Conventional reliability analysis methods assume that a simulation model is able to represent the real physics accurately. However, this assumption may not always hold as the simulation model could be biased due to simplifications and idealizations. Simulation models are approximate mathematical representations of real-world systems and thus cannot exactly imitate the real-world systems. The accuracy of a simulation model is especially critical when it is used for the reliability calculation. Therefore, a simulation model should be validated using prototype testing results for reliability analysis. However, in practical engineering situation, experimental output data for the purpose of model validation is limited due to the significant cost of a large number of physical testing. Thus, the model validation needs to be carried out to account for the uncertainty induced by insufficient experimental output data as well as the inherent variability existing in the physical system and hence in the experimental test results. Therefore, in this study, a confidence-based model validation method that captures the variability and the uncertainty, and that corrects model bias at a user-specified target confidence level, has been developed. Reliability assessment using the confidence-based model validation can provide conservative estimation of the reliability of a system with confidence when only insufficient experimental output data are available.
Without confidence-based model validation, the designed product obtained using the conventional reliability-based design optimization (RBDO) optimum could either not satisfy the target reliability or be overly conservative. Therefore, simulation model validation is necessary to obtain a reliable optimum product using the RBDO process. In this study, the developed confidence-based model validation is integrated in the RBDO process to provide truly confident RBDO optimum design. The developed confidence-based model validation will provide a conservative RBDO optimum design at the target confidence level. However, it is challenging to obtain steady convergence in the RBDO process with confidence-based model validation because the feasible domain changes as the design moves (i.e., a moving-target problem). To resolve this issue, a practical optimization procedure, which terminates the RBDO process once the target reliability is satisfied, is proposed. In addition, the efficiency is achieved by carrying out deterministic design optimization (DDO) and RBDO without model validation, followed by RBDO with the confidence-based model validation. Numerical examples are presented to demonstrate that the proposed RBDO approach obtains a conservative and practical optimum design that satisfies the target reliability of designed product given a limited number of experimental output data.
Thus far, while the simulation model might be biased, it is assumed that we have correct distribution models for input variables and parameters. However, in real practical applications, only limited numbers of test data are available (parameter uncertainty) for modeling input distributions of material properties, manufacturing tolerances, operational loads, etc. Also, as before, only a limited number of output test data is used. Therefore, a reliability needs to be estimated by considering parameter uncertainty as well as biased simulation model. Computational methods and a process are developed to obtain confidence-based reliability assessment. The insufficient input and output test data induce uncertainties in input distribution models and output distributions, respectively. These uncertainties, which arise from lack of knowledge – the insufficient test data, are different from the inherent input distributions and corresponding output variabilities, which are natural randomness of the physical system.