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摘要:
为了满足变循环发动机(VCE)性能寻优控制(PSC)需求,提出了一种基于序列二次约束二次规划(SQCQP)算法的性能寻优控制算法,通过罚函数将二次约束二次规划(QCQP)子问题转化为适应度函数,并提出一种改进微分进化(IDE)算法求解QCQP子问题,以获得最优的搜索方向。与序列二次规划(SQP)算法相比,本文提出的基于IDE算法求解QCQP子问题的SQCQP算法(IDE-SQCQP)能在更少的迭代次数下寻到更优的解。将IDE-SQCQP算法应用于变循环发动机的性能寻优控制中,数字仿真结果表明,在最大推力寻优控制中,IDE-SQCQP算法用时比SQP算法减少16.81%,优化效果提升了21.50%,在最小油耗寻优控制中,IDE-SQCQP算法用时比SQP算法减少14.90%,优化效果提升了31.03%,达到了算法提出的目的。
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关键词:
- 变循环发动机(VCE) /
- 性能寻优控制(PSC) /
- 序列二次约束二次规划(SQCQP)算法 /
- 微分进化算法 /
- 序列二次规划(SQP)算法
Abstract:In order to meet the demands of the variable cycle engine (VCE) performance seeking control (PSC), a new PSC method based on the sequential quadratically constrained quadratic programming (SQCQP) algorithm was proposed. The sub-problem of the quadratically constrained quadratic programming (QCQP) was changed to fitness function by penalty function, and an improved differential evolution (IDE) algorithm was proposed to solve the QCQP sub-problem and to get the global optimal searching direction. Compared with the widely-used sequential quadratic programming (SQP) algorithm, the improved differential evolution-sequential quadratically constrained quadratic programming (IDE-SQCQP) algorithm can find a better solution by less iterations. The IDE-SQCQP algorithm is applied to performance seeking control of the variable cycle engine. The simulation results show that, in the maximum thrust mode, IDE-SQCQP algorithm takes 16.81% less time than SQP while thrust is enhanced by 21.50%, and in the minimum fuel-consumption mode, it takes 14.90% less time than SQP algorithm while fuel-consumption is dropped by 31.03%. The algorithm achieves the goal of proposal.
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表 1 测试函数
Table 1. Test functions
编号 测试函数 Prob1 Prob2 Prob3 Prob4 表 2 SQP算法与IDE-SQCQP算法的测试结果对比
Table 2. Comparison of test results between SQP and IDE-SQCQP algorithms
算法 测试函数 x0 Niter 寻优结果f(x) 参考最优值f(x) SQP Probl [l, l] 3 6.777 777 777 774 569 6.7 [5, 5] 4 6.777 777 777 777 770 Prob2 [1, 1] l5 l. 836 82l 753 924 569 1.836 82178 [2, 2] 50 2.520 727 612 805 417 Prob3 [4, 2, l, l, 8, 7, l, 0.5] 50 3.947 372 022 706 715 3.951 163 406 [l, l, l, l, 6.l, 6.l, l, l] 50 3.950 744 454 322 580 Prob4 [7, l, 0.5, 8] 50 -5.689 567 423 597 13l -5.739 820 386 [7, 0.l, 0.l, 7] 50 -5.740 096 689 116 705 IDE-SQCQP Probl [1, 1] 2 6.777 762 345 747 336 6.7 [5, 5] 2 6.777 762 347 781 540 Prob2 [1, 1] 7 1.836 818 809 380 766 1.836 821 78 [2, 2] 26 1.836 818 906 828 806 Prob3 [4, 2, l, l, 8, 7, l, 0.5] 19 3.951 178 934 326 082 3.951 163406 [l, l, l, l, 6.l, 6.l, l, l] ll 3.951 176 013 300 333 Prob4 [7, l, 0.5, 8] l3 -5.739 763 870 783 301 -5.739 820 386 [7, 0.l, 0.l, 7] 2l -5.739 771 048 390 224 注:x0—搜索的起始值;Niter—寻优过程的迭代次数。 表 3 IDE算法参数设置
Table 3. Parameter setting of IDE algorithm
参数 数值或范围 Fdv 0.2~1.0 Gmax 50 Np 50 αF 0.3 μ 1/3 τ 0.5 -
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