摘要
在现代航空推进系统中,涡轮盘是航空发动机的关键部件,其工作条件非常严酷。为了减少或避免涡轮盘破坏性故障的发生,亟需采用有效方法进行涡轮盘优化设计,以便改善涡轮盘内部的温度及应力分布状况,提高涡轮盘的设计品质。因此,本文以发动机涡轮盘结构优化设计问题为应用背景,对复杂结构设计的优化方法和近似技术进行了研究和探讨。
在复杂结构设计的优化方法上,主要研究了现代智能优化算法中的遗传算法和差分进化算法,重点解决已有遗传算法和差分进化算法在求解复杂约束优化问题时存在的早熟收敛、局部收敛、优化后期收敛速度慢等问题,提出有效的解决方法和优化算法。在近似技术方面,主要研究函数全局近似方法中的Kriging响应面法近似技术,重点解决已有Kriging响应面法在近似求解复杂优化设计问题时存在的函数评价次数多和计算量大的问题。
首先,在分析遗传算法原理的基础上,针对传统遗传算法不适合求解复杂约束优化问题的缺陷,提出一种能够处理复杂约束条件的约束分级与排序方法。基于该方法和改进的遗传算子,提出一种求解约束优化问题的基于约束分级与排序的遗传算法。数值试验表明,该算法具有较好的稳定性和全局寻优能力,能够有效求解连续变量约束优化问题和连续-离散混合变量约束优化问题。
其次,在分析差分进化算法原理的基础上,针对原始差分进化算法在求解约束全局优化问题时存在陷入局部最优的缺陷,提出一种改进的差分进化算法。该算法采用基于规则的方法进行种群个体的比较及选择,实现复杂约束条件的处理；并利用种群相似度和最优变异操作改善种群进行全局范围搜索的多样性,提高算法跳出局部最优的能力。数值试验表明,该算法具有较好的稳定性、收敛速度和全局寻优能力,不仅能有效求解连续变量约束优化问题,也适用于离散变量或混合变量优化问题。
再次,针对原始差分进化算法后期收敛速度慢和不适合求解约束全局优化问题的缺陷,提出一种鲁棒的存档差分进化算法。该算法利用柔性处理算子扩展对不同类型优化问题的适用性；利用存档算子、迭代控制以及效率处理算子避免在设计空间中不必要的重复搜索,从而提高算法的局部搜索效率和最终解的精确度。数值试验表明,该算法具有较好的稳定性、收敛速度和全局寻优能力,对不同类型优化问题的适用性好,不仅适用于无约束优化问题,而且适用于连续变量和连续-离散混合变量约束优化问题。
然后,为了解决复杂工程优化设计中设计精度和计算代价之间的矛盾,针对已有的Kriging方法计算量较大的缺陷,从样本处理、试验样本选取和近似优化框架三个方面进行改进,并将改进的Kriging方法与现代智能优化方法相结合,提出一种基于Kriging的近似优化方法,为复杂结构优化问题的求解提供一种计算代价低且计算精度能够满足工程需要的有效途径。计算结果表明,基于Kriging的近似优化方法能够在优化计算结果满足工程精度要求的前提下,显著减少优化设计的仿真分析次数,降低计算代价。
最后,针对具有热-惯性离心载荷耦合作用特点的涡轮盘结构优化问题,建立涡轮盘优化设计模型及载荷分析模型,用基于Kriging的近似优化方法进行涡轮盘的近似优化设计,并对所获得的近似最优设计方案采用有限元方法进行仿真分析和验证。结果表明,采用基于Kriging的近似优化方法所获得的涡轮盘优化设计方案是一种重量轻、应力分布合理、材料有效利用率高的可行设计方案；近似优化设计的计算精度能够满足工程需要,计算代价小。
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.
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