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研究生：	林昱廷 Lin, Yu-Ting
論文名稱：	利用類神經網路訓練與可變步階簡易共軛梯度法進行史特靈引擎最佳化設計 Optimal Design of Stirling Engines by Neural Network Training Algorithm and Variable-Step Simplified Conjugate-Gradient Method
指導教授：	鄭金祥 Cheng, Chin-Hsiang
學位類別：	博士 Doctor
系所名稱：	工學院 - 航空太空工程學系 Department of Aeronautics & Astronautics
論文出版年：	2021
畢業學年度：	109
語文別：	英文
論文頁數：	99
中文關鍵詞：	VSCGM 、最佳化、設計方法、史特靈引擎、自由活塞式史特靈引擎、Gamma型史特靈引擎
外文關鍵詞：	VSCGM, Optimization, Design algorithm, Stirling engine, Free-piston Stirling engine, Gamma-type Stirling engine
相關次數：	點閱：99 下載：6
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本研究發展一史特靈引擎設計的新穎最佳化方法，此方法結合可變步階簡易簡易共軛梯度法(VSCGM)及類神經網路。與現有的梯度導向方法相比，例如：共軛梯度法(CGM)、簡易共軛梯度法(SCGM)，可變步階簡易共軛梯度法(VSCGM)具有較佳與較快的收斂性，同時也兼具可自訂目標函數格式之彈性。同時，本方法之強健性也在本研究中獲得證實。
本研究先以一低溫差Gamma型史特靈引擎作為最佳化的目標。以三維電腦輔助流場分析(CFD)產生之資料訓練一類神經網路作為求解器。結果顯示指示功與熱效率分別增進了102.93%及5.24%。
然而，由於自由活塞式史特靈引擎與傳統史特靈引擎的運作特性差異，原本的可變步階簡易共軛梯度法需要加入兩項搜尋策略：喚醒策略、逆比較策略。透過此最佳化設計方法，除了可以依據現有的自由活塞式史特靈引擎進行多參數最佳化，也可以任意給定參數，將原本無法運作的自由活塞式史特靈引擎調整至可運作區的最佳化參數組合。本研究忠實呈現將原本不會動的自由活塞式史特靈引擎調整至可成功運作並具有23.998公厘的移氣器穩定振幅。本設計方法與一般最佳化過程不同的地方在於，不會因為引擎落入不可運作區而停止搜尋，而是透過前述策略維持設計方法持續運作。同時，透過此方法也可以識別出自由活塞式史特靈引擎之可運作區與不可運作區，並提供做為應用設計或選定引擎的運作條件之參考。

This study is mainly focus on developing a novel optimization process and design for a Stirling engine by combining the variable-step simplified conjugate gradient method (VSCGM) and the neural network training algorithm. The VSCGM method is a modified version of conjugate gradient method (CGM) and the simplified conjugate gradient method (SCGM). Compared with existing gradient-based methods, VSCGM provides a greatly accelerated convergence speed and also maintains the flexibility related to defining the form of the objective function. Also, the robustness testing for the VSCGM method is carried out by showing the same optimal result with different initial guesses.
In the present study, the optimal design of a low-temperature-differential gamma-type Stirling engine and a free-piston Stirling engine were used as testing cases. For the gamma-type Stirling engine, a direct-solution provider was trained using a backpropagation neural network based on the simulation samples provided from the three-dimensional computational fluid dynamic simulation package (CFD). The optimal design of the gamma-type Stirling engine shows that the indicated power and thermal efficiency were increased by 102.93% and 5.24%, respectively.
Due to the different operating characteristics of free piston Stirling engines and traditional Stirling engines, for the free-piston Stirling engine, two strategies are added to the VSCGM: the wake-up strategy, and the backward-comparison strategy. Therefore, a novel design algorithm for a free-piston Stirling engine was completed. Through the use of this design algorithm, the optimization not only can starting from the existing free-piston Stirling engine design parameters, but also can search from an inoperable region or any arbitrarily given free-piston Stirling engine. In this study, a comparison of automatic tuning of a free-piston Stirling engine with a set of inoperable design parameters to an operable one with a steady displacer amplitude of 23.998mm is made. The advantage of this algorithm is that the search process for the optimal design parameters does not stop in the inoperable region. This algorithm can proceed and identify both operable and inoperable zones. The engine designer can also use this identification data as a reference to determine operating requirements for such engines.

摘要  I
第一章 前言  III
第二章 最佳化與設計方法  IV
第三章 類神經網路訓練方法與理論模式  V
第四章 結合類神經網路與可變步階簡易共軛梯度法之討論  VI
第五章 結論 VII
ABSTRACT  VIII
致謝 X
CONTENTS XI
LIST OF TABLES XIII
LIST OF FIGURES XIV
NOMENCLATURE XVI

CHAPTER 1	INTRODUCTION	1
1.1	STIRLING ENGINE	1
1.2	OPTIMIZATION METHOD	4
1.3	THEORETICAL MODEL OF A STIRLING ENGINE	7
1.4	NEURAL NETWORK	8
1.5	MOTIVATION	11

CHAPTER 2	OPTIMIZATION METHOD AND DESIGN ALGORITHM	13
2.1	VARIABLE-STEP SIMPLIFIED CONJUGATE GRADIENT METHOD	13
2.2	SEARCH STRATEGIES INTEGRATED WITH VSCGM	19
2.2.1	Wake-up Strategy	19
2.2.2	Backward-comparison Strategy	20

