Spectral Analysis for Signal Detection and Classification : Reducing Variance and Extracting Features

Spectral analysis encompasses several powerful signal processing methods. The papers in this thesis present methods for finding good spectral representations, and methods both for stationary and non-stationary signals are considered. Stationary methods can be used for real-time evaluation, analysing shorter segments of an incoming signal, while non-stationary methods can be used to analyse the instantaneous frequencies of fully recorded signals. All the presented methods aim to produce spectral representations that have high resolution and are easy to interpret. Such representations allow for detection of individual signal components in multi-component signals, as well as separation of close signal components. This makes feature extraction in the spectral representation possible, relevant features include the frequency or instantaneous frequency of components, the number of components in the signal, and the time duration of the components. Two methods that extract some of these features automatically for two types of signals are presented in this thesis. One adapted to signals with two longer duration frequency modulated components that detects the instantaneous frequencies and cross-terms in the Wigner-Ville distribution, the other for signals with an unknown number of short duration oscillations that detects the instantaneous frequencies in a reassigned spectrogram. This thesis also presents two multitaper methods that reduce the influence of noise on the spectral representations. One is designed for stationary signals and the other for non-stationary signals with multiple short duration oscillations. Applications for the methods presented in this thesis include several within medicine, e.g. diagnosis from analysis of heart rate variability, improved ultrasound resolution, and interpretation of brain activity from the electroencephalogram

An Algorithm for the Continuous Morlet Wavelet Transform

This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet. The energy values of the Wavelet transform are compared with the power spectrum of the Fourier transform. Useful definitions for power spectra are given. The focus of the work is on simple measures to evaluate the transform with the Morlet wavelet in an efficient way. The use of the transform and the defined values is shown in some examples.Comment: 15 pages, 4 figures, revised for MSS

Développement d’une procédure non intrusive basée sur la propagation des ondes élastiques pour l’évaluation de l’état des structures en béton enfouies du réseau de distribution d’Hydro-Québec

Depuis l’automne 2011, des travaux de recherches ont été réalisés par le groupe de recherche en géotechnique de l’Université de Sherbrooke afin de développer une méthode d’inspection non-destructive permettant l’évaluation de l’état de dégradation du toit des structures enfouies du réseau de distribution d’Hydro-Québec (chambre de raccordement). En plus d’être non-destructive, la méthode développée se doit d’être réalisable depuis la surface du sol et donc ne pas nécessiter d’accès direct à la structure. Cette thèse explique en détail le processus de recherche réalisé depuis l’automne 2013 qui a mené au développement d’un outil permettant de faire l’inspection d’une structure souterraine à l’aide de l’étude de la propagation des ondes élastiques dans le sol. Premièrement, un survol de l’état des connaissances montre que les méthodes géophysiques peuvent offrir une alternative intéressante aux méthodes d’inspections traditionnelles. Cette revue montre également que la propagation des ondes élastiques peut être simulée à l’aide de différentes méthodes analytiques, semi-analytiques et numériques. Deuxièmement, il est montré que les algorithmes utilisés dans cette thèse permettent l’identification et la séparation dans le domaine vitesse-fréquence de différents groupes d’ondes présents dans divers types de signaux sismiques. Ces algorithmes permettent également le calcul de l’énergie et des vitesses de groupe et de phase des différents groupes d’ondes identifiés. Troisièmement, la méthode de la matrice de propagation et des simulations numériques en 2D montrent que l’énergie et les vitesses de propagation du mode fondamental des ondes de Rayleigh varient en fonction de la profondeur d’une structure souterraine. Il est notamment montré que la présence d’une structure souterraine agit comme un guide d’onde entrainant une variation importante de la vitesse de groupe près d’une fréquence nommée phase d’Airy. Des simulations numériques en 2D réalisées sur des structures dont la surface comporte des anomalies permet de montrer que la présence de ces dernières entraîne des variations importantes de l’énergie et des vitesses de propagations des ondes élastiques calculées à partir de la variation de l’accélération verticale mesurée à la surface du modèle. Ces observations ont mené à l’élaboration d’un protocole d’inspection qui a par la suite été testée sur de vraies structures construites sur le site expérimental de l’IREQ. Ces essais sur le site expérimental ont permis de confirmer que la profondeur et l’état de dégradation de la surface du toit d’une structure souterraine affectent l’énergie et la vitesse de propagation des ondes élastiques. Quatrièmement, des simulations numériques en 3D ont été réalisées afin d’améliorer le protocole d’inspection et d’évaluer l’effet de la présence du puits d’accès reliant la structure à la surface du terrain. Ces simulations ont permis de développer un nouveau protocole d’inspection et de montrer que la présence du puits d’accès n’empêche pas la détection d’anomalies présentes à la surface d’une structure. L’efficacité de ce nouveau protocole a également été validée en réalisant de nouveaux essais sur le site expérimental de l’IREQ. Finalement, il est montré que la présence d’un revêtement rigide à la surface du sol n’empêche pas la caractérisation du profil souterrain se trouvant sous un revêtement rigide lorsque la source se trouve directement en contact avec le sol

