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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.

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.

Design optimization techniques are widely used to drive designs toward a global or a near global optimal solution. However, the achieved optimal solution often appears to be the only choice that an engineer/designer can select as the final design. This is caused by either problem topology or by the nature of optimization algorithms to converge quickly in local/global optimal or both. Problem topology can be unimodal or multimodal with many local and/or global optimal solutions. For multimodal problems, most global algorithms tend to exploit the global optimal solution quickly but at the same time leaving the engineer with only one choice of design. The paper explores the application of genetic algorithms (GA), simulated annealing (SA), and mixed integer problem sequential quadratic programming (MIPSQP) to find multiple local and global solutions using single objective optimization formulation.

Genetic Algorithms have proved to be very useful as global search methods for multi-dimensional optimization problems. One drawback, however, is that they are inefficient from the point of view of the number of function evaluations. This paper presents a two phase approach to optimization, using Game Theory in an initial step which provides a family of designs which are close to the Pareto frontier. The starting population for the genetic algorithm is then selected from the non-dominated designs produced in the first phase. This ensures that the genetic algorithm starts with a population of points which are already optimized to a large degree.

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.

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.

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.

Robustness/Reliability Assessment and Optimization (RRAO) is often computationally expensive because obtaining accurate Uncertainty Quantification (UQ) may require a large number of design samples. This is especially true where computationally expensive high fidelity CAE simulations are involved. Approximation methods such as the Polynomial Chaos Expansion (PCE) and other Response Surface Methods (RSM) have been used to reduce the number of time-consuming design samples needed. However, for certain types of problems require the RRAO, one of the first question to consider is which method can provide an accurate and affordable UQ for a given problem. To answer the question, this paper tests the PCE, RSM and pure sampling based approaches on each of the three selected test problems: the Ursem Waves mathematical function, an automotive muffler optimization problem, and a vehicle restraint system optimization problem.

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.