Modelling and identification of non-linear deterministic systems in the delta-domain

This paper provides a formulation for using the delta-operator in the modelling of non-linear systems. It is shown that a unique representation of a deterministic non-linear auto-regressive with exogenous input (NARX) model can be obtained for polynomial basis functions using the delta-operator and expressions are derived to convert between the shift- and delta- domain. A delta-NARX model is applied to the identification of a test problem (a Van-der-Pol oscillator): a comparison is made with the standard shift operator non-linear model and it is demonstrated that the delta-domain approach improves the numerical properties of structure detection, leads to a parsimonious description and provides a model that is closely linked to the continuous-time non-linear system in terms of both parameters and structure

Maximum-likelihood estimation of delta-domain model parameters from noisy output signals

Fast sampling is desirable to describe signal transmission through wide-bandwidth systems. The delta-operator provides an ideal discrete-time modeling description for such fast-sampled systems. However, the estimation of delta-domain model parameters is usually biased by directly applying the delta-transformations to a sampled signal corrupted by additive measurement noise. This problem is solved here by expectation-maximization, where the delta-transformations of the true signal are estimated and then used to obtain the model parameters. The method is demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast

Adaptive cancelation of self-generated sensory signals in a whisking robot

Sensory signals are often caused by one's own active movements. This raises a problem of discriminating between self-generated sensory signals and signals generated by the external world. Such discrimination is of general importance for robotic systems, where operational robustness is dependent on the correct interpretation of sensory signals. Here, we investigate this problem in the context of a whiskered robot. The whisker sensory signal comprises two components: one due to contact with an object (externally generated) and another due to active movement of the whisker (self-generated). We propose a solution to this discrimination problem based on adaptive noise cancelation, where the robot learns to predict the sensory consequences of its own movements using an adaptive filter. The filter inputs (copy of motor commands) are transformed by Laguerre functions instead of the often-used tapped-delay line, which reduces model order and, therefore, computational complexity. Results from a contact-detection task demonstrate that false positives are significantly reduced using the proposed scheme

World statistics drive learning of cerebellar internal models in adaptive feedback control : a case study using the optokinetic reflex

The cerebellum is widely implicated in having an important role in adaptive motor control. Many of the computational studies on cerebellar motor control to date have focused on the associated architecture and learning algorithms in an effort to further understand cerebellar function. In this paper we switch focus to the signals driving cerebellar adaptation that arise through different motor behavior. To do this, we investigate computationally the contribution of the cerebellum to the optokinetic reflex (OKR), a visual feedback control scheme for image stabilization. We develop a computational model of the adaptation of the cerebellar response to the world velocity signals that excite the OKR (where world velocity signals are used to emulate head velocity signals when studying the OKR in head-fixed experimental laboratory conditions). The results show that the filter learnt by the cerebellar model is highly dependent on the power spectrum of the colored noise world velocity excitation signal. Thus, the key finding here is that the cerebellar filter is determined by the statistics of the OKR excitation signal

Longitudinal vehicle dynamics : a comparison of physical and data-driven models under large-scale real-world driving conditions

Mathematical models of vehicle dynamics will form essential components of future autonomous vehicles. They may be used within inverse or forward control loops, or within predictive learning systems. Often, nonlinear physical models are used in this context, which, though conceptually simple (especially for decoupled, longitudinal dynamics), may be computationally costly to parameterise and also inaccurate if they omit vehicle-specific dynamics. In this study we sought to determine the relative merits of a commonly used nonlinear physical model of vehicle dynamics versus data-driven models in large-scale real-world driving conditions. To this end, we compared the performance of a standard nonlinear physical model with a linear state-space model and a neural network model. The large-scale experimental data was obtained from two vehicles; a Lancia Delta car and a Jeep Renegade sport utility vehicle. The vehicles were driven on regular, public roads, during normal human driving, across a range of road gradients. Both data-driven models outperformed the physical model. The neural network model performed best for both vehicles; the state-space model performed almost as well as the neural network for the Lancia Delta, but fell short for the Jeep Renegade whose dynamics were more strongly nonlinear. Our results suggest that the linear data-driven model gives a good trade-off in accuracy and simplicity, whilst the neural network model is most accurate and is extensible to more nonlinear operating conditions, and finally that the widely used physical model may not be the best choice for control design

