Applications of Transient Signal Analysis Using the Concept of Recurrence Plot Analysis

Abstract

Transient signals are universally characterized by a short duration and a broad spectrum which are often present in various phenomena such as sudden acoustic pressure changes, seismic waves, electrical discharges, etc. In order to efficiently monitor the systems where they happen, it is very important that the signals generated by transient phenomena be detected, located and characterized. This significantly helps to better understand their effects in the given application context. This paper presents new tools derived from the concept of Recurrence Plot Analysis (RPA) and applied on three real applications. Two of the applications concern the detection, localization and characterization of the electrical partial discharges (measured from photovoltaic panels and on electrical cables, respectively). Another application refers to the quantification of the water hammer effect using two acoustic sensors placed on a pipe line.

New Approach of UAV Movement Detection and Characterization Using Advanced Signal Processing Methods Based on UWB Sensing

“…Starting from the difference between each two successive scan lines (Equation (2)) that is considered as a time series [ 43 , 44 ], the construction of the phase space is given by the transition from the initial values of the time series to a vector that defines the new representation space. This vector is obtained by introducing two new parameters: Time delay and phase space dimension .…”

“…This vector is obtained by introducing two new parameters: Time delay and phase space dimension . Thus, the equation that defines the new vector is [ 43 , 44 ]: where are the axis vector units. The choice of the parameters and can be found in [ 44 ].…”

“…This method ( Figure 6 ) allows investigating the trajectory of the m -dimensional phase space through a two-dimensional representation of the pair-wise distance, a representation called the recurrence plot. Mathematically, this is expressed as the distance matrix, a form of representation of the distances between all pair-wise trajectory points and provides a two-dimensional alternative to represent the trajectory [ 43 , 44 ]: where , is the number of samples of the signal and in our paper, is the Euclidian distance. For this application, we chose the Euclidean distance, because our purpose is to best highlight sudden changes in the phase space trajectory, these changes corresponding to the UWB pulses of the movement [ 43 ].…”

“…Next, the time-distributed recurrence (TDR) is defined in order to highlight the sudden changes in the trajectory [ 43 ]: …”

“…The advantage of this method is that it is a non-parametric method and it can be analyzed for many types of signals [ 43 , 44 ].…”