Identification of Complex Nonlinearities Using Cubic Splines with Automatic Discretization
One of the major challenges in nonlinear system identification is the selection of appropriate mathematical functions to model the observed nonlinearities. In this context, piecewise polynomials, or splines, offer a simple and flexible representation basis requiring limited prior knowledge. The generally-adopted discretization for splines consists in an even distribution of their control points, termed knots. While this may prove successful for simple nonlinearities, a more advanced strategy is needed for nonlinear restoring forces with strong local variations. The present paper specifically introduces a two-step methodology to select automatically the location of the knots. It proposes to derive an initial model, using nonlinear subspace identification, and incorporating cubic spline basis functions with fixed and equally-spaced abscissas. In a second step, the location of the knots is optimized iteratively by minimizing a least-squares cost function. A single-degree-of-freedom system with a discontinuous stiffness characteristic is considered as a case study.
KeywordsNonlinear system identification Frequency-domain subspace algorithm Cubic splines Nonsmooth nonlinearity Automatic splines discretization Constrained nonlinear optimization
The authors T. Dossogne and J.P. Noël are Research Fellow (FRIA fellowship) and Postdoctoral Researcher, respectively, of the Fonds de la Recherche Scientifique FNRS which is gratefully acknowledged.
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