Citation: | ZHAI Yuyao, SHI Xianjun, YANG Shuai, et al. Multi-objective test optimization selection based on NSGA-Ⅱ under unreliable test conditions[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(4): 792-801. doi: 10.13700/j.bh.1001-5965.2020.0036(in Chinese) |
Since test optimization selection plays a vital role in the test design of various equipment systems, in the testability design of various types of equipment, test unreliable factors seriously affect the optimization of test selection. First, this paper describes the mathematical model of the multi-objective optimization selection problem under unreliable test conditions. Second, under this mathematical model, the test cost, missed detection rate, and false alarm rate are used as the optimization goals, and the fault detection rate and isolation rate are constraints. Thus, a multi-objective optimization problem was established. Third, the NSGA-Ⅱ algorithm, a fast Non-dominated multi-objective optimization Sorting Genetic Algorithm-Ⅱ with an elite retention strategy, was proposed to optimize the proposed multi-objective problem. Using the NSGA-Ⅱ algorithm, a set of Pareto optimal solutions are obtained, and the optimal test combination can be selected according to actual needs. Finally, an example analysis is performed on a certain equipment, three sets of optimal solutions are obtained, which can meet the optimal selection under different needs, and the feasibility and effectiveness of the mathematical model and multi-objective optimization algorithm are verified.
[1] |
刘建敏, 刘远宏, 冯辅周, 等. 基于贪婪算法的测试优化选择[J]. 兵工学报, 2014, 35(12): 2109-2115.
LIU J M, LIU Y H, FENG F Z, et al. The optimization selection of tests based on greedy algorithm[J]. Acta Armamentarii, 2014, 35(12): 2109-2115(in Chinese).
|
[2] |
蒋荣华, 王厚军, 龙兵. 基于离散粒子群算法的测试选择[J]. 电子测量与仪器学报, 2008, 22(2): 11-15.
JIANG R H, WANG H J, LONG B. Test selection based on binary particle swarm optimization[J]. Journal of Electronic Measurement and Instrument, 2008, 22(2): 11-15(in Chinese).
|
[3] |
朱喜华, 李颖晖, 李宁, 等. 基于改进离散粒子群算法的传感器布局优化设计[J]. 电子学报, 2013, 41(10): 2104-2108.
ZHU X H, LI Y H, LI N, et al. Optimal sensor placement design based on improved discrete PSO algorithm[J]. Acta Electronica Sinica, 2013, 41(10): 2104-2108(in Chinese).
|
[4] |
雷华军, 秦开宇. 基于改进量子进化算法的测试优化选择[J]. 仪器仪表学报, 2013, 34(4): 838-844.
LEI H J, QIN K Y. Optimal test selection based on improved quantum-inspired evolutionary algorithm[J]. Chinese Journal of Scientific Instrument, 2013, 34(4): 838-844(in Chinese).
|
[5] |
雷华军, 秦开宇. 测试不可靠条件下基于量子进化算法的测试优化选择[J]. 电子学报, 2017(10): 154-162.
LEI H J, QIN K Y. Optimal selection of imperfect tests based on improved quantum-inspired evolutionary algorithm[J]. Acta Electronica Sinica, 2017(10): 154-162(in Chinese).
|
[6] |
张钊旭, 王志杰, 李建辰, 等. 基于搜寻者算法的测试性优化分配方法[J]. 鱼雷技术, 2018, 26(1): 53-56.
ZHANG Z X, WANG Z J, LI J C, et al. Optimal allocation method of testability based on seeker optimization algorithm[J]. Torpedo Technology, 2018, 26(1): 53-56(in Chinese).
|
[7] |
邓露, 许爱强, 吴忠德. 基于遗传算法的故障样本优化选取方法[J]. 系统工程与电子技术, 2015, 37(7): 1703-1708.
DENG L, XU A Q, WU Z D. Method of failure simple optimal selection based on genetic algorithm[J]. System Engineering and Electronics, 2015, 37(7): 1703-1708(in Chinese).
|
[8] |
周虎, 胡海峰, 刘清竹, 等. 基于故障-测试相关模型的运载火箭测试点优化设计方法[J]. 载人航天, 2018, 81(1): 38-44.
ZHOU H, HU H F, LIU Q Z, et al. An optimization method for test points of manned launch vehicle based on fault-test dependency model[J]. Manned Spaceflight, 2018, 81(1): 38-44(in Chinese).
|
[9] |
陈希祥, 邱静, 刘冠军. 基于混合二进制粒子群-遗传算法的测试优化选择研究[J]. 仪器仪表学报, 2009, 30(8): 1674-1680.
