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系統識別號 U0026-1807201817033400
論文名稱(中文) 深度學習於重力波資料分析之運用
論文名稱(英文) Deep learning applied to data analysis of gravitational wave
校院名稱 成功大學
系所名稱(中) 物理學系
系所名稱(英) Department of Physics
學年度 106
學期 2
出版年 107
研究生(中文) 陳孟佑
研究生(英文) Meng-You Chen
學號 L26054140
學位類別 碩士
語文別 英文
論文頁數 52頁
口試委員 指導教授-游輝樟
口試委員-許祖斌
口試委員-林俊鈺
中文關鍵字 機器學習  重力波分析  卷積類神經網路  擬合匹配 
英文關鍵字 Machine learning  Gravitational wave analysis  Convolution Neuron Network(CNN)  Matched filtering 
學科別分類
中文摘要 這篇論文使用重力波解析波形加上不同形式的雜訊,仿造重力波干涉儀所偵測到的訊號,作為訓練卷積類神經網路的資料集,並產生足以在高雜訊資料中辨識重力波訊號的判別模型。目前,重力波觀測主要使用匹配濾波器來分析干涉儀的觀測時序資料,而我們是採用機器學習的方法,使用不同的結構及超參數建構並訓練卷積類神經網路,以判斷觀測資料中是否包含重力波樣板,並針對淺層及深層的類神經網路進行探討。此概念是啟發自George 及Huerta的論文。

在第二章中,我們對機器學習做一個初步的介紹。第三章利用了Sin-
Gaussian函數加上雜訊的一個簡單模型,演示LIGO如何利用白化及匹配濾波器偵測重力波訊號。接著,我們說明此研究所使用的卷積類神經網路結構以及訓練資料製備策略。第四章展示了研究的成果:我們發現,相較於高斯雜訊,以白化雜訊製備出的資料集所訓練出的機器學習模型,對於不同訊雜比的測試資料有較平滑的敏感度表現。另外,針對層數上的比較,四層卷積層加上兩層全連接層的結構相較於其他結構表現來的好。最後,我們隨機偏移了訓練資料集中的重力波波峰,研究對於訓練模型的影響。我們發現,該模型對不同訊雜比測試資料的判別敏感度曲線明顯變差了,我們預期需要更細緻的超參數調教,或是較長的訓練步數。最後,第五章總結了本研究,並提出一些類神經網路可以進行改善的方法。
英文摘要 This article uses analytical gravitational waveforms superposed with di erent types of noise to simulate the LIGO detection data. The LIGO uses the matched filtering technique to detect gravitational waves in a laser interferometer. Here, we use the machine learning method to decide whether there is a gravitational wave signal in a simulated waveform. Inspired by George and Huerta's paper, we use di erent convolution neuron network (CNN) architectures and hyperparameters to t our detector's data and study the behaviors for both shallow and deep neuron networks.

In chapter 2, we introduce the CNN and some terminologies in machine learning.In chapter 3, we use a noisy sin-Gaussian function as a toy model to demonstrate the
standard LIGO approach of whitening and matched ltering for detecting signals. Then we introduce the neuron network architecture and the initial data preparation in our machine learning scheme.

In chapter 4, we demonstrate our result. We found our model shows a smoother sensitivity-versus-signal-to-noise-ratio curve for testing data with white noise than those
with Gaussian noise. Our neuron network architecture consisted of four convolution layers and two fully connected layers yield much better results compared to other architectures. Then, we vary the dataset with randomly shifted waveform peaks to mimic
real detection scenario, the behavior becomes worse and needs further study.

In chapter 5, we summarize results and propose some improvements to our neuron network.
論文目次 Chinese abstract i
Abstract ii
Acknowledgments iii
Contents iv
List of Figures vi
List of Tables vii
1 Introduction and Motivation 1
1.1 Gravitation Wave 1
1.2 Machine learning 2
2 Machine Learning Theory 4
2.1 Linear regression 4
2.2 Artificial neural network(ANN) 6
2.3 Deep neural network(DNN) 7
2.4 Back propagation 7
2.5 Activate function 8
2.6 Loss function and Cost function 10
2.6.1 Loss function 10
2.6.2 Cost function 11
2.7 Traditional neural network 11
2.8 Convolution neural network(CNN) 14
2.9 Training set , Validation set, Test set 19
3 Method 20
3.1 Traditional method in gravitational wave analysis 20
3.1.1 Whitening 20
3.1.2 Matched filtering 20
3.2 Using machine learning to identify noise and gravitational wave 21
3.2.1 Prepare waveform data 21
3.2.2 Input data setting 22
3.2.3 Designing neural networks 22
3.3 Cost function setting and training stage 26

4 Result and Analysis 28
4.1 Traditional method in gravitational wave analysis 28
4.1.1 Whitening 28
4.1.2 Matched filtering 31
4.2 Using machine learning to identify noise and gravitational wave 32
4.2.1 Random noise and Gaussian noise adding in waveform compare32
4.3 The simplified neuron network and depth neuron network compare 34
4.3.1 White noise 34
4.3.2 Gaussian noise 35
4.4 The waveform peak randomly shift with 0.2s sensitivity test 36
4.4.1 Shallow neuron network 37
4.4.2 Depth neuron network 38
4.4.3 Complex neuron network 39
5 Conclusion and Outlook40
5.1 Conclusion 40
5.2 Outlook 41
The least-square method42
Quadratic cost function compared cross-entropy cost function 44
B.1 Quadratic cost function 44
B.2 Cross-entropy cost function46
C Mathematic convolutional Operation48
D Waveform template and signal relation50
Bibliography 52

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