基于软计算的结构优化设计
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摘要
本文应用软计算方法中神经网络、遗传算法进行结构优化设计。针对神经网络在机构优化设计中网络结构难以确定的问题，进行了神经网络在结构优化设计中的映射性能和训练特性的研究；以此为基础，构造了一种适于结构优化设计的结构自适应BP神经网络，使得BP神经网络具有了一定的自我完善能力。利用该网络的快速映射能力代替结构优化设计中的有限元计算，并利用遗传算法作为搜索策略进行全局搜索寻优，成功实现了某型航空发动机涡轮盘的结构优化计算，取得较好的效果。论文还对连续体结构优化问题的样本选取问题进行了初步的分析，提出了一种样本优化的方法。
Some methods of soft computing were used in the field of engineering structural optimization, including BP (Back Propagating) neural network and genetic arithmetic . Aiming at the problem that it is difficult to find a suitable structure of neural network in the structural optimization, the author conducted some researches on the mapping ability and training properties of BP neural network in the structural optimization and constituted a self-adapting BP neural network. The network was used to take the place of FEM (Finite Element Method) for it's fast mapping ability in structure optimization and the genetic arithmetic was used as the searching method to accomplish global optimization. A turbine disk of areo-engine was optimized successfully with this method. Beside, the author has analyzed the way of getting suitable training samples, and carried out a method in which the training samples were optimized.
Some methods of soft computing were used in the field of engineering structural optimization, including BP (Back Propagating) neural network and genetic arithmetic . Aiming at the problem that it is difficult to find a suitable structure of neural network in the structural optimization, the author conducted some researches on the mapping ability and training properties of BP neural network in the structural optimization and constituted a self-adapting BP neural network. The network was used to take the place of FEM (Finite Element Method) for it's fast mapping ability in structure optimization and the genetic arithmetic was used as the searching method to accomplish global optimization. A turbine disk of areo-engine was optimized successfully with this method. Beside, the author has analyzed the way of getting suitable training samples, and carried out a method in which the training samples were optimized.
引文
1．袁亚湘，孙文瑜．最优化理论与方法．科学出版社，1999．
2．张智星，孙春在，(日)水谷英二．神经——模糊和软计算．西安交通大学出版社，2000．
3．Michael BM,Anthony J C. Multilayer neural networks and adaptive nonlinear control of agile agile anti-aid missiles[R]. AIAA-97-3540.
4．王天华，王平洋，范明天．遗传算法、模糊逻辑和运输模型在配电网空间负荷预测中的应用．电网技术，1999，23(1)：24～28．
5．张青，王殊，杨宗凯．模糊神经网络在火灾探测中的应用．电路与系统学报，1997，2(3)：51～55．
6．乔俊伟，詹永麟，施光林．基于结构的拟神经网络建模与优化方法研究 机械工程学报，2002，38(1)：71～74．
7．李文勇，李泉永．利用神经网络进行近似分析的结构优化设计，广西科学，2001，8(2)：86～89．
8．沈谦，王涛．结构优化的RBF神经网络学习算法，微电子学与计算机，2000，4，
14～18．
9．黄胜伟，王德信．结构优化设计中神经网络方法的应用，建筑技术开发，2002，29(4)，63～65．
10. Soh Chee-Kiong, Yang Jiaping. Optimal layout of bridge trusses by genetic algorithms Computer-Aided Civil and Infrastructure Engineering, 1998,13:247～254.
11．戚德虎，康继昌．BP神经网络的设计．计算机工程与设计．1998，19(4)．
12．申铉国，张铁强．人工神经网络在机械部件设计中的应用研究．机械工程学报，1992，28(6)．
13．许素强，夏人伟．结构优化方法研究综述．航空学报，1995，16，(4)．
14．张氢，孙国正．基于神经网络的优化设计专家系统．机械科学与技术，1999，18(6)．
15. D. Anderson, E.L. Hines, S.J. Arthur, E.L. Eiap. Application of Artificial Neural Networks to the Prediction of Minor Axis Steel Connections. Computers & Structures, 1997,63(4).
16．马海全，温卫东．含连续／离散变量结构优化中的神经网络与变尺度模拟退火方法．南京航空航天大学学报，2001，33(3)：237～240．
17．陆金桂，余俊，王浩，陈新度，周济，肖世德．基于人工神经网络的结构近似分析方法的研究．中国科学(A辑)，24(6)．
18. Keunedy M P,Chua L O. Neural networks for nonlinear programming. IEEE Trans. Circuits Systems, 1988,35:554～562.
19. Satoshi Matssuda. "Optimal" Hopfield network for combinatorial Optimization with linear cost function .IEEE Trans, on Neural Network, 1998,9(6):1319～1329.
