Identification of continuous-time models for nonlinear dynamic systems from discrete data

A new iOFR-MF (iterative orthogonal forward regression--modulating function) algorithm is proposed to identify continuous-time models from noisy data by combining the MF method and the iOFR algorithm. In the new method, a set of candidate terms, which describe different dynamic relationships among the system states or between the input and output, are first constructed. These terms are then modulated using the MF method to generate the data matrix. The iOFR algorithm is next applied to build the relationships between these modulated terms, which include detecting the model structure and estimating the associated parameters. The relationships between the original variables are finally recovered from the model of the modulated terms. Both nonlinear state-space models and a class of higher order nonlinear input–output models are considered. The new direct method is compared with the traditional finite difference method and results show that the new method performs much better than the finite difference method. The new method works well even when the measurements are severely corrupted by noise. The selection of appropriate MFs is also discussed

Modelling the Nonlinear Oscillations Due to Vertical Bouncing Using a Multi-Scale Restoring Force System Identification Method

Human vertical bouncing motion is studied using a system identification method. A multi-scale mathematical model is identified directly from real experimental data to characterise the nonlinear oscillation associated with the vertical bouncing. A new method which combines the restoring force surface (RFS) method and the iterative orthogonal forward regression (iOFR) algorithm is proposed to determine the model structure and estimate the associated parameters. Two types of sub-models are used to study the nonlinear oscillations in different scales. Results show that the model predicted outputs provide excellent predictions of the experimental data and the models are capable of reproducing the nonlinear oscillations in both time and frequency domain

Sparse, interpretable and transparent predictive model identification for healthcare data analysis

Data-driven modelling approaches play an indispensable role in analyzing and understanding complex processes. This study proposes a type of sparse, interpretable and transparent (SIT) machine learning model, which can be used to understand the dependent relationship of a response variable on a set of potential explanatory variables. An ideal candidate for such a SIT representation is the well-known NARMAX (nonlinear autoregressive moving average with exogenous inputs) model, which can be established from measured input and output data of the system of interest, and the final refined model is usually simple, parsimonious and easy to interpret. The performance of the proposed SIT models is evaluated through two real healthcare datasets

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

Structure optimisation of input layer for feed-forward NARX neural network

This paper presents an optimization method for reducing the number of input channels and the complexity of the feed-forward NARX neural network (NN) without compromising the accuracy of the NN model. By utilizing the correlation analysis method, the most significant regressors are selected to form the input layer of the NN structure. Applications of vehicle handling and ride model identification are presented in this paper to demonstrate the optimization technique. The optimal input layer structure and the optimal number of neurons for the NN models are investigated and the results show that the optimised NN model requires significantly less coefficients and training time while maintains high simulation accuracy compared with that of the unoptimised model

Estimation and tracking of rapidly time-varying broadband acoustic communication channels

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2006This thesis develops methods for estimating wideband shallow-water acoustic communication channels. The very shallow water wideband channel has three distinct features: large dimension caused by extensive delay spread; limited number of degrees of freedom (DOF) due to resolvable paths and inter-path correlations; and rapid fluctuations induced by scattering from the moving sea surface. Traditional LS estimation techniques often fail to reconcile the rapid fluctuations with the large dimensionality. Subspace based approaches with DOF reduction are confronted with unstable subspace structure subject to significant changes over a short period of time. Based on state-space channel modeling, the first part of this thesis develops algorithms that jointly estimate the channel as well as its dynamics. Algorithms based on the Extended Kalman Filter (EKF) and the Expectation Maximization (EM) approach respectively are developed. Analysis shows conceptual parallels, including an identical second-order innovation form shared by the EKF modification and the suboptimal EM, and the shared issue of parameter identifiability due to channel structure, reflected as parameter unobservability in EKF and insufficient excitation in EM. Modifications of both algorithms, including a two-model based EKF and a subspace EM algorithm which selectively track dominant taps and reduce prediction error, are proposed to overcome the identifiability issue. The second part of the thesis develops algorithms that explicitly find the sparse estimate of the delay-Doppler spread function. The study contributes to a better understanding of the channel physical constraints on algorithm design and potential performance improvement. It may also be generalized to other applications where dimensionality and variability collide.Financial support for this thesis research was provided by the Office of Naval Research and the WHOI Academic Program Office