本研究的目的是要提出一個系統動力模型(System Dynamics Model；以下簡稱SDM)與類神經網路(Artificial Neural Network；以下簡稱ANN)之間的轉換法，用以輔助建構SDM並設計其中的政策。SDM與ANN都是將建模者的知識儲存在圖形的結構之中。ANN又能夠從一組多變量的時間序列軌跡中學習出一組數值的傳遞結構。因此我們將先把SDM轉換成一種特殊的ANN－部分遞迴網路(Partial Recurrent Network；以下簡稱PRN)，並證明兩者具有相同的數值傳遞限制。再將PRN的學習法與建模過程整合，而形成一套學習機制，便可以輔助建模者建構SDM。也就是由模型的草圖開始，由PRN學習出幾個可能的結構，再由建模者選擇。另外，以同樣的精神，也可以將SDM-PRN轉換法應用來設計SDM中的政策。因為PRN可以從歷史軌跡學習出結構，當然也可以從建模者設定的較佳軌跡中，學習出較佳的結構。本研究也實證了上述兩個應用的有效性及使用性，結果都非常令人滿意。

This paper presents a model transformation between System Dynamics Model (SDM) and Artificial Neural Network (ANN) to aid model construction and policy design. We first point out a similarity between a System Dynamics Model (SDM) and an artificial neural network, in which both store knowledge majorly in the structure (or linkages) of a model. Then, we design a method that can map a SDM to a special design Partial Recurrent Network (PRN), and prove in mathematics that they two operate under the same numerical propagation constraints. With the established foundation, we then showed that the SDM-PRN transformation could aid SDM construction in the following way: (1) start from an initial skeleton of a PRN model (mapping from an initial SDM), (2) incarnate its structure by learning and (3) convert it back to a corresponding SDM. This approach integrates the capability of neural network learning with a traditional process, which thus makes model construction more systematic and much easier for common people. In the same philosophy, the SDM-PRN transformation could also aid SD policy design. Since any PRN can learn some structures from a historical time series pattern, it can also learn a better structure from a better pattern set by designer. We have investigated the effectiveness and usefulness of two application of the SDM-PRN transformation described above and the results are satisfactory.

摘要 I
ABSTRACT II
目錄 III
表目錄 V
圖目錄 VI
第一章 導論 1
第一節 研究背景 1
第二節 研究動機及問題 1
第三節 研究目的 3
第四節 論文架構 4
第二章 文獻探討 5
第一節 系統動力學回顧 5
第二節 系統動力建模程序回顧 9
第三節 正規化政策設計方法回顧 15
第四節 類神經網路回顧 21
第三章 SDM-PRN模型轉換法 29
第一節 結構之對應 29
第二節 數值限制式之對應 41
第三節 實證 50
第四章 模型轉換法應用之一：輔助建模 55
第一節 問題之定義 56
第二節 模型之建構 57
第三節 結構之學習 58
第四節 模型之解釋 62
第五節 實證 65
第六節 輔助建模工具之設計 79
第五章 模型轉換法應用之二：整體性政策設計 82
第一節 政策設計程序 82
第二節 實證 83
第六章 結論及未來研究方向 103
附錄一 107
參考文獻 116
中文部分： 116
英文部分： 116

中文部分：
[1] 陳加屏，民88，系統動力學模式結構層次高槓桿決策函數產生法之研究，中山大學企業管理系博士論文。
[2] 郭進隆譯，民83，第五項修練：學習型組織的藝術與實務，台北，天下文化出版公司。原著作者：Peter M. Senge。
[3] 齊若蘭譯，民84，第五項修練實踐篇－思考、演練與超越，台北，天下文化出版公司。原著作者：Peter M. Senge等。
英文部分：
[1] An, G. “The Effects of Adding Noise during Backpropagation Training on a Generalization Performance,” Neural Computation (8), 1996, pp. 643-647.
[2] Aussem, A. “Dynamical Recurrent Neural Networks towards Prediction and Modeling of Dynamical Systems,” Neurocomputing (28), 1999, pp. 207-232.