20. Kate Smith ,et al. Neural technigues for combinational optimization with applications. IEEE Trans, on Neural Network, 1998,9(6):1301～1317.
21. Z.P. Szewczyk. A.K, Noor. A hybrid neuro-computing/numerical strategy for nonlinear structure analysis. Computer & Structure. 1996, 58(4):661～667.
22. W.M. Jenkins Neural network-Based approximation for timefural analysis, in: Development in Neural Networks and structural Engineering. BHV Topping civil-comppress Edin, UK.,1995,25～35.
23．唐小兵，沈从武，陈定方．神经网络与遗传算法结合在结构优化设计中的应用．武汉交通科技大学学报，1999，23(5)，477～479．
24．路志峰．基于BP神经网络和遗传算法的结构优化设计 南京航空航天大学，2001．
25. B. Fritzke. Growing cell structures—a self-organizing network for unsupervised and supervised learning. Neural Network, 1994, 7(9): 1411～1460.
26. S. Jockusch, H. Ritter.Self-organizing maps: local competition and evolutionary optimization .Neural Networks, 1994,7(8):1229～1239
27. Y. Zheng, et al. The effect of concave and convex weight adjustments in self-organizing maps. IEEE Trans on Neural Networks , 1996, 7(1): 87～96.
28．吴郢，阎平凡．结构自适应自组织神经网络的研究．电子学报，1999，27(7)：55～58．
29．孙功星，朱科军，戴长江，戴贵亮．任务自适应神经网络结构研究．核电子学与探测技术，1999，19(3)：164～168．
30．张翔，宋星原，夏军．短期洪水预报的变结构神经网络模型．水电能源科学，2002，20(1)：12～14．
31．牛东晓，乞建勋，邢棉．建筑工程造价预测的变结构神经网络模型研究．华北电力大学学报，2001，28(4)：1～4．
32．王石刚，刘莉等．结构优化的GA算法．应用力学学报1995．12(3)：106～110．
33．陈新度，秦叶，陈新，余俊．遗传算法在离散变量结构优化设计中的应用．华中理工大学学报，1997，25〔8〕：44～46．
34. Han Yingshi, Ouo Pengfei. A hybrid genetic algorithm for structural optimization with discete variables ,In : Proceedings of the First China—Japan-Korea Joint Symposium on Optimization of Structural and Mechanical System, Xi'an, China, 1999-10-31～11-04. Xi'an: Xidian University Press, 1999.157～164.
35. Yeh I-Cheng. Hybrid genetic algorithms for optimization of truss structures . Computer-Aided Civil and Infrastructure Engineering, 1999,14:199～206.
36. Ghasemi M R, Hinton E, Wood R.D. Optimization of trusses using genetic algorithms for discrete and continuous variables .Engineering Computations, 1999,16(3):272～301.
37. Rajeev S, Krishnamoothy C S. Discrete optimization of structures using genetic algorithms. Journal of Structural Engineering, 118(5): 1233～1250.
38. Kita E, Tanie H .Topology and shape optimization of continuum structures using GA and BEM-Structural Optimization, 1999,17,130～139.
39. Yamakawa Hiroshi systems using genetic algorithm. In: Gu Y X ed. Proceedings of the First China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical System ,Xi'an, China, 1999-10-31 11-04. Xi'an:Xidian University Press, 1999.109～116.
40. Sugimoto Masahiro, Yamakawa hiroshi. A study on simultaneous optimization
by parallel genetic algorithms. In: Gu Y X ed. Proceedings of the First China—Japan-Korea Joint Symposium on Optimization of Structural and Mechanical System, Xi'an, China, 1999-10-31～11-04. Xi'an:Xidian University Press, 1999.241～248.
41. Hajela P, Lee E, Cho H. Genetic algorithms in topologic design of grillage structure. Computer-Aided Civil and Infrastructure Engineering, 1998,13:13～22.
42. Ewing M S, Downs K. Optimization of a Rectangular Cross-section Wingbox Using Genetic Algorithms. AIAA-96-1536-CP. 1996.1858～1867.
43. Burczynski Tadeusz, Koko Grzegorz. Topology optimization using boundary elements and genetic algorithms. In: Idelsohn S ,Ouate E, Drorkiu E, eds. Computational Mechanics New Trends and Applications. CIMNB. Barcelona, 1998,1～12 .
44. Galante M, Cerrolaza M ,Annicchiarico W .Optimization of structural and finite element models via genetic algorithms. Structural Optimization, SAMPE J, 1994,30(3):127～137.
