基于自适应差分进化算法的变循环发动机模型求解方法研究

Solving Variable Cycle Engine Model Based on Adaptive Differential Evolution Algorithm

关键词:  变循环发动机  模型求解  非线性方程组  差分进化算法  自适应机制

Key words:  Variable cycle engine  Model solving  Nonlinear equations  Differential evolution algorithm  Adaptive mechanism

摘要:

为了降低传统迭代算法在求解变循环发动机非线性模型时对初值的依赖性，将模型的求解问题转换为求最小值的优化问题，引入差分进化算法进行模型的求解，并提出一种自适应差分进化算法。自适应差分进化算法借助轮盘赌选择法，利用种群的进化经验可以自适应地选择最适合当前种群的差分策略与算法控制参数。针对变循环发动机四个典型工作点的模型求解问题，研究了标准差分进化算法的控制参数对其性能的影响，获取了标准差分进化算法在求解四个典型工作点时的最优控制参数组合，对比分析了自适应差分进化算法与标准差分进化算法的性能差异，最后研究了种群规模对自适应差分进化算法性能的影响。结果表明：标准差分进化算法在求解发动机模型时具有较好的鲁棒性，在求解不同工作点时算法的最优控制参数并不完全相同；相比于使用最优控制参数的标准差分进化算法，自适应差分进化算法可以在不影响算法鲁棒性的情况下提升效率50%以上；减少自适应差分进化算法的种群规模会在提升算法效率的同时破坏鲁棒性。

Abstract:

In order to reduce the dependence of the traditional iterative algorithm on the initial value in solving the nonlinear model of variable cycle engine， the model solving problem was converted to the optimization problem of finding the minimum value. Differential evolution algorithm was introduced to solve the model，and an adaptive differential evolution algorithm was proposed. Using the evolution experience and roulette selection method， adaptive differential evolution algorithm can adaptively select the differential strategy and algorithm control parameters that are most suitable for the current population. For the model solving problem of the four typical operating points of the variable cycle engine， the effects of the control parameters of standard differential evolution algorithm on its performance were studied. And the optimal combinations of control parameters of standard differential evolution algorithm in solving the four typical operating points were obtained. The performance difference between adaptive differential evolution algorithm and standard differential evolution algorithm was compared. Finally， the effects of population size on the performance of adaptive differential evolution algorithm were studied. The results show that standard differential evolution algorithm has pretty robustness in solving engine model， and its optimal control parameters are not completely the same when solving different operating points. Compared with standard differential evolution algorithm using the best control parameters， adaptive differential evolution algorithm can increase the efficiency by more than 50% without affecting the robustness of the algorithm. Reducing the population size of adaptive differential evolution algorithm will improve the efficiency while destroying the robustness of the algorithm.