Initial estimates of the linear subsystems of Wiener–Hammerstein models

The iterative optimizations often used to identify Wiener–Hammerstein models, pairs of linear filters separated by memoryless nonlinearities, require good initial estimates of the linear elements in order to avoid them getting caught in local minima. Previous work has shown that initial estimates of the two linear elements can be formed by splitting the poles and zeros of the best linear approximation of the Wiener–Hammerstein system between the two linear elements, an approach which can generate a large number of initializations. This paper develops a scanning technique that can efficiently evaluate each of the proposed initializations using estimates of some carefully constructed nonlinear characteristics of the system, estimates which can be formed using linear system identification techniques after some data pre-processing. This approach results in a much smaller number, often only one, of potential starting points for the optimization. The proposed algorithm is demonstrated using a Monte Carlo simulation using data from the SYSID 2009 Wiener–Hammerstein Benchmark system.