Abstract
Two methods are proposed for identifying the component elements of a Wiener cascade that is comprised of a dynamic linear element (L) followed by a static nonlinearity (N). Both methods avoid potential problems of instability in a procedure presented by Paulin [M. G. Paulin, Biol. Cybern. 69: 67–76, 1993], which itself is a modification of a method described earlier by Hunter and Korenberg [I. W. Hunter and M. J. Korenberg, Biol. Cybern. 55: 135–144, 1996]. The latter method is a rapidly convergent iterative procedure that produces accurate estimates of the L and N elements from short data records, provided that the static nonlinearity N is invertible. Subsequently, Paulin introduced a modification that removed this limitation and enabled identification of Wiener cascades with nonmonotonic static nonlinearities. However, Paulin presented his modification employing an autoregressive moving average (ARMA) model representation for the dynamic linear element. To remove the possibility that the estimated ARMA model could be unstable, we recast the procedure by utilizing instead a rapid method for finding an impulse response representation for the dynamic linear element. However, in this form the procedure did not have good convergence properties, so we introduced two key ideas, both of which provide effective alternatives for identifying Wiener cascades whether or not the static nonlinearities therein are invertible. The new procedures are illustrated on challenging examples involving high-degree polynomial static nonlinearities, of odd or even symmetry, a high-pass linear element, and output noise corruption of 50%. © 1999 Biomedical Engineering Society.
PAC99: 8710+e, 0210Nj, 0250-r
Similar content being viewed by others
REFERENCES
Busgang, J. J. Cross correlation functions of amplitudedistorted Gaussian signals. MIT Res. Lab. Elec. Tech. Rep. 216:1–14, 1952.
Hunter, I. W. Experimental comparison of Wiener and Hammerstein cascade models of frog muscle fiber mechanics. Biophys. J. 49:81a, 1986.
Hunter, I. W., and M. J. Korenberg. The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biol. Cybern. 55:135–144, 1986.
Korenberg, M. J. Identification of biological cascades of linear and static nonlinear systems. Proceedings of the Midwest Symposium on Circuit Theory. 18.2:1–9, 1973.
Korenberg, M. J. Identifying nonlinear difference equation and functional expansion representations: The fast orthogonal algorithm. Ann. Biomed. Eng. 16:123–142, 1988.
Korenberg, M. J. Parallel cascade identification and kernel estimation for nonlinear systems. Ann. Biomed. Eng. 19:429–455, 1991.
Korenberg, M. J., S. B. Bruder, and P. J. McIlroy. Exact orthogonal kernel estimation from finite data records: Extending Wiener's identification of nonlinear systems. Ann. Biomed. Eng. 16:201–214, 1988.
Maksym, G. N., R. E. Kearney, and J. H. Bates. Nonparametric block-structured modeling of lung tissue strip mechanics. Ann. Biomed. Eng. 26:242–252, 1998.
Paulin, M. G. A method for constructing data-based models of spiking neurons using a dynamic linear-static nonlinear cascade. Biol. Cybern. 69:67–76, 1993.
Rice, J. R. A theory of condition. J. Numer. Anal. 3:287–310, 1966.
Sakai, H. M., and K.-I. Naka. Signal transmission in the catfish retina. V. Sensitivity and circuit. J. Neurophysiol. 58:1329–1350, 1987.
Spekreijse, H., and H. Oosting. Linearizing: A method for analyzing and synthesizing nonlinear systems. Kybernetik 7:22–31, 1970.
Trad, C. H., B. A. Horwitz, and E. D. Lipson. Light-induced absorbance changes in extract of Phycomyces sporangiophores: Modifications in night-blind mutants. J. Photochem. Photobiol., B 1:305–314, 1988.
Trad, C. H., and E. D. Lipson. Biphasic fluence-response curves and derived action spectra for light-induced absorption changes in Phycomyces mycelium. J. Photochem. Photobiol. 1:169–180, 1987.
Trad, C. H. and E. D. Lipson. Electrophoretic analysis of proteins from Phycomyces mutants with abnormal trophisms. Biochem. Genet. 27:355–365, 1989.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Korenberg, M.J., Hunter, I.W. Two Methods for Identifying Wiener Cascades Having Noninvertible Static Nonlinearities. Annals of Biomedical Engineering 27, 793–804 (1999). https://doi.org/10.1114/1.232
Issue Date:
DOI: https://doi.org/10.1114/1.232