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姓名	林宏霖(Hong-lin Lin)  查詢紙本館藏	畢業系所	物理學系
論文名稱	使用最大相似法以改進校正之誤差分析 (Improvement of error estimation of calibration by maximum likelihood method)
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摘要(中)	重力波的觀測是本世紀以來最重要的發現之一，從 1974 年 Hulse 跟 Taylor 發現了雙星運動會散發能量開始，直到 2015 年美國重力播觀測天文台 LIGO 直 接的觀測到重力波的訊號;近十年來從當初的雙黑洞融合訊號，到最新的觀測 紀錄總共已經觀測到了高達 90 個事件。 重力波的觀測是利用探測公里級的雷射干涉儀上的反射鏡之位移求得，因 為重力波大小只有10公尺，所以需要用上最先進的科技才有辦法達到相對應 的敏感度，也因為重力波的訊號與其他天文觀測息息相關，所以觀測到的數值 精確度也是一個大課題，這也為什麼是校正工作之所以必要。 KAGRA 是一個座落在日本的公里級重力波觀測天文台，在 2020 年加入了 重力波觀測網路，他有著兩大特點，分別是位在地底與低溫系統，位在地底可 以有效的減少地震造成的噪音，而低溫系統可以有效的減少熱擾動的噪音 本篇論文將以模擬的校正測量資料作為研究對象，使用最大相似法建立一 個分析程式，並將其結果與原先有的貝氏統計法做比較，要驗證兩個方法的結 果可以一致，並且最大相似法擁有比原先方法更快速的計算速度，藉由這個交 互比對的分析程式，我們可以獲得更可靠的分析結果與更快的分析程式
摘要(英)	The observation of Gravitational Waves(GW) is one of the most exciting dis- coveries of this century. Since 1974, Hulse and Taylor discovered the binary star system emits energies, people realized the prediction of GW from general rela- tivity is possible. In 2015, an advanced Laser Interferometer Gravitational wave Observatory called aLIGO succeed in directly detecting the GW signals from a binary black hole merger. During this decade, with advanced Virgo and KA- GRA’s joining, the sensitivity dramatically increases, and the events discovered increased from that binary black hole system to 90 events in the latest catalog. The observation of GW is detecting the displacement of test masses in the km- scale observatory, with the most frontier technologies applied, the requirements of detecting the GW strain is can be satisfied. As the GW becomes one of the important cosmological resources, the accuracy of the sources is required to reach with other astronomy research. This is why the calibration of the response of the interferometer is crucial, the error estimation of calibration is a crucial part of the parameter estimation of the GW source. KAGRA, the third km-scale GW observatory located in Japan, Gifu, joined the observation network in April 2020 and features two unique technologies - underground and cryogenic. KAGRA is the first observatory built on the under- ground site, in order to reduce the seismic noise, and the cryogenic system is to reduce the thermal noise. In this thesis, we discuss the error estimation analysis based on the simu- lated frequency domain calibration data of KAGRA during the period O3GK in April 2020. We develop a calibration pipeline based on the maximum likelihood method to crosscheck with the previous pipeline based on the Bayesian method. The maximum likelihood method provides a faster pipeline for crosscheck in the ratio around. By crosscheck between these two method, and the results proves that these two are consistence, so that we can improve the accuracy of GW observation with more reliable parameters and faster pipeline.
