Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG

The identification of nonlinear time-varying systems using linear-in-the-parameter models is investigated. A new efficient Common Model Structure Selection (CMSS) algorithm is proposed to select a common model structure. The main idea and key procedure is: First, generate K 1 data sets (the first K data sets are used for training, and theK 1 th one is used for testing) using an online sliding window method; then detect significant model terms to form a common model structure which fits over all the K training data sets using the new proposed CMSS approach. Finally, estimate and refine the time-varying parameters for the identified common-structured model using a Recursive Least Squares (RLS) parameter estimation method. The new method can effectively detect and adaptively track the transient variation of nonstationary signals. Two examples are presented to illustrate the effectiveness of the new approach including an application to an EEG data set

Modelling and Prediction of Global Magnetic Disturbance in Near-Earth Space: a Case Study for Kp Index using NARX Models

Severe geomagnetic disturbances can be hazardous for mod-ern technological systems. The reliable forecast of parameters related to thestate of the magnetosphere can facilitate the mitigation of adverse effects ofspace weather. This study is devoted to the modeling and forecasting of theevolution of the Kp index related to global geomagnetic disturbances. Through-out this work the Nonlinear AutoRegressive with eXogenous inputs (NARX)methodology is applied. Two approaches are presented: i) a recursive slid-ing window approach, and ii) a direct approach. These two approaches arestudied separately and are then compared to evaluate their performances.It is shown that the direct approach outperforms the recursive approach, butboth tend to produce predictions slightly biased from the true values for lowand high disturbances

Nonlinear System Identification of Neural Systems from Neurophysiological Signals

The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a small amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention

Time-varying nonlinear causality detection using regularized orthogonal least squares and multi-wavelets with applications to EEG

A new transient Granger causality detection method is proposed based on a time-varying parametric modelling framework, and is applied to real EEG signals to reveal the causal information flow during motor imagery (MI) tasks. The time-varying parametric modelling approach employs a nonlinear autoregressive with external input (NARX) model, whose parameters are approximated by a set of multiwavelet basis functions. A regularized orthogonal least squares (ROLS) algorithm is then used to produce a parsimonious or sparse regression model and estimate the associated model parameters. The time-varying Granger causality between nonstationary signals can be detected accurately by making use of both the good approximation properties of multi-wavelets and the good generalization performance of the ROLS in the presence of high-level noise. Two simulation examples are presented to demonstrate the effectiveness of the proposed method for both linear and nonlinear causal detection respectively. The proposed method is then applied to real EEG signals of MI tasks. It follows that transient causal information flow over the time course between various sensorimotor related channels can be successfully revealed during the whole reaction processes. Experiment results from these case studies confirm the applicability of the proposed scheme and show its utility for the understanding of the associated neural mechanism and the potential significance for developing MI tasks based brain-computer interface (BCI) systems

Prediction of Kp Index Using NARMAX Models with A Robust Model Structure Selection Method

The severity of global magnetic disturbances in Near-Earth space can crucially affect human life. These geomagnetic disturbances are often indicated by a Kp index, which is derived from magnetic field data from ground stations, and is known to be correlated with solar wind observations. Forecasting of Kp index is important for understanding the dynamic relationship between the magnetosphere and solar wind. This study presents 3 hours ahead prediction for Kp index using the NARMAX model identified by a novel robust model structure detection method. The identified models are evaluated using 4 years of Kp data. Overall, the models with robust structure can produce very good Kp forecast results and provide transparent and compact representations of the relationship between Kp index and solar wind variables. The robustness and conciseness of the models can highly benefit the space weather forecast tasks

Neural network-based parametric system identification: a review

Parametric system identification, which is the process of uncovering the inherent dynamics of a system based on the model built with the observed inputs and outputs data, has been intensively studied in the past few decades. Recent years have seen a surge in the use of neural networks (NNs) in system identification, owing to their high approximation capability, less reliance on prior knowledge, and the growth of computational power. However, there is a lack of review on neural network modelling in the paradigm of parametric system identification, particularly in the time domain. This article discussed the connection in principle between conventional parametric models and three types of NNs including Feedforward Neural Networks, Recurrent Neural Networks and Encoder-Decoder. Then it reviewed the advantages and limitations of related research in addressing two major challenges of parametric system identification, including the model interpretability and modelling with nonstationary realisations. Finally, new challenges and future trends in neural network-based parametric system identification are presented in this article

n

Electroencephalograms (EEG) signals are of interest because of their relationship with physiological activities, allowing a description of motion, speaking, or thinking. Important research has been developed to take advantage of EEG using classification or predictor algorithms based on parameters that help to describe the signal behavior. Thus, great importance should be taken to feature extraction which is complicated for the Parameter Estimation (PE)–System Identification (SI) process. When based on an average approximation, nonstationary characteristics are presented. For PE the comparison of three forms of iterative-recursive uses of the Exponential Forgetting Factor (EFF) combined with a linear function to identify a synthetic stochastic signal is presented. The one with best results seen through the functional error is applied to approximate an EEG signal for a simple classification example, showing the effectiveness of our proposal

