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Identification of Hammerstein models with cubic spline nonlinearities
Erika J Dempsey1, David T Westwick
1Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB T2N 1N4 Canada.
IEEE Transactions on Bio-Medical Engineering
|February 10, 2004
Summary
This study introduces a new system identification algorithm using cubic splines for nonlinear system modeling. Cubic splines improve Hammerstein model accuracy for electromyography (EMG) data compared to traditional polynomials.
Area of Science:
- Biomedical Engineering
- Systems Biology
- Nonlinear Dynamics
Background:
- Block structured models are crucial for analyzing complex systems.
- Representing static nonlinearities accurately is a key challenge in system identification.
- Traditional polynomial-based nonlinearities may limit model predictive power.
Purpose of the Study:
- To introduce a novel system identification algorithm for Hammerstein systems.
- To evaluate the efficacy of cubic splines in representing static nonlinearities.
- To compare cubic spline-based models against polynomial-based models for biological signal analysis.
Main Methods:
- Developed a system identification algorithm for Hammerstein structures.
- Employed cubic splines to model the static nonlinear component.
- Utilized a separable least squares Levenberg-Marquardt optimization.
- Modeled linear dynamics using a finite impulse response filter.
Main Results:
- Cubic spline-based Hammerstein models demonstrated superior accuracy in simulations.
- The algorithm was successfully applied to electromyogram (EMG) data from a spinal cord injured patient.
- Cubic spline models provided more accurate predictions of reflex EMG compared to polynomial models, including on novel data.
Conclusions:
- Cubic splines offer a more accurate representation of static nonlinearities in Hammerstein models.
- The proposed system identification algorithm enhances predictive capabilities for biological signals.
- This approach holds promise for improved analysis of physiological data in clinical settings.