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Available methodologies for model bias identification are mainly regression-based approaches, such as Gaussian process, Bayesian inference-based models and so on. Accuracy and efficiency of these methodologies may degrade for characterizing the model bias when more system inputs are considered in the prediction model due to the curse of dimensionality for regression-based approaches. This paper proposes a copula-based approach for model bias identification without suffering the curse of dimensionality. The main idea is to build general statistical relationships between the model bias and the model prediction including all system inputs using copulas so that possible model bias distributions can be effectively identified at any new design configurations of the system. Two engineering case studies whose dimensionalities range from medium to high will be employed to demonstrate the effectiveness of the copula-based approach.

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.

This paper attempts to integrate a derivative-free probability analysis method to Reliability-Based Robust Design Optimization (RBRDO). The Eigenvector Dimension Reduction (EDR) method is used for the probability analysis method. It has been demonstrated that the EDR method is more accurate and efficient than the Second-Order Reliability Method (SORM) for reliability and quality assessment. Moreover, it can simultaneously evaluate both reliability and quality without any extra expense. Two practical engineering problems (vehicle side impact and layered bonding plates) are used to demonstrate the effectiveness of the EDR method.

Researchers desire to evaluate system reliability uniquely and efficiently. Despite its strong technical demand, little progress has been made on system reliability analysis in the last two decades. Up to now, bound methods for system reliability prediction have been dominant. For system reliability bounds, the second order bound method gives fairly accurate prediction for system reliability assuming that the probabilities of second-order joint events are accurately obtained. Two primary challenges in system reliability analysis are evaluation of the probabilities of second-order joint events and no unique system reliability for design optimization. Firstly, the greatest technical demand is found in an accurate and efficient method to numerically evaluate the probability of a second-order joint event.

This paper presents an innovative approach for quality engineering using the Eigenvector Dimension Reduction (EDR) Method. Currently industry relies heavily upon the use of the Taguchi method and Signal to Noise (S/N) ratios as quality indices. However, some disadvantages of the Taguchi method exist such as, its reliance upon samples occurring at specified levels, results to be valid at only the current design point, and its expensiveness to maintain a certain level of confidence. Recently, it has been shown that the EDR method can accurately provide an analysis of variance, similar to that of the Taguchi method, but is not hindered by the aforementioned drawbacks of the Taguchi method. This is evident because the EDR method is based upon fundamental statistics, where the statistical information for each design parameter is used to estimate the uncertainty propagation through engineering systems.