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Reliability-based Robust Optimization Design Based on Specular Reflection Algorithm

Qi Qisong Wang Jun Xu Gening Fan Xiaoning

戚其松, 王君, 徐格宁, 范小宁. 基于镜面反射算法的可靠性稳健优化设计研究. 自动化学报, 2017, 43(8): 1457-1464. doi: 10.16383/j.aas.2017.e150129
引用本文: 戚其松, 王君, 徐格宁, 范小宁. 基于镜面反射算法的可靠性稳健优化设计研究. 自动化学报, 2017, 43(8): 1457-1464. doi: 10.16383/j.aas.2017.e150129
Qi Qisong, Wang Jun, Xu Gening, Fan Xiaoning. Reliability-based Robust Optimization Design Based on Specular Reflection Algorithm. ACTA AUTOMATICA SINICA, 2017, 43(8): 1457-1464. doi: 10.16383/j.aas.2017.e150129
Citation: Qi Qisong, Wang Jun, Xu Gening, Fan Xiaoning. Reliability-based Robust Optimization Design Based on Specular Reflection Algorithm. ACTA AUTOMATICA SINICA, 2017, 43(8): 1457-1464. doi: 10.16383/j.aas.2017.e150129

基于镜面反射算法的可靠性稳健优化设计研究

doi: 10.16383/j.aas.2017.e150129
基金项目: 

the National Natural Science Foundation of China 51275329

Reliability-based Robust Optimization Design Based on Specular Reflection Algorithm

Funds: 

the National Natural Science Foundation of China 51275329

More Information
    Author Bio:

    Jun Wang is a Ph.D.candidate at Taiyuan University of Science and Technology, China.Her research interests include intelligent optimization algorithm and hydraulic servo control system.E-mail:best_wangj@126.com

    Gening Xu received the Ph.D.degree from Tongji University, China.He is currently a Professor of Taiyuan University of Science and Technology.His research interests include theory and method of structure design and analysis and structure reliability design.E-mail:xugening@sina.com

    Xiaoning Fan received the Ph.D.degree from Dalian University of Technology, China.She is currently a Professor of Taiyuan University of Science and Technology.Her research interests include computational intelligence, optimization design and structure fatigue life evaluation.E-mail:fannyfxn@163.com

    Corresponding author: Qisong Qi is a Ph.D.candidate at Taiyuan University of Science and Technology, China.His research interests include intelligent optimization algorithm, structure reliability design and structure design of Crane.Corresponding author of this paper.E-mail:qiqisong_19870328@126.com
  • 摘要: 本文通过模拟镜子反射光线的能力,提出了一种全新的全局优化方法-镜面反射算法(Specular Reflection Algorithm).镜面反射算法不仅具有全局收敛、计算效率高,适合求解高维、多峰的复杂函数等优点,而且算法的自适应能力强,能够根据不同的优化对象,自适应调整参数,以达到最好的优化效果.本文利用4个典型的优化问题验证该算法的计算能力,并同经典的粒子群算法、果蝇算法和模拟退火算法比较.最后,以桥式起重机桥架结构为研究对象,将镜面反射算法和稳健可靠性设计方法相结合对其进行优化设计,证明了镜面反射算法具有很高的工程研究价值,而且可以预见算法能够广泛的同生产实际结合,创造更大的价值.
    Recommended by Associate Editor Qinglai Wei
  • Fig.  1  Coordinate update of the specular reflection system.

    Fig.  2  Optimization flow chart of the SRA.

    Fig.  3  Three-dimensional surface of test function.

    Fig.  4  Iteration curve of sphere.

    Fig.  5  Iteration curve of griewank.

    Fig.  6  Iteration curve of rosenbrock.

    Fig.  7  Iteration curve of restrigin.

    Fig.  8  Mechanical model diagram and sectional dimension.

    Table  Ⅰ  JUDGEMENT OF $\xi$

    Value of $\xi$ N =2 N =10 N=20 N=50 N = 100
    Optimal solution (10-6) Iteration times Optimal solution (10-6) Iteration times Optimal solution (10-6) Optimal solution (103) Optimal solution (10-6) Optimal solution (103) Optimal solution (10-6) Optimal solution (104)
    0.4 4.7776 402.70 7.1895 1103 7.2883 2.0369 8.9324 6.1015 9.5844 1.4945
    0.5 3.3845 341.04 6.4267 940.12 7.3111 1.8001 8.4771 5.3149 9.6383 1.2586
    0.6 3.9884 737.76 5.4844 936.46 7.2327 1.6802 9.0155 4.8292 9.3691 1.1344
    0.7 3.5625 515.18 6.9587 810.24 7.2858 1.5971 8.5419 4.4544 9.5971 1.0679
    0.8 4.2770 509.46 6.7379 747.90 7.5046 1.4992 8.8811 4.2697 9.3384 1.0741
    0.9 4.0589 259.08 6.3850 732.90 7.4304 1.4562 8.3421 4.2036 9.4009 1.0976
    1.0 4.9287 193.26 5.9257 694.18 6.8977 1.3677 8.3414 4.3603 9.5947 1.1404
    1.1 4.6702 142.60 6.1496 674.28 8.0852 1.2946 9.4538 4.2854 9.4944 1.1889
    1.2 4.6250 142.42 5.8875 626.54 7.7654 1.3608 8.6969 4.4775 9.6771 1.2434
    1.3 5.1501 139.08 6.5208 654.72 7.2172 1.4050 8.9588 4.5342 9.5792 1.3215
    1.4 5.4409 131.02 5.6072 695.40 6.9556 1.4699 8.9053 4.6930 9.6898 1.3675
    1.5 4.7099 103.72 5.7050 675.02 7.6612 1.4740 9.0472 4.8329 9.5134 1.4173
    1.6 4.7625 93.82 5.8038 713.20 6.4546 1470 8.9756 4.8634 9.7748 1.4768
    1.7 4.9327 91.94 4.9871 783.90 5.8034 1.6036 9.1825 5.0851 9.6612 1.4985
    1.8 5.9076 87.32 5.4104 856.30 7.1143 1.6917 8.7372 5.3202 9.4446 1.5536
    1.9 4.9402 82.44 5.5724 832.12 6.4092 1.8641 8.7754 5.5962 9.6617 1.6423
    2.0 4.7168 89.08 4.8307 998.300 5.7508 2.0544 8.1780 6.3700 9.4975 2.5117
    下载: 导出CSV

