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A copula-based approach for model bias characterization was previously proposed [18] aiming at improving prediction accuracy compared to other model characterization approaches such as regression and Gaussian Process. This paper proposes an adaptive copula-based approach for model bias identification to enhance the available methodology. The main idea is to use cluster analysis to preprocess data, then apply the copula-based approach using information from each cluster. The final prediction accumulates predictions obtained from each cluster. Two case studies will be used to demonstrate the superiority of the adaptive copula-based approach over its predecessor.

To date, model validation metric is prominently designed for non-dynamic model responses. Though metrics for dynamic responses are also available, they are specifically designed for the vehicle impact application and uncertainties are not considered in the metric. This paper proposes the validation metric for general dynamic system responses under uncertainty. The metric makes use of the popular U-pooling approach and extends it for dynamic responses. Furthermore, shape deviation metric was proposed to be included in the validation metric with the capability of considering multiple dynamic test data. One vehicle impact model is presented to demonstrate the proposed validation metric.

Model validation is a process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model. In reliability based design, the intended use of the model is to identify an optimal design with the minimum cost function while satisfying all reliability constraints. It is pivotal that computational models should be validated before conducting the reliability based design. This paper presents an ensemble approach for model bias prediction in order to correct predictions of computational models. The basic idea is to first characterize the model bias of computational models, then correct the model prediction by adding the characterized model bias. The ensemble approach is composed of two prediction mechanisms: 1) response surface of model bias, and 2) Copula modeling of a series of relationships between design variables and the model bias, between model prediction and the model bias.

Analytical models (math or computer simulation models) are typically built on the basis of many assumptions and simplifications and hence model prediction could be inaccurate in intended applications. Model validation is thus critical to quantify and improve the degree of accuracy of these models. So far, little work considers model validation for various design configurations so that model prediction is accurate in the intended design space. Furthermore, there is a lack of effective approaches that can be used to quantify model accuracy considering different number of experimental data. To overcome these limitations, objective of this paper is to develop a model validation approach for various design configurations with a reference metric for model accuracy check considering different number of experimental data.