﻿ 成本约束的表决冗余系统可靠度优化与分配
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1. 西北工业大学 自动化学院, 西安 710129;
2. 中国航空工业集团公司 第一飞机设计研究院, 阎良 710000;
3. 西北工业大学 自动化学院, 西安 710129

Reliability-redundancy optimization and allocation of voting system under cost constraint
Liu Zhijun1, Gao Yakui2, Zhang Weiguo3
1. School of Automation, Northwestern Polytechnical University, Xi'an 710129, China;
2. The First Aircraft Institute, Aviation Industry Corporation of China, Yanliang 710000, China;
3. School of Automation, Northwestern Polytechnical University, Xi'an 710129, China
Abstract:Voting-redundancy structure was adopted in a system to maximize the system reliability under the cost constraint. With the combination of the augmented Lagrangian multiplier method and the fish swarm algorithm, a hybrid method was employed to optimize and allocate the system reliability and redundancies. In the meanwhile, the relationship between the reliability and the cost was not only analyzed, but also the impact of the voter failure rate on the system reliability was discussed. Finally, simulation results based on the longitudinal pitch motion flight control system of a certain type aircraft verify that the quaternion configuration is more appropriate to maintain an optimal system reliability taking into account the cost limit. In addition, in the case of a single voter, the voter reliability should be selected as high as possible. Most of the actual project systems select more voters redundancies structure to avoid the impact of single voter failure on the system reliability.
Key words: reliability     redundancy     voters     augmented Lagrangian multiplier method     fish swarm algorithm

 图 1 具有表决的冗余系统可靠度框图Fig. 1 Reliability-redundancy diagram of voting system

1) 各组件单元只有两种状态,即工作或失效;

2) 同一子系统的组件具有相同的可靠度;

3) 各组件单元以及各子系统相互独立;

4) 各表决器的结构和失效率具有一致性.

 图 2 分配算法流程Fig. 2 Allocation algorithm process

 测试函数 理论最优值f(x*) fbest AFS_aL 文献[16] G02 -0.803 6 -0.804 3 -0.792 52 G06 -6 961.81 -6 961.9 -6 961.45 G10 7 049.25 7 055.47 7 070.56
2 仿真分析

 组件可靠度 子系统可靠度 冗余 系统可靠度 组件1 组件2 组件3 组件4 子系统1 子系统2 子系统3 子系统4 0.827 870 35 0.517 855 84 0.924 564 65 0.966 996 62 0.982 233 71 0.713 794 43 0.998 380 09 0.999 994 22 4,4,4,5 0.699 973 17 0.839 367 58 0.878 870 07 0.871 566 23 0.696 113 51 0.985 418 3 0.993 536 75 0.992 342 1 0.967 726 3 4,4,4,5 0.940 196 25 0.827 738 95 0.585 593 34 0.853 023 04 0.515 916 42 0.982 195 01 0.803 807 55 0.988 699 85 0.831 762 51 4,4,4,5 0.649 252 48 0.847 414 31 0.658 549 74 0.975 111 02 0.517 223 04 0.987 415 97 0.881 542 09 0.999 939 48 0.833 287 65 4,4,4,5 0.725 290 28 0.827 549 0.581 305 87 0.559 498 84 0.749 182 03 0.982 138 97 0.798 598 97 0.771 054 43 0.984 182 45 4,4,4,5 0.595 199 2

 组件可靠度 子系统可靠度 系统总成本 系统可靠度 组件1 组件2 组件3 组件4 子系统1 子系统2 子系统3 子系统4 0.827 852 19 0.664 376 2 0.916 895 86 1.093 448 9 3.313 408 77 2.658 550 48 3.667 583 46 5.467 244 52 15.104 787 2 0.699 973 17 0.848 590 98 0.881 711 52 0.810 468 39 0.804 843 13 3.394 363 94 3.526 846 07 3.241 873 56 4.024 215 67 14.187 299 2 0.940 196 25 0.827 623 26 0.688 428 33 0.783 495 89 0.744 314 70 3.310 493 03 2.753 713 30 3.133 983 57 3.721 573 51 12.919 763 4 0.649 252 48 0.864 008 68 0.718 858 37 1.138 666 06 0.744 666 07 3.456 034 74 2.875 433 48 4.554 664 26 3.723 330 33 14.609 492 8 0.725 290 28 0.827 292 65 0.686 810 87 0.563 968 44 0.829 793 61 3.309 170 58 2.747 243 48 2.255 873 76 4.148 968 07 12.461 255 9 0.595 199 2

