Research and Validation of Lightning Location Based on Particle Swarm Optimization Algorithm

Abstract

In the lightning monitoring systems, positioning calculation is directly related to the results of the detection accuracy. In this paper, the concept of the particle swarm optimization (PSO) algorithm for lightning location estimation was brought in. The PSO overcome the disadvantages of iterative method, such as the difficulty in finding initial and going to diverge. The numerical simulation results show that: the algorithm can obtained lightning point steadily and accurately, and converge quickly. Therefore, the PSO algorithm on lightning location is feasible. Introduction In the lightning monitoring systems, positioning calculation is directly related to the results of the detection accuracy [1]. The algorithms of lightning location generally use Taylor series and least squares iterative algorithm,which have the shortcomings such as difficult to determine the initial value or easy to diverge. Based on the above, this paper introduces the PSO into the lightning location, and make the numerical simulation and validation. Lightning location Based on Particle Swarm Optimization Algorithm Brief review of the PSO theory and algorithm. The PSO is an effective global optimization algorithms. The basic idea of the PSO is to achieve searching for optimal solutions in complex spatial through collaboration and information sharing among groups of individuals. The PSO adopts Speed-Shift model for action [2]. In each generation population, the particles will track the two extremes: one is the optimal solution the particle itself found so far, namely its extreme [3]; the other is the optimal solution the whole population found so far, namely the global extremum [4]. These two extremes continuously adjust the position of the particle which can be found the optimal solution within a few iterations. PSO can be described as: Let PSO search in an n-dimensional space, the population consists of N particles X = {XX1,XX2, ... ,XXNN}. Each particle location Xii = {xxii1, xxii2, ... , xxiiii} represents a solution of the problem. The particles search for the new solutions by constantly adjusting their positions. Particles by continuously adjust their position (xxiiii) to search for a new solution. Each particle can remember their optimal solutions they have searched for, and the best position (ppgg) the entire particle swarm have went by, which is also the optimal solution searched currently, denoted ppgg. In addition, each particle has a velocity, denoted by Vii = {vvii1, vvii2, ... vviiii}, while the latter two are found, each particle will update their own pace according to Eq. 1. vvii(tt + 1) = wwvi(tt) + cc1RRmm1(ppii − xxii(tt) + cc2RRmm2(ppgg − xxii(tt) (1) xxii(tt + 1) = xxii(tt) + vvii(tt + 1) (2) Where vviiii(tt + 1) represents the i-th particle velocity at t + 1 iterations. ww is the inertia weight, and it can reduce the flight speed of the particle and prevent search divergence; cc1 , cc2 is International Conference on Intelligent Systems Research and Mechatronics Engineering (ISRME 2015) © 2015. The authors Published by Atlantis Press 815 acceleration constant, generally take cc1 = cc2 = 2 ;RRmm1,RRmm2 for n × n -dimensional diagonal matrix, the diagonal elements are random number between [0,1]. In addition, the speed of the particles will not be too large, and you can set the speed limit(vvmmmmmm). That is, in Eq. 1 when vvii(tt + 1) > vvmmmmmm, vvii(tt + 1) = vvmmmmmm; when vvii(tt + 1) < vvmmmmmm,vvii(tt + 1) = −vvmmmmmm. Inertia weight ww is given by Eq. 3: w = (wstart − wend) × (MaxDT−iter) MaxDT + wweeiiii (3) Where MaxDT is the maximum number of iterations; Iter is the current iteration number; wstart,wend were initial inertia weight and termination inertia weight, wstart = 0.9,wend = 0.4. PSO implementation steps are as follows: (1) Initialized. Set various parameters PSO algorithm have been involved. (2) Calculate the fitness of each particle (fitness). Store the best place Pbest of each particle and fitness. Choose the best fitness position of the particle from the population as Gbest of populations; (3) Update state of the particles according to Eq. 1 and Eq.2; (4) If the current situation reaches the maximum number of iterations or final result is less than the convergence precision, stop the iterative and output the optimal solution. Otherwise go to step (2). Start Initialize the particle position and initial velocity randomly throughout the search space Calculate the fitness of each particle Update Pbest and Gbest of each particle Update the velocity and position of each particle, according to the Eq. 1 and Eq.2 If the termination condition is satisfied