Real-time spectral modelling of audio for creative sound transformation

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

The application of auditory signal processing principles to the detection, tracking and association of tonal components in sonar.

A steady signal exerts two complementary effects on a noisy acoustic environment: one is to add energy, the other is to create order. The ear has evolved mechanisms to detect both effects and encodes the fine temporal detail of a stimulus in sequences of auditory nerve discharges. Taking inspiration from these ideas, this thesis investigates the use of regular timing for sonar signal detection. Algorithms that operate on the temporal structure of a received signal are developed for the detection of merchant vessels. These ideas are explored by reappraising three areas traditionally associated with power-based detection. First of all, a time-frequency display based on timing instead of power is developed. Rather than inquiring of the display, "How much energy has been measured at this frequency? ", one would ask, "How structured is the signal at this frequency? Is this consistent with a target? " The auditory-motivated zero crossings with peak amplitudes (ZCPA) algorithm forms the starting-point for this study. Next, matters related to quantitative system performance analysis are addressed, such as how often a system will fail to detect a signal in particular conditions, or how much energy is required to guarantee a certain probability of detection. A suite of optimal temporal receivers is designed and is subsequently evaluated using the same kinds of synthetic signal used to assess power-based systems: Gaussian processes and sinusoids. The final area of work considers how discrete components on a sonar signal display, such as tonals and transients, can be identified and organised according to auditory scene analysis principles. Two algorithms are presented and evaluated using synthetic signals: one is designed to track a tonal through transient events, and the other attempts to identify groups of comodulated tonals against a noise background. A demonstration of each algorithm is provided for recorded sonar signals

Towards Real-Time Non-Stationary Sinusoidal Modelling of Kick and Bass Sounds for Audio Analysis and Modification

Sinusoidal Modelling is a powerful and flexible parametric method for analysing and processing audio signals. These signals have an underlying structure that modern spectral models aim to exploit by separating the signal into sinusoidal, transient, and noise components. Each of these can then be modelled in a manner most appropriate to that component's inherent structure. The accuracy of the estimated parameters is directly related to the quality of the model's representation of the signal, and the assumptions made about its underlying structure. For sinusoidal models, these assumptions generally affect the non-stationary estimates related to amplitude and frequency modulations, and the type of amplitude change curve. This is especially true when using a single analysis frame in a non-overlapping framework, where biased estimates can result in discontinuities at frame boundaries. It is therefore desirable for such a model to distinguish between the shape of different amplitude changes and adapt the estimation of this accordingly. Intra-frame amplitude change can be interpreted as a change in the windowing function applied to a stationary sinusoid, which can be estimated from the derivative of the phase with respect to frequency at magnitude peaks in the DFT spectrum. A method for measuring monotonic linear amplitude change from single-frame estimates using the first-order derivative of the phase with respect to frequency (approximated by the first-order difference) is presented, along with a method of distinguishing between linear and exponential amplitude change. An adaption of the popular matching pursuit algorithm for refining model parameters in a segmented framework has been investigated using a dictionary comprised of sinusoids with parameters varying slightly from model estimates, based on Modelled Pursuit (MoP). Modelling of the residual signal using a segmented undecimated Wavelet Transform (segUWT) is presented. A generalisation for both the forward and inverse transforms, for delay compensations and overlap extensions for different lengths of Wavelets and the number of decomposition levels in an Overlap Save (OLS) implementation for dealing with convolution block-based artefacts is presented. This shift invariant implementation of the DWT is a popular tool for de-noising and shows promising results for the separation of transients from noise