45. Rodolphe G, Riche Le, Catherine Knopf-Lenoir, Raphael T Haftka. A segregated genetic algorithm for constrained structural optimization. In: Proceedings of the 6th international Conference on Genetic Algorithms, 1995.558～565.
46. Byon O (Ben G), Nishi Y, Sato S. Optimization lamination of hybrid thick-walled cylindrical shell under external Pressure by using a genentic algorithm, J Thermoplastic Composite Materials, 1998, 11:417～428.
47. Savic D A, Evans K E, Silberhorn Thorsten. A genetic algorithm-based system for the optimal design of laminate. Computer-Aided Civil and Infrastructure Engineering, 1999, 14: 187～197.
48. Venter Gerhard, Haftka R T. A Two Species Genetic Algorithm for Designing Composite Laminates Subjected to Uncertainty. AIAA-96-1535-CP, 1996,1848～1857.
49．唐文艳，顾元宪．遗传算法在结构优化中的研究进展．力学进展，2002，32(1)，26～40．
2．张智星，孙春在，(日)水谷英二．神经——模糊和软计算．西安交通大学出版社，2000．
3．Michael BM,Anthony J C. Multilayer neural networks and adaptive nonlinear control of agile agile anti-aid missiles[R]. AIAA-97-3540.
4．王天华，王平洋，范明天．遗传算法、模糊逻辑和运输模型在配电网空间负荷预测中的应用．电网技术，1999，23(1)：24～28．
5．张青，王殊，杨宗凯．模糊神经网络在火灾探测中的应用．电路与系统学报，1997，2(3)：51～55．
6．乔俊伟，詹永麟，施光林．基于结构的拟神经网络建模与优化方法研究 机械工程学报，2002，38(1)：71～74．
7．李文勇，李泉永．利用神经网络进行近似分析的结构优化设计，广西科学，2001，8(2)：86～89．
8．沈谦，王涛．结构优化的RBF神经网络学习算法，微电子学与计算机，2000，4，
14～18．
9．黄胜伟，王德信．结构优化设计中神经网络方法的应用，建筑技术开发，2002，29(4)，63～65．
10. Soh Chee-Kiong, Yang Jiaping. Optimal layout of bridge trusses by genetic algorithms Computer-Aided Civil and Infrastructure Engineering, 1998,13:247～254.
11．戚德虎，康继昌．BP神经网络的设计．计算机工程与设计．1998，19(4)．
12．申铉国，张铁强．人工神经网络在机械部件设计中的应用研究．机械工程学报，1992，28(6)．
13．许素强，夏人伟．结构优化方法研究综述．航空学报，1995，16，(4)．
14．张氢，孙国正．基于神经网络的优化设计专家系统．机械科学与技术，1999，18(6)．
15. D. Anderson, E.L. Hines, S.J. Arthur, E.L. Eiap. Application of Artificial Neural Networks to the Prediction of Minor Axis Steel Connections. Computers & Structures, 1997,63(4).
16．马海全，温卫东．含连续／离散变量结构优化中的神经网络与变尺度模拟退火方法．南京航空航天大学学报，2001，33(3)：237～240．
17．陆金桂，余俊，王浩，陈新度，周济，肖世德．基于人工神经网络的结构近似分析方法的研究．中国科学(A辑)，24(6)．
18. Keunedy M P,Chua L O. Neural networks for nonlinear programming. IEEE Trans. Circuits Systems, 1988,35:554～562.
19. Satoshi Matssuda. "Optimal" Hopfield network for combinatorial Optimization with linear cost function .IEEE Trans, on Neural Network, 1998,9(6):1319～1329.
20. Kate Smith ,et al. Neural technigues for combinational optimization with applications. IEEE Trans, on Neural Network, 1998,9(6):1301～1317.
21. Z.P. Szewczyk. A.K, Noor. A hybrid neuro-computing/numerical strategy for nonlinear structure analysis. Computer & Structure. 1996, 58(4):661～667.
22. W.M. Jenkins Neural network-Based approximation for timefural analysis, in: Development in Neural Networks and structural Engineering. BHV Topping civil-comppress Edin, UK.,1995,25～35.
23．唐小兵，沈从武，陈定方．神经网络与遗传算法结合在结构优化设计中的应用．武汉交通科技大学学报，1999，23(5)，477～479．
24．路志峰．基于BP神经网络和遗传算法的结构优化设计 南京航空航天大学，2001．
25. B. Fritzke. Growing cell structures—a self-organizing network for unsupervised and supervised learning. Neural Network, 1994, 7(9): 1411～1460.
