Convex-Model Based Analysis And Design For Structural And Multidisciplinary Systems Under Uncertainty

In this paper, the uncertainty analysis and design problems for structural and multidisciplinary system were investigated in detail base on a non-probabilistic approach that is convex model theory. Two types of convex models were considered simultaneously to account for uncertainties: the ellipsoidal model and the interval model. A relatively systematic research that involves safety evaluation, performance variation analysis and design under uncertainty for structural and multidisciplinary systems was performed. The main content is as follows:1, A robust reliability index, which can be used as a measure of safety of system with both ellipsoidal models and interval parameters, was proposed. A comparison of the reliability index and the failure frequency calculated by Monte Carlo simulation method was presented by a simple example.2, Using the reliability index as a design constraint, a non-probabilistic reliability based optimization model was constructed so that the result optimum design could resist a given level of uncertainties. A sequential linearization method that is easily integrated into sequential linear programming (SLP) algorithm was developed to solve this problem. A simple example was given to demonstrate the proposed approach.3, A computationally efficient technique for calculating the variation intervals of coupling variables of multidisciplinary system was developed. The first-order Taylor approximation combined with global sensitivity equations (GSE) is used to estimate the intervals of the end performance of multidisciplinary system. The sensitivity information needed in this method is often a byproduct for many gradient-based optimization algorithms, so this approach can be easily integrated with a non-deterministic optimization framework to perform robust design for multidisciplinary system. The method is validated using Monte Carlo simulation in application to an electronic packaging problem. The results show that it can give a good approximation for the uncertainty intervals of the coupling variables with small amount of calculation when the uncertainty level is low.4, The proposed robust reliability index was extended to evaluate the safety of multidisciplinary system. Because of the iterative nature of the multidisciplinary system analysis, the reliability analysis requires a double loop procedure and is generally verytime consuming. To improve computing efficiency, a new formulation was constructed according to the idea of SAND. In this formulation, only a single loop is required and all analyses can be conducted concurrently at the individual discipline-level. The method was validated and compared with the All-in-One reliability analysis approach in application to an electronic packaging problem.5, Two optimization models for multidisciplinary feasible robust design were constructed, the All-in-One model and the Collaborative Robust Design model. The All-in-One method is a directly extension of the robust feasibility concept for single disciplinary system. The latter method is an adaptation of the traditional deterministic Collaborative Optimization (CO) framework, which employs decomposition techniques that decouple analysis tools in order to facilitate disciplinary autonomy and parallel execution. Both models were implemented and compared in application to a multidisciplinary test problem.6, The post-optimality analysis techniques quantitatively approach how the optimum solutions change with respect to optimization parameters without re-optimizing the problem. In recent years, these techniques have been used by several multidisciplinary design optimization (MDO) frameworks. The goal of this research is to create global surrogate models in the whole parameter space, especially by Kriging method. A piecewise Kriging scheme is proposed in order to reduce the influence of possibly salutations of the optimum solutions on the accuracy of Kriging model as a result of changes of the active constrains set. A simple structural optimization problem is used to demonstrate the improvement on accuracy.