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Technical Paper

Comparing Uncertainty Quantification with Polynomial Chaos and Metamodel-Based Strategies for Computationally Expensive CAE Simulations and Optimization Applications

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.
Journal Article

Methods to Find Best Designs Among Infeasible Design Data Sets for Highly Constrained Design Optimization Problems

In recent years, the use of engineering design optimization techniques has grown multifold and formal optimization has become very popular among design engineers. However, the real world problems are turning out to be involved and more challenging. It is not uncommon to encounter problems with a large number of design variables, objectives and constraints. The engineers’ expectation, that an optimization algorithm should be able to handle multi-objective, multi-constrained data is leading them to apply optimization techniques to truly large-scale problems with extremely large number of constraints and objectives. Even as newer and better optimization algorithms are being developed to tackle such problems, more often than not, the optimization algorithms are unable to find a single feasible design that satisfies all constraints.
Journal Article

Multidisciplinary Design Optimization of Vehicle Weight Reduction

Multidisciplinary Design Optimization (MDO) is often required in aircraft design to address the multidisciplinary feasibility issues due to the disciplines, for example, aerodynamics, propulsion, and structures, are heavily coupled. However, in automobile designs, can we apply different type of MDO decomposition originated from aircraft design, to some MDO problem, for example, a vehicle weight reduction example? Also, to effectively and efficiently accommodate design changes, multi-party collaboration between discipline specialists, and fast decision making, a web-based MDO platform with knowledge-based repository for resource sharing, capability of version control, and enhancing data security, is very much needed. Two types of MDO decomposition: All-at-Once (AAO) and Collaborative Optimization (CO) are formulated for the weight reduction example. A typical six-step MDO process, from building single discipline work flow to comparing optimization results, is illustrated step-by-step.
Journal Article

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

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.
Journal Article

Optimization Strategies to Explore Multiple Optimal Solutions and Its Application to Restraint System Design

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.
Technical Paper

Study of Optimization Strategy for Vehicle Restraint System Design

Vehicle restraint systems are optimized to maximize occupant safety and achieve high safety ratings. The optimization formulation often involves the inclusion or exclusion of restraint features as discrete design variables, as well as continuous restraint design variables such as airbag firing time, airbag vent size, inflator power level, etc. The optimization problem is constrained by injury criteria such as Head Injury Criterion (HIC), chest deflection, chest acceleration, neck tension/compression, etc., which ensures the vehicle meets or exceeds all Federal Motor Vehicle Safety Standard (FMVSS) requirements. Typically, Genetic Algorithms (GA) optimizations are applied because of their capability to handle discrete and continuous variables simultaneously and their ability to jump out of regions with multiple local optima, particularly for this type of highly non-linear problems.