Research On Analytical Target Cascading And Time Dependent Reliability Basaed Design Optimization For Complex System

Engineering design is a complicated process, which involves multiple disciplines and multi-level systems. This is further complicated due to the presence of uncertainty. It is hard for traditional design optimization methods to find the optimal solution of the complex system design, and the design efficiency is low. Multidisciplinary design optimization (MDO) is an impressive method for the complex system design. By coordinating the couplings between disciplines or sub-systems, MDO can converge to the system optimal solution, and it can reduce the design cycle time with concurrent design. Analytical target cascading (ATC) is one kind of MDO methods to solve multi-level hierarchically decomposed system design optimization problem. ATC can converge to the system optimum by enabling top level design targets to be cascaded down to the lowest level of the modeling hierarchy, and formulating target coordination optimization problem in each level. In this dissertation, the target cascading and coordination methodologies are studied, and the reliability analysis and design optimization methods are developed to consider the effects of the uncertainty.In the ATC method, the top design targets are cascaded for each lower level subsystems, if targets cascaded to subsystems are not achievable or compatible, feedback is required resulting in an iterative target cascading process. In the initial design stage, interval targets can improve the feasibility and flexibility of subsystems, reduce the unnecessary process redesign. In the ATC formulation, the couplings between disciplines and subsystems are coordinated by solving the target coordination design optimization problem in each level. A weighted-sum objective function is formulated in each level to coordinate the inconsistency between design response and assigned targets in each level. The weighting coefficients represent the relative importance of the inconsistency. The system converges by setting proper weighting coefficients. However, the weights setting is a problem depended, it is hard to set proper weighting coefficents for complex system, and improper selections of the weights will lead to converge slowly or converge to the local optimum. To avoid the problems associated with the weights, new target coordination methods are developed in this dissertation.Due to the presence of uncertainty, to make reliable decision, it is necessary to consider the effects of uncertainty to the system. For the highly nonlinear performance functions or limit state functions, and the existence of many most probable failure points (MPP), traditional MPP based first order reliability method or second order reliability method may be inaccurate to calculate the probability of failure. Therefore, it is needed to analyze the probability distribution of the limit state function in the design domain. Due to the degradation and some random loads are time variant, to guarantee the reliable of the system in the whole life cycle, it is important to develop design optimization method based on the time dependent reliability constraints.Based on the above problems, some models are developed in this dissertation. All these models extend the traditional MDO method to consummate the theoretical system of MDO and have a wider application in the engineering practices.(1) Developing a new ATC method for achieving flexibility in hierarchical multilevel system design optimization based on reliability constraints.In the initial stage of design, it is hard to set accurate feasible targets. In this dissertation, a new method for achieving flexibility in hierarchical multilevel system design optimization based on reliability constraints is proposed. Instead of point valued targets, system will set interval targets for each subsystem, and each subsystem solves the design optimization problem within the target intervals. Interval targets provide a freedom to the subsystem, achieve the true concurrent design. Therefore, the convergence efficiency is improved. The uncertainty analysis for the engineering system based on reliability constraints guarantees the reliability and accuracy of the system.(2) Developing two ATC coordination methods based on Pareto multi-objective GA method, and bounded target coordination method.To avoid weights setting, two new coordinating methods are proposed: Pareto multi-objective GA coordination method and bounded target coordination method. In the Pareto multi-objective GA coordination method, all the Pareto solutions are provided for each level design optimization problem, each level subsystem can choose the satisfied design points form the solution set. In the bounded target coordination method, bounds are built and updated based on the response of subsystems to the assigned targets during the optimization process. Linear approximation functions of the response of subsystems and common variables are formulated in system level for coordinating the common variables of subsystems. Further, transform the multi-objective model into a single objective design optimization problem, which avoid weights setting, and provide information for target setting based on the sensitivity analysis. Therefore, efficiency and accuracy of system design optimization are improved.(3) Developing two uncertainty analysis methods based on maximum entropy principleThe high order moments are calculated to analyze the PDF and CDF of the limit state functions. In this dissertation, the moment generating function combined the operation of universal generating function are used to calculate the high order moments of the limit state function. Due to the lack of information for some random variables, the distribution of the design variables can not be determined, and the bootstrap method is used to analyze the certainty intervals of the statistic distribution. Finally, the maximum entropy principle is used to calculate the PDF and CDF of the limit state function.(4) Developing a new system design optimization method under time-dependent reliability constraintsTraditional reliability based design optimization methods did not consider time-variant degeneration and loads with stochastic process. In this dissertation, the time-dependent reliability analysis methods are studied, and a new system design optimization formulation is proposed. In the proposed method, the effects of the time-variant loads to the reliability are considered. Therefore, the reliability of the system within the life cycle time is guaranteed.