This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 1 Measurement System Based on Electrostatic Sensors to Detect Moving Charged Debris With Planar-Isotropic Accuracy Tommaso Addabbo, Member, IEEE, Ada Fort, Member, IEEE, Marco Mugnaini, Member, IEEE, Enza Panzardi , and Valerio Vignoli, Member, IEEE Abstract— We present a measurement system capable to detect and reconstruct the trajectory of moving charged debris expelled with the exhaust gases or circulating in the lubricating oil of engines, aero-engines, or gas turbines. The measurement tech- nique is based on a circular array of three electrostatic sensors used to estimate the trajectory, the charge, and the velocity of a moving charged particle. We discuss methods to process the information provided by the sensors, combining physical models and the geometrical characteristics of the sensor array, providing a theoretical characterization of the measurement accuracy, which is shown to be not dependent on the direction of the particle motion with respect to the sensor placement. The information obtained with the measurement system can be used to reject false positives when the sensors and the front-end electronics are used in noisy environments. Index Terms—Charge amplifier, condition monitoring, debris monitoring, electrostatic sensor, gas turbomachines. I. I NTRODUCTION T HE electrostatic detection of charged debris has been proposed in the literature for the condition monitoring of engines, aero-engines, or gas turbines [1]–[18]. The debris expelled with the exhaust gas or circulating in the lubricating oil can be electrically charged with charge levels that depend on several factors, among which the debris material and its size, the type of the mechanical fault, the temperature, and other physical properties of the medium [1], [3], [13], [19]. Different authors have shown that the measurement of the debris charge, velocity, and trajectory can provide useful sup- plementary information for the machine condition monitoring to provide early warning of potential failures, such that pre- ventive or predictive maintenance actions may be taken. The charge signal provided by an electrostatic sensor depends on the debris speed and the distance of the debris trajectory from the sensing equipment [3]. Furthermore, depending on the bandwidth of the measurement instrumentation chain, the mea- sured signal may result distorted due to some filtering effects, as discussed in [3] and [4]. To improve the measurement Manuscript received March 20, 2018; revised May 23, 2018; accepted June 19, 2018. The Associate Editor coordinating the review process was Massimo Lazzaroni. (Corresponding author: Enza Panzardi.) The authors are with the Department of Information Engineering and Mathematics, University of Siena, 53100 Siena, Italy (e-mail: panzardi@ dii.unisi.it). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2018.2853938 detection range, or to cover extended sections of the conduit transporting the monitored flow, arrays of sensors have been proposed [20]. However, in these solutions, the information redundancy obtained when using more than one sensor has not been conveniently exploited to derive methods increasing the measurement reliability in terms of false positive detection rejection. Indeed, in the considered application, the sensors are typically housed in hazardous environments, in which the electric side of the measurement system may be excited by a number of undesired stimuli, especially due to the electromagnetic bursts generating noisy spikes. Nowadays, the solutions proposed in the literature are based on sensor arrays arranged according to layouts orthogonal to the conduit flow. This choice allows for estimating a limited set of features related to the flowing charged particles, i.e., the information provided by the measurement system is limited by the chosen layout of the sensor array. Further information can be obtained using different sensor array layouts, exploiting also the geometrical dimension parallel to the nominal flow direction. As shown in the following, measurement systems based on this approach provide more accurate measurements and result more reliable in terms of false positive detection rejection. In this paper, we extend the results published in [21], discussing the theoretical foundations of a novel measurement system based on three electrostatic sensors, capable to estimate the direction of the moving particle, as well as its velocity, charge, and trajectory. This paper is based on the theoretical models and experiments presented in [3] and [4], and we show that the measurement setup has planar-isotropic directivity, providing a measurement accuracy not dependent on the orientation of the particle motion with respect to the sensor placement. This paper is organized as follows. In Section II, we present the proposed measurement setup discussing how to estimate the particle trajectory and velocity. In Section III, we briefly recall the theoretical models presented in [3] to verify the theoretical calculations emulating the involved physics and discuss the proposed measurement technique showing that the results are not dependent on the debris direction. The conclusion and references close this paper. II. MEASUREMENT SETUP We focus on an elementary layout, discussing geometries based on three sensors. The structure has to be understood as 0018-9456 © 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.