability that one solution dominates the other in terms of each uncertain objective. Second, such an operator can be flexibly used and combined with many existing multi-objective optimization frameworks and techniques by just substituting their standard comparison operator, thus easily enabling the Pareto front optimization of problems with multiple uncertain objectives. Third, a new benchmark for evaluating uncertainty-aware optimization techniques is introduced by incorporating different types of uncertainties into a well-known benchmark for multi-objective optimization problems. Fourth, the new comparison operator and benchmark suite are integrated into an existing multi-objective optimization framework that features a selection of multi-objective optimization problems and algorithms. Fifth, the efficiency in terms of performance and execution time of the proposed comparison operator is evaluated on the introduced uncertainty benchmark. Finally, statistical tests are applied giving evidence of the superiority of the new comparison operator in terms of \epsilon -dominance and attainment surfaces in comparison to previously proposed approaches.

Enhancement of Labyrinth Seals Efficiency by Means of a Multi-Objective Optimization Technique

2018 ◽  
Author(s):  
Mikhail Gritckevich ◽  
Kunyuan Zhou ◽  
Vincent Peltier ◽  
Markus Raben ◽  
Olga Galchenko
Keyword(s):  
Optimization Technique ◽  
Leakage Flow ◽  
Multi Objective Optimization ◽  
Labyrinth Seals ◽  
Engine Operation ◽  
Turbine Engine ◽  
Multi Objective ◽  
Single Objective ◽  
Ansys Workbench ◽  
Comprehensive Study

A comprehensive study of several labyrinth seals has been performed in the framework of both single-objective and multi-objective optimizations with the main focus on the effect of stator grooves formed due to the rubbing during gas turbine engine operation. For that purpose, the developed optimization workflow based on the DLR-AutoOpti optimizer and ANSYS-Workbench CAE environment has been employed to reduce the leakage flow and windage heating for several seals. The obtained results indicate that the seal designs obtained from optimizations without stator grooves have worse performance during the lifecycle than those with the stator grooves, justifying the importance of considering this effect for real engineering applications.

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