Nonlinear modeling of cortical responses to mechanical wrist perturbations using the NARMAX method

Objective: Nonlinear modeling of cortical responses (EEG) to wrist perturbations allows for the quantification of cortical sensorimotor function in healthy and neurologically impaired individuals. A common model structure reflecting key characteristics shared across healthy individuals may provide a reference for future clinical studies investigating abnormal cortical responses associated with sensorimotor impairments. Thus, the goal of our study is to identify this common model structure and therefore to build a nonlinear dynamic model of cortical responses, using nonlinear autoregressivemoving-average model with exogenous inputs (NARMAX). Methods: EEG was recorded from ten participants when they were receiving continuous wrist perturbations. A common model structure detection method was developed for identifying a common NARMAX model structure across all participants, with individualized parameter values. The results were compared to conventional subject-specific models. Results: The proposed method achieved 93.91% variance accounted for (VAF) when implementing a one-step-ahead prediction and around 50% VAF for a k-step ahead prediction (k = 3), without a substantial drop of VAF as compare to subject-specific models. The estimated common structure suggests that the measured cortical response is a mixed outcome of the nonlinear transformation of external inputs and local neuronal interactions or inherent neuronal dynamics at the cortex. Conclusion: The proposed method well determined the common characteristics across subjects in the cortical responses to wrist perturbations. Significance: It provides new insights into the human sensorimotor nervous system in response to somatosensory inputs and paves the way for future translational studies on assessments of sensorimotor impairments using our modeling approach

Significant indicators and determinants of happiness: Evidence from a UK survey and revealed by a data-driven systems modelling approach

This study aims to establish a quantitative relationship between lifestyle and happiness in the UK based on over 10,000 surveyed samples with 63 lifestyle variables from the UK Understanding Society Data. Transparent parametric models are built and a number of significant explanatory variables (lifestyle indicators) have been identified using a systems engineering modelling approach. Specifically; based on the traditional orthogonal forward regression (OFR) algorithm; the study introduces a new metrics; with which the impacts of lifestyle variables (and/or their interactions) can be quantitatively measured and identified one by one. These identified significant indicators provide a meaningful parsimonious representation of the relationship between happiness and lifestyle; revealing how happiness quantitatively depends on lifestyle; and how the lifestyle variables interactively affect happiness. For example; the quantitative results of a linear model indicate that lifestyle variables such as 'health'; 'income'; and 'retirement'; impacts happiness significantly. Furthermore; the results of a bilinear model show that some interaction variables such as 'retired' together with 'elder'; 'fair health' together with 'low-income' and so on; are significantly related to happiness

A Novel Approach for Modeling Neural Responses to Joint Perturbations Using the NARMAX Method and a Hierarchical Neural Network

The human nervous system is an ensemble of connected neuronal networks. Modeling and system identification of the human nervous system helps us understand how the brain processes sensory input and controls responses at the systems level. This study aims to propose an advanced approach based on a hierarchical neural network and non-linear system identification method to model neural activity in the nervous system in response to an external somatosensory input. The proposed approach incorporates basic concepts of Non-linear AutoRegressive Moving Average Model with eXogenous input (NARMAX) and neural network to acknowledge non-linear closed-loop neural interactions. Different from the commonly used polynomial NARMAX method, the proposed approach replaced the polynomial non-linear terms with a hierarchical neural network. The hierarchical neural network is built based on known neuroanatomical connections and corresponding transmission delays in neural pathways. The proposed method is applied to an experimental dataset, where cortical activities from ten young able-bodied individuals are extracted from electroencephalographic signals while applying mechanical perturbations to their wrist joint. The results yielded by the proposed method were compared with those obtained by the polynomial NARMAX and Volterra methods, evaluated by the variance accounted for (VAF). Both the proposed and polynomial NARMAX methods yielded much better modeling results than the Volterra model. Furthermore, the proposed method modeled cortical responded with a mean VAF of 69.35% for a three-step ahead prediction, which is significantly better than the VAF from a polynomial NARMAX model (mean VAF 47.09%). This study provides a novel approach for precise modeling of cortical responses to sensory input. The results indicate that the incorporation of knowledge of neuroanatomical connections in building a realistic model greatly improves the performance of system identification of the human nervous system