SUMMARYMetamodels are widely used to facilitate the analysis and optimization of engineering systems that involve computationally expensive simulations. Kriging is a metamodelling technique that is well known for its ability to build surrogate models of responses with non-linear behaviour. However, the assumption of a stationary covariance structure underlying Kriging does not hold in situations where the level of smoothness of a response varies significantly. Although non-stationary Gaussian process models have been studied for years in statistics and geostatistics communities, this has largely been for physical experimental data in relatively low dimensions. In this paper, the non-stationary covariance structure is incorporated into Kriging modelling for computer simulations. To represent the non-stationary covariance structure, we adopt a non-linear mapping approach based on parameterized density functions. To avoid over-parameterizing for the high dimension problems typical of engineering design, we propose a modified version of the non-linear map approach, with a sparser, yet flexible, parameterization. The effectiveness of the proposed method is demonstrated through both mathematical and engineering examples. The robustness of the method is verified by testing multiple functions under various sampling settings. We also demonstrate that our method is effective in quantifying prediction uncertainty associated with the use of metamodels.
Summary: Information, communication, and navigation devices need to be evaluated for ease-of-use and safety while driving. Lab tests, if validated, can evaluate prototype designs faster, more economically, and earlier than on-road tests. The Static Load Test was evaluated for its ability to predict on-road driver performance while using in-vehicle devices. In this test, participants perform various in-vehicle tasks in a lab while viewing a videotaped road scene on a monitor, tapping a brake pedal when a central or peripheral light is observed. For the on-road comparison test, the device, tasks, and lights are the same, but the participants also drive the vehicle while performing the tasks and responding to the lights. In both the lab and road tests, ten driver performance variables were measured. Our goal was to produce a linear model to predict an on-road variable from the lab data with low residual error, high percent variance explained, and few errors in classifying tasks as meeting or not meeting on-road driver performance criteria. Separate test data from a replicated Static Load Test at an independent lab were used to further validate the models. The results indicate a simple, inexpensive, and low-fidelity Static Load Test can accurately predict a number of on-road driver performance variables suitable for assessing the safety and ease-of-use of advanced in-vehicle devices while driving.
Metamodels are widely used to facilitate the analysis and optimization of engineering systems that involve computationally expensive simulations. Kriging is a metamodeling technique that is well known for its ability to build surrogate models of responses with nonlinear behavior. However, the assumption of a stationary covariance structure underlying Kriging does not hold in situations where the level of smoothness of a response varies significantly. Although nonstationary Gaussian process models have been studied for years in statistics and geostatistics communities, this has largely been for physical experimental data in relatively low dimensions. In this paper, the nonstationary covariance structure is incorporated into Kriging modeling for computer simulations. To represent the nonstationary covariance structure, we adopt a nonlinear mapping approach based on a parameterized density functions. To avoid over-parameterizing for the high dimension problems typical of engineering design, we propose a modified version of the nonlinear map approach, with a sparser, yet flexible, parameterization. The effectiveness of the proposed method is demonstrated through both mathematical and engineering examples. The robustness of the method is verified by testing multiple functions under various sampling settings. We also demonstrate that our method is effective in quantifying prediction uncertainty associated with the use of metamodels.
Delivering reliable, high-quality products at low cost has become the key to survival in today's global economy. The presence of uncertainty in the analysis and design of engineering systems has always been recognized. Traditional deterministic analysis accounts for these uncertainties through the use of empirical safety factors. These safety factors are derived from past experience and do not provide quantifiable measures of the frequency at which failure will occur.Engineering design usually involves a trade-off between maximizing reliability at the component or system level while achieving cost targets. In contrast to the traditional deterministic design, probabilistic analysis provides the required information for optimum design and accomplishes both goals simultaneously. In the automotive industry, quality products are vehicles whose specifications, as manufactured, meet customer requirements. Given the uncertainties in loads, materials, and manufacturing, modern methods of reliability analysis should be used to ensure automotive quality in terms of reliability measures.In large-scale systems, often encountered in the automotive and aerospace industries among others, reliability predictions based on expensive full-scale tests are not economically feasible. Efficient computational methods represent a far better alternative. The first requirement of a computational reliability analysis is to develop a quantitative model of the behavior of interest. Subsequently, the statistical behavior is defined for all random variables involved in the limit-state function that separates the failure and the Zissimos P. Mourelatos
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