Robust And Multi-disciplinary Design Optimization With Applications On Tolerance Design

Nowadays engineering systems are becoming more and more complex. The first challenge in the design and optimization of such systems is the existence of uncertainties in parameters and design variables. Uncertainty plays a critical role, as a small amount of uncertainty could make an optimal design solution infeasible. It is necessary to develop efficient robust optimization(RO) approaches to find a solution that is both optimal and insensitive to uncertainty.Second, most engineering systems, like gas engines, involve multiple disciplines which share design variables and may be coupled with each other. In multi-disciplinary design optimization(MDO) problems, multiple optimization sub-problems with consistency constraints have to be solved in a more efficient manner so that their applicability for real-world engineering systems may be enhanced. In this regard, efficient MDO methods are necessary to handle these MDO problems with shared variables including global and coupling variables.Both types of design optimization problems suffer from computational inefficiency, due to multi-level(or so called nested) optimization structures used to handle the robust constraints in RO or consistency constraints in multi-level MDO problems. This dissertation concentrates on new RO and MDO methodology development to improve their computational efficiencies.The internal combustion engine(ICE), or to be more specific, the gas engine, is a typical complex nonlinear multi-disciplinary system. Uncertainties in dimensions and clearances of key components have great impacts on the engine’s performance and cost. Traditional tolerance designs for ICEs are conducted based on the designers’ experiences with very limited help of an optimization process. Furthermore, there has been limited study to focus on the tolerances of individual components with design autonomy and discipline synthesis at the system level. In this regard, tolerance designs of ICEs become a critical issue in the above two perspectives.This dissertation first handles single-disciplinary RO problems that have uncertain parameters and design variables existing in objective functions, constraint functions, or both. Secondly, the dissertation focuses on the development of an efficient MDO algorithm. Accordingly, the proposed work includes four Research Thrusts. In Research Thrust 1, Sequential Quadratic Programing for Robust Optimization(SQP-RO) is proposed to solve single-objective continuous nonlinear optimization problems with interval uncertainties. In Research Thrust 2, an advanced SQP-RO(A-SQP-RO) algorithm with a single-looped structure is proposed and tested, which proves to be more efficient than SQP-RO. In Research Thrust 3, a novel sequential MOO(S-MOO) approach and a sequential MDO(S-MDO) approach are proposed. These approaches give full optimization autonomy to each subsystem in the initial optimization stage, and then during the sequential optimization stage, each iteration can be solved in parallel without the nested optimization structure, so that the computational efficiency can be significantly improved. Based on the previously proposed approaches, in Research Thrust 4, SQP-RO and A-SQP-RO have been applied to solve the robust optimization problems for engine tolerance design, and a novel multi-disciplinary tolerance design optimization problem for gas engines is proposed and solved using S-MDO with the assistance of Gaussian process.In addition to the tolerance design of gas engines, numerous numerical and engineering examples are used in the dissertation to demonstrate the applicability and efficiency of the proposed approaches. It is shown that the proposed RO approaches can obtain robust optimal solutions with only less than five times of the number of function calls used by the corresponding deterministic cases. The proposed S-MOO can obtain comparable solutions of MOO problems with those solved by MOGA, and S-MDO can obtain comparable solutions with those from IDF, MDF, and CO for MDO problems, both using a much less number of function calls. For the multi-disciplinary tolerance design of gas engines, critical dimensions are shrunken while non-critical dimensions are released to improve the system performance while decreasing the manufacturing cost.