Study On Optimization Method And Approximation Technology For Complex Structural Design

In modern aviation propulsion systems, turbine discs usually working under extremely hard conditions are key parts of aero-engine. In order to improve the distribution of temperature and stresses in turbine discs, and better their quality so as to prevent them from being destroyed, effective method and technology are desirable for design optimization of them. Therefore, the optimization method and approximation technology for complex structural design are investigated in this work, which has the application background of the structural design optimization of the turbine disc.On the optimization method, genetic algorithms and differential evolution algorithms are mainly analyzed so as to bring forward some effective methods with good performance on convergence and global searching ability for complex optimization problems. On the approximation technology, kriging response surface method is mainly studied so as to solve the problems of function evaluations and calculations for complex design optimization.Firstly, based on the analysis of genetic algorithms, a constrained ranking and sorting method is proposed so as to deal with complex constraints that always hamper genetic algorithms. Furthermore, a genetic algorithm with constrained ranking and sorting is proposed by using the constrained ranking and sorting method and improved genetic operators. Numerical experimentation indicated that the proposed algorithm has good stability and global searching ability when it is used for solving constrained optimization problems with continuous or discrete variables.Secondly, based on the analysis of differential evolution algorithms, a modified differential evolution algorithm is provided for constrained global optimization problems instead of the original one that is probably trapped in local optima. The modified algorithm introduces a rule-based way to select comparatively the individuals from population and to handle complex constraints. The diversity of population in global search is improved via population similarity and best mutation operation, which enables the algorithm to jump over any local minimum trap. Experimental results demonstrated the stability, efficiency and global search ability of the proposed algorithm for constrained optimization problems with continuous or discrete variables.Thirdly, a robust archived differential evolution algorithm is put forward for efficiently solving various optimization problems. The proposed algorithm uses a flexibility processing operator for various type optimization problems. Furthermore, an archiving operator, an iterative control operator and an efficiency processing operator are designed and embedded in the algorithm, which can not only avoid unnecessary search in the optimization process, but also improve the local searching efficiency and the final searching quality. Experimental results based on a suite of six well-known optimization problems and comparisons with previously reported results revealed that the proposed algorithm is reliable, efficient, fast and robust in global optimization. It is able to solve not only unconstrained optimization problems, but also constrained optimization problems with continuous, discrete or mixed continuous-discrete variables.Fourthly, general kriging method is improved by means of experimental sample handling, experimental sample selection and approximate optimization strategy. Furthermore, a kriging based approximate optimization method is proposed by combining the improved kriging method and modern intelligent optimization method, which provides an effective approach to the solution of complex structural optimization problems. Numerical experimentation indicated that the proposed method can reduce simulations and computations with a sufficient precision for practical optimization problems.Finally, the design optimization model and design analysis model for the minimum-mass shape design of turbine discs under thermal and mechanical loads are built. The kriging based approximate optimization method is applied to the design optimization of the general turbine disc, and the final optimal design is analyzed and validated by means of finite element method. Experimental results demonstrated that the optimal solution obtained by the proposed method is a light and feasible design that has reasonable stress distribution and high material utilization; besides, the approximate optimization method achieves a sufficient precision with low computational cost.