Topics in Gravitational-Wave Astrophysics

In this dissertation we study the applicability of different waveform models in gravitational wave searches for comparable mass binary black holes. We determine the domain of applicability of the computationally inexpensive closed form models, and the same for the semi-analytic models that have been calibrated to Numerical Relativity simulations (and are computationally more expensive). We further explore the option of using hybrid waveforms, constructed by numerically stitching analytic and numerical waveforms, as filters in gravitational wave detection searches. Beyond matched-filtering, there is extensive processing of the filter output before a detection candidate can be confirmed. We utilize recent results from Numerical Relativity to study the ability of LIGO searches to make detections, using (recolored) detector data. Lastly, we develop a waveform model, using recent self-force results, that captures the complete binary coalescence process. The self-force formalism was developed in the context of extreme mass-ratio binaries, and we successfully extend it to model intermediate mass-ratios

NRTidalv3: A New and Robust Gravitational-Waveform Model for High-Mass-Ratio Binary Neutron Star Systems with Dynamical Tidal Effects

For the analysis of gravitational-wave signals, fast and accurate gravitational-waveform models are required. These enable us to obtain information on the system properties from compact binary mergers. In this article, we introduce the NRTidalv3 model, which contains a closed-form expression that describes tidal effects, focusing on the description of binary neutron star systems. The model improves upon previous versions by employing a larger set of numerical-relativity data for its calibration, by including high-mass ratio systems covering also a wider range of equations of state. It also takes into account dynamical tidal effects and the known post-Newtonian mass-ratio dependence of individual calibration parameters. We implemented the model in the publicly available LALSuite software library by augmenting different binary black hole waveform models (IMRPhenomD, IMRPhenomX, and SEOBNRv5_ROM). We test the validity of NRTidalv3 by comparing it with numerical-relativity waveforms, as well as other tidal models. Finally, we perform parameter estimation for GW170817 and GW190425 with the new tidal approximant and find overall consistent results with respect to previous studies

Adaptive spline fitting with particle swarm optimization

In fitting data with a spline, finding the optimal placement of knots can significantly improve the quality of the fit. However, the challenging high-dimensional and non-convex optimization problem associated with completely free knot placement has been a major roadblock in using this approach. We present a method that uses particle swarm optimization (PSO) combined with model selection to address this challenge. The problem of overfitting due to knot clustering that accompanies free knot placement is mitigated in this method by explicit regularization, resulting in a significantly improved performance on highly noisy data. The principal design choices available in the method are delineated and a statistically rigorous study of their effect on performance is carried out using simulated data and a wide variety of benchmark functions. Our results demonstrate that PSO-based free knot placement leads to a viable and flexible adaptive spline fitting approach that allows the fitting of both smooth and non-smooth functions.Comment: Accepted version; Typo corrected in equation 3; Minor changes to tex

Adaptive spline fitting with particle swarm optimization

In fitting data with a spline, finding the optimal placement of knots can significantly improve the quality of the fit. However, the challenging high-dimensional and non-convex optimization problem associated with completely free knot placement has been a major roadblock in using this approach. We present a method that uses particle swarm optimization (PSO) combined with model selection to address this challenge. The problem of overfitting due to knot clustering that accompanies free knot placement is mitigated in this method by explicit regularization, resulting in a significantly improved performance on highly noisy data. The principal design choices available in the method are delineated and a statistically rigorous study of their effect on performance is carried out using simulated data and a wide variety of benchmark functions. Our results demonstrate that PSO-based free knot placement leads to a viable and flexible adaptive spline fitting approach that allows the fitting of both smooth and non-smooth functions

Accurate and rapid gravitational waveform models for binary black hole coalescences

