臺灣博碩士論文加值系統

在本文中，我們提出了兩種改良式的微分進化演算法(differential evolution algorithm，DEA)，稱為田口微分進化演算法（Taguchi-differential evolution algorithm，TDEA）及可調整式田口微分進化演算法（adjustable Taguchi-differential evolution algorithm，ATDEA）。其演算法應用於模式簡化（model reduction），降階模型的動作使得模擬、分析或是控制設計能夠更容易。TDEA修改了傳統DEA突變之法則。我們利用田口實驗法具有的系統規劃參數設計理念，應用於突變機制中，取代了傳統DEA在突變機制中隨機產生擾動向量的動作，提升了避免搜索過程中陷入局部解的機率。
然而在搜尋最佳解時，最大的問題在於無法得知其範圍是多大，故ATDEA引入了搜尋空間擴大機制（search space expansion scheme），讓搜尋範圍空間成為動態，使得搜索效率能提升。
我們將試舉幾個測試函數，說明TDEA及ATDEA比傳統DEA擁有較佳的尋優能力。最後利用TDEA及ATDEA去做模式簡化的應用，最後並與傳統DEA及文獻中提出的DEA來作分析比較。

In this thesis, the problems of model reduction are solved by using two improved differential evolution algorithms (DEA), which are called Taguchi-differential evolution algorithm (TDEA) and adjustable Taguchi-differential evolution algorithm（ATDEA）. The use of a reduced-order model makes it easier to implement analyses, simulations and control designs. The proposed TDEA is modified from the traditional DEA with mutation operation. The systematic reasoning ability of the Taguchi method can promote the mutation efficiency. The Taguchi method applied into mutation operation and replaced the action of perturbed vectors were chosen randomly in the tradition DEA. TDEA can avoid premature convergence with controllable deteriorating probability.
However, the biggest problem in optimal solution is that we can’t know the range of searching. Here, we incorporate a search space expansion scheme in the ATDEA approach and let search space dynamical. The efficiency will be promoted.
It will also be shown that the TDEA and ATDEA perform batter than traditional DEA by using some benchmark test functions. Finally, we use TDEA and ATDEA to solve examples of model reduction. Simulation results show that the proposed TDEA and ATDEA approaches can obtain better performances than the traditional DEA and the existing DEA reported recently in the literature.

中文摘要 i
英文摘要 ii
誌謝 iv
目錄 v
表目錄 vii
圖目錄 viii
第一章、序論 1
1.1 研究動機與目的 1
1.2 論文架構 3
第二章、理論基礎 4
2.1 微分進化演算法 4
2.2 田口實驗法 9
2.2.1 直交表 9
2.2.2 實驗配置與結果分析 10
第三章、田口微分進化演算法 17
3.1 前言 17
3.2 輪盤式選擇 17
3.3 田口式突變 18
3.4 搜尋空間擴大機制 24
3.5 TDEA及ATDEA流程 25
3.5.1 TDEA流程 25
3.5.2 ATDEA流程 27
3.6 標竿型函數測試 29
第四章、模式簡化應用 36
4.1 問題描述 36
4.2 模擬結果 37
4.2.1 例子一 37
4.2.2 例子二 65
4.3 結果分析 75
第五章、結論與未來展望 76
5.1 結論 76
5.2 未來展望 76
參考文獻 77

[1] A. J. Hugo, P.A. Taylor and J, D, Wright, 1996, “Approximate dynamic models for recycle systems”, Ind. End. Chem. Res., vol. 35, no. 2, pp.485-487.
[2] Y. S. Zhong, 2001, “Extreme stability margins of interval systems”, IEE Proceedings on Control Theory and Applications, vol.148, no. 1, pp.77-80.
[3] C. S. Hsieh and C. Hwang, 1989, “Model reduction of continuous-time systems using a modified Routh approximation method”, IEE Proceedings on Control Theory and Applications, vol.136, no. 4, pp.151-156.
[4] X. Tai, H. Zhang and Y. Sun, 2006, “A minimum output information loss method for stochastic model reduction”, IEEE Proceedings of 6th World Congress on Intelligent Control and Automation, pp. 1186-1190.
[5] P. Houlis and V. Sreeram, 2006, “A parametrized controller reduction technique”, IEEE Proceedings of 45th on Decision and Control, pp. 3430-3435.
[6] X. X. Huang, W. Y. Yan and K. L. Teo, 2001, “ near-optimal model reduction”, IEEE Trans. Automat. Contr, vol. 46, no. 8, pp. 1279-1284.
[7] A. Ferrante, W. Krajewski, A. Lepschy and U. Viaro, 1999, “Convergent algorithms for model reduction”, Automatica, vol. 35, pp. 75-79.
[8] S. L. Cheng and C. Hwang, 2001, “Optimal approximation of linear systems by a differential evolution algorithm”, IEEE Trans. Sys., Man and Cyber., vol. 31, no.6, pp. 698-707
[9] A. Megretski, 2006, “H-infinity model reduction with guaranteed suboptimality bound”, IEEE Proceedings of the 2006 American Control Conference, pp. 448-453.
[10] K. M. Grigoriadis, 1995, “Optimal model reduction via linear matrix inequalities: Continuous- and discrete-time cases”, Syst. Contr. Lett., vol. 26, no. 5, pp. 321-333.
[11] J. F. Leu and C. Hwang, 2001, “Optimal model reduction using genetic algorithms”, J. of the Chinese Institute of Engineers, vol. 24, no. 5, pp. 607-618.
[12] D. Kavranoglu and M. Bettayeb, 1994, “Characterization and computation of the solution to the optimal approximation problem,” IEEE Trans. Automat. Contr., vol. 39, pp. 1899–1904.
[13] R. Storn, 1997, “Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces”, J. Global. vol. 11, pp. 341–359.
[14] R. Storn and K.Price, 1995, “Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces”, Technical Report TR-95-012, International Computer Science Institute, Berkeley, USA.
[15] R. Storn and K. Price, 1996, “Minimizing the real functions of the ICEC’96 contest by differential evolution”, Proceedings IEEE Conference on Evolutionary Computation, pp. 842-844.
[16] 蘇朝墩，2002，品質工程，中華民國品質學會，台北，台灣。
[17] 周至宏，2005，”實驗設計與品質工程”上課講義，國立高雄第一科技大學系統與控制工程研究所，高雄，台灣。
[18] D. E. Goldberg, 1989, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Massachusetts.
[19] T. Y. Guo and C. Hwang, 1996, “Optimal reduced-order models for unstable and nonminimum-phase systems”, IEEE Trans. Circuits Syst. I, vol. 43, no. 9, pp. 800-805.
[20] P. J. Parker and B.D.O. Anderson, 1987, “Unstable rational function approximation”, Int. J. Contr., vol. 46, no. 5, pp. 1783-1801.
[21] K. Glover, 1984, “All optimal Hankel-norm approximations of linear multivariable systems and their -error bounds”, Int. J. Contr., vol. 39, no. 6, pp. 1115-1193.