Operator-Based Truncation Scheme Based on the Many-Body Fermion Density Matrix

In [S. A. Cheong and C. L. Henley, cond-mat/0206196 (2002)], we found that the many-particle eigenvalues and eigenstates of the many-body density matrix $\rho_B$ of a block of $B$ sites cut out from an infinite chain of noninteracting spinless fermions can all be constructed out of the one-particle eigenvalues and one-particle eigenstates respectively. In this paper we developed a statistical-mechanical analogy between the density matrix eigenstates and the many-body states of a system of noninteracting fermions. Each density matrix eigenstate corresponds to a particular set of occupation of single-particle pseudo-energy levels, and the density matrix eigenstate with the largest weight, having the structure of a Fermi sea ground state, unambiguously defines a pseudo-Fermi level. We then outlined the main ideas behind an operator-based truncation of the density matrix eigenstates, where single-particle pseudo-energy levels far away from the pseudo-Fermi level are removed as degrees of freedom. We report numerical evidence for scaling behaviours in the single-particle pseudo-energy spectrum for different block sizes $B$ and different filling fractions \nbar. With the aid of these scaling relations, which tells us that the block size $B$ plays the role of an inverse temperature in the statistical-mechanical description of the density matrix eigenstates and eigenvalues, we looked into the performance of our operator-based truncation scheme in minimizing the discarded density matrix weight and the error in calculating the dispersion relation for elementary excitations. This performance was compared against that of the traditional density matrix-based truncation scheme, as well as against a operator-based plane wave truncation scheme, and found to be very satisfactory.Comment: 22 pages in RevTeX4 format, 22 figures. Uses amsmath, amssymb, graphicx and mathrsfs package

Sparse Bayesian Nonlinear System Identification using Variational Inference

IEEE Bayesian nonlinear system identification for one of the major classes of dynamic model, the nonlinear autoregressive with exogenous input (NARX) model, has not been widely studied to date. Markov chain Monte Carlo (MCMC) methods have been developed, which tend to be accurate but can also be slow to converge. In this contribution, we present a novel, computationally efficient solution to sparse Bayesian identification of the NARX model using variational inference, which is orders of magnitude faster than MCMC methods. A sparsity-inducing hyper-prior is used to solve the structure detection problem. Key results include: 1. successful demonstration of the method on low signal-to-noise ratio signals (down to 2dB); 2. successful benchmarking in terms of speed and accuracy against a number of other algorithms: Bayesian LASSO, reversible jump MCMC, forward regression orthogonalisation, LASSO and simulation error minimisation with pruning; 3. accurate identification of a real world system, an electroactive polymer; and 4. demonstration for the first time of numerically propagating the estimated nonlinear time-domain model parameter uncertainty into the frequency-domain

An analysis of TB epidemiology from a primary care perspective using the General Practice Research Database

Background: TB is a growing public health problem. Most research focuses on secondary care. This, the largest study of TB in primary care to date, aims to investigate aspects of TB epidemiology by examining the role of primary care in case detection, management and outcomes. Methods: Using data from the General Practice Research Database a case-control and a self-controlled study were undertaken to investigate TB pre-diagnosis and a self-controlled and cohort study to describe and quantify TB morbidity and mortality post-diagnosis. Results: 3032 TB cases and 15,160 matched controls were analysed. The pre-TB studies showed that cases had higher consultation rates, consulted on multiple occasions often with recurrent respiratory infections and experienced a diagnostic delay of up-to-4months. Strengths of association between symptoms, respiratory diseases and TB were also noted. The case-control study also showed that male gender, smoking and chronic disease were independent risk factors for TB. Post-TB, patients who survived at least 18months had no increase in morbidity but TB led to a slight increase in all-cause mortality (adjusted HR:1.53) and a case fatality rate at one year of 6.5%. Mortality was highest in the first year post-diagnosis. Undiagnosed pulmonary TB, older age, male gender, malignancy and chronic disease were all associated with a worse prognosis. At 10 years, TB cases had a 70% chance of survival compared to 79% for patients’ without-TB. Conclusions: Diagnosing TB in primary care remains a challenge due to its variable and non-specific nature but a window of opportunity exists from 4months following first presentation. Combining knowledge of the strength of association between TB, its symptoms and respiratory diagnoses, TB risk factors and raising awareness of newer investigations and local referral processes could help GPs make an earlier diagnosis. This research indicates a need for improved patient and professional awareness of TB and emphasises the need for earlier diagnosis

A temporal-to-spatial neural network for classification of hand movements from electromyography data

Deep convolutional neural networks (CNNs) are appealing for the purpose of classification of hand movements from surface electromyography (sEMG) data because they have the ability to perform automated person-specific feature extraction from raw data. In this paper, we make the novel contribution of proposing and evaluating a design for the early processing layers in the deep CNN for multichannel sEMG. Specifically, we propose a novel temporal-to-spatial (TtS) CNN architecture, where the first layer performs convolution separately on each sEMG channel to extract temporal features. This is motivated by the idea that sEMG signals in each channel are mediated by one or a small subset of muscles, whose temporal activation patterns are associated with the signature features of a gesture. The temporal layer captures these signature features for each channel separately, which are then spatially mixed in successive layers to recognise a specific gesture. A practical advantage is that this approach also makes the CNN simple to design for different sample rates. We use NinaPro database 1 (27 subjects and 52 movements + rest), sampled at 100 Hz, and database 2 (40 subjects and 40 movements + rest), sampled at 2 kHz, to evaluate our proposed CNN design. We benchmark against a feature-based support vector machine (SVM) classifier, two CNNs from the literature, and an additional standard design of CNN. We find that our novel TtS CNN design achieves 66.6% per-class accuracy on database 1, and 67.8% on database 2, and that the TtS CNN outperforms all other compared classifiers using a statistical hypothesis test at the 2% significance level