A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems

Dynamical epidemic suppression using stochastic prediction and control

We consider the effects of noise on a model of epidemic outbreaks, where the outbreaks appear. randomly. Using a constructive transition approach that predicts large outbreaks, prior to their occurrence, we derive an adaptive control. scheme that prevents large outbreaks from occurring. The theory inapplicable to a wide range of stochastic processes with underlying deterministic structure.Comment: 14 pages, 6 figure

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

The contribution of organisational factors to vicarious trauma in mental health professionals: a systematic review and narrative synthesis

Background: The negative impact of trauma work has been well documented in mental health professionals. There are three main phenomena used to describe these effects: Secondary Traumatic Stress (STS), Vicarious Trauma (VT) and Compassion Fatigue (CF). To date, the majority of research has focused on the contribution of individual level factors. However, it is imperative to also understand the role of organizational factors. Objectives: This review examines the role of organizational factors in ameliorating or preventing STS, VT, and CF in mental health professionals. We further aimed to identify specific elements of these factors which are perceived to be beneficial and/or detrimental in mitigating against the effects of STS, VT, and CF. Method: Studies were identified by searching the electronic databases Medline, PsycINFO, Embase, Web of Science and SCOPUS with final searches taking place on 10 March 2021. Results: Twenty-three quantitative studies, eight qualitative studies, and five mixed methods studies were included in the final review. A narrative synthesis was conducted to analyse the findings. The results of the review highlight the importance of regular supervision within supportive supervisory relationships, strong peer support networks, and balanced and diverse caseloads. The value of having an organizational culture which acknowledges and validates the existence of STS was also imperative. Conclusions: Organizations have an ethical responsibility to support the mental health professionals they employ and provide a supportive environment which protects them against STS. This review provides preliminary evidence for the types of support that should be offered and highlights the gaps in the literature and where future research should be directed. Further research is needed to evaluate which strategies–and under what conditions–best ameliorate and prevent STS

Generalised coherent point drift for group-wise registration of multi-dimensional point sets

In this paper we propose a probabilistic approach to group-wise registration of unstructured high-dimensional point sets. We focus on registration of generalised point sets which encapsulate both the positions of points on surface boundaries and corresponding normal vectors describing local surface geometry. Richer descriptions of shape can be especially valuable in applications involving complex and intricate variations in geometry, where spatial position alone is an unreliable descriptor for shape registration. A hybrid mixture model combining Student’s t and Von-Mises-Fisher distributions is proposed to model position and orientation components of the point sets, respectively. A group-wise rigid and non-rigid registration framework is then formulated on this basis. Two clinical data sets, comprising 27 brain ventricle and 15 heart shapes, were used to assess registration accuracy. Significant improvement in accuracy and anatomical validity of the estimated correspondences was achieved using the proposed approach, relative to state-of-the-art point set registration approaches, which consider spatial positions alone

Improved model identification for non-linear systems using a random subsampling and multifold modelling (RSMM) approach

In non-linear system identification, the available observed data are conventionally partitioned into two parts: the training data that are used for model identification and the test data that are used for model performance testing. This sort of 'hold-out' or 'split-sample' data partitioning method is convenient and the associated model identification procedure is in general easy to implement. The resultant model obtained from such a once-partitioned single training dataset, however, may occasionally lack robustness and generalisation to represent future unseen data, because the performance of the identified model may be highly dependent on how the data partition is made. To overcome the drawback of the hold-out data partitioning method, this study presents a new random subsampling and multifold modelling (RSMM) approach to produce less biased or preferably unbiased models. The basic idea and the associated procedure are as follows. First, generate K training datasets (and also K validation datasets), using a K-fold random subsampling method. Secondly, detect significant model terms and identify a common model structure that fits all the K datasets using a new proposed common model selection approach, called the multiple orthogonal search algorithm. Finally, estimate and refine the model parameters for the identified common-structured model using a multifold parameter estimation method. The proposed method can produce robust models with better generalisation performance

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