關鍵字(中)	★ 校正	關鍵字(英)	★ Calibration
論文目次	1 Introduction 1 2 Science 3 2.1 EinsteinequationandGravitationalwave . . . . . . . . . . . . . . 3 2.2 Sources.................................. 9 2.2.1 CompactBinaryCoalescence(CBC) . . . . . . . . . . . . . 9 2.2.2 ContinuousWave........................ 13 2.2.3 Burst............................... 14 2.2.4 StochasticGravitationalWaves................ 15 2.3 PreviousObservation.......................... 16 2.3.1 WorldwideObservation.................... 16 2.3.2 O3GK .............................. 17 2.4 Discussion................................ 18 2.4.1 ExpectedscienceinO4..................... 18 2.4.2 BNSandHubbleconstant................... 18 2.4.3 2ndpeakofBNS ........................ 20 2.4.4 Intermediatemassblackhole................. 21 2.4.5 KAGRA’sadvantage...................... 21 3 Gravitational Wave detectors 25 3.1 Introduction ............................... 25 3.2 PrincipleofGWobservation...................... 25 3.3 Worldwideobservatory ........................ 31 3.3.1 LIGO............................... 31 3.3.2 KAGRA ............................. 32 3.3.3 Virgo............................... 32 3.4 InstrumentofKAGRA ......................... 32 3.5 Discussion................................ 33 4 Calibration 37 4.1 IntroductionofCalibration....................... 37 4.2 DARMmodel .............................. 39 4.3 Calibrationinstruments ........................ 40 4.4 Reconstructionpipeline ........................ 44 4.5 Errorestimation............................. 46 4.6 Discussion................................ 48 4.6.1 ComparisonofPCALamongLVK .............. 48 4.6.2 PcalabsoluteerrorandHubbleconstant. . . . . . . . . . . 49 4.6.3 GcalandNcal.......................... 49 4.6.4 KAGRA’scontrolmodel.................... 50 4.7 Goalofthisthesis............................ 50 5 DARM modeling 53 5.1 Introduction ............................... 53 5.2 Actuationfunction ........................... 55 5.2.1 Suspensioninstruments .................... 56 5.2.2 DAC ............................... 56 5.2.3 Coildriver............................ 57 5.2.4 AnalogAA/AIfilter ...................... 59 5.2.5 Anti-Dewhiteningfilter .................... 60 5.2.6 DigitalAA/AIfilter ...................... 62 5.2.7 Timedelay............................ 63 5.3 Coilmatrix................................ 64 5.4 CoilVA .................................. 65 5.5 Sensingfunction............................. 66 5.5.1 ADC ............................... 66 5.5.2 Whiteningfilter......................... 67 5.5.3 Whiteningfilterforinnerdetector . . . . . . . . . . . . . . 69 5.5.4 Anti-Whitening......................... 71 5.5.5 AA/AIfilter........................... 73 5.5.6 DigitalAA/AIfilter ...................... 73 5.5.7 Timedelay............................ 75 5.6 Trans ................................... 77 5.7 Pcalmodeling .............................. 78 5.7.1 OpticalFollowerServo..................... 78 5.8 Stackedresidualfiltermodel...................... 79 5.8.1 ResidualAfunction ...................... 80 5.8.2 ResidualCfunction ...................... 81 5.8.3 ResidualPcalfunction..................... 82 5.9 Discussion................................ 83 6 Parameter estimation of interferometer 85 6.1 Introduction ............................... 85 6.2 Simulationdataset ........................... 85 6.3 Maximumlikelihoodmethod ..................... 90 6.4 Parameterestimation.......................... 92 6.5 ComparisonwithMCMC ....................... 95 6.5.1 Responsefunction ....................... 98 6.6 Discussion................................ 99 6.6.1 Results of the maximum likelihood method . . . . . . . . . 99 6.6.2 ComparisonwithpyDARM.................. 99 7 Discussion 101 7.1 ComparisonbetweenLIGOandKAGRA . . . . . . . . . . . . . . 101 7.2 Crosscheckresult ............................ 102 7.3 Futurework ............................... 103 8 Conclusion 105 A AAAI measurement 107 A.1 IntroductionofAA/AI......................... 107 A.2 Motivation................................ 107 A.3 Overviewofmeasurement....................... 108 A.4 DigitalMeasurement.......................... 108 A.4.1 Overview ............................ 108 A.4.2 Hardware ............................ 109 A.4.3 measurementdetails...................... 110 A.4.4 Circuitandmodel ....................... 111 A.4.5 AnalysisProcess ........................ 111 A.4.6 FittingResult .......................... 112 A.4.7 Result .............................. 114 A.5 Modelcalculations ........................... 115 A.5.1 Overview ............................ 115 A.5.2 Notchfiter............................ 116 A.5.3 Lowpassfilter ......................... 118 A.5.4 Simultaneously(Notch+Low pass) filter . . . . . . . . . . . 119 A.5.5 Comparison........................... 123 A.5.6 FittingResult .......................... 124 A.6 Analogmeasurement.......................... 125 A.6.1 Overview ............................ 125 A.6.2 Hardwaresetup......................... 125 A.6.3 Fittingresult........................... 126 A.7 Re-measurement ............................ 128 A.8 Summary................................. 130 Bibliography 131
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指導教授	井上優貴(Yuki Inoue)	審核日期	2023-4-10
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