The first direct gravitational wave detection by LIGO and Virgo in 2015 marked the beginning of the gravitational wave astronomy era. Gravitational waves are an excellent tool to prove general relativity and unveil compact objects' dynamics in the universe. Over the years, we observe more signals from coalescing black hole binaries. Signals from the detectors are filtered through numerous waveform templates coming from theoretical predictions. Some models are more accurate but slow, and the others are less accurate but fast. We face ever-increasing demands for accuracy, speed, and parameter coverage of waveform models with more detections. Thus, we investigate strategies to speed up waveform generation without losing much accuracy for future signal analysis. In this dissertation, we present our approach as follows: 1. developing a method to dynamically tune less accurate (but fast) models with a more accurate (but slow) models through an iterative dimensionality reduction technique, 2. investigating the performance of regression methods, including machine learning for higher dimensions, 3. adding eccentricity to quasicircular analytical models through fitting technique. We analyze our results' faithfulness and prospects to speed up waveform generation. Our methods can readily be applied to reduce the complexity and time of building a new waveform model. Additionally, we build a python package pyrex to carry out the quasicircular turned eccentric computation. This study is crucial for the development of models which include more parameters

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms

Digital Filter Design Using Improved Artificial Bee Colony Algorithms

Digital filters are often used in digital signal processing applications. The design objective of a digital filter is to find the optimal set of filter coefficients, which satisfies the desired specifications of magnitude and group delay responses. Evolutionary algorithms are population-based meta-heuristic algorithms inspired by the biological behaviors of species. Compared to gradient-based optimization algorithms such as steepest descent and Newton’s like methods, these bio-inspired algorithms have the advantages of not getting stuck at local optima and being independent of the starting point in the solution space. The limitations of evolutionary algorithms include the presence of control parameters, problem specific tuning procedure, premature convergence and slower convergence rate. The artificial bee colony (ABC) algorithm is a swarm-based search meta-heuristic algorithm inspired by the foraging behaviors of honey bee colonies, with the benefit of a relatively fewer control parameters. In its original form, the ABC algorithm has certain limitations such as low convergence rate, and insufficient balance between exploration and exploitation in the search equations. In this dissertation, an ABC-AMR algorithm is proposed by incorporating an adaptive modification rate (AMR) into the original ABC algorithm to increase convergence rate by adjusting the balance between exploration and exploitation in the search equations through an adaptive determination of the number of parameters to be updated in every iteration. A constrained ABC-AMR algorithm is also developed for solving constrained optimization problems.There are many real-world problems requiring simultaneous optimizations of more than one conflicting objectives. Multiobjective (MO) optimization produces a set of feasible solutions called the Pareto front instead of a single optimum solution. For multiobjective optimization, if a decision maker’s preferences can be incorporated during the optimization process, the search process can be confined to the region of interest instead of searching the entire region. In this dissertation, two algorithms are developed for such incorporation. The first one is a reference-point-based MOABC algorithm in which a decision maker’s preferences are included in the optimization process as the reference point. The second one is a physical-programming-based MOABC algorithm in which physical programming is used for setting the region of interest of a decision maker. In this dissertation, the four developed algorithms are applied to solve digital filter design problems. The ABC-AMR algorithm is used to design Types 3 and 4 linear phase FIR differentiators, and the results are compared to those obtained by the original ABC algorithm, three improved ABC algorithms, and the Parks-McClellan algorithm. The constrained ABC-AMR algorithm is applied to the design of sparse Type 1 linear phase FIR filters of filter orders 60, 70 and 80, and the results are compared to three state-of-the-art design methods. The reference-point-based multiobjective ABC algorithm is used to design of asymmetric lowpass, highpass, bandpass and bandstop FIR filters, and the results are compared to those obtained by the preference-based multiobjective differential evolution algorithm. The physical-programming-based multiobjective ABC algorithm is used to design IIR lowpass, highpass and bandpass filters, and the results are compared to three state-of-the-art design methods. Based on the obtained design results, the four design algorithms are shown to be competitive as compared to the state-of-the-art design methods

A Consolidated Review of Path Planning and Optimization Techniques: Technical Perspectives and Future Directions

In this paper, a review on the three most important communication techniques (ground, aerial, and underwater vehicles) has been presented that throws light on trajectory planning, its optimization, and various issues in a summarized way. This kind of extensive research is not often seen in the literature, so an effort has been made for readers interested in path planning to fill the gap. Moreover, optimization techniques suitable for implementing ground, aerial, and underwater vehicles are also a part of this review. This paper covers the numerical, bio-inspired techniques and their hybridization with each other for each of the dimensions mentioned. The paper provides a consolidated platform, where plenty of available research on-ground autonomous vehicle and their trajectory optimization with the extension for aerial and underwater vehicles are documented