[3] Bailey, R., Bras, B. and Allen, J. K., “Using Response Surfaces to Improve the Search for Satisfactory Behavior in System Dynamics Models,” System Dynamics Review (16:2), 2000, pp. 75-90.
[4] Bensoussan, A., Hurst, E. G. and Näslund, B., Management Application of Modern Control Theory, North Holland, Amsterdam, 1974.
[5] Burns, J. R., and Malone D. W. “Optimization Techniques Applied to the Forrester Model of the World,” IEEE Transaction on Systems, Man, and Cybernetics (4:2), 1974, pp. 164-171.
[6] Clemson, B., Tang, Y., Pyne, J. and Unal R., “Efficient Methods for Sensitivity Analysis,” System Dynamics Review (11:1), 1995, pp. 31-49.
[7] Cooper, D. R. and Emory C. W. Business Research Methods, Irwin, Chicago, 1995.
[8] Coyle, R. G., Management System Dynamics, Wiley, New York, 1977.
[9] Coyle, R. G. “The Use of Optimisation Methods for Policy Design in a System Dynamics Model,” System Dynamics Reviews (1), 1985, pp. 81-92.
[10] DeRusso, P., Roy, R. and Close, C., State Variables for Engineers, Wiley, 1965.
[11] Dolado, J. J. “Qualitative Simulation and System Dynamics,” System Dynamics Reviews (8:1), 1992, pp. 55-81.
[12] Elman, J. L. “Finding Structure in Time,” Cognitive Science (14), 1990, pp. 179-211.
[13] Forrester, J. W. Industrial Dynamics, MIT Press, Cambridge, MA, 1961.
[14] Forrester, J. W. “Industrial Dynamics-After the First Decade,” Management Science (14:7), 1968a, pp. 393-415.
[15] Forrester, J. W. Principles of Systems, MIT Press, Cambridge, MA, 1968b.
[16] Forrester, J. W., World Dynamics, Wright-Allen, Cambridge, Mass., 1971.
[17] Forrester, J. W. “System Dynamics, Systems Thinking, and Soft OR,” System Dynamics Review (10:2-3), 1994, pp. 245-256.
[18] Graham, A. K., “Parameter Formulation and Estimation in System Dynamics Models,” working paper, System Dynamics Group, MIT, Cambridge, MA, 1976.
[19] Gunter, B., “Statistically Designed Experiments,” Quality Progress (74), 1990.
[20] Hair J. F. Jr., Anderson, R. E., Tatham, R. L. and Black, W. C. Multivariate Data Analysis, Prentice-Hall, Upper Saddle River, NJ, 1998.
[21] Holmstrom, L. and Koistinen, P. “Using Additive Noise in Back-propagation Training,” IEEE Transaction on Neural Networks (3), 1992, pp. 24-38.
[22] Jordan, M. I. “Attractor Dynamics and Parallelism in a Connectionist Sequential Machine,” in Proceedings of the Eighth Annual Conference of the Cognitive Science Society, Hillsdale, NJ, 1986, pp. 531-546.
[23] Kivijärvi, H. and Tuominen, M., “Solving Economic Optimal Control Problems with System Dynamics,” System Dynamics Review (2:2), 1986, pp. 138-150.
[24] Kleijnen, J. P. C., “Sensitivity Analysis and Optimization of System Dynamics Models: Regression Analysis and Statistical Design of Experiments”, System Dynamics Review (11:4), 1995, pp. 275-288.
[25] Kohonen, T. Self-Organization and Associative Memory, Springer-Verlag, Berlin, 1988.
[26] McCullagh, P. and Nelder, J. A. Generalized Linear Models 2nd ed., Chapman & Hall, London, 1989.
[27] Mohapatra, P. K. J. and Sharma, S. K. “Synthetic Design of Policy Decisions in System Dynamics Models: A Modal Control Theoretical Approach,” System Dynamics Review (1), 1985, pp. 63-80.
[28] Nie, J. “Nonlinear Time Series Forecasting: A Fuzzy-neural Approach,” Neurocomputing (16), 1997, pp. 63-76.
