## International Summer Research Program in Gravitational-Wave Physics:

Research Experiences for Undergraduates around the world

**INFN and Università di Pisa**

- Study of multichannel correlations between noise and environmental data in Virgo:

The analysis of a statistical dependence between the interferometer noise and the signals coming from environmental sensors (seismometers, magnetometers etc.) is important in order to understand the mechanisms which couple external fluctuations to the channel used for the detection of gravitational waves. In this project it is proposed to investigate such dependence using several methods. In the simplest case, the dependence is linear, and can be quantified using coherence and its multichannel generalizations.

More complicated and interesting scenarios can exist: for example one noise source can be modulated by another one. The most direct generalization of coherence in this nonlinear scenario is the bi-coherence, together with other statistics derived from polyspectra.

We are investigating the possibility of implementing tools, based on these techniques, that could be used to help during and after the commissioning of advanced Virgo. We are particularly interested in understanding the possibility of building efficient algorithms for blind noise separation (such as independent component analysis), the basic idea being to try to disentangle and classify noise sources and noise events using multichannel data.

The main motivation for this project is to stimulate interaction with the detector experts, in order to provide a physical interpretation of the results. The student will be involved both in the analysis and in the implementation of the algorithms, with the possibility of modulating the mix between these two activities according to her/his personal interest.

**Mentor:**Giancarlo Cella

**Related Project 2009:**"Detecting and Characterizing Nonlinear Signal Components in VIRGO Data Channels" - Efficient strategies for cavity locking:

In an interferometric detector of gravitational waves laser light is coupled to resonant cavities. These are built with suspended mirrors whose relative distance must be maintained stable up to a small fraction of the laser's wavelength. The typical displacement induced by seismic motion is larger than that, and the cavity must be stabilized with an active feedback.

Typically the error signal is available during the free motion of the mirrors only for a quite short time, namely when the mirror cross the resonance condition. This is particularly true for a high finesse cavity. In a direct approach big feedback forces must be applied for this reason: stabilization is difficult and reintroduction of additional noise in the system is possible. In this project more efficient strategies useful to get the cavity locked will be investigated. The basic idea is to use information got during the resonance crossing and to predict in a probabilistic way the mirror motion using the dynamic of the system, which can be modeled by a set of oscillators coupled to stochastic forces. Model parameters are only partially known in a real situation, and must be learned by the stabilization system. The student will interface with a numerical simulation of the cavity (a "black box") and will implement and tune a control algorithm based on the Kalman filter or on the particle filter approach.

A required skill is some experience in programming (C and/or MATLAB).

**Mentor:**Giancarlo Cella

**Past IREU Projects**

**Other Prior Projects**