在電子封裝領域裡，主要的趨勢皆是傾向於更輕，更小與更多功能。若來看封裝技術的演進，由DIP(Dual In-line Packaging)、SOP/TSOP(Small Outline Packaging / Thin Small Outline Packaging)、QFP/TQFP(Quad Flat Packaging / Thin Quad Flat Packaging)、BGA(Ball Grid Array) 發展到更小體積更高密度的的覆晶封裝(Flip Chip, FC)以及晶圓級封裝(Wafer Level Packaging, WLP)等。
封裝結構中其中一項重要的議題為可靠度，有非常多的因素會影響其可靠度，例如:封裝結構尺寸、材料性質、製程技術等皆是影響因素，在設計產品的流程中，通常使用實驗的方法如熱循環負載試驗(Thermal Cycling Test)來測試所設計的產品是否能通過訂定的疲勞壽命標準，透過這樣的方式來確保所設計之產品發行後能在使用期限中正常不失效。但在實務上，若以電子封裝可靠度實驗來測試每一個設計其花費的成本與時間會相當的高，導致產品上市時間延宕，開發成本上升，導致企業競爭力的大幅降低。
為了改善上述缺點，有限單元分析(Finite Element Analysis, FEA)已被廣泛的應用在可靠度測試上，只需要少量的實驗驗證數據便可以大幅降低評估產品可靠度之時間，節省開發產品之成本。在本研究當中利用ANSYS軟體來模擬晶圓級封裝在熱循環負載下所產生的等效塑性應變增量，再使用Coffin-Manson 模型來預測錫球之疲勞壽命，再模擬中利用體積權重概念來固定錫球應力集中處網格大小，此外再利用實驗的數據對比模擬的結果，來驗證模擬分析之結果與其可信度。
雖然有限單元分析(Finite Element Analysis, FEA)對比實驗試誤方式(Design on Experiment, DOE)已減少了大量的時間與成本，但由不同的研究員所得到的模擬結果也不盡相同。本研究目的就是將機器學習(Machine Learning, ML)應用在評估封裝結構可靠度上。既可以更加地減少預測不同結構可靠度預估之時間，也可以降低由不同研究人員所模擬結果之誤差。在本研究中結合了有限單元分析與機器學習，由經過認證的模擬結果建構資料庫，透過此資料庫訓練獲得預估模型，使得壽命預估流程更加有效率。
在機器學習模型的選擇上，本研究選擇使用的為循環神經網路(Recurrent Neural Network, RNN)，再與基本的人工神經網路(Artificial Neural Network, ANN)做比較。在機器學習當中，最關鍵的部分就在於資料，好的資料品質可以使模型得到更好的結果，因此在本研究也探討根據不同的訓練數據大小、分布對於訓練後預估模型表現的影響。

In the field of electronic packaging, the main trend is toward lighter, smaller and more functional. In the evolution of packaging technology, from DIP (Dual in-line Packaging), SOP/TSOP (Small Outline Packaging / Thin Small Packaging), QFP/TQFP (Quad Flat Packaging / Thin Quad Flat Packaging), BGA (Ball Grid Array) to smaller, higher density package like Flip Chip (FC) and Wafer Level Packaging (WLP).
One of the important issues in the package structure is reliability. There are many factors that affect its reliability. For example, package structure size, material properties, process technology, etc. are all influencing factors. In the process of designing products, the experimental method is usually used, such as the Thermal Cycling Test, to test whether the designed product can pass the fatigue life standard, and in this way ensures that the designed product will not fail during the service period. However, in practice, if the reliability test is executed by experiment method, the cost and time spent will be quite high, resulting in delayed product launch time and rising development costs, even further caused a significant reduction in the competitiveness of enterprises.
In order to improve the above shortcomings, Finite Element Analysis (FEA) has been widely used in reliability assessment. Only a small amount of experimental data is needed to verified the simulation then we can greatly reduce the time spent and cost for evaluating product reliability. In this study, ANSYS software was used to simulate the equivalent plastic strain increment in Wafer-Level Package under thermal cycling load. The Coffin-Manson strain based model and fixed mesh size were used to predict the fatigue life of the solder ball. Finally, the simulation results are compared with the simulation results to verify the the simulation analysis and its credibility.
Although using the Finite Element Analysis (FEA) has reduced a lot of time spent and cost compared to Design on Experiment (DOE). The simulation results obtained by different researchers are not totally same. The purpose of this study is to apply Machine Learning (ML) to assess the reliability of electronic package structure. It can not only reduce the time spent for predicting the reliability prediction of different structures, but also eliminate the variance of the results simulated by different researchers. In this study, combined with finite element analysis and machine learning, a database built by verified simulation results, and the estimation model was trained through this database, making the reliability life prediction process more efficient.
In the choice of machine learning model, this study chose to use the Recurrent Neural Network (RNN) and compare it with the basic Artificial Neural Network (ANN). The effects of different training data sizes and distributions on the performance of the regression model are also discussed.

