Recursive algorithm for interaction prediction in Hammerstein system identification with experimental studies

The paper presents a fully recursive algorithm for building a nonlinear block-oriented model of a dynamic system on the basis of noise-corrupted data. Hidden internal signal in the Hammerstein structure is firstly predicted to compute the best possible model of the second (linear dynamic) block of the system. Asymptotically, the algorithm reaches an equilibrium point when the predictor becomes equivalent to the characteristic of the nonlinear block. Nonlinear static element is treated as a black box, and the predictor is based on non-parametric kernel regression or orthogonal expansion estimation method. The crucial contribution lies in the fact that the algorithm computes the offset (bias) between the input-output regression function and the nonlinear characteristic, which allows to get optimal model of the whole system. Experimental studies include both iterative convex optimisation procedure and its recursive version, wherein measurement data need not to be stored in memory. As a real data example - thermal analysis of chalcogenide glasses was modelled with an algorithm updated to the Hammerstein system with ARMAX block.