 组件可靠度 子系统可靠度 冗余 系统可靠度 组件1 组件2 组件3 组件4 子系统1 子系统2 子系统3 子系统4 0.993 563 65 0.993 563 65 0.989 348 52 0.991 963 44 0.999 999 06 0.999 999 99 0.999 999 94 0.999 999 98 5,5,5,5 0.999 998 971 0.993 449 59 0.992 592 15 0.985 354 14 0.981 125 91 0.999 999 99 0.999 998 38 0.999 999 77 0.999 999 38 5,4,5,5 0.999 997 522 0.972 748 35 0.989 807 77 0.999 681 12 0.987 508 11 0.999 997 30 0.999 999 95 0.999 999 999 9 0.999 999 88 5,5,5,5 0.999 997 13 0.986 005 09 0.980 471 15 0.975 740 703 0.997 153 12 0.999 999 81 0.999 999 28 0.999 998 302 0.999 999 999 6 5,5,5,5 0.999 997 396 0.995 826 63 0.999 420 99 0.998 936 37 0.993 428 72 0.999 999 71 0.999 999 999 0.999 999 995 0.999 999 991 4,4,4,5 0.999 999 695

 组件可靠度 子系统可靠度 系统总成本 系统可靠度 组件1 组件2 组件3 组件4 子系统1 子系统2 子系统3 子系统4 1.460 582 2 1.342 910 46 1.308 411 28 1.277 088 07 7.302 911 01 6.714 552 3 6.542 056 38 6.385 440 36 26.944 960 1 0.999 998 971 1.808 468 3 1.320 819 49 1.244 719 48 1.166 095 51 9.042 341 7 5.283 277 97 6.223 597 38 4.945 748 56 26.379 694 6 0.999 997 522 1.380 792 4 1.270 677 55 2.010 140 25 1.219 747 78 6.903 962 01 6.353 387 75 10.050 701 26 6.098 738 91 29.406 789 9 0.999 997 13 1.580 718 48 1.168 492 65 1.1437 910 7 1.411 999 27 7.903 592 37 5.842 463 23 5.718 955 35 7.059 996 37 26.525 007 3 0.999 997 396 1.943 709 6 1.721 372 07 1.769 212 71 1.303 256 13 7.774 838 42 6.885 488 29 7.076 850 82 6.516 280 66 28.253 458 2 0.999 999 695

 图 3 冗余对系统可靠度的影响Fig. 3 Iimpact of redundancy on system reliability

 图 4 冗余对子系统可靠度的影响Fig. 4 Impact of redundancy on subsystems reliability

 图 5 成本与组件可靠度的关系Fig. 5 Reliability relationship between costs and components

 图 6 表决器对系统可靠度的影响Fig. 6 Impact of voters on system reliability

 图 7 表决器对子系统可靠度的影响Fig. 7 Impact of voters on subsystems reliability

1) 分配结果进一步证明了该算法具有较强的全局收敛性和较好的算法稳定性;

2) 证明了采用余度配置可以大大提高系统的可靠度,改善系统的可靠性;

3) 仿真分析了表决器的失效率对系统可靠度的影响,说明改善系统的可靠度不仅要恰当地配置系统冗余,同时也要注意改善表决器的可靠度.因此,目前在实际工程中,除了采用组件系统冗余,同时也注重表决器结构的冗余配制,保证系统更可靠地工作.

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#### 文章信息

Liu Zhijun, Gao Yakui, Zhang Weiguo

Reliability-redundancy optimization and allocation of voting system under cost constraint

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(12): 1747-1753.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0765