CHEN X X, QIU J, LIU G J. Optimal test selection based on hybrid BPSO and GA[J]. Chinese Journal of Scientific Instrument, 2009, 30(8): 1674-1680(in Chinese).
|
[10] |
代西超, 南建国, 黄雷, 等. 基于改进遗传模拟退火算法的测试优化选择[J]. 空军工程大学学报(自然科学版), 2016, 17(2): 70-75.
DAI X C, NAN J G, HUANG L, et al. An optimal test selection based on improved genetic simulated annealing algorithm[J]. Journal of Air Force Engineering University(Natural Science Edition), 2016, 17(2): 70-75(in Chinese).
|
[11] |
QIU J, TAN X D, LIU G J, et al. Test selection and optimization for PHM based on failure evolution mechanism model[J]. Journal of Systems Engineering and Electronics, 2013, 24(5): 780-792.
|
[12] |
ZHANG S G, LIU C R, HU Z, et al. Testability evaluation of the systems with multi-outcome imperfect tests[J]. Applied Mechanics and Materials, 2013, 303(306): 407-410.
|
[13] |
ZHANG S G, PATTIPATI K R, HU Z, et al. Optimal selection of imperfect tests for fault detection and isolation[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2013, 43(6): 1370-1384.
|
[14] |
ZHANG S G, PATTIPATI K R, HU Z, et al. Dynamic coupled fault diagnosis with propagation and observation delays[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2013, 43(6): 1424-1439.
|
[15] |
LI F. Dynamic modeling, sensor placement design, and fault diagnosis of nuclear desalination systems[D]. Tennessee: University of Tennessee, 2011: 20-30.
|
[16] |
PAN J L, YE X H, XUE Q. An heuristic genetic algorithm solve test point selecting with unreliable test[C]//International Workshop on Computer Science & Engineering. Piscataway: IEEE Press, 2010: 227-232.
|
[17] |
杨光, 刘冠军, 李金国, 等. 基于故障检测和可靠性约束的传感器布局优化[J]. 电子学报, 2006, 34(2): 348-351.
YANG G, LIU G J, LI J G, et al. Optmial sensor placement based on various fault detectability and reliability criteria[J]. Acta Electronica Sinica, 2006, 34(2): 348-351(in Chinese).
|
[18] |
叶晓慧, 潘佳梁, 王红霞, 等. 基于动态贪婪算法的不可靠测试点选择[J]. 北京理工大学学报, 2010, 30(11): 1350-1354.
YE X H, PAN J L, WANG H X, et al. Test set selection under unreliable test based on a new dynamic greedy algorithm[J]. Transactions of Beijing Institute of Technology, 2010, 30(11): 1350-1354(in Chinese).
|
[19] |
DENG S, JING B, YANG Z. Test point selection strategy under unreliable test based on heuristic particle swarm optimization algorithm[C]//2012 IEEE Conference on Prognostics and System Health Management. Piscataway: IEEE Press, 2012: 1-6.
|
[20] |
RAGHAVAN V, SHAKERI M, PATTIPATI K. Test sequencing algorithms with unreliable tests[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 1999, 29(4): 347-357.
|
[21] |
RUAN S, YU F, MEIRINA C, et al. Dynamic multiple fault diagnosis with imperfect tests[J]. Autotestcon, 2003, 39(6): 1224-1236.
|
[22] |
杨鹏. 基于相关性模型的诊断策略优化设计技术[D]. 长沙: 国防科技大学, 2008: 47-50.
YANG P. Optimization technology of design for diagnostic strategy based on dependency model[D]. Changsha: National University of Defense Technology, 2008: 47-50(in Chinese).
|
[23] |
翟禹尧, 史贤俊, 吕佳朋. 基于广义随机Petri网的导弹系统测试性建模与指标评估方法研究[J]. 兵工学报, 2019, 40(10): 2070-2079.
ZHAI Y Y, SHI X J, LV J P. Research on evaluation method for testability index and modeling of missile system based on GSPN[J]. Acta Armamentarii, 2019, 40(10): 2070-2079(in Chinese).
|
[24] |
SRINIVAS N, DEB K. Muiltiobjective optimization using nondominated sorting in genetic algorithms[J]. Evolutionary Computation, 2014, 2(3): 221-248.
|
[25] |
DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-Ⅱ[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182-197.
|
[26] |
陈希祥, 邱静, 刘冠军. 测试不确定条件下基于贝叶斯网络的装备测试优化选择技术[J]. 中国机械工程, 2011, 22(4): 379-384.
