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

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

Peptide mass fingerprinting using field-programmable gate arrays

The reconfigurable computing paradigm, which exploits the flexibility and versatility of field-programmable gate arrays (FPGAs), has emerged as a powerful solution for speeding up time-critical algorithms. This paper describes a reconfigurable computing solution for processing raw mass spectrometric data generated by MALDI-TOF instruments. The hardware-implemented algorithms for denoising, baseline correction, peak identification, and deisotoping, running on a Xilinx Virtex-2 FPGA at 180 MHz, generate a mass fingerprint that is over 100 times faster than an equivalent algorithm written in C, running on a Dual 3-GHz Xeon server. The results obtained using the FPGA implementation are virtually identical to those generated by a commercial software package MassLynx

A cellular automata modelling of dendritic crystal growth based on Moore and von Neumann neighbourhood

An important step in understanding crystal growth patterns involves simulation of the growth processes using mathematical models. In this paper some commonly used models in this area are reviewed, and a new simulation model of dendritic crystal growth based on the Moore and von Neumann neighbourhoods in cellular automata models are introduced. Simulation examples are employed to find ap- propriate parameter configurations to generate dendritic crystal growth patterns. Based on these new modelling results the relationship between tip growth speed and the parameters of the model are investigated

Multiscale time series modelling with an application to the relativistic electron intensity at the geosynchronous orbit

In this paper, a Bayesian system identification approach to multiscale time series modelling is proposed, where multiscale means that the output of the system is observed at one(coarse) resolution while the input of the system is observed at another (One) resolution. The proposed method identifies linear models at different levels of resolution where the link between the two resolutions is realised via non-overlapping averaging process. This averaged time series at the coarse level of resolution is assumed to be a set of observations from an implied process so that the implied process and the output of the system result in an errors-in-variables ARMAX model at the coarse level of resolution. By using a Bayesian inference and Markov Chain Monte Carlo (MCMC) method, such a modelling framework results in different dynamical models at different levels of resolution at the same time. The new method is also shown to have the ability to combine information across different levels of resolution. An application to the analysis of the relativistic electron intensity at the geosynchronous orbit is used to illustrate the new method

A simple scalar coupled map lattice model for excitable media

A simple scalar coupled map lattice model for excitable media is intensively analysed in this paper. This model is used to explain the excitability of excitable media, and a Hopf-like bifurcation is employed to study the different spatio-temporal patterns produced by the model. Several basic rules for the construction of these kinds of models are proposed. Illustrative examples demonstrate that the sCML model is capable of generating complex spatiotemporal patterns

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

Characterising spatio-temporal dynamical systems in the frequency domain

In this paper a new concept, spatio-temporal generalised frequency response functions (STGFRF), is introduced for the first time to characterise spatio-temporal dynamical systems in the frequency domain. A probing method is developed to calculate the STGFRFs for both continuous and discrete spatio-temporal systems

Identification of the transition rule in a modified cellular automata model: the case of dendritic NH4Br crystal growth

A method of identifying the transition rule, encapsulated in a modified cellular automata (CA) model, is demonstrated using experimentally observed evolution of dendritic crystal growth patterns in NH4Br crystals. The influence of the factors, such as experimental set-up and image pre-processing, colour and size calibrations, on the method of identification are discussed in detail. A noise reduction parameter and the diffusion velocity of the crystal boundary are also considered. The results show that the proposed method can in principle provide a good representation of the dendritic growth anisotropy of any system

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