Volterra Series Truncation and Kernel Estimation of Nonlinear Systems in the Frequency Domain

The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description. But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed. The new algorithm provides a powerful tool to determine which terms should be included in the Volterra series expansion and to estimate the kernels and thus solves the two problems all together. The estimated results are compared with those determined using the analytical expressions of the kernels to validate the method. To further evaluate the effectiveness of the method, the physical parameters of the system are also extracted from the measured kernels. Simulation studies demonstrates that the new approach not only can truncate the Volterra series expansion and estimate the kernels of a weakly nonlinear system, but also can indicate the applicability of the Volterra series analysis in a severely nonlinear system case

The wavelet-NARMAX representation : a hybrid model structure combining polynomial models with multiresolution wavelet decompositions

A new hybrid model structure combing polynomial models with multiresolution wavelet decompositions is introduced for nonlinear system identification. Polynomial models play an important role in approximation theory, and have been extensively used in linear and nonlinear system identification. Wavelet decompositions, in which the basis functions have the property of localization in both time and frequency, outperform many other approximation schemes and offer a flexible solution for approximating arbitrary functions. Although wavelet representations can approximate even severe nonlinearities in a given signal very well, the advantage of these representations can be lost when wavelets are used to capture linear or low-order nonlinear behaviour in a signal. In order to sufficiently utilise the global property of polynomials and the local property of wavelet representations simultaneously, in this study polynomial models and wavelet decompositions are combined together in a parallel structure to represent nonlinear input-output systems. As a special form of the NARMAX model, this hybrid model structure will be referred to as the WAvelet-NARMAX model, or simply WANARMAX. Generally, such a WANARMAX representation for an input-output system might involve a large number of basis functions and therefore a great number of model terms. Experience reveals that only a small number of these model terms are significant to the system output. A new fast orthogonal least squares algorithm, called the matching pursuit orthogonal least squares (MPOLS) algorithm, is also introduced in this study to determine which terms should be included in the final model

A Nonlinear Smoothing Algorithm for Chaotic and Non-Chaotic Time Series

A new NARMA based smoothing algorithm is introduced for chaotic and non-chaotic time series. The new algorithm employs a cross validation method to determine the smoother structure, requires very little user interaction and can be combined with wavelet thresholding to further enhance the noise reduction. Numerical examples are included to illustrate the application of the new algorithm

The Effects of Noise Reduction on the Prediction Accuracy of Time Series

A new iterative smoothing method based on the extended Kalman filter is introduced to smooth noisy chaotic time series. Two examples are given to illustrate the smoothing method. The smoothing method is then employed as a noise prior to identification and prediction. Three different prediction methods are introduced and the prediction performance is compared using three nonlinear examples. Superior predictive performance is obtained by the prediction method that employs the pre-processing step on the data

Time Series Prediction Using Support Vector Machines, the Orthogonal and the Regularised Orthogonal Least Squares Algorithms

Generalisation properties of support vector machines, orthogonal least squares and other variants of the orthogonal least squares algorithms are studied in this paper. In particular the zero-order regularised orthogonal least squares algorithm that has been proposed in (Chen et al. 1996) and the first order regularised orthogonal least squares algorithm which can be obtained using the cost function support vector machines will be discussed. Simple noisy sine and sinx functions are used to show that overfitting in the orthogonal least squares algorithm can be greatly reduced if the free parameters of the algorithm are selected properly. Results on three chaotic time series show that the orthiogonal least squares algorithm is slightly inferior compared to the other three algorithms. However, the strength of the orthogonal least squares algorithm lies in the ability to obtain a very concise or parsimonious model and the algorithm has the fewest number of free parameters compared to the other algorithms

Nonlinear Fisher Discriminant Analysis Using a Minimum Squared Error Cost Function and the Orthogonal Least Squares Algorithm.

The nonlinear discriminant function obtained using a minimum squared error cost function can be shown to be directly related to the nonlinear Fisher discriminant. With the squared error cost function, the orthogonal least squares algorithm can be used to find a parsimonious description of the nonlinear discriminant function. Two simple classification techniques will be introduced and tested on a number of real and artificial data sets. The results show that the new classification technique can often perform favourably with other state of the art classification techniques

A New Direct Approach of Computing Multi-Step Ahead Predictions for Nonlinear Models

A new direct approach of computing multi-step ahead predictions for nonlinear time series is introduced. The covariance of the parameter estimates associated with, and the mean squared k-step ahead prediction errors of the new direct approach are smaller than those obtained using the conventional direct approach. Numerical examples are included to illustrate the application of the new direct approach

Aeroelastic Model Structure Computation for Envelope Expansion

Structure detection is a procedure for selecting a subset of candidate terms, from a full model description, that best describes the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modeling may be of critical importance in the development of robust, parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion that may save significant development time and costs. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of non-linear aeroelastic systems. The LASSO minimises the residual sum of squares with the addition of an l(Sub 1) penalty term on the parameter vector of the traditional l(sub 2) minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudo-linear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. Applicability of this technique for model structure computation for the F/A-18 (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) Active Aeroelastic Wing project using flight test data is shown for several flight conditions (Mach numbers) by identifying a parsimonious system description with a high percent fit for cross-validated data

SyPRID sampler: A large-volume, high-resolution, autonomous, deep-ocean precision plankton sampling system

AbstractThe current standard for large-volume (thousands of cubic meters) zooplankton sampling in the deep sea is the MOCNESS, a system of multiple opening–closing nets, typically lowered to within 50m of the seabed and towed obliquely to the surface to obtain low-spatial-resolution samples that integrate across 10s of meters of water depth. The SyPRID (Sentry Precision Robotic Impeller Driven) sampler is an innovative, deep-rated (6000m) plankton sampler that partners with the Sentry Autonomous Underwater Vehicle (AUV) to obtain paired, large-volume plankton samples at specified depths and survey lines to within 1.5m of the seabed and with simultaneous collection of sensor data. SyPRID uses a perforated Ultra-High-Molecular-Weight (UHMW) plastic tube to support a fine mesh net within an outer carbon composite tube (tube-within-a-tube design), with an axial flow pump located aft of the capture filter. The pump facilitates flow through the system and reduces or possibly eliminates the bow wave at the mouth opening. The cod end, a hollow truncated cone, is also made of UHMW plastic and includes a collection volume designed to provide an area where zooplankton can collect, out of the high flow region. SyPRID attaches as a saddle-pack to the Sentry vehicle. Sentry itself is configured with a flight control system that enables autonomous survey paths to low altitudes. In its verification deployment at the Blake Ridge Seep (2160m) on the US Atlantic Margin, SyPRID was operated for 6h at an altitude of 5m. It recovered plankton samples, including delicate living larvae, from the near-bottom stratum that is seldom sampled by a typical MOCNESS tow. The prototype SyPRID and its next generations will enable studies of plankton or other particulate distributions associated with localized physico-chemical strata in the water column or above patchy habitats on the seafloor

FDG-PET imaging, EEG and sleep phenotypes as translational biomarkers for research in Alzheimer's disease

Peer reviewedPublisher PD