Spatio-temporal System Identification Research Articles

A Spatial Frequency Domain Analysis of the Belousov–Zhabotinsky Reaction

A nonlinear spatio-temporal system identification and analysis approach is used to study the dynamical behavior of the Belousov–Zhabotinsky (BZ) chemical reaction process. In our previous study [Guo et al., 2010],, the dynamical behavior of the BZ reaction in the spatial-temporal domain has been analyzed by identifying a coupled map lattice (CML) model of the process directly from experimental data from a real BZ reaction experiment. In this paper, the frequency domain analysis of the dynamics near equilibrium is carried out by mapping the obtained CML model into higher order spatial frequency response functions to reveal the nonlinear coupling and modulation between the various initial spectral components in the process. As far as we are aware, this is the first study of any real spatio-temporal system using a spatio-temporal domain identification and frequency domain analysis approach.

Model term selection for spatio-temporal system identification using mutual information

A new mutual information based algorithm is introduced for term selection in spatio-temporal models. A generalised cross validation procedure is also introduced for model length determination and examples based on cellular automata, coupled map lattice and partial differential equations are described.

An adaptive wavelet neural network for spatio-temporal system identification

Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks (AWNN) is introduced for spatio-temporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimization (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework.

Spatiotemporal system identification on nonperiodic domains using Chebyshev spectral operators and system reduction algorithms

A system identification methodology based on Chebyshev spectral operators and an orthogonal system reduction algorithm is proposed, leading to a new approach for data-driven modeling of nonlinear spatiotemporal systems on nonperiodic domains. A continuous model structure is devised allowing for terms of arbitrary derivative order and nonlinearity degree. Chebyshev spectral operators are introduced to realm of inverse problems to discretize that continuous structure and arrive with spectral accuracy at a discrete form. Finally, least squares combined with an orthogonal system reduction algorithm are employed to solve for the parameters and eliminate the redundancies to achieve a parsimonious model. A numerical case study of identifying the Allen-Cahn metastable equation demonstrates the superior accuracy of the proposed Chebyshev spectral identification over its finite difference counterpart.

Lattice Dynamical Wavelet Neural Networks Implemented Using Particle Swarm Optimization for Spatio–Temporal System Identification

In this brief, by combining an efficient wavelet representation with a coupled map lattice model, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNNs), is introduced for spatio-temporal system identification. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimization (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the OPP algorithm, significant wavelet neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer. The resultant network model, obtained in the first stage, however, may be redundant. In the second stage, an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network. An example for a real spatio-temporal system identification problem is presented to demonstrate the performance of the proposed new modeling framework.

Neighborhood Detection for the Identification of Spatiotemporal Systems

Neighborhood detection and local state vector construction for the identification of spatiotemporal systems is considered in this paper. Determining the neighborhood size both in the space and time domain can considerably reduce the complexity of the set of candidate model terms for the identification of coupled map lattice models. The computation requirements of the model identification algorithm can also be greatly reduced instead of the more direct identification approach of searching over the entire spatiotemporal neighborhood in the original space. In this paper, a new neighborhood detection method is introduced based on embedding theory for nonlinear dynamical systems to produce an initial spatiotemporal neighborhood for the identification of spatiotemporal systems. Numerical examples are provided to demonstrate the feasibility and applicability of the new neighborhood detection method.

THE IDENTIFICATION OF COMPLEX SPATIOTEMPORAL PATTERNS USING COUPLED MAP LATTICE MODELS

Many complex and interesting spatiotemporal patterns have been observed in a wide range of scientific areas. In this paper, two kinds of spatiotemporal patterns including spot replication and Turing systems are investigated and new identification methods are proposed to obtain Coupled Map Lattice (CML) models for this class of systems. Initially, a new correlation analysis method is introduced to determine an appropriate temporal and spatial data sampling procedure for the identification of spatiotemporal systems. A new combined Orthogonal Forward Regression and Bayesian Learning algorithm with Laplace priors is introduced to identify sparse and robust CML models for complex spatiotemporal patterns. The final identified CML models are validated using correlation-based model validation tests for spatiotemporal systems. Numerical results illustrate the identification procedure and demonstrate the validity of the identified models.

Locally Regularized Spatiotemporal Modeling and Model Comparison for Functional MRI

In this work we treat fMRI data analysis as a spatiotemporal system identification problem and address issues of model formulation, estimation, and model comparison. We present a new model that includes a physiologically based hemodynamic response and an empirically derived low-frequency noise model. We introduce an estimation method employing spatial regularization that improves the precision of spatially varying noise estimates. We call the algorithm locally regularized spatiotemporal (LRST) modeling. We develop a new model selection criterion and compare our model to the SPM-GLM method. Our findings suggest that our method offers a better approach to identifying appropriate statistical models for fMRI studies.

A signal estimation approach to functional MRI.

In the last half decade, fast methods of magnetic resonance imaging have led to the possibility, for the first time, of non-invasive dynamic brain imaging. This has led to an explosion of work in the Neurosciences. From a signal processing viewpoint the problems are those of nonlinear spatio-temporal system identification. In this paper, we develop new methods of identification using novel spatial regularization. We also develop a new model comparison technique and use that to compare our method with existing techniques on some experimental data.

The Representation and Identification of Spatio-Temporal Systems: An Example of Population Diffusion in North-West England

The Representation and Identification of Spatio-Temporal Systems: An Example of Population Diffusion in North-West England