Gravitational Wave Searches of Binary Compact Objects using Particle Swarm Optimization and modifications

Saha, Swarnendu (2025) Gravitational Wave Searches of Binary Compact Objects using Particle Swarm Optimization and modifications. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Swarnendu Saha (20MS152)) 20MS152_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (12MB)

Abstract

Gravitational wave (GW) astronomy has emerged as a powerful tool for exploring compact objects and testing general relativity. This thesis explores GW signal modeling, detection methodologies, and advanced search techniques using optimization frameworks. The study emphasizes waveform generation, matched filtering, and a modified version of Particle Swarm Optimization (PSO) for improved parameter estimation of binary compact objects. Each chapter builds systematically towards a coherent framework that combines physics, computation, and data analysis. Chapter 1: Background Studies introduces the theoretical foundations of general relativity and gravitational waves. It outlines Einstein’s field equations, the quadrupole formula, and the physics of compact binary inspirals. Various GW sources are discussed, including binary black holes, neutron stars, and exotic systems like EMRIs and cosmic strings. The chapter concludes with a discussion of current observational landscapes and the importance of gravitational wave detection in modern astrophysics. Chapter 2: Detectors and Detection Techniques explores the evolution of GW detectors, including early resonant bar detectors and the interferometric design of LIGO. It delves into the nature of noise (seismic, thermal, quantum shot, and Newtonian) that affects detection sensitivity. A substantial focus is placed on time-series data analysis methods such as Fourier transforms, periodograms, and statistical detection techniques. Matched filtering for stationary and colored noise is formally introduced. Chapter 3: Waveform Generation and Matched Filtering provides both analytical and numerical approaches to waveform generation. The chirp waveform is modeled in the Newtonian approximation, and numerical waveforms using approximants like IMRPhenom are discussed. This chapter further explains the matched filtering algorithm, with implementation results for waveform matching and detection using template banks. Various plots illustrate match values across parameter space, showing the effectiveness of the method. Chapter 4: Particle Swarm Optimization for Mass Parameter Estimation introduces PSO, a metaheuristic algorithm inspired by the social behavior of swarms. It discusses the underlying dynamics, swarm behavior, and control parameters. The algorithm is implemented to estimate binary component masses from GW signals by maximizing match values with respect to waveform templates. Reflective boundary conditions and constraint handling techniques are also implemented and tested. Chapter 5: Modified PSO with Gaussian Perturbations explores algorithmic enhancements to the classical PSO by incorporating Gaussian noise into the cognitive and social coefficients. This stochastic modification is intended to improve convergence and avoid local optima. Different mathematical formulations (additive and multiplicative perturbations) are tested. Theoretical interpretations and simulation results demonstrate improved robustness in parameter recovery under noisy conditions. Chapter 6: Observations presents a detailed comparison of match values for various PSO and template bank searches. It includes multiple runs, statistical summaries, and convergence diagnostics to assess consistency, reliability, and estimation error. The figures support the effectiveness of modified PSO under different configurations and parameter regimes. Chapter 7: Conclusion summarizes the entire study, discussing the limitations of fixed template banks and the advantages of PSO as a flexible, data-driven approach to parameter estimation. A comparative table contrasts classical and PSO-based methods. The chapter concludes by highlighting the potential of PSO in large-scale gravitational wave pipelines and recommending further improvements through multi-objective optimization and hybrid algorithms. Appendices provide detailed Python implementations and pseudocode for all algorithms, simulations, and waveform generation routines discussed in the main chapters. These include standard PSO, template bank search, Gaussian-perturbed PSO, and analytical waveform modeling. The appendices serve as a valuable resource for reproducibility and future enhancements. This thesis demonstrates a comprehensive approach to gravitational wave data analysis by integrating theoretical physics, numerical simulations, and optimization algorithms, showcasing the interdisciplinary strength of gravitational wave science.

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