Identification of time-varying systems using multiresolution wavelet models

Identification of linear and nonlinear time-varying systems is investigated and a new wavelet model identification algorithm is introduced. By expanding each time-varying coefficient using a multiresolution wavelet expansion, the time-varying problem is reduced to a time invariant problem and the identification reduces to regressor selection and parameter estimation. Several examples are included to illustrate the application of the new algorithm

Multiscale Forecasting Models Based on Singular Values for Nonstationary Time Series

Time series are valuable sources of information for supporting planning activities. Transport, fishery, economy and finances are predominant sectors concerned into obtaining information in advance to improve their productivity and efficiency. During the last decades diverse linear and nonlinear forecasting models have been developed for attending this demand. However the achievement of accuracy follows being a challenge due to the high variability of the most observed phenomena. In this research are proposed two decomposition methods based on Singular Value Decomposition of a Hankel matrix (HSVD) in order to extract components of low and high frequency from a nonstationary time series. The proposed decomposition is used to improve the accuracy of linear and nonlinear autoregressive models. The evaluation of the proposed forecasters is performed through data coming from transport sector and fishery sector. Series of injured persons in traffic accidents of Santiago and Valparaíso and stock of sardine and anchovy of central-south Chilean coast are used. Further, for comparison purposes, it is evaluated the forecast accuracy reached by two decomposition techniques conventionally used, Singular Spectrum Analysis (SSA) and decomposition based on Stationary Wavelet Transform (SWT), both joint with linear and nonlinear autoregressive models. The experiments shown that the proposed methods based on Singular Value Decomposition of a Hankel matrix in conjunction with linear or nonlinear models reach the best accuracy for one-step and multi-step ahead forecasting of the studied time series.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Crosswind stability of vehicles under nonstationary wind excitation

This work has studied the crosswind stability of vehicles under nonstationary wind excitation in various scenarios. Railway vehicles running on curved and straight track with varying vehicle speed are studied. Road vehicles are classified into different categories. For each vehicle class, a corresponding worst-case vehicle model has been built. As the wind excitation on the vehicle is a stochastic process, a risk analysis has to be carried out and failure probabilities are computed and analyzed

Crosswind stability of vehicles under nonstationary wind excitation

This work has studied the crosswind stability of vehicles under nonstationary wind excitation in various scenarios. Railway vehicles running on curved and straight track with varying vehicle speed are studied. Road vehicles are classified into different categories. For each vehicle class, a corresponding worst-case vehicle model has been built. As the wind excitation on the vehicle is a stochastic process, a risk analysis has to be carried out and failure probabilities are computed and analyzed

A multiple beta wavelet-based locally regularized ultraorthogonal forward regression algorithm for time-varying system identification with applications to EEG

Time-varying (TV) nonlinear systems widely exist in various fields of engineering and science. Effective identification and modeling of TV systems is a challenging problem due to the nonstationarity and nonlinearity of the associated processes. In this paper, a novel parametric modeling algorithm is proposed to deal with this problem based on a TV nonlinear autoregressive with exogenous input (TV-NARX) model. A new class of multiple beta wavelet (MBW) basis functions is introduced to represent the TV coefficients of the TV-NARX model to enable the tracking of both smooth trends and sharp changes of the system behavior. To produce a parsimonious model structure, a locally regularized ultraorthogonal forward regression (LRUOFR) algorithm aided by the adjustable prediction error sum of squares (APRESS) criterion is investigated for sparse model term selection and parameter estimation. Simulation studies and a real application to EEG data show that the proposed MBW-LRUOFR algorithm can effectively capture the global and local features of nonstationary systems and obtain an optimal model, even for signals contaminated with severe colored noise

Adaptive Multi-Output Gradient RBF Tracker For Nonlinear and Nonstationary Regression

Multioutput regression of nonlinear and nonstationary data is largely understudied in both machine learning and control communities. This article develops an adaptive multioutput gradient radial basis function (MGRBF) tracker for online modeling of multioutput nonlinear and nonstationary processes. Specifically, a compact MGRBF network is first constructed with a new two-step training procedure to produce excellent predictive capacity. To improve its tracking ability in fast time-varying scenarios, an adaptive MGRBF (AMGRBF) tracker is proposed, which updates the MGRBF network structure online by replacing the worst performing node with a new node that automatically encodes the newly emerging system state and acts as a perfect local multioutput predictor for the current system state. Extensive experimental results confirm that the proposed AMGRBF tracker significantly outperforms existing state-of-the-art online multioutput regression methods as well as deep-learning-based models, in terms of adaptive modeling accuracy and online computational complexity.</p

Defining and applying prediction performance metrics on a recurrent NARX time series model.

International audienceNonlinear autoregressive moving average with exogenous inputs (NARMAX) models have been successfully demonstrated for modeling the input-output behavior of many complex systems. This paper deals with the proposition of a scheme to provide time series prediction. The approach is based on a recurrent NARX model obtained by linear combination of a recurrent neural network (RNN) output and the real data output. Some prediction metrics are also proposed to assess the quality of predictions. This metrics enable to compare different prediction schemes and provide an objective way to measure how changes in training or prediction model (Neural network architecture) affect the quality of predictions. Results show that the proposed NARX approach consistently outperforms the prediction obtained by the RNN neural network

Functional MRI data analysis : Detection, estimation and modelling

Ph.DDOCTOR OF PHILOSOPH

Predicting Physical Time Series Using Dynamic Ridge Polynomial Neural Networks

Forecasting naturally occurring phenomena is a common problem in many domains of science, and this has been addressed and investigated by many scientists. The importance of time series prediction stems from the fact that it has wide range of applications, including control systems, engineering processes, environmental systems and economics. From the knowledge of some aspects of the previous behaviour of the system, the aim of the prediction process is to determine or predict its future behaviour. In this paper, we consider a novel application of a higher order polynomial neural network architecture called Dynamic Ridge Polynomial Neural Network that combines the properties of higher order and recurrent neural networks for the prediction of physical time series. In this study, four types of signals have been used, which are; The Lorenz attractor, mean value of the AE index, sunspot number, and heat wave temperature. The simulation results showed good improvements in terms of the signal to noise ratio in comparison to a number of higher order and feedforward neural networks in comparison to the benchmarked techniques