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Technical Paper

Comparing Robust Design Optimization and Reliability Based Optimization Formulations for Practical Aspects of Industry Problems

2015-04-14
2015-01-0471
Need for accounting Robustness and Reliability in engineering design is well understood and being researched. However, the actual practice of applying robustness and reliability methods to high fidelity CAE based simulations, especially during optimization is just starting to gain traction in last few years. Availability of computing power is helping the use of such methods, but, at the same time the demand for modeling stochastic behavior with high fidelity CAE simulations and considering large number of stochastic variables still makes it prohibitive. Typically, Robust Design Optimization (RDO) formulations calculate mean and standard deviation of responses based on sampling. On the other hand Reliability Based Design Optimization (RBDO) formulations have been using methods like First Order Reliability Method (FORM) or Second Order Reliability Method (SORM) which require nested optimization to evaluate joint probability distribution and reliability factor.
Technical Paper

Application of Hybrid Optimization Algorithm to Automotive Design Problems and Performance Comparison with Other Standard Optimizers

2015-04-14
2015-01-1355
With the increase in computational capability, there is an increase in classes of engineering optimization problems that are considered solvable. Not all problems benefit from similar types of approaches when searching for an optimal solution. Some have objective functions that can be described as largely unimodal while others have complex behavior with multiple local optima. Further, there are problems that have behavior that is not clearly apparent due to the involvement of CAD/CAE tools and high number of inputs/factors. There has been a push to combine dissimilar optimization approaches in order to tackle such hard-to-solve problems for a variety of reasons. One such combination is the “Hybrid” optimization algorithm developed by ESTECO for their commercial optimization software “modeFRONTIER”. This paper gives the reader some examples and results from problems where the Hybrid algorithm has proved to be a worthy choice.
Journal Article

Effective Decision Making and Data Visualization Using Partitive Clustering and Principal Component Analysis (PCA) for High Dimensional Pareto Frontier Data

2015-04-14
2015-01-0460
Decision making in engineering design is complicated, especially when dealing with high-dimensional data. Modern software tools are able to produce a large amount of data while performing optimization studies. A typical optimization problem with many objectives may produce 100s or even 1000s of Pareto Optimal solutions. It is a challenge to analyze this data and make a decision about which design/s to choose for further testing or as a final design. To tackle the problem, two data analysis techniques are used in this paper. Partitive Clustering (PC) is used to locate groups of similar designs in the dataset while Principal Component Analysis (PCA) is used to reduce the dimensionality of the data and visualize it in two and three dimensions. Although these techniques can be used independently, when used together, they prove to be a tremendous help in decision making. This paper underlines the benefit of using these two methods together.
Technical Paper

Multi-objective Optimization of a Charge Air Cooler using modeFRONTIER

2008-04-14
2008-01-0886
In order for an automotive charge air cooler (CAC) to function efficiently, the flow of air through the cross tubes should be as uniform as possible. The position of the inlet and outlet, as well as the shape of the header tanks, are generally the most important determinants of the flow uniformity, and therefore of the cooling performance of the system. In an attempt to achieve this goal of flow uniformity, however, the effect on pressure loss in the system must also be considered. Further, the cost of the CAC tanks, which is directly related to the amount of material, should be minimized. Finally, the physical space in which the CAC can be located is limited by other underhood components and vehicle styling features. This presents an optimization problem with four conflicting objectives: to reduce the pressure loss in the system, to increase the uniformity of flow in the tubes, to minimize the tank material and to conform to the package volume.
Technical Paper

Self Organizing Maps (SOM) for Design Selection in Multi-Objective Optimization using modeFRONTIER

2008-04-14
2008-01-0874
Self Organizing Maps (SOM) has evolved as a very useful visualization and data analysis tool for high dimensional data. Visualization and analysis of Pareto data for multi-objective optimization problems with more than three objectives is also a challenge. This paper will investigate the application of SOM for visualization and design selection for multi-objective Pareto data. The SOM is applied to investigate the spread of Pareto front as well as to investigate trade-off between objectives. The visualization and selection strategy is applied to mathematical test problem to explain the concept. Later it is also applied to real world automotive design problem of engine optimization.
Journal Article

Efficient Stochastic Optimization using Chaos Collocation Method with modeFRONTIER

2008-04-14
2008-01-1429
Robust Design Optimization (RDO) using traditional approaches such as Monte Carlo (MC) sampling requires tremendous computational expense. Performing a RDO for problems involving time consuming CAE analysis may not even be possible within time constraints. In this paper a new stochastic modeling technique based on chaos collocation method is used to measure the mean and standard deviation (σ) for uncertain output parameters. For a given accuracy, chaos collocation method requires far less sample evaluations compared to MC. The efficient evaluation of mean and std. deviation terms using chaos collocation method makes it quite attractive to be used with RDO methods. In this work the RDO of an automotive engine design is performed employing chaos collocation method.
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