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Parallel cascade identification and kernel estimation for nonlinear systems.

M J Korenberg1

  • 1Department of Electrical Engineering, Queen's University, Kingston, Ontario, Canada.

Annals of Biomedical Engineering
|January 1, 1991
PubMed
Summary
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This study introduces a parallel cascade model to represent nonlinear systems using linear and nonlinear elements. This method accurately identifies system kernels and distinguishes deterministic from random behavior.

Area of Science:

  • System identification
  • Nonlinear dynamics
  • Signal processing

Background:

  • Nonlinear systems are challenging to model and identify.
  • Volterra series offer a representation but can be computationally intensive.
  • Previous methods often require specific input signal properties.

Purpose of the Study:

  • To develop a novel parallel cascade representation for discrete-time finite-memory nonlinear systems.
  • To establish a method for identifying nonlinear system kernels from input-output data without restrictive input assumptions.
  • To apply this framework for accurate kernel estimation and distinguishing signal behaviors.

Main Methods:

  • Utilizing parallel cascades of dynamic linear (LN) and static nonlinear elements.
  • Extending Palm's work to represent Volterra series with finite parallel LN paths.

Related Experiment Videos

  • Developing an identification technique applicable to arbitrary input signals (non-Gaussian, non-white).

    • Main Results:

    • Any finite-order Volterra system can be exactly represented by a finite number of parallel LN paths.
    • An upper bound on the number of required parallel LN paths is determined.
    • Accurate measurement of nonlinear system kernels, even with long memory, is achieved.
    • Significant terms for nonlinear difference equation models are identified.

    Conclusions:

    • The parallel cascade model provides an exact and efficient representation for a broad class of nonlinear systems.
    • The identification method is robust, requiring only a single input-output record and no specific input signal properties.
    • Kernel estimation using this approach aids in understanding system dynamics and signal characteristics, offering an alternative to chaos-based analysis.