    Table  Ⅱ  NUMERICAL CALCULATION FUNCTION

    Name Expression Interval of convergence Global extreme Dimension
    Sphere $f_1 = \sum\limits_{i = 1}^n {x_i^2 }$ $x_i\in [-50,50]$ 0 (0, 0, $\ldots$ , 0) $n$ = 30 100
    Griewank $f_2 = 1 + \sum\limits_{i = 1}^n {\left( {\frac{x_i^2 }{4000}} \right) -\prod\limits_{i = 1}^n {\cos \left( {\frac{x_i }{\sqrt i }} \right)} }$ $x_i\in [-600,600]$ 0 (0, 0, $\ldots$ , 0) $n$ = 30 100
    Rosenbrock $f_3 = \sum\limits_{i = 1}^{n - 1} {[100(x_{i + 1}-x_i^2 )^2 + (x_i-1)^2]}$ $x_i\in [-100,100]$ 0 (1, 1, $\ldots$ , 1) $n$ = 30 100
    Restrigin $f_4 = \sum\limits_{i = 1}^n {[10 + x_i^2-10\cos (2\pi x_i )]}$ $x_i\in [-5.0, 5.0]$ 0 (0, 0, $\ldots$ , 0) $n$ = 30 100
    下载: 导出CSV

    Table  Ⅲ  CALCULATION RESULTS OF TEST FUNCTION

    Name PSO
    (n = 30) [10]
    Kalman swarm
    (n = 30) [10]
    Chaos ant colony optimization
    (n = 30)[10]
    Chaos PSO
    (n = 30) [10]
    New chaos PSO
    (n = 30) [10]
    SRA
    (n = 30)
    SRA
    (n = 100)
    Sphere 3.7004×102 4.723 3.815×10-1 2.4736×10-3 2.0729×10-9 1.1080×10-24 2.3160×10-12
    Griewank 2.61×107 3.28×103 23.414 6.8481×10-2 9.9051×10-11 4.6629×10-15 2.7978×10-14
    Rosenbrock 13.865 9.96×10-1 4.669×10-1 1.0404×10-2 2.9068×10-4 9.8730×10-7 6.1173×10-5
    Restrigin 1.0655×102 53.293 22.6361 9.5258×10-1 4.3741×10-4 3.9373×10-21 8.7727×10-7
    下载: 导出CSV

    Table  Ⅳ  CALCULATION RESULTS

    Design method Design variables (mm) Objective function (mm2) Reliability Sensitivity of reliability/(10-3)
    x1 x2 x3 x4 x5 A Rv $\frac{\partial R_v}{\partial S}$ $\frac{\partial R_v}{\partial F}$ $\frac{\partial R_v}{\partial E}$ $\frac{\partial R_v}{\partial \rho}$
    SRA Optimization 6 6 205 635 257 10 704 0.5071 14.3985 0.0017 9.15×10-9 0.0011
    Reliability Optimization 6 6 258 632 310 11 304 0.9968 13.0816 0.0015 8.77×10-9 0.0010
    Robust Reliability Optimization 6 6 324 595 376 11 652 0.9813 12.6270 0.0015 9.23×10-9 0.0010
    PSO Optimization 10 6 185 567 619 11 544 0.5314 13.0714 0.0015 9.8×10-9 0.0010
    Reliability Optimization 7 7 222 605 276 12 334 0.9806 12.9119 0.0015 9.73×10-9 0.0011
    Robust Reliability Optimization 9 6 302 534 354 12 780 0.9810 11.5262 0.0013 1.01×10-8 0.0010
    FOA Optimization 9 6 190 581 633 11 328 0.5132 13.3500 0.0016 9.64×10-9 0.0010
    Reliability Optimization 6 6 491 532 543 13 068 0.9802 11.3697 0.0013 1.01×10-8 9.95×10-4
    Robust Reliability Optimization 8 11 237 536 299 16 576 1.0 11.6479 0.0013 1.27×10-9 0.0013
    Note: The index of reliability R0 = 0.98 is deflned.
    下载: 导出CSV
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  • 收稿日期:  2015-08-04
  • 录用日期:  2016-02-01
  • 刊出日期:  2017-08-20

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