A framework for combining model calibration with model-based optimization in virtual engineering design workflows

In recent years, the development of complex engineering products has seen a movement towards increasing levels of virtualisation using expensive black-box simulations. One of the main factors driving this trend is the rapid increase in available computational resources. As computational capabilities are further developed, projects which used to be infeasible are now possible.

When using a virtual engineering design process, once the structure of the simulation model has been built, there is a need to perform both calibration and optimization in order to ensure that the resulting outputs presented to a decision maker correctly represent the optimal solutions. Both of these stages require the use of model evaluations to determine the efficacy of new parameterizations and designs. Such usage becomes a problem when there is only a limited budget of evaluations available within the design process for both stages. This problem is reinforced further by the current practice of considering the two stages as separate problems where there is only a limited transfer of knowledge between them, rather than a linked process.

The question that is posed within this research is whether there would be any benefits to adopting a linked approach to the calibration and optimization of expensive multi-objective design problems.

In order to determine an answer to this question, it is first essential to set out a mathematical formulation for the joint problem of calibration and optimisation. In order to assess any newly developed methods, it is necessary to devise a set of benchmark problems that contain both model parameters and control inputs that are required to be determined. This is achieved through the adaptation of pre-existing problems from the optimization literature as well as the development of a new component that fits within the Walking Fish Group (WFG) framework. A new alternating combined methodology is developed with the aim of gaining information within more relevant areas of the search space to improve the efficiency of the evaluations used. This new alternating method is further expanded to incorporate surrogates with the aim of improving knowledge sharing between the stages of model calibration and optimization. It is found that the use of the new alternating method can improve the final parameter sets obtained by the calibration, when compared to the classical approach. The extended alternating approach also offers superior calibration, in addition to achieving faster improvement in convergence of the optimiser to the true Pareto front of optimal designs.