26. S. Jockusch, H. Ritter.Self-organizing maps: local competition and evolutionary optimization .Neural Networks, 1994,7(8):1229～1239
27. Y. Zheng, et al. The effect of concave and convex weight adjustments in self-organizing maps. IEEE Trans on Neural Networks , 1996, 7(1): 87～96.
28．吴郢，阎平凡．结构自适应自组织神经网络的研究．电子学报，1999，27(7)：55～58．
29．孙功星，朱科军，戴长江，戴贵亮．任务自适应神经网络结构研究．核电子学与探测技术，1999，19(3)：164～168．
30．张翔，宋星原，夏军．短期洪水预报的变结构神经网络模型．水电能源科学，2002，20(1)：12～14．
31．牛东晓，乞建勋，邢棉．建筑工程造价预测的变结构神经网络模型研究．华北电力大学学报，2001，28(4)：1～4．
32．王石刚，刘莉等．结构优化的GA算法．应用力学学报1995．12(3)：106～110．
33．陈新度，秦叶，陈新，余俊．遗传算法在离散变量结构优化设计中的应用．华中理工大学学报，1997，25〔8〕：44～46．
34. Han Yingshi, Ouo Pengfei. A hybrid genetic algorithm for structural optimization with discete variables ,In : Proceedings of the First China—Japan-Korea Joint Symposium on Optimization of Structural and Mechanical System, Xi'an, China, 1999-10-31～11-04. Xi'an: Xidian University Press, 1999.157～164.
35. Yeh I-Cheng. Hybrid genetic algorithms for optimization of truss structures . Computer-Aided Civil and Infrastructure Engineering, 1999,14:199～206.
36. Ghasemi M R, Hinton E, Wood R.D. Optimization of trusses using genetic algorithms for discrete and continuous variables .Engineering Computations, 1999,16(3):272～301.
37. Rajeev S, Krishnamoothy C S. Discrete optimization of structures using genetic algorithms. Journal of Structural Engineering, 118(5): 1233～1250.
38. Kita E, Tanie H .Topology and shape optimization of continuum structures using GA and BEM-Structural Optimization, 1999,17,130～139.
39. Yamakawa Hiroshi systems using genetic algorithm. In: Gu Y X ed. Proceedings of the First China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical System ,Xi'an, China, 1999-10-31 11-04. Xi'an:Xidian University Press, 1999.109～116.
40. Sugimoto Masahiro, Yamakawa hiroshi. A study on simultaneous optimization
by parallel genetic algorithms. In: Gu Y X ed. Proceedings of the First China—Japan-Korea Joint Symposium on Optimization of Structural and Mechanical System, Xi'an, China, 1999-10-31～11-04. Xi'an:Xidian University Press, 1999.241～248.
41. Hajela P, Lee E, Cho H. Genetic algorithms in topologic design of grillage structure. Computer-Aided Civil and Infrastructure Engineering, 1998,13:13～22.
42. Ewing M S, Downs K. Optimization of a Rectangular Cross-section Wingbox Using Genetic Algorithms. AIAA-96-1536-CP. 1996.1858～1867.
43. Burczynski Tadeusz, Koko Grzegorz. Topology optimization using boundary elements and genetic algorithms. In: Idelsohn S ,Ouate E, Drorkiu E, eds. Computational Mechanics New Trends and Applications. CIMNB. Barcelona, 1998,1～12 .
44. Galante M, Cerrolaza M ,Annicchiarico W .Optimization of structural and finite element models via genetic algorithms. Structural Optimization, SAMPE J, 1994,30(3):127～137.
45. Rodolphe G, Riche Le, Catherine Knopf-Lenoir, Raphael T Haftka. A segregated genetic algorithm for constrained structural optimization. In: Proceedings of the 6th international Conference on Genetic Algorithms, 1995.558～565.
46. Byon O (Ben G), Nishi Y, Sato S. Optimization lamination of hybrid thick-walled cylindrical shell under external Pressure by using a genentic algorithm, J Thermoplastic Composite Materials, 1998, 11:417～428.
47. Savic D A, Evans K E, Silberhorn Thorsten. A genetic algorithm-based system for the optimal design of laminate. Computer-Aided Civil and Infrastructure Engineering, 1999, 14: 187～197.
48. Venter Gerhard, Haftka R T. A Two Species Genetic Algorithm for Designing Composite Laminates Subjected to Uncertainty. AIAA-96-1535-CP, 1996,1848～1857.
49．唐文艳，顾元宪．遗传算法在结构优化中的研究进展．力学进展，2002，32(1)，26～40．