CHEN X X, QIU J, LIU G J. Optimal test selection of materiel based on bayesian network under test uncertainty[J]. China Mechanical Engineering, 2011, 22(4): 379-384(in Chinese).
|
[1] | MA J,LI R Y,ZHANG Q Y,et al. Network time reliability evaluation method based on uncertainty theory[J]. Journal of Beijing University of Aeronautics and Astronautics,2025,51(4):1267-1276 (in Chinese). doi: 10.13700/j.bh.1001-5965.2023.0191. |
[2] | LI Qian, KONG Qingyu, YANG Jian, XU Guipeng, BEN Yueyang. Research on cooperative hunting algorithm of AUV cluster based on multi-objective task assignment[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2025.0107 |
[3] | GU Zhirong, DING Jianyang, CHAI Zhilei. TC-NSGA-II:Multi-Objective Optimization Algorithm for TSN-CAN Gateway Congestion Scheduling[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2025.0031 |
[4] | WEN G,YUAN L F,WANG X D,et al. Loading optimization of irregular unit load device based on improved NSGA-Ⅱ algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics,2025,51(3):992-1004 (in Chinese). doi: 10.13700/j.bh.1001-5965.2023.0149. |
[5] | HU Gengshuo, JIAO Jian, HU Langxiao, JING Yongfeng. Reliability modeling and evaluation method of IMA under dynamic reconfiguration[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2024.0188 |
[7] | YAN X B,FANG Y W,PENG W S. Multi-objective Harris Hawk optimization algorithm based on adaptive Gaussian mutation[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(8):2636-2645 (in Chinese). doi: 10.13700/j.bh.1001-5965.2022.0686. |
[8] | LI R N,FENG X,YAO Y P,et al. Multi-objective optimization of airport runway construction schemes based on improved genetic algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(12):3720-3728 (in Chinese). doi: 10.13700/j.bh.1001-5965.2022.0893. |
[9] | LI J,YANG D K,HONG X B,et al. Soil moisture algorithm testing of interference signal inversion with GNSS linearly polarized antenna[J]. Journal of Beijing University of Aeronautics and Astronautics,2024,50(3):874-885 (in Chinese). doi: 10.13700/j.bh.1001-5965.2022.0282. |
[10] | ZHANG Fan, LIU Wan, GUO Yong-yan, CENG Zhi-chun, HE Qian-wei, ZHAO Zhong. The application and practice of black box testing technology in Fluid Simulation Software[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0621 |
[11] | ZHU Qi-tao, LI Hong-shuang. A mixed reliability analysis method based on direct probability integral[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0498 |
[12] | WANG Yang-guang, YAO Yuan-zhi, YU Neng-hai. Cover Selection Method for Batch Image Steganography with Multivariate Optimization[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0380 |
[13] | MA Su-gang, DUAN Shuai-peng, HOU Zhi-qiang, YU Wang-sheng, PU Lei, YANG Xiao-bao. Multi-object tracking algorithm based on dual-branch feature enhancement and multi-level trajectory association[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0472 |
[14] | ZHANG J F,YOU L B,ZHOU M,et al. Multi-objective arrival sequencing and scheduling based on point merge system[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(1):66-73 (in Chinese). doi: 10.13700/j.bh.1001-5965.2021.0199. |
[15] | LEI J Y,LEI Q N,LI H B,et al. A mesh parameterization method and life reliability-based optimization for turbine blade[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(10):2651-2659 (in Chinese). doi: 10.13700/j.bh.1001-5965.2021.0708. |
[16] | SHI X D,LI R P,ZHAO H X,et al. Non-standard interface aviation RF cable test method based on TRL[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(9):2207-2217 (in Chinese). doi: 10.13700/j.bh.1001-5965.2021.0645. |
[17] | WANG L Y,CHEN W H,JIANG Y S,et al. Measurement of ejection factor of new resin matrix composites[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(11):2960-2967 (in Chinese). doi: 10.13700/j.bh.1001-5965.2022.0056. |
[18] | YANG B,HE Y Z,XU F,et al. Using improved genetic algorithm for software fault localization aided test case generation[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(9):2279-2288 (in Chinese). doi: 10.13700/j.bh.1001-5965.2022.0524. |
[19] | ZHAO Yue-qing, LIN De-zhi, CHEN Hui, TANG Jia-li, CHEN Ping. Performance test and constitutive model selection of diaphragms in hot diaphragm forming[J]. Journal of Beijing University of Aeronautics and Astronautics. doi: 10.13700/j.bh.1001-5965.2023.0350 |
[20] | KANG Rui, LIU Haoran, ZHANG Qingyuan, YU Li, ZHAI Guofu. Function oriented belief reliability design and optimization of new torsion spring electrical connectors[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(9): 1745-1756. doi: 10.13700/j.bh.1001-5965.2022.0323 |