Detecting a stochastic background of gravitational waves in the presence of non-Gaussian noise: A performance of generalized cross-correlation statistic

We discuss a robust data analysis method to detect a stochastic background of gravitational waves in the presence of non-Gaussian noise. In contrast to the standard cross-correlation (SCC) statistic frequently used in the stochastic background searches, we consider a {\it generalized cross-correlation} (GCC) statistic, which is nearly optimal even in the presence of non-Gaussian noise. The detection efficiency of the GCC statistic is investigated analytically, particularly focusing on the statistical relation between the false-alarm and the false-dismissal probabilities, and the minimum detectable amplitude of gravitational-wave signals. We derive simple analytic formulae for these statistical quantities. The robustness of the GCC statistic is clarified based on these formulae, and one finds that the detection efficiency of the GCC statistic roughly corresponds to the one of the SCC statistic neglecting the contribution of non-Gaussian tails. This remarkable property is checked by performing the Monte Carlo simulations and successful agreement between analytic and simulation results was found.Comment: 15 pages, 8 figures, presentation and some figures modified, final version to be published in PR

Data analysis strategies for the detection of gravitational waves in non-Gaussian noise

In order to analyze data produced by the kilometer-scale gravitational wave detectors that will begin operation early next century, one needs to develop robust statistical tools capable of extracting weak signals from the detector noise. This noise will likely have non-stationary and non-Gaussian components. To facilitate the construction of robust detection techniques, I present a simple two-component noise model that consists of a background of Gaussian noise as well as stochastic noise bursts. The optimal detection statistic obtained for such a noise model incorporates a natural veto which suppresses spurious events that would be caused by the noise bursts. When two detectors are present, I show that the optimal statistic for the non-Gaussian noise model can be approximated by a simple coincidence detection strategy. For simulated detector noise containing noise bursts, I compare the operating characteristics of (i) a locally optimal detection statistic (which has nearly-optimal behavior for small signal amplitudes) for the non-Gaussian noise model, (ii) a standard coincidence-style detection strategy, and (iii) the optimal statistic for Gaussian noise.Comment: 5 pages RevTeX, 4 figure

Fault detection in operating helicopter drive train components based on support vector data description

The objective of the paper is to develop a vibration-based automated procedure dealing with early detection of mechanical degradation of helicopter drive train components using Health and Usage Monitoring Systems (HUMS) data. An anomaly-detection method devoted to the quantification of the degree of deviation of the mechanical state of a component from its nominal condition is developed. This method is based on an Anomaly Score (AS) formed by a combination of a set of statistical features correlated with specific damages, also known as Condition Indicators (CI), thus the operational variability is implicitly included in the model through the CI correlation. The problem of fault detection is then recast as a one-class classification problem in the space spanned by a set of CI, with the aim of a global differentiation between normal and anomalous observations, respectively related to healthy and supposedly faulty components. In this paper, a procedure based on an efficient one-class classification method that does not require any assumption on the data distribution, is used. The core of such an approach is the Support Vector Data Description (SVDD), that allows an efficient data description without the need of a significant amount of statistical data. Several analyses have been carried out in order to validate the proposed procedure, using flight vibration data collected from a H135, formerly known as EC135, servicing helicopter, for which micro-pitting damage on a gear was detected by HUMS and assessed through visual inspection. The capability of the proposed approach of providing better trade-off between false alarm rates and missed detection rates with respect to individual CI and to the AS obtained assuming jointly-Gaussian-distributed CI has been also analysed

Detection of multiplicative noise in stationary random processes using second- and higher order statistics

This paper addresses the problem of detecting the presence of colored multiplicative noise, when the information process can be modeled as a parametric ARMA process. For the case of zero-mean multiplicative noise, a cumulant based suboptimal detector is studied. This detector tests the nullity of a specific cumulant slice. A second detector is developed when the multiplicative noise is nonzero mean. This detector consists of filtering the data by an estimated AR filter. Cumulants of the residual data are then shown to be well suited to the detection problem. Theoretical expressions for the asymptotic probability of detection are given. Simulation-derived finite-sample ROC curves are shown for different sets of model parameters

