Identification of binary cellular automata from spatiotemporal binary patterns using a fourier representation

The identification of binary cellular automata from spatio-temporal binary patterns is investigated in this paper. Instead of using the usual Boolean or multilinear polynomial representation, the Fourier transform representation of Boolean functions is employed in terms of a Fourier basis. In this way, the orthogonal forward regression least-squares algorithm can be applied directly to detect the significant terms and to estimate the associated parameters. Compared with conventional methods, the new approach is much more robust to noise. Examples are provided to illustrate the effectiveness of the proposed approach

A comparison of polynomial and wavelet expansions for the identification of chaotic coupled map lattices

A comparison between polynomial and wavelet expansions for the identification of coupled map lattice (CML) models for deterministic spatio-temporal dynamical systems is presented in this paper. The pattern dynamics generated by smooth and non-smooth nonlinear maps in a well-known 2-dimensional CML structure are analysed. By using an orthogonal feedforward regression algorithm (OFR), polynomial and wavelet models are identified for the CML’s in chaotic regimes. The quantitative dynamical invariants such as the largest Lyapunov exponents and correlation dimensions are estimated and used to evaluate the performance of the identified models

Neighbourhood detection and indentification of spatio-temporal dynamical systems using a coarse-to-fine approach

A novel approach to the determination of the neighbourhood and the identification of spatio-temporal dynamical systems is investigated. It is shown that thresholding to convert the pattern to a binary pattern and then applying cellular automata (CA) neighbourhood detection methods can provide an initial estimate of the neighbourhood. A coupled map lattice model can then be identified using the CA detected neighbourhood as the initial conditions. This provides a coarse-to-fine approach for neighbourhood detection and identification of coupled map lattice models. Three examples are used to demonstrate the application of the new approach

An extended orthogonal forward regression algorithm for system identification using entropy

In this paper, a fast identification algorithm for nonlinear dynamic stochastic system identification is presented. The algorithm extends the classical Orthogonal Forward Regression (OFR) algorithm so that instead of using the Error Reduction Ratio (ERR) for term selection, a new optimality criterion —Shannon’s Entropy Power Reduction Ratio(EPRR) is introduced to deal with both Gaussian and non-Gaussian signals. It is shown that the new algorithm is both fast and reliable and examples are provided to illustrate the effectiveness of the new approach

Identification of partial differential equation models for a class of multiscale spatio-temporal dynamical systems

In this paper, the identification of a class of multiscale spatio-temporal dynamical sys-tems, which incorporate multiple spatial scales, from observations is studied. The proposed approach is a combination of Adams integration and an orthogonal least squares algorithm, in which the multiscale operators are expanded, using polynomials as basis functions, and the spatial derivatives are estimated by finite difference methods. The coefficients of the polynomials can vary with respect to the space domain to represent the feature of multiple scales involved in the system dynamics and are approximated using a B-spline wavelet multi-resolution analysis (MRA). The resulting identified models of the spatio-temporal evolution form a system of partial differential equations with different spatial scales. Examples are provided to demonstrate the efficiency of the proposed method

Consistent parameter identification of partial differential equation models from noisy observations

This paper introduces a new residual-based recursive parameter estimation algorithm for linear partial differential equations. The main idea is to replace unmeasurable noise variables by noise estimates and to compute recursively both the model parameter and noise estimates. It is proven that under some mild assumptions the estimated parameters converge to the true values with probability one. Numerical examples that demonstrate the effectiveness of the proposed approach are also provided

Multiscale modelling and identification of a class of lattice dynamical systems

A new multiscale modelling framework is introduced to describe a class of lattice dynamical systems (LDS), which can be used to model natural systems involving multiphysics and the multi-resolution facets of a single spatio-temporal dynamical system. The emphasis of the paper is on the multi-resolution facets, with respect to the spatial domain, of a single spatio-temporal dynamical system by using a Haar wavelet decomposition technique. A multiscale identification method for such systems is then proposed, which can be considered as a dual of the multigrid method. The proposed identification method involves three steps: the system dynamics at some specific scale of interest are identified using a recursive least-squares algorithm; the residual is then projected onto coarser scales using Haar wavelets and the parameter estimation errors are minimized; and finally a coarse correction procedure is applied to the original scale. An outstanding advantage of the proposed identification method is a saving on the computational costs. Numerical examples are provided to demonstrate the application of the proposed new approach

Multiscale identification of spatio-temporal dynamical systems using a wavelet multiresolution analysis

In this paper, a new algorithm for the multiscale identification of spatio-temporal dynamical systems is derived. It is shown that the input and output observations can be represented in a multiscale manner based on a wavelet multiresolution analysis. The system dynamics at some specific scale of interest can then be identified using an orthogonal forward leastsquares algorithm. This model can then be converted between different scales to produce predictions of the system outputs at different scales. The method can be applied to both multiscale and conventional spatio-temporal dynamical systems. For multiscale systems, the method can generate a parsimonious and effective model at a coarser scale while considering the effects from finer scales. Additionally, the proposed method can be used to improve the performance of the identification when measurements are noisy. Numerical examples are provided to demonstrate the application of the proposed new approach

Spatio-temporal generalised frequency response functions

The concept of generalised frequency response functions (GFRFs), which were developed for nonlinear system identification and analysis, is extended to continuous spatio-temporal dynamical systems normally described by partial differential equations (PDEs). The paper provides the definitions and interpretation of spatio-temporal generalised frequency response functions for linear and nonlinear spatio-temporal systems based on an impulse response procedure. A new probing method is also developed to calculate the GFRFs. Both the Diffusion equation and Fisher’s equation are analysed to illustrate the new frequency domain methods

Spatio-temporal generalised frequency response functions over unbounded spatial domains

The concept of generalised frequency response functions (GFRFs), which were developed for nonlinear system identification and analysis, is extended to continuous spatio-temporal dynamical systems normally described by partial differential equations (PDEs). The paper provides the definitions and interpretation of spatio-temporal generalised frequency response functions for linear and nonlinear spatio-temporal systems, defined over unbounded spatial domains, based on an impulse response procedure. A new probing method is also developed to calculate the GFRFs. Both the Diffusion equation and Fisher’s equation are analysed to illustrate the new frequency domain methods