State-of-Charge Estimation of Lithium-Ion Battery Pack Based on Improved RBF Neural Networks

Algorithm 2

Compact RBF modelling algorithm using the PSO method.

Require: selected input variable matrix in equation (2), the variable upper/lower bounds and the velocity upper/lower bounds , the size of the population , the maximum number of iterations , the crossover factors , and the acceleration of the particle velocity .
Ensure: the SOC vector of the battery pack .
(1)	Initialization:, .
(2)Whiledo
(3)Initialization: Set the initial centers and widths of the RBF basis function, where , thus the initial nonlinear parameters are . Set the initial velocity .
(4)for to do
(5) construct the candidate RBF basis vectors.
(6) calculate the matrix using and the recursive matrix using Algorithm 1, respectively.
(7) calculate the vector using .
(8) Find the candidate regressor that gives the minimal PRESS error, and record the minimal PRESS error (index , minimal PRESS error ) and the best position of each particle .
(9) compare to the last best position using , obtain the global optimal position .
(10) update velocity and position using
	where and denote the velocity and particle at iteration for selection, and is the random numbers.
(11)end for
(12)add the candidate feature with the minimal PRESS error to the regression matrix , .
(13)end while
(14)Identification: calculate the linear coefficients using equation (11).