Time-Domain Analysis of Sensor-to-Sensor Transmissibility Operators with Application to Fault Detection.

In some applications, multiple measurements are available, but the driving input that gives rise to those outputs may be unknown. This raises the question as to whether it is possible to model the response of a subset of sensors based on the response of the remaining sensors without knowledge of the driving input. To address this issue, we develop time-domain sensor-to-sensor models that account for nonzero initial conditions. The sensor-to-sensor model is in the form of a transmissibility operator, that is, a rational function of the differentiation operator. What is essential in defining the transmissibility operator is that it must be independent of both the initial condition and inputs of the underlying system, which is assumed to be time-invariant. The development is carried out for both single-input, single-output and multi-input, multi-output transmissibility operators. These time-domain sensor-to-sensor models can be used for diagnostics and output prediction. We show that transmissibility operators may be unstable, noncausal, and of unknown order. Therefore, to facilitate system identification, we consider a class of models that can approximate transmissibility operators with these properties. This class of models consists of noncausal finite impulse response models based on a truncated Laurent expansion. These models are shown to approximate the Laurent expansion inside the annulus between the asymptotically stable pole of largest modulus and the unstable pole of smallest modulus. By delaying the measured pseudo output relative to the measured pseudo input, the identified finite impulse response model is a noncausal approximation of the transmissibility operator. The causal (backward-shift) part of the Laurent expansion is asymptotically stable since all of its poles are zero, while the noncausal (forward-shift) part of the Laurent expansion captures the unstable and noncausal components of the transmissibility operator. This dissertation also develops a time-domain framework for both single-input, single-output and multi-input, multi-output transmissibilities that account for nonzero initial conditions for both force-driven and displacement-driven structures. We show that motion transmissibilities in force-driven and displacement-driven structures are equal when the locations of the forces and prescribed displacements are identical.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113623/1/khaledfj_1.pd

A Fast Gradient Approximation for Nonlinear Blind Signal Processing

When dealing with nonlinear blind processing algorithms (deconvolution or post-nonlinear source separation), complex mathematical estimations must be done giving as a result very slow algorithms. This is the case, for example, in speech processing, spike signals deconvolution or microarray data analysis. In this paper, we propose a simple method to reduce computational time for the inversion of Wiener systems or the separation of post-nonlinear mixtures, by using a linear approximation in a minimum mutual information algorithm. Simulation results demonstrate that linear spline interpolation is fast and accurate, obtaining very good results (similar to those obtained without approximation) while computational time is dramatically decreased. On the other hand, cubic spline interpolation also obtains similar good results, but due to its intrinsic complexity, the global algorithm is much more slow and hence not useful for our purpose

A Postdramatic Composer in Search of a Dramatic Aesthetic, or, the Apotheosis and Decline of Andrew Lloyd Webber

Andrew Lloyd Webber has been associated with a type of musical the­ater that disregards the conventions of the character-driven musical play, offering, instead, a stream of impressive and loosely connected au­ral and visual images. His compositional method could be easily de­scribed as "postdramatic," prioritizing the audiovisual intensity of the individual dramatic moment, rather than its insertion into a coherent narrative structure. However, a closer reading of Lloyd Webber's musico-dramatic texts can reveal the composer's consistent effort to develop a more traditionally dramatic musical aesthetic. This experimentation with more dramatic models of musical composition produced Lloyd Webber's biggest commercial triumph, The Phantom of the Opera, but can also be considered responsible for his subsequent demise. The present paper will try to trace these developments in Lloyd Webber's composi­tional method, offering, at the same time, a sociological reading of his aesthetic that explains the reasons for the composer's vast popularity in postmodern culture as well as the reasons for his decline

