Resumen de Quantifying uncertainty in complex automotive crashworthiness computational models: development of methodologies and implementation in vps/pamcrash
Marc Rocas Alonso
The automotive industry is constantly involved in the development of new methodologies and projects with the aim of reducing costs. During the vehicle design process, one of the most significant cost arises from building and testing prototypes for a valid crashworthiness performance. Mathematical crash models play an important role to get a solid knowledge of the structure, aiming to achieve a successful Euro NCAP test. However, the complex nature of a crash model hinders to obtain a robust design to guarantee a good performance. Currently, in the context of crashworthiness models, particular attention is focused to uncertainties affecting the design process. Despite important improvements in modeling uncertainty quantification, theoretical simulations and experimental models are not still in perfect correlation. Starting from a computational crash model that reproduces the behaviour of the structure system, the aim of uncertainty quantification is modeling the sources of uncertainty (lack of knowledge and natural variability) from the input parameters to the output responses.
This doctoral thesis presents an uncertainty quantification methodology for complex crashworthiness models, assessing the robustness of the models and supporting decision making. Due to the high computational cost of crash models (around 18 hours for a full VPS/Pamcrash model), the use of raw Monte Carlo methods for uncertainty quantification is often unaffordable. To overcome this limitation, in the first part of the thesis a review of the state-of-the-art is presented. The most relevant methods are implemented for a benchmark problem of interest for SEAT. However, some weaknesses are detected for classic approaches to deal with complex crash models. Input variability leads to nonlinear problems with high dimensional outputs. In addition, the behaviour of crash structures may have multiple hidden structure modes that can be a challenging task to be predicted. Detecting and describing these behaviours to quantify probabilities, statistics and sensitivity analysis (among other measures) can provide a potential tool for robust analysis for the SEAT portfolio.
To overcome this problem, the use of metamodels (surrogate models) is a well established approach, substituting the full order model (based on a limited number of training runs of the full order model at selected points of the input variables) for uncertainty quantification. In this doctoral thesis several techniques are studied, Ordinary Kriging, Polynomial Response Surface and a new novel surrogate strategy based on the Proper Generalized Decomposition denoted by Separated Response Surface. However, uncertainty inputs, nonlinear behaviours and large number of degrees of freedom for the outcome leads to solve high dimensional problems where the metamodel jeopardizes efficiency. Thus, previous to define a metamodel, a dimensionality reduction technique (for this thesis, kernel Principal Component Analysis) presents advantages to simplify the outcome description with the aim of building a posteriori efficient metamodel.
This thesis develops a methodology combining dimensionality reduction and surrogate modeling for uncertainty quantification of crash problems, aiming to perform a minimum number of full order simulations, using a data-driven adaptive approach. The proposed methodology is tested for an industrial benchmark problem, demonstrating its performance for obtaining robust information of the system for multi-purpose analyses.
