臺灣博碩士論文加值系統

本研究提出一模糊比例微分控制器最佳化演算法以解決工程最佳化問題，工程設計問題通常有兩個特性：設計變數在目標函數與限制條件常具有單調性。而且，此目標函數與限制條件常為內隱式函數，也就是不能以設計變數來表示其外顯形式。
傳統的數值最佳化演算法在處理工程最佳化問題時將其視為一單純的數學問題，而工程方面的相關知識往往將其忽略，發展此模糊比例微分控制器最佳化演算法於工程最佳化問題，此動機為取代使用單純數值資訊來獲得新的迭代設計點，並運用模糊規則將工程知識如設計變數的單調性與限制條件的有效性，導入至最佳化演算法之中。
本論文發展此模糊比例微分控制器最佳化演算法透過三個階段，在前兩個階段之中，此最佳化演算法使用一最佳化準則方法來解決特定的工程最佳化問題。在第三階段中，則是將此模糊比例微分控制器最佳化演算法應用至一般的工程最佳化問題上，而此問題具有單調性的特性，並且，這些應用的工程最佳化問題亦常見於文獻之中來驗證最佳化演算法的實用性，最後，運用本論文發展的模糊比例微分控制器最佳化演算法都可成功的獲得最佳解，且在不同的初始值與移動限制下此最佳化演算法亦有不錯的強健性。

This paper proposes a fuzzy proportional-derivative (PD) controller optimization engine for engineering optimization problems. Engineering design problems have two characteristics: the design variables are often monotonic in the objective function and constraints. Moreover, the objective function and constraints are often implicit functions which cannot be expressed explicitly in terms of design variables.
Traditional numerical optimization algorithms treat engineering optimization problems as pure mathematical problems. Engineering heuristics are totally ignored. The idea of using the fuzzy PD controller in engineering optimization is that, instead of using purely numerical information to obtain the new design point in the next iteration, engineering knowledge, such as monotonicity of the design variables and activities of the constraints, are be modeled in the optimization algorithm using fuzzy rules.
The fuzzy PD controller optimization engine is developed through three stages. In the first two stages, the optimization engine is applied to solve engineering optimization problems with optimality criteria methods. In the third stage, the fuzzy PD controller optimization engine is extended to apply on more general engineering optimization problems with monotonicity. Several engineering design optimization problems commonly seen in research literature are used to demonstrate the practicality of the fuzzy PD controller optimization engine. Numerical optimal solutions are successfully obtained in all problems. The fuzzy PD controller seems to be robust to various initial design points and move limits.

Chapter 1. Introduction 1
Chapter 2. The concept of fuzzy proportion-derivative controller optimization engine 5
2.1 Fuzzy optimization 5
2.2. The concept of fuzzy PD controller optimization engine 7
Chapter 3. The First stage development of the fuzzy PD controller optimization engine 10
3.1. The procedure of fuzzy PD controller optimization engine 10
3.2 A structural optimization example 11
3.2.1 Preparing the optimization model 11
3.2.2 Preparing the fuzzy PD controller 12
3.2.3 Defining the initial values and parameters 13
3.2.4 The optimum results 14
3.3 A blow moulding process parameter optimization example 17
3.3.1. Preparing the optimization model 18
3.3.2 Preparing the fuzzy PD controller 19
3.3.3 Defining the initial values and the fuzzy data 20
3.3.4. The optimum results 20
3.4 Discussion 23
3.4.1 Comparison with the fully stressed design method 23
3.4.2 Using different quantization values of inputs and outputs 26
Chapter 4. The second stage development of the fuzzy PD controller optimization engine 32
4.1 Monotonicity Analysis 32
4.2 A hydraulic cylinder design optimization example 34
4.2.1 Formulating the optimization model 34
4.2.2 Monotonicity Analysis and the preparation of optimization criterion 35
4.2.3 Preparing the fuzzy PD controller 39
4.2.4 Defining the initial values and parameters 42
4.2.5 The optimization results 44
4.3 A vehicular jack design optimization example 47
4.3.1 Formulating the optimization model 47
4.3.2 Monotonicity Analysis and preparation of the optimization criterion 48
4.3.3 Defining the initial values and parameters 55
4.3.4 The optimization results 57
4.4 An air tank design optimization example 61
4.4.1 Formulating the optimization model 61
4.4.2 Monotonicity Analysis and preparation of the optimization criterion 62
4.4.3 Defining the initial values and parameters 66
4.4.4 The optimization results 67
4.5 Discussion 69
4.5.1 Using different initial values of the design variables 69
4.5.2 Comparison with the fuzzy proportional control optimization engine 72
4.5.3 Conclusion of this chapter 73
Chapter 5. The third stage development of the fuzzy PD controller optimization engine 75
5.1 The fuzzy PD controller optimization engine for more general engineering design optimization problems 75
(1) For design variables with one critical constraints 77
(2) For design variables with a conditionally critical set 78
(3) For design variables whose monotonicity signs are “indeterminate” in the objective function of the final monotonicity table output by MONO 78
5.2 An air tank design optimization problem 78
5.2.1 Formulating the optimization model 78
5.2.2 Monotonicity Analysis 80
5.2.3 Preparing the fuzzy PD controller 84
5.2.4 Defining the initial values and move limits of the design variables 87
5.2.5 The optimization results 89
5.3 A vehicular jack design optimization problem 94
5.3.1 Formulating the optimization model 94
5.3.2 Monotonicity Analysis 96
5.3.3 Defining the initial values and move limits of the design variables 100
5.3.4 The optimization results 102
5.4 Discussion 107
Chapter 6. Engineering design optimization examples 112
6.1 Three-bar truss design optimization problem 112
6.1.1 Formulating the optimization model 112
6.1.2 Monotonicity Analysis 114
6.1.3 Defining the initial values and move limits of the design variables 116
6.1.4 The optimization results 116
6.2 A tension/compression spring design optimization problem 118
6.2.1 Formulating the optimization model 118
6.2.2 Monotonicity Analysis 119
6.2.3 Defining the initial values and move limits of the design variables 121
6.2.4 Optimization Results 122
6.3 Tubular column design optimization problem 123
6.3.1 Formulating the optimization model 123
6.3.2 Monotonicity Analysis 125
6.3.3 Defining the initial values and move limits of the design variables 127
6.3.4 The optimization results 128
6.4 Welded beam design optimization problem 129
6.4.1 Formulating the optimization model 129
6.4.2 Monotonicity Analysis 132
6.4.3 Defining the initial values and move limits of the design variables 134
6.4.4 The optimization results 135
6.5 Speed reducer design optimization problem 137
6.5.1 Formulating the optimization model 137
6.5.2 Monotonicity Analysis 141
6.5.3 Defining the initial values and move limits of the design variables 144
6.5.4 The optimization results 145
6.6 Heat exchange design optimization example 148
6.6.1 Formulating the optimization model 148
6.6.2 Monotonicity Analysis 151
6.6.3 Defining the initial values and move limits of the design variables 154
6.6.4 The optimization results 155
Chapter 7. Conclusions and discussion 158
Reference 161
Biography 165

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