摘要 I
Abstract II
目錄 IV
圖目錄 VII
表目錄 X
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 研究目標 9
第二章 基礎理論 10
2.1 有限單元法基礎理論[23] 10
2.1.1 線彈性有限單元理論 10
2.1.2 材料非線性理論 14
2.1.3 數值方法及收斂準則 15
2.2 材料硬化法則 17
2.2.1 等向硬化法則 17
2.2.2 動態硬化法則 18
2.3 Chaboche模型 19
2.4 錫球外型預測 21
2.5 封裝結構可靠度之預測方法 23
2.5.1 Coffin-Manson應變法 23
2.5.2 Darveaux 能量密度法 24
2.5.3 修正型能量密度法 24
2.7 機器學習 25
2.7.1 機器學習演算法 27
2.7.2 資料前處理 29
2.7.3 人工神經網路(Artificial Neural Network) 31
2.7.4 啟動函數(Activation Function) 32
2.7.5 損失函數(Loss function) 34
2.7.6 回歸模型最佳化演算法 35
2.7.7 誤差反向傳播法(Backpropagation) 40
2.7.8 增量學習(Incremental Learning) 42
2.8 循環神經網路(Recurrent Neural Network) 43
2.8.1 雙向循環神經網路(Bidirectional RNN) 45
2.8.2 長短期記憶(Long Short-Term Memory, LSTM) 46
2.8.3 循環門控單元（Gate Recurrent Unit, GRU） 49
第三章 WLCSP有限單元模型之建立 51
3.1 有限單元模型基本假設 53
3.2 材料參數之設定 53
3.3 網格劃分 55
3.4 邊界條件設定 56
3.5 溫度負載設定 57
3.6 WLCSP模型 57
3.6.1 TV1模擬設定 58
3.6.2 TV2模擬設定 59
3.6.3 TV3模擬設定 60
3.6.4 TV4模擬設定 61
3.6.5 TV5模擬設定 63
3.7 WLCSP有限單元模型驗證 64
第四章 結果與討論 65
4.1 機器學習訓練及測試資料 65
4.2 定義ANN以及RNN模型輸入 79
4.3 超參數選定之過程 81
4.3.1 前處理方法比較 82
4.3.2 損失函數結果之比較 85
4.4 人工神經網路訓練結果 92
4.4.1 不同數據分布對於結果之影響 92
4.5 循環神經網路訓練結果. 95
4.5.1 不同數據分布對於結果之影響 95
4.5.2 多對一Vanilla RNN/LSTM/GRU模型 97
4.5.3 多對多RNN模型 99
4.5.4 多對多雙向RNN模型 102
4.6 結果比較與討論 105
4.7 增量學習(Incremental Learning)初步結果 115
4.7.1 10次迭代結果 116
4.7.2 100次迭代結果 117
第五章 結論與建議未來工作 120
參考資料 121

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