Acoustic Condition Monitoring & Fault Diagnostics for Industrial Systems

Condition monitoring and fault diagnostics for industrial systems is required for cost reduction, maintenance scheduling, and reducing system failures. Catastrophic failure usually causes significant damage and may cause injury or fatality, making early and accurate fault diagnostics of paramount importance. Existing diagnostics can be improved by augmenting or replacing with acoustic measurements, which have proven advantages over more traditional vibration measurements including, earlier detection of emerging faults, increased diagnostic accuracy, remote sensors and easier setup and operation. However, industry adoption of acoustics remains in relative infancy due to vested confidence and reliance on existing measurement and, perceived difficulties with noise contamination and diagnostic accuracy. Researched acoustic monitoring examples typically employ specialist surface-mount transducers, signal amplification, and complex feature extraction and machine learning algorithms, focusing on noise rejection and fault classification. Usually, techniques are fine-tuned to maximise diagnostic performance for the given problem. The majority investigate mechanical fault modes, particularly Roller Element Bearings (REBs), owing to the mechanical impacts producing detectable acoustic waves. The first contribution of this project is a suitability study into the use of low-cost consumer-grade acoustic sensors for fault diagnostics of six different REB health conditions, comparing against vibration measurements. Experimental results demonstrate superior acoustic performance throughout but particularly at lower rotational speed and axial load. Additionally, inaccuracies caused by dynamic operational parameters (speed in this case), are minimised by novel multi-Support Vector Machine training. The project then expands on existing work to encompass diagnostics for a previously unreported electrical fault mode present on a Brush-Less Direct Current motor drive system. Commonly studied electrical faults, such as a broken rotor bar or squirrel cage, result from mechanical component damage artificially seeded and not spontaneous. Here, electrical fault modes are differentiated as faults caused by issues with the power supply, control system or software (not requiring mechanical damage or triggering intervention). An example studied here is a transient current instability, generated by non-linear interaction of the motor electrical parameters, parasitic components and digital controller realisation. Experimental trials successfully demonstrate real-time feature extraction and further validate consumer-grade sensors for industrial system diagnostics. Moreover, this marks the first known diagnosis of an electrically-seeded fault mode as defined in this work. Finally, approaching an industry-ready diagnostic system, the newly released PYNQ-Z2 Field Programmable Gate Array is used to implement the first known instance of multiple feature extraction algorithms that operate concurrently in continuous real-time. A proposed deep-learning algorithm can analyse the features to determine the optimum feature extraction combination for ongoing continuous monitoring. The proposed black-box, all-in-one solution, is capable of accurate unsupervised diagnostics on almost any application, maintaining excellent diagnostic performance. This marks a major leap forward from fine-tuned feature extraction performed offline for artificially seeded mechanical defects to multiple real-time feature extraction demonstrated on a spontaneous electrical fault mode with a versatile and adaptable system that is low-cost, readily available, with simple setup and operation. The presented concept represents an industry-ready all-in-one acoustic diagnostic solution, that is hoped to increase adoption of acoustic methods, greatly improving diagnostics and minimising catastrophic failures

Sparse Signal Representation of Ultrasonic Signals for Structural Health Monitoring Applications

Assessment of the integrity of structural components is of great importance for aerospace systems, land and marine transportation, civil infrastructures and other biological and mechanical applications. Guided waves (GWs) based inspections are an attractive mean for structural health monitoring. In this thesis, the study and development of techniques for GW ultrasound signal analysis and compression in the context of non-destructive testing of structures will be presented. In guided wave inspections, it is necessary to address the problem of the dispersion compensation. A signal processing approach based on frequency warping was adopted. Such operator maps the frequencies axis through a function derived by the group velocity of the test material and it is used to remove the dependence on the travelled distance from the acquired signals. Such processing strategy was fruitfully applied for impact location and damage localization tasks in composite and aluminum panels. It has been shown that, basing on this processing tool, low power embedded system for GW structural monitoring can be implemented. Finally, a new procedure based on Compressive Sensing has been developed and applied for data reduction. Such procedure has also a beneficial effect in enhancing the accuracy of structural defects localization. This algorithm uses the convolutive model of the propagation of ultrasonic guided waves which takes advantage of a sparse signal representation in the warped frequency domain. The recovery from the compressed samples is based on an alternating minimization procedure which achieves both an accurate reconstruction of the ultrasonic signal and a precise estimation of waves time of flight. Such information is used to feed hyperbolic or elliptic localization procedures, for accurate impact or damage localization