[29] Oja, E. and Wang, L. “Robust Fitting by Nonlinear Neural Units,” Neural Netowkrs (9:3), 1996, pp. 435-444.
[30] Poggio, T. A. and Girosi, F. “Networks for Approximation and Learning,” Proceedings of the IEEE (78:9), 1990, pp. 1481-1497.
[31] Powell, M. J. D., “An efficient method for finding the minimum of function of several variables without calculating derivatives,” Comput. J. (7), 1964, pp. 155-162.
[32] Randers, J. “Guidelines for Model Conceptualization,” in Elements of the system dynamics method Randers, J. (eds.), MIT Press, Cambridge, Mass., 1980.
[33] Richardson, G. P. and Paugh A. L. III, Introduction to System Dynamics Modeling with DYNAMO, MIT Press, Cambridge, Mass., Reprinted by Productivity Press, Protland, Ore., 1981.
[34] Richmond, B., Vescuso, P. and Peterson, S., An Acdemic User’s Guide to STELLA, High Performance System, Hanover, NH, 1987.
[35] Roberts, N. Andersen, D. F., Deal, R. M., Garet, M. S. and Shaffer, W. A. Introduction to Computer Simulation: the System Dynamics Modeling Approach, Addison-Wesley, Mass., 1983.
[36] Sarle, W. S. Neural Network FAQ Part III, ftp:// ftp.sas.com/ pub/ neural/ FAQ3.html, 2000.
[37] Scarselli, F. and Tsoi, A. C. “Universal Approximation Using Feedforward Neural Networks: A Survey of Some Existing Methods, and Some New Results,” Neural Networks (11:1), 1998, pp. 15-37.
[38] Senge, P. M. The Fifth Discipline: The Art and Practice of the Learning Organization, Doubleday, New York, 1990.
[39] Senge, P. M. et al. (eds.) The Fifth Discipline Fieldbook: Strategies and Tools for Building a Learning Organization, Doubleday, New York, 1994.
[40] Sharp, J. A., “Sensitivity Analysis: Mehtods for System Dynamics Models,” working paper, System Dynamics Research Group, University of Bradford, Bradford, Yorkshire, U. K., 1976.
[41] Starr, P. J. “Modeling Issues and Decisions in System Dynamics,” TIMS Studies in the Management Science (14), 1980, pp. 45-59.
[42] Taguchi, G. and Konishi, S., Orthogonal Arrays and Linear Graphs, American Supplier Institute, Dearborn, Mich., 1987.
[43] Talavage, J. J. “Modal Analysis to Aid System Dynamics Simulation,” TIMS Studies in the Management Sciences (14), 1980, pp. 229-240.
[44] Tank-Nielsen, C., “Sensitivity Analysis in System Dynamics,” in Elemnets of the System Dynamics Method, (eds.) Randers, J., MIT Press, Cambridge, Mass., Reprinted by Productivity Press, Portland, Ore., 1980.
[45] Werbos, P. J., “Backpropagation Through Time: What It Does and How to Do It,” Proceedings of the IEEE (78:10), 1990, pp. 1550-1560.
[46] Winston, P. H. Artificial Intelligence, Addison-Wesley, Reading, Mass., 1992.
[47] Wolstenholme, E. F., “Defence Operational Analysis Using System Dynamics,” European Journal of Operational Research, forthcoming, 1987.
[48] Wolstenholme, E. F., System Enquiry: A System Dynamics Approach, Wiley, New York, 1990.
[49] Wolstenholme, E. F. and Al-Alusi, A. -S., “System Dynamics and Heuristic Optimization in Defense Analysis,” System Dynamics Reviews (3:2), 1987, pp. 102-115.
[50] Young, S. H. and Chen, C. P., “A Heuristic Mathematical Method for Improving the Behavior of Forrester’s Market Growth Model,” in Proceeding of 16th International Conference of the System Dynamics Socity, 1998.
[51] Zell, A. et al. SNNS User Manual Version 4.1, Stuttgart, German, 1995.
[52] Zhang, G. and Hu, M. Y. “Neural Network Forecasting of the British Pound/US dollar Exchange Rate,” Omega (26:4), 1998, pp. 495-506.