Parameter reduction in nonlinear state-space identification of hysteresis

Abstract

Hysteresis is a highly nonlinear phenomenon, showing up in a wide variety of science and engineering problems. The identification of hysteretic systems from input-output data is a challenging task. Recent work on black-box polynomial nonlinear state-space modeling for hysteresis identification has provided promising results, but struggles with a large number of parameters due to the use of multivariate polynomials. This drawback is tackled in the current paper by applying a decoupling approach that results in a more parsimonious representation involving univariate polynomials. This work is carried out numerically on input-output data generated by a Bouc-Wen hysteretic model and follows up on earlier work of the authors. The current article discusses the polynomial decoupling approach and explores the selection of the number of univariate polynomials with the polynomial degree, as well as the connections with neural network modeling. We have found that the presented decoupling approach is able to reduce the number of parameters of the full nonlinear model up to about 50%, while maintaining a comparable output error level.

Data driven discrete-time parsimonious identification of a nonlinear state-space model for a weakly nonlinear system with short data record

“…PNLSS-I DEC model can be seen as the model with a dimensionality reduction step to reduce the dimensionality of the multivariate nonlinear polynomial function in PNLSS and PNLSS-I models. This model structure can be a good choice in certain cases where dynamic nonlinearities are involved [36]. Finally, promising results were obtained despite having structural limitations in both model structures to deal with the influence of process noise present in the cascaded water-tanks benchmark problem.…”

“…Even though in the decoupled model, the number of parameters have been reduced to 84, in this particular benchmark, the number of data points were limited to 1024, therefore the possibility to choose the degrees of freedom w.r.t above mentioned variables was very limited, hence the performance of PNLSS-I DEC model structure could not be improved further. For a fair comparison and evaluation of different parameters on the performance of PNLSS-I DEC , the readers are kindly referred to [36] In the context of this benchmark, NLSS2 model performance is best on the full benchmark validation dataset (see Table 4). One reason could be due to its better generalisation performance (i.e.…”