Bayes meets Bach: applications of Bayesian statistics to audio restoration

Memoryless nonlinear distortion can be present in audio signals, from recording to reproduction: bad quality or amateurishly operated equipments, physically degraded media and low quality reproducing devices are some examples where nonlinearities can naturally appear. Another quite common defect in old recordings are the long pulses, caused in general by the reproduction of disks with deep scratches or severely degraded magnetic tapes. Such defects are characterized by an initial discontinuity in the waveform, followed by a low-frequency transient of long duration. In both cases audible artifacts can be created, causing an unpleasant experience to the listener. It is then important to develop techniques to mitigate such defects, having at hand only the degraded signal, in a way to recover the original signal. In this thesis, techniques to deal with both problems are presented: the restoration of nonlinearly degraded recordings is tackled in a Bayesian context, considering both autoregressive models and sparsity in the DCT domain for the original signal, as well as through a deterministic solution also based on sparsity; for the suppression of long pulses, a parametric approach is revisited with the addition of an efficient initialization procedure, and a nonparametric modeling via Gaussian process is also presented.Distorções não-lineares podem aparecer em sinais de áudio desde o momento da sua gravação até a posterior reprodução: equipamentos precários ou operados de maneira indevida, mídias fisicamente degradadas e baixa qualidade dos aparelhos de reprodução são somente alguns exemplos onde não-linearidades podem aparecer de modo natural. Outro defeito bastante comum em gravações antigas são os pulsos longos, em geral causados pela reprodução de discos com arranhões muito profundos ou fitas magnéticas severamente degradadas. Tais defeitos são caracterizados por uma descontinuidade inicial na forma de onda, seguida de um transitório de baixa frequência e longa duração. Em ambos os casos, artefatos auditivos podem ser criados, causando assim uma experiência ruim para o ouvinte. E importante então desenvolver técnicas para mitigar tais efeitos, tendo como base somente uma versão do sinal degradado, de modo a recuperar o sinal original não degradado. Nessa tese são apresentadas técnicas para lidar com esses dois problemas: o problema de restaurar gravações corrompidas com distorções não-lineares é abordado em um contexto bayesiano, considerando tanto modelos autorregressivos quanto de esparsidade no domínio da DCT para o sinal original, bem como por uma solução determinística também em usando esparsidade; para a supressão de pulsos longos, uma abordagem paramétrica é revisitada, junto com o acréscimo de um eficiente procedimento de inicialização, sendo também apresentada uma abordagem não-paramétricausando processos gaussianos

System Identification of Wrist Stiffness in Parkinson's Disease Patients

The purpose of this work is to investigate the characteristics of motor control systems in Parkinson's disease patients. ARMAX system identification was performed to identify the intrinsic and reflexive, the non-controllable and controllable, components of wrist stiffness, enabling a better understanding of the problems associated with Parkinson's disease. The results show that the intrinsic stiffness dynamics represent the vast majority of the total stiffness in the wrist joint and that the reflexive stiffness dynamics are attributable to a tremor commonly found in Parkinson's disease patients. It was found that Parkinsonian rigidity, a symptom of Parkinson's disease, interferes with the known and traditional methods for separating intrinsic and reflexive components. Resolving this problem could lead to early detection of Parkinson's disease in patients not exhibiting typical symptoms, analytical measurement of the severity of the disease, and as a testing mechanism for the effectiveness of new medicines

Methods for Model Complexity Reduction for the Nonlinear Calibration of Amplifiers Using Volterra Kernels

Volterra models allow modeling nonlinear dynamical systems, even though they require the estimation of a large number of parameters and have, consequently, potentially large computational costs. The pruning of Volterra models is thus of fundamental importance to reduce the computational costs of nonlinear calibration, and improve stability and speed, while preserving accuracy. Several techniques (LASSO, DOMP and OBS) and their variants (WLASSO and OBD) are compared in this paper for the experimental calibration of an IF amplifier. The results show that Volterra models can be simplified, yielding models that are 4–5 times sparser, with a limited impact on accuracy. About 6 dB of improved Error Vector Magnitude (EVM) is obtained, improving the dynamic range of the amplifiers. The Symbol Error Rate (SER) is greatly reduced by calibration at a large input power, and pruning reduces the model complexity without hindering SER. Hence, pruning allows improving the dynamic range of the amplifier, with almost an order of magnitude reduction in model complexity. We propose the OBS technique, used in the neural network field, in conjunction with the better known DOMP technique, to prune the model with the best accuracy. The simulations show, in fact, that the OBS and DOMP techniques outperform the others, and OBD, LASSO and WLASSO are, in turn, less efficient. A methodology for pruning in the complex domain is described, based on the Frisch–Waugh–Lovell (FWL) theorem, to separate the linear and nonlinear sections of the model. This is essential because linear models are used for equalization and cannot be pruned to preserve model generality vis-a-vis channel variations, whereas nonlinear models must be pruned as much as possible to minimize the computational overhead. This methodology can be extended to models other than the Volterra one, as the only conditions we impose on the nonlinear model are that it is feedforward and linear in the parameters

Repetitive control of electrical stimulation for tremor suppression

Tremor is a rapid uncontrollable back-and-forth movement of a body part often seen in patients with neurological conditions such as Multiple Sclerosis (MS) and Parkinson’s disease. This debilitating oscillation can be suppressed by applying functional electrical stimulation (FES) within a closedloop control system. However current implementations use classical control methods and have proved capable of only limited performance. This paper develops a novel application of repetitive control (RC) that exploits the capability of learning from experience to enable complete suppression of the tremor. The proposed control structure is applied to suppress tremor at the wrist via FES regulated co-contraction of wrist extensors/flexors. Experimental evaluation is performed using a validated wristrig and results are compared against classical feedback control designs to establish the efficacy of the approach