Multidisciplinary Uncertain Design Optimization Besed On Convex Model Theory

Complex engineering system usually involves coupled multidisciplinaries, and it usually contains uncertainties. Therefore, it is necessary to investigate multidisciplinary uncertain design optimization methods to meet engineering requirement. However, it is very difficult to obtain the distribution of uncertain variables because of the large number of variables and the complex relationship that exists between variables. Convex model theory has advantages in handling non-deterministic problems with a few uncertainties information, and it's likely applied in engineering problems. Both convex model theory and multidisciplinary optimization theory are newly developed methodology for complex engineering system. Therefore, study on the integration of the two theories can improve their theoretical system. Based on convex model theory, this dissertation mainly focuses on investigating multidisciplinary uncertain design optimization method and providing fundamental understanding for multidisciplinary design optimization in engineering applications. As a result, the following studies are carried out in this dissertation:(1) First, the technique for calculating the variation ranges of multidisciplinary system is investigated based on convex model theory. Gauss-Sidel iteration method is utilized to calculate the variation intervals of coupling variables, and then the variation intervals of the other state variables can be obtained. A reliability analysis method of multidisciplinary system is proposed based on convex model. First order reliability analysis is used to calculate the non-probabilistic reliability index, and the multidisciplinary feasible method is applied to perform multidisciplinary analysis.(2) A method is suggested to solve the multidisciplinary optimization problem with uncertainties both in objective function and constraints. Based on the method of order relation of interval number, the uncertain objective function is transformed into two deterministic objective functions, and then the deterministic objective functions are linear weighted to get a single-objective function. The uncertain inequality constrains are converted into deterministic inequality constrains through modified possibility degree. The state variables are obtained through Gauss-Sidel iteration. The constraint optimization problem is changed into non-constraint optimization problem by penalty function method, and multidisciplinary feasible method is used as optimization strategy. (3) A multidisciplinary robust design optimization method is presented to solve the optimization problem of multidisciplinary design with uncertainties in constraints. Uncertain variables are assumed as convex model and genetic algorithm is applied to solve the maximum values of constraint intervals. The values of constraints can be obtained after possibility degree level is predetermined. Bi-level integrated system synthetic method is used as multidisciplinary optimization solver. Numerical example is investigated to demonstrate the efficiency of the method. The method can provide the necessary theoretical basis for multidisciplinary uncertain design optimization.(4) A sequential multidisciplinary optimization and reliability assessment method based on convex model is proposed to improve computational efficiency. The conventional reliability-based multidisciplinary design optimization strategy has tri-level loops:the first level is an optimization in the deterministic space, the second one is a reliability analysis in the probabilistic space, and the third one is the multidisciplinary analysis. The cental idea of sequential optimization and reliability assessment method is to decouple the reliability analysis from multidisciplinary optimization with sequential cycles of reliability analysis and multidisciplinary optimization. In the method, the reliability analysis method is performance measure approach, and multidisciplinary feasible method or bi-level integrated system synthesis is used to optimize the multidisciplinary system.(5) A sensitivity information updating method is developed to improve computational efficiency in multidisciplinary uncertain design optimization. This method aimed at reducing the number of disciplinary analysis called by sensitivity analysis. At first, the linear and insensitive terms in sensitivity information are identified, and then the values of the linear and insensitive terms are temporarily kept invariable for multiple multidisciplinary design optimization cycles. The true sensitivity information is replaced by approximated sensitivity information. The sensitivity information updating method is integrated into multidisciplinary uncertain design optimization method.