Parametric modeling of photometric signals

This paper studies a new model for photometric signals under high flux assumption. Photometric signals are modeled by Gaussian autoregressive processes having the same mean and variance denoted Constraint Gaussian Autoregressive Processes (CGARP's). The estimation of the CGARP parameters is discussed. The Cramér Rao lower bounds for these parameters are studied and compared to the estimator mean square errors. The CGARP is intended to model the signal received by a satellite designed for extrasolar planets detection. A transit of a planet in front of a star results in an abrupt change in the mean and variance of the CGARP. The Neyman–Pearson detector for this changepoint detection problem is derived when the abrupt change parameters are known. Closed form expressions for the Receiver Operating Characteristics (ROC) are provided. The Neyman–Pearson detector combined with the maximum likelihood estimator for CGARP parameters allows to study the generalized likelihood ratio detector. ROC curves are then determined using computer simulations

Cross-Correlation Detection of Point Sources in WMAP First Year Data

We apply a Cross-correlation (CC) method developed previously for detecting gamma-ray point sources to the WMAP first year data by using the Point-Spread Function of WMAP and obtain a full sky CC coefficient map. Analyzing this map, we find that the CC method is a powerful tool to examine the WMAP foreground residuals which can be further cleaned accordingly. Evident foreground signals are found in WMAP foreground cleaned maps and Tegmark cleaned map. In this process 101 point-sources are detected, and 26 of them are new sources besides the originally listed WMAP 208 sources. We estimate the flux of these new sources and verify them by another method. As a result, a revised mask file based on the WMAP first year data is produced by including these new sources.Comment: 14 pages, 10 figures; accepted for publication by ChJA

Classification of chirp signals using hierarchical bayesian learning and MCMC methods

This paper addresses the problem of classifying chirp signals using hierarchical Bayesian learning together with Markov chain Monte Carlo (MCMC) methods. Bayesian learning consists of estimating the distribution of the observed data conditional on each class from a set of training samples. Unfortunately, this estimation requires to evaluate intractable multidimensional integrals. This paper studies an original implementation of hierarchical Bayesian learning that estimates the class conditional probability densities using MCMC methods. The performance of this implementation is first studied via an academic example for which the class conditional densities are known. The problem of classifying chirp signals is then addressed by using a similar hierarchical Bayesian learning implementation based on a Metropolis-within-Gibbs algorithm

Line-robust statistics for continuous gravitational waves: safety in the case of unequal detector sensitivities

The multi-detector F-statistic is close to optimal for detecting continuous gravitational waves (CWs) in Gaussian noise. However, it is susceptible to false alarms from instrumental artefacts, for example quasi-monochromatic disturbances ('lines'), which resemble a CW signal more than Gaussian noise. In a recent paper [Keitel et al 2014, PRD 89 064023], a Bayesian model selection approach was used to derive line-robust detection statistics for CW signals, generalising both the F-statistic and the F-statistic consistency veto technique and yielding improved performance in line-affected data. Here we investigate a generalisation of the assumptions made in that paper: if a CW analysis uses data from two or more detectors with very different sensitivities, the line-robust statistics could be less effective. We investigate the boundaries within which they are still safe to use, in comparison with the F-statistic. Tests using synthetic draws show that the optimally-tuned version of the original line-robust statistic remains safe in most cases of practical interest. We also explore a simple idea on further improving the detection power and safety of these statistics, which we however find to be of limited practical use.Comment: 21 pages, 11 figures, updated to match published versio

Deep Learning for Real-time Gravitational Wave Detection and Parameter Estimation: Results with Advanced LIGO Data

The recent Nobel-prize-winning detections of gravitational waves from merging black holes and the subsequent detection of the collision of two neutron stars in coincidence with electromagnetic observations have inaugurated a new era of multimessenger astrophysics. To enhance the scope of this emergent field of science, we pioneered the use of deep learning with convolutional neural networks, that take time-series inputs, for rapid detection and characterization of gravitational wave signals. This approach, Deep Filtering, was initially demonstrated using simulated LIGO noise. In this article, we present the extension of Deep Filtering using real data from LIGO, for both detection and parameter estimation of gravitational waves from binary black hole mergers using continuous data streams from multiple LIGO detectors. We demonstrate for the first time that machine learning can detect and estimate the true parameters of real events observed by LIGO. Our results show that Deep Filtering achieves similar sensitivities and lower errors compared to matched-filtering while being far more computationally efficient and more resilient to glitches, allowing real-time processing of weak time-series signals in non-stationary non-Gaussian noise with minimal resources, and also enables the detection of new classes of gravitational wave sources that may go unnoticed with existing detection algorithms. This unified framework for data analysis is ideally suited to enable coincident detection campaigns of gravitational waves and their multimessenger counterparts in real-time.Comment: 6 pages, 7 figures; First application of deep learning to real LIGO events; Includes direct comparison against matched-filterin

Singular Gaussian Measures in Detection Theory

No abstract availabl