Polynomial model tree (POLYMOT) — A new training algorithm for local model networks with higher degree polynomials

A new training algorithm for nonlinear system identification with local models of higher polynomial degree is presented in this paper. Usually the local models are linearly parameterized and those parameters are typically estimated by some least squares approach. For the utilization of higher degree polynomials this procedure is no longer feasible since the amount of parameters grows rapidly with the number of physical inputs and the polynomial degree. Thus a new learning strategy with the aid of stepwise regression is developed to estimate only the most significant parameters. The included partitioning algorithm which is based on the LOLIMOT algorithm decides in each step between increasing the number of parameters of the worst local model and splitting this model to create two new ones. A comparison of a LOLIMOT and POLYMOT trained exhaust emission model shows the benefits of the proposed new learning strategy.