This content is not included in your SAE MOBILUS subscription, or you are not logged in.
Comparing Uncertainty Quantification with Polynomial Chaos and Metamodel-Based Strategies for Computationally Expensive CAE Simulations and Optimization Applications
Technical Paper
2015-01-0437
ISSN: 0148-7191, e-ISSN: 2688-3627
Annotation ability available
Sector:
Language:
English
Abstract
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. Results of the UQ are compared thoroughly and recommendations based on the empirical results are made as the design guidelines to engineers.
Recommended Content
Authors
Citation
Xue, Z., Marchi, M., Parashar, S., and Li, G., "Comparing Uncertainty Quantification with Polynomial Chaos and Metamodel-Based Strategies for Computationally Expensive CAE Simulations and Optimization Applications," SAE Technical Paper 2015-01-0437, 2015, https://doi.org/10.4271/2015-01-0437.Also In
References
- Clarich, A., Pediroda, V., and Poloni, C., “A competitive Game Approach for Multi-objective Robust Design Optimization,” Proceedings of the AIAA 1st Intelligent Systems Technical Conference, Chicago, IL, 2004, doi:10.2514/6.2004-6511.
- Pediroda, V., Parussini, L., Poloni, C., Parashar, S. et al., “Efficient Stochastic Optimization using Chaos Collocation Method with modeFRONTIER,” SAE Int. J. Mater. Manf. 1(1):747-753, 2009, doi:10.4271/2008-01-1429.
- Parashar, S., Clarich, A., Geremia, P., and Otani, A., “Reverse Multi-Objective Robust Design Optimization (R-MORDO) Using Chaos Collocation Based Robustness Quantification for Engine Calibration,” 13th AIAA/ISSMO Conference, Fort Worth, TX, 2010, doi:10.2514/6.2010-9038.
- Wiener, N., “The homogeneous chaos,” Amer. J. Math. 60(4): 897-936, 1938, doi:10.2307/2371268.
- Xiu, D. and Karniadakis, G. E., “The Wiener-Askey polynomial chaos for stochastic differential equations,” SIAM J. Sci. Comput. 24(2):619-644, 2002, doi:10.1137/S1064827501387826.
- Poles, S. and Lovison, A., “A polynomial chaos approach to multiobjective optimization,” Dagstuhl Seminar Proceedings 09041, Hybrid and Robust Approaches to Multiobjective Optimization, 2009, http://drops.dagstuhl.de/opus/volltexte/2009/2000.
- Rasmussen, C. E. and Williams, C. K. I., “Gaussian Processes for Machine Learning,” MIT Press, 2006, ISBN 026218253X.
- Rökkönen, J., “Continuous Multimodal Global Optimization with Differential Evolution-Based Methods,” PhD Thesis, Lappeenranta University of Technology, 2009.
- modeFRONTIER® is a product of ESTECO srl, (www.esteco.com)
- Turco, A., “MetaHybrid: Combining Metamodels and Gradient-Based Techniques in a Hybrid Multi-Objective Genetic Algorithm,” Learning and Intelligent Optimization, 5th International Conference, LION 5, Rome, Italy, 2011, doi:10.1007/978-3-642-25566-3_22.
- http://en.wikipedia.org/wiki/Truncated_normal_distribution
- GT-Power® is a product of Gamma Technologies (www.gtisoft.com)
- Rigoni, E. and Turco, A., “Metamodels for Fast Multi-objective Optimization: Trading Off Global Exploration and Local Exploitation,” 8th International Conference, Simulated Evolution and Learning 2010, Lecture Notes in Computer Science, 6457: 523-532, 2010.
- Xue, Z., Parashar, S., Li, G., and Fu, Y., “Optimization Strategies to Explore Multiple Optimal Solutions and Its Application to Restraint System Design,” SAE Int. J. Passeng. Cars - Mech. Syst. 5(1):540-551, 2012, doi:10.4271/2012-01-0578.
- Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T., “A fast and elitist multiobjective genetic algorithm: NSGA-II,” Evolutionary Computation, IEEE Transactions on, 6(2):182-197, 2002, doi:10.1109/4235.996017.