Sensitivity analysis for multidisciplinary design optmization - Maginot, Jeremy (Cranfield University, 2007)
When designing a complex industrial product, the designer often has to optimise simultaneously multiple conflicting criteria. Such a problem does not usually have a unique solution, but a set of non-dominated solutions known as Pareto solutions. In this context, the progress made in the development of more powerful but more computationally demanding numerical methods has led to the emergence of multi-disciplinary optimisation (MDO). However, running computationally expensive multi-objective optimisation procedures to obtain a comprehensive description of the set of Pareto solutions might not always be possible. The aim of this research is to develop a methodology to assist the designer in the multi-objective optimisation process. As a result, an approach to enhance the understanding of the optimisation problem and to gain some insight into the set of Pareto solutions is proposed. This approach includes two main components. First, global sensitivity analysis is used prior to the optimisation procedure to identify non- significant inputs, aiming to reduce the dimensionality of the problem. Second, once a candidate Pareto solution is obtained, the local sensitivity is computed to understand the trade-offs between objectives. Exact linear and quadratic approximations of the Pareto surface have been derived in the general case and are shown to be more accurate than the ones found in literature. In addition, sufficient conditions to identify non-differentiable Pareto points have been proposed. Ultimately, this approach enables the designer to gain more knowledge about the multi-objective optimisation problem with the main concern of minimising the computational cost. A number of test cases have been considered to evaluate the approach. These include algebraic examples, for direct analytical validation, and more representative test cases to evaluate its usefulness. In particular, an airfoil design problem has been developed and implemented to assess the approach on a typical engineering problem. The results demonstrate the potential of the methodology to achieve a reduction of computational time by concentrating the optimisation effort on the most significant variables. The results also show that the Pareto approximations provide the designer with essential information about trade-offs at reduced computational cost.