Lingzhong Guo

State-Space Reconstruction and Spatio-Temporal Prediction of Lattice Dynamical Systems

This paper addresses the problems of state space reconstruction and spatio-temporal prediction for lattice dynamical systems. It is shown that the state space of any finite lattice dynamical system can be embedded into a reconstruction space for almost every, in the sense of prevalence, smooth measurement mapping as long as the dimension of the reconstruction space is larger than twice the size of the lattice. Based on this result, an input-output spatio-temporal dynamical relation for each site within the lattice is derived and used for spatio-temporal prediction of the system. In the case of infinite lattice dynamical systems, an approach based on constructing local lattice dynamical systems is proposed. It is shown that the finite dimensional results can be directly applied to the local modelling and spatio-temporal prediction for infinite lattice dynamical systems. Two numerical examples are provided to demonstrate the proposed theory and approach

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.

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.

Identification of Partial Differential Equation Models for Continuous Spatio-Temporal Dynamical Systems

The identification of a class of continuous spatio-temporal dynamical systems from observations is presented in this paper. The proposed approach is a combination of implicit Adams integration and an orthogonal least-squares algorithm, in which the operators are expanded using polynomials as basis functions, and the spatial derivatives are estimated by finite difference methods. The resulting identified models of the spatio-temporal evolution form a system of partial differential equations. Examples are provided to demonstrate the efficiency of the proposed method

Identification of coupled map lattice models for spatio-temporal patterns using wavelets

This paper introduces a new approach for the identification of coupled map lattice models of complex spatio-temporal patterns from measured data. The nonlinear functionals describing the evolution of the spatio-temporal patterns are constructed using B-spline wavelet and scaling functions. This provides a multiresolution approximation for the underlying spatio-temporal dynamics. An orthogonal least squares algorithm is used to determine the suitable terms from wavelet functions to form an accurate representation of the nonlinear spatio-temporal dynamics. Three examples are used to demonstrate the application of the proposed new approach.

An iterative orthogonal forward regression algorithm

A novel iterative learning algorithm is proposed to improve the classic Orthogonal Forward Regression (OFR) algorithm in an attempt to produce an optimal solution under a purely OFR framework without using any other auxiliary algorithms. The new algorithm searches for the optimal solution on a global solution space while maintaining the advantage of simplicity and computational efficiency. Both a theoretical analysis and simulations demonstrate the validity of the new algorithm.

Estimation of spatial derivatives and identification of continuous spatio-temporal dynamical systems

A new approach for the estimation of spatial derivatives and the identification of a class of continuous spatio-temporal dynamical systems from experimental data is presented in this study. The proposed identification approach is a combination of implicit Adams integration and an orthogonal forward regression algorithm (OFR), in which the operators are expanded using polynomials as basis functions. The noisy experimental data are de-noised by using biorthogonal spline wavelet filters and the spatial derivatives are estimated using a multiresolution analysis method. Finally, a bootstrap method is applied to refine the identified parameters from the OFR algorithm. The resulting identified models of the spatio-temporal evolution form a system of partial differential equations. Examples are provided to demonstrate the efficiency of the proposed method.

A NEIGHBORHOOD SELECTION METHOD FOR CELLULAR AUTOMATA MODELS

A new neighborhood selection method is presented for both deterministic and probabilistic cellular automata models. The detection criteria are built explicitly on the corresponding contribution whi...

Neighbourhood detection and identification 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.

Ultra-Orthogonal Forward Regression Algorithms for the Identification of Non-Linear Dynamic Systems

A new ultra-least squares (ULS) criterion is introduced for system identification. Unlike the standard least squares criterion which is based on the Euclidean norm of the residuals, the new ULS criterion is derived from the Sobolev space norm. The new criterion measures not only the discrepancy between the observed signals and the model prediction but also the discrepancy between the associated weak derivatives of the observed and the model signals. The new ULS criterion possesses a clear physical interpretation and is easy to implement. Based on this, a new Ultra-Orthogonal Forward Regression (UOFR) algorithm is introduced for nonlinear system identification, which includes converting a least squares regression problem into the associated ultra-least squares problem and solving the ultra-least squares problem using the orthogonal forward regression method. Numerical simulations show that the new UOFR algorithm can significantly improve the performance of the classic OFR algorithm.