CHAPTER 3	NEURAL NETWORK TRAINING METHOD	21
3.1	THE STRUCTURE OF A NEURAL NETWORK	  21
3.2	TRAINING OF A BACKPROPAGATION NEURAL NETWORK	25

CHAPTER 4	COMBINATION OF THE NEURAL NETWORK AND THE VARIABLE-STEP SIMPLIFIED CONJUGATE GRADIENT METHOD	32
4.1	GAMMA-TYPE STIRLING ENGINE	32
4.2	OPTIMIZATION OF A GAMMA-TYPE STIRLING ENGINE	41
4.2.1	Objective Function	41
4.2.2	Optimal Design with VSCGM	42
4.2.3	Comparison of the VSCGM and SCGM Performance	44
4.2.4	Robustness of the VSCGM	45
4.3	THEORETICAL MODEL OF THE FREE-PISTON STIRLING ENGINE	46
4.4	THE OPTIMIZATION OF A FREE-PISTON STIRLING ENGINE	53
4.4.1	Regular Optimization with the VSCGM	53
4.4.2	VSCGM with the Wake-up Strategy	56
4.4.3	VSCGM with the Backward-comparison Strategy	57

CHAPTER 5	CONCLUSIONS	60
REFERENCES	62


LIST OF TABLES
TABLE 4-1	COMPUTATIONAL FLUID DYNAMICS (CFD) SIMULATION FRAMEWORK	66
TABLE 4-2	PARAMETERS WITH THE BASELINE CASE	67
TABLE 4-3	CFD COMPUTATION RESULTS	68
TABLE 4-4	MEAN SQUARED ERROR AND REGRESSION VALUE OF TRAINING	70
TABLE 4-5	PARAMETERS WITH FIVE-PARAMETER OPTIMIZATION	71
TABLE 4-6	FREE-PISTON STIRLING ENGINE DESIGN PARAMETERS	72



LIST OF FIGURES
FIGURE 2-1	THE ADJUSTMENT OF STEPSIZE IS ACCORDING TO THE RATIO OF THE SEARCHING DIRECTIONS	73
FIGURE 2-2	THE FLOW CHART OF VARIABLE-STEP SIMPLIFIED CONJUGATE GRADIENT METHOD	74
FIGURE 2-3	DIAGRAM OF THE ARTIFICIAL-INTELLIGENCE DESIGN ALGORITHM FOR FREE-PISTON STIRLING ENGINE	75
FIGURE 2-4	THE VARIABLE UPDATE MECHANISM OF WAKE-UP STRATEGY	76
FIGURE 2-5	THE INTEGRATION OF WAKE-UP STRATEGY WITH VSCGM	77
FIGURE 2-6	THE UPDATING SOLUTION OF BACKWARD-COMPARISON STRATEGY	78
FIGURE 2-7	THE INTEGRATION OF BACKWARD COMPARISON STRATEGY WITH VSCGM	79
FIGURE 3-1	DIAGRAM OF NEURAL NETWORK WITH 2 HIDDEN LAYERS IN PROCESSING ELEMENT FORM	80
FIGURE 3-2	DIAGRAM OF NEURAL NETWORK WITH 2 HIDDEN LAYERS IN NEURON FORM	81
FIGURE 4-1	GEOMETRICAL PARAMETERS OF A LOW-TEMPERATURE-DIFFERENTIAL GAMMA-TYPE STIRLING ENGINE	82
FIGURE 4-2	THE NEURAL NETWORK OF A GAMMA-TYPE STIRLING ENGINE INTEGRATED IN PROCESSING NODE AND NEURON FORM	83
FIGURE 4-3	DATA EXPANSION AFTER TRIANGULATION-BASED INTERPOLATION	84
FIGURE 4-4	ERROR HISTOGRAM OF NEURAL NETWORK TRAINING	86
FIGURE 4-5	REGRESSION DISTRIBUTION OF NEURAL NETWORK TRAINING	87
FIGURE 4-6	COMPARISON BETWEEN VSCGM AND SCGM	88
FIGURE 4-7	OPTIMIZATION PROCESSES WITH FOUR DIFFERENT INITIAL GUESSES	89
FIGURE 4-8	DIAGRAM OF A FREE-PISTON STIRLING ENGINE	90
FIGURE 4-9	OPTIMIZATION FOR MAXIMUM AMPLITUDE OF DISPLACER WITH VSCGM	91
FIGURE 4-10	COMPARISON OF THE PRESSURE-VOLUME PLOTS BEFORE AND AFTER VSCGM	92
FIGURE 4-11	OBJECTIVE FUNCTION VARIATION AND WAKE-UP STRATEGY IN INOPERABLE ZONE	93
FIGURE 4-12	OPTIMIZATION WITH VSCGM AND WAKE-UP STRATEGY	94
FIGURE 4-13	OPTIMIZATION WITH VSCGM AND BACK-COMPARISON STRATEGY	95
FIGURE 4-14	OPTIMIZATION WITH VSCGM AND BACK-COMPARISON STRATEGY	96
FIGURE 4-15	THE FREE-PISTON STIRLING ENGINE PROTOTYPE DESIGN FOLLOW BY THE RESULT PROVIDED BY THE DESIGN ALGORITHM	97
FIGURE 4-16	MECHANICAL PARTS OF THE PROTOTYPE FREE-PISTON STIRLING ENGINE	98
FIGURE 4-17	THE ASSEMBLY OF THE PROTOTYPE FREE-PISTON STIRLING ENGINE	99
                                    

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校內：2022-07-16公開
校外：2023-07-16公開

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