  System identification uses measurements of a dynamic system's input and
output to reconstruct a mathematical model for that system. These can be
mechanical, electrical, physiological, among others. Since most of the systems
around us exhibit some form of nonlinear behavior, nonlinear system
identification techniques are the tools that will help us gain a better
understanding of our surroundings and potentially let us improve their
performance. One model that is often used to represent nonlinear systems is the
polynomial NARX model, an equation error model where the output is a polynomial
function of the past inputs and outputs. That said, a major disadvantage with
the polynomial NARX model is that the number of parameters increases rapidly
with increasing polynomial order. Furthermore, the polynomial NARX model is a
black-box model, and is therefore difficult to interpret. This paper discusses
a decoupling algorithm for the polynomial NARX model that substitutes the
multivariate polynomial with a transformation matrix followed by a bank of
univariate polynomials. This decreases the number of model parameters
significantly and also imposes structure on the black-box NARX model. Since a
non-convex optimization is required for this identification technique,
initialization is an important factor to consider. In this paper the decoupling
algorithm is developed in conjunction with several different initialization
techniques. The resulting algorithms are applied to two nonlinear benchmark
problems: measurement data from the Silver-Box and simulation data from the
Bouc-Wen friction model, and the performance is evaluated for different
validation signals in both simulation and prediction.
