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We have recently proposed a new method for integrating design optimization with model validation by means of a sequential approach that uses variable-size local domains of the design space and statistical bootstrap techniques. Our work was motivated by the fact that global model validation may be neither affordable nor necessary. The method proceeds iteratively by obtaining test data at a design point, constructing around it a local domain in which the model is considered valid, and optimizing the design within this local domain. Due to test variability, it is important to know how many tests are needed to size each local domain of the sequential optimization process. Conducting an unnecessarily large number of tests may be inefficient, while a small number of tests may be insufficient to achieve the desired validity level. In this paper, we introduce a technique to determine the number of tests required to account for their variability by sizing the local domains accordingly. The goal is to achieve a desired level of model validity in each domain using the correlation between model data at the center and any other point in the local domain. To make the method more cost-effective we avoid generating some testsby statistically predicting a set of local domains along the optimization process. The proposed technique is illustrated with a piston design example. [ABSTRACT FROM AUTHOR]

Optimization is an indispensable tool in decision based design (DBD). There is an emerging consensus in DBD that the only correct objective to maximize is the decision maker's utility from a design. However, a utility function assessed a priori may not capture the preferences of the decision maker over the entire design space. As a result, when the optimizer searches for the optimal design, it may traverse (or end up) in regions in the design space where the preference order among different solutions is different from that used to build the utility function. For a highly non-convex design space, this can lead to convergence to a grossly suboptimal design depending on where we start the solution search. In this article, we propose two approaches to address this issue. First, we track the trajectory of the solution as generated by the optimizer and generate ranking questions that are presented to the designer to verify the correctness of the utility function, and second we propose backtracking rules if a local utility function is very different from the initially assessed function. We demonstrate our methodology using a mathematical example and a welded-beam design problem. [ABSTRACT FROM AUTHOR]

Simulation-based design optimization utilizes computational models that rely on assumptions and approximations. There is a need therefore, to ensure that the obtained designs will exhibit the desired behavior as anticipated given the model predictions. The common approach to accomplish that is to validate the utilized computational models prior to the design optimization process. However, this is practically an impossible task especially for design problems with high-dimensional design and parameter spaces. We have recently proposed a different approach for maximizing confidence in the designs generated during a sequential simulation-based optimization process based on calibrating the computational models when necessary and within local subdomains of the design space. In that work, the size of the local domains was held fixed and not linked to uncertainty, and the confidence in designs was quantified using Bayesian hypothesis testing. In this article, we present an improved methodology. Specifically, we use a statistical methodology to account for uncertainty and to determine the size of the local domains at each stage of the sequential design optimization process using parametric bootstrapping that involves maximum likelihood estimators of model parameters. The sequential process continues until the local domain does not change from stage to stage during the design optimization process, ensuring convergence to an optimal design. The proposed methodology is illustrated with the design of a thermal insulator using one-dimensional, linear heat conduction in a solid slab with heat flux boundary conditions. [ABSTRACT FROM AUTHOR]