Multifractal characterization and fuzzy classification of lightning strike maps

This paper investigates optimal classification of lightning strike maps (LSMs), using regular and fuzzy K-means classifiers. It also describes a novel approach for measurements of the physical LSMs. Lightning strikes are physical phenomena, which have adverse effects on power transmission. Modelling and classification of the LSMs can lead to prediction of their time-space behaviour, and enhance the protection of the existing and new power systems and transmission lines. Prediction requires the classification of the simulated results and physical data, and comparing them together using characterization. Since the LSMs are highly nonlinear, nonstationary, and stochastic, ordinary models and analyses are incapable of simulating and characterizing these phenomena. Since self-affinity of such maps is an indication of multifractality, percolation models and complexity measures such as the Renyi fractal dimension spectrum (RS) and Mandelbrot singularity spectrum (MS) are utilized. The data of the LSMs have been obtained through the Canadian Lightning Detection Network (CLDN) for Manitoba in the year 2002. The data have been characterized by both the RS and MS. Features have been extracted using the RS. Classification employed the regular and fuzzy K-means methods. For each classification method, 50 tests have been utilized, and classification performance for 2 to 15 classes has been investigated through Davis-Bouldin criterion. The fuzzy K-means classifier identified 6 optimal classes with a confidence level of 0.78, while the regular K-means algorithm could not distinguish the classes.