Single-Sensor Source Localization Using Electromagnetic Time Reversal and Deep Transfer Learning: Application to Lightning

Electromagnetic Time Reversal (EMTR) has been used to locate different types of electromagnetic sources. We propose a novel technique based on the combination of EMTR and Machine Learning (ML) for source localization. We show for the first time that ML techniques can be used in conjunction with EMTR to reduce the required number of sensors to only one for the localization of electromagnetic sources in the presence of scatterers. In the EMTR part, we use 2D-FDTD method to generate 2D profiles of the vertical electric field as RGB images. Next, in the ML part, we take advantage of transfer learning techniques by using the pretrained VGG-19 Convolutional Neural Network (CNN) as the feature extractor tool. To the best of our knowledge, this is the first time that the knowledge of pretrained CNNs is applied to simulation-generated images. We demonstrate the skill of the developed methodology in localizing two kinds of electromagnetic sources, namely RF sources with a bandwidth of 0.1–10 MHz and lightning impulses. For the localization of lightning, based on the experimental recordings in the Säntis region, the new approach enables accurate 2D lightning localization using only one sensor, as opposed to current lightning location systems that need at least two sensors to operate.

On Practical Implementation of Electromagnetic Models of Lightning Return-Strokes

Hamidreza Karami

In electromagnetic models, the return-stroke channel is represented as an antenna excited at its base by either a voltage or a current source. To adjust the speed of the current pulse propagating in the channel to available optical observations, different representations for the return-stroke channel have been proposed in the literature using different techniques to artificially reduce the propagation speed of the current pulse to values consistent with observations. In this paper, we present an analysis of the available electromagnetic models in terms of their practical implementation. Criteria used for the analysis are the ease of implementation of the models, the numerical accuracy and the needed computer resources, as well as their ability to reproduce a desired value for the speed of the return stroke current pulse. Using the CST-MWS software, which is based on the time-domain finite-integration technique, different electromagnetic models were analyzed, namely (A) a wire embedded in a fictitious half-space dielectric medium (other than air), (B) a wire embedded in a fictitious coating with permittivity (epsilon(r)) and permeability (mu(r)), and (C) a wire in free-space loaded by distributed series inductance and resistance. It is shown that, by adjusting the parameters of each model, it is possible to reproduce a desired value for the speed of the current pulse. For each of the considered models, we determined the values for the adjustable parameters that allow obtaining the desired value of the return speed. Model A is the least expensive in terms of computing resources. However, it requires two simulation runs to obtain the electromagnetic fields. A variant of Model B that includes a fictitious dielectric/ferromagnetic coating is found to be more efficient to control the current speed along the channel than using only a dielectric coating. On the other hand, this model requires an increased number of mesh cells, resulting in higher memory and computational time. The presence of an inhomogeneous medium generates, in addition, unphysical fluctuations on the resulting current distributions. These fluctuations, which strongly depend on the size of the coating as well as on its electric and magnetic properties, can be attenuated by considering conductive losses in the coating. Considering the efficiency in terms of the required computer resources and ease of implementation, we recommend the use of Model C (wire loaded by distributed inductance and resistance).

Mdpi Ag2016

Efficient Analysis of Shielding Effectiveness of Metallic Rectangular Enclosures Using Unconditionally Stable Time-Domain Integral Equations

Hamidreza Karami, Michael Mattes, Juan Ramon Mosig

This paper proposes an efficient modeling technique for transient electromagnetic analysis of a rectangular metallic enclosure with multiple apertures, using the surface equivalent principle (SEP) and integral equations. The SEP is used to replace the apertures by perfect electric conductor surfaces while introducing appropriate magnetic current densities on both sides of the apertures. As a result, the problem is reduced to two independent regions. The first region is outside the enclosure for which the free-space Green's function with the aid of image theory can be used to obtain the total fields in it. The second region is the inside of the enclosure and a closed-form expression is then derived for its time-domain dyadic Green's function. Finally, the governing time-domain magnetic field integral equation (TD-MFIE) for the structure is derived by enforcing the continuity of the tangential magnetic field at the apertures. To eliminate the late time instabilities in solving the resultant TD-MFIE, an unconditionally stable marching-on-in degree scheme is used. A new accelerated algorithm is proposed for the internal problem that relies on the separation of time and space in the cavity Green's function. The validity of the proposed method is confirmed by comparing the simulation results of several case studies with those obtained using the frequency-domain methods and CST microwave studio.

2014

Localizing the Source of an Epidemic Using Few Observations

Brunella Marta Spinelli

Localizing the source of an epidemic is a crucial task in many contexts, including the detection of malicious users in social networks and the identification of patient zeros of disease outbreaks. The difficulty of this task lies in the strict limitations on the data available: In most cases, when an epidemic spreads, only few individuals, who we will call sensors, provide information about their state. Furthermore, as the spread of an epidemic usually depends on a large number of variables, accounting for all the possible spreading patterns that could explain the available data can easily result in prohibitive computational costs. Therefore, in the field of source localization, there are two central research directions: The design of practical and reliable algorithms for localizing the source despite the limited data, and the optimization of data collection, i.e., the identification of the most informative sensors. In this dissertation we contribute to both these directions. We consider network epidemics starting from an unknown source. The only information available is provided by a set of sensor nodes that reveal if and when they become infected. We study how many sensors are needed to guarantee the identification of the source. A set of sensors that guarantees the identification of the source is called a double resolving set (DRS); the minimum size of a DRS is called the double metric dimension (DMD). Computing the DMD is, in general, hard, hence estimating it with bounds is desirable. We focus on G(N,p) random networks for which we derive tight bounds for the DMD. We show that the DMD is a non-monotonic function of the parameter p, hence there are critical parameter ranges in which source localization is particularly difficult. Again building on the relationship between source localization and DRSs, we move to optimizing the choice of a fixed number K of sensors. First, we look at the case of trees where the uniqueness of paths makes the problem simpler. For this case, we design polynomial time algorithms for selecting K sensors that optimize certain metrics of interest. Next, turning to general networks, we show that the optimal sensor set depends on the distribution of the time it takes for an infected node u to infect a non-infected neighbor v, which we call the transmission delay from u to v. We consider both a low- and a high-variance regime for the transmission delays. We design algorithms for sensor placement in both cases, and we show that they yield an improvement of up to 50% over state-of-the-art methods. Finally, we propose a framework for source localization where some sensors (called dynamic sensors) can be added while the epidemic spreads and the localization progresses. We design an algorithm for joint source localization and dynamic sensor placement; This algorithm can handle two regimes: offline localization, where we localize the source after the epidemic spread, and online localization, where we localize the source while the epidemic is ongoing. We conduct an empirical study of offline and online localization and show that, by using dynamic sensors, the number of sensors we need to localize the source is up to 10 times less with respect to a strategy where all sensors are deployed a priori. We also study the resistance of our methods to high-variance transmission delays and show that, even in this setting, using dynamic sensors, the source can be localized with less than 5% of the nodes being sensors.