引力波天文学及数据处理相关问题
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摘要
近年来,引力波探测器不断地升级,即将达到一个全新的灵敏度。第一个引力波的直接探测有希望于近几年发生。下一代地面和空间引力波探测器正处于计划中。因此,有必要研究引力波天文学发展引力波数据处理技术,为不久的探测做好准备。本论文立足于此,主要工作共分三个部分。
第一部分中,我们作为第一个中国的小组参加了模拟LISA数据处理挑战项目(MLDC)。我们设计算法分析了双白矮星的几组数据,并利用遗传算法加速反演波源的物理参数。结果显示,我们的算法可以成功探测出大噪声中的微弱引力波信号,同时准确反演出波源的参数。
第二部分中,我们考虑了多个LISA探测器的联合角分辨率问题,利用一个化简模型,给出了任意组LISA探测器的联合角分辨率的详细推导和结果。然后,我们把化简模型推广到更一般的情况。我们的结果可以为多个空间引力波探测器的联合角分辨率提供一个快速的估计,并可为多个空间引力波探测器的轨道设计提供参考。
对一组参数化的引力波信号的探测和参数估计,需要数值上找到一个待估计参数的函数的极值。这个函数是和引力波观测数据相关的。观测数据中的强噪声,会使这个函数呈现高度的多模态并含有大量的极值。这会导致信号检测程序的计算量过大,进而影响了检测结果所能提供的科学信息。随机优化算法可以为减少计算量提供一种途径。在第三部分中,我们报告了粒子群算法在引力波数据处理中的第一次应用。我们将粒子群算法应用到LIGO的致密双星绕转所释放的引力波信号的检测中。结果显示,粒子群算法可以有效地找到多模态函数的极值,为引力波数据处理提供了一种新方法。
Not until recently, gravitational wave(GW) detectors are being upgraded to promis-ing sensitivity level. Hopefully, a first direct GW detection will be made in the near future. In the meanwhile, future ground-based and space-borne GW detectors are be-ing planned. It is good time to investigate GW astronomy and design GW data analysis techniques in preparation. This thesis is devoted to the field, and consists of three major parts.
In the first part, we participate Mock LISA Data Challenge(MLDC) as a first Chinese group. We design an algorithm to analyze the galactic binary blind data sets and implement genetic algorithm in the parameter search step. It turns out that our algorithms can detect the GW signal buried in large measurement noise and estimate the physical parameters precisely.
In the second part, we present a detailed derivation of the angular resolution of arbitrary sets of Laser Interferometer Space Antenna(LISA) constellations with a toy model for GW signals, and further generalized to more complicated cases with slowly varying GW signals of well-defined frequency at any time instant. For future space-borne LISA-like GW detectors, our results may serve as a conservative quick estimate of the detector's angular resolution and hopefully moreover a reference for the config-uration designs.
The detection and estimation of gravitational wave signals belonging to a parame-terized family of waveforms requires, in general, the numerical maximization of a data-dependent function of the signal parameters. Due to noise in the data, the function to be maximized is often highly multi-modal with numerous local maxima. Searching for the global maximum then becomes computationally expensive, which in turn can limit the scientific scope of the search. Stochastic optimization is one possible approach to reducing computational costs in such applications. In the third part, we report result-s from a first investigation of the Particle Swarm Optimization (PSO) method in this context. The method is applied to a testbed motivated by the problem of detection and estimation of a binary inspiral signal. Our results show that PSO works well in the presence of high multi-modality, making it a viable candidate method for further applications in GW data analysis.
第一部分中,我们作为第一个中国的小组参加了模拟LISA数据处理挑战项目(MLDC)。我们设计算法分析了双白矮星的几组数据,并利用遗传算法加速反演波源的物理参数。结果显示,我们的算法可以成功探测出大噪声中的微弱引力波信号,同时准确反演出波源的参数。
第二部分中,我们考虑了多个LISA探测器的联合角分辨率问题,利用一个化简模型,给出了任意组LISA探测器的联合角分辨率的详细推导和结果。然后,我们把化简模型推广到更一般的情况。我们的结果可以为多个空间引力波探测器的联合角分辨率提供一个快速的估计,并可为多个空间引力波探测器的轨道设计提供参考。
对一组参数化的引力波信号的探测和参数估计,需要数值上找到一个待估计参数的函数的极值。这个函数是和引力波观测数据相关的。观测数据中的强噪声,会使这个函数呈现高度的多模态并含有大量的极值。这会导致信号检测程序的计算量过大,进而影响了检测结果所能提供的科学信息。随机优化算法可以为减少计算量提供一种途径。在第三部分中,我们报告了粒子群算法在引力波数据处理中的第一次应用。我们将粒子群算法应用到LIGO的致密双星绕转所释放的引力波信号的检测中。结果显示,粒子群算法可以有效地找到多模态函数的极值,为引力波数据处理提供了一种新方法。
Not until recently, gravitational wave(GW) detectors are being upgraded to promis-ing sensitivity level. Hopefully, a first direct GW detection will be made in the near future. In the meanwhile, future ground-based and space-borne GW detectors are be-ing planned. It is good time to investigate GW astronomy and design GW data analysis techniques in preparation. This thesis is devoted to the field, and consists of three major parts.
In the first part, we participate Mock LISA Data Challenge(MLDC) as a first Chinese group. We design an algorithm to analyze the galactic binary blind data sets and implement genetic algorithm in the parameter search step. It turns out that our algorithms can detect the GW signal buried in large measurement noise and estimate the physical parameters precisely.
In the second part, we present a detailed derivation of the angular resolution of arbitrary sets of Laser Interferometer Space Antenna(LISA) constellations with a toy model for GW signals, and further generalized to more complicated cases with slowly varying GW signals of well-defined frequency at any time instant. For future space-borne LISA-like GW detectors, our results may serve as a conservative quick estimate of the detector's angular resolution and hopefully moreover a reference for the config-uration designs.
The detection and estimation of gravitational wave signals belonging to a parame-terized family of waveforms requires, in general, the numerical maximization of a data-dependent function of the signal parameters. Due to noise in the data, the function to be maximized is often highly multi-modal with numerous local maxima. Searching for the global maximum then becomes computationally expensive, which in turn can limit the scientific scope of the search. Stochastic optimization is one possible approach to reducing computational costs in such applications. In the third part, we report result-s from a first investigation of the Particle Swarm Optimization (PSO) method in this context. The method is applied to a testbed motivated by the problem of detection and estimation of a binary inspiral signal. Our results show that PSO works well in the presence of high multi-modality, making it a viable candidate method for further applications in GW data analysis.
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