Exploiting prior knowledge during automatic key and chord estimation from musical audio

Chords and keys are two ways of describing music. They are exemplary of a general class of symbolic notations that musicians use to exchange information about a music piece. This information can range from simple tempo indications such as “allegro” to precise instructions for a performer of the music. Concretely, both keys and chords are timed labels that describe the harmony during certain time intervals, where harmony refers to the way music notes sound together. Chords describe the local harmony, whereas keys offer a more global overview and consequently cover a sequence of multiple chords. Common to all music notations is that certain characteristics of the music are described while others are ignored. The adopted level of detail depends on the purpose of the intended information exchange. A simple description such as “menuet”, for example, only serves to roughly describe the character of a music piece. Sheet music on the other hand contains precise information about the pitch, discretised information pertaining to timing and limited information about the timbre. Its goal is to permit a performer to recreate the music piece. Even so, the information about timing and timbre still leaves some space for interpretation by the performer. The opposite of a symbolic notation is a music recording. It stores the music in a way that allows for a perfect reproduction. The disadvantage of a music recording is that it does not allow to manipulate a single aspect of a music piece in isolation, or at least not without degrading the quality of the reproduction. For instance, it is not possible to change the instrumentation in a music recording, even though this would only require the simple change of a few symbols in a symbolic notation. Despite the fundamental differences between a music recording and a symbolic notation, the two are of course intertwined. Trained musicians can listen to a music recording (or live music) and write down a symbolic notation of the played piece. This skill allows one, in theory, to create a symbolic notation for each recording in a music collection. In practice however, this would be too labour intensive for the large collections that are available these days through online stores or streaming services. Automating the notation process is therefore a necessity, and this is exactly the subject of this thesis. More specifically, this thesis deals with the extraction of keys and chords from a music recording. A database with keys and chords opens up applications that are not possible with a database of music recordings alone. On one hand, chords can be used on their own as a compact representation of a music piece, for example to learn how to play an accompaniment for singing. On the other hand, keys and chords can also be used indirectly to accomplish another goal, such as finding similar pieces. Because music theory has been studied for centuries, a great body of knowledge about keys and chords is available. It is known that consecutive keys and chords form sequences that are all but random. People happen to have certain expectations that must be fulfilled in order to experience music as pleasant. Keys and chords are also strongly intertwined, as a given key implies that certain chords will likely occur and a set of given chords implies an encompassing key in return. Consequently, a substantial part of this thesis is concerned with the question whether musicological knowledge can be embedded in a technical framework in such a way that it helps to improve the automatic recognition of keys and chords. The technical framework adopted in this thesis is built around a hidden Markov model (HMM). This facilitates an easy separation of the different aspects involved in the automatic recognition of keys and chords. Most experiments reviewed in the thesis focus on taking into account musicological knowledge about the musical context and about the expected chord duration. Technically speaking, this involves a manipulation of the transition probabilities in the HMMs. To account for the interaction between keys and chords, every HMM state is actually representing the combination of a key and a chord label. In the first part of the thesis, a number of alternatives for modelling the context are proposed. In particular, separate key change and chord change models are defined such that they closely mirror the way musicians conceive harmony. Multiple variants are considered that differ in the size of the context that is accounted for and in the knowledge source from which they were compiled. Some models are derived from a music corpus with key and chord notations whereas others follow directly from music theory. In the second part of the thesis, the contextual models are embedded in a system for automatic key and chord estimation. The features used in that system are so-called chroma profiles, which represent the saliences of the pitch classes in the audio signal. These chroma profiles are acoustically modelled by means of templates (idealised profiles) and a distance measure. In addition to these acoustic models and the contextual models developed in the first part, durational models are also required. The latter ensure that the chord and key estimations attain specified mean durations. The resulting system is then used to conduct experiments that provide more insight into how each system component contributes to the ultimate key and chord output quality. During the experimental study, the system complexity gets gradually increased, starting from a system containing only an acoustic model of the features that gets subsequently extended, first with duration models and afterwards with contextual models. The experiments show that taking into account the mean key and mean chord duration is essential to arrive at acceptable results for both key and chord estimation. The effect of using contextual information, however, is highly variable. On one hand, the chord change model has only a limited positive impact on the chord estimation accuracy (two to three percentage points), but this impact is fairly stable across different model variants. On the other hand, the chord change model has a much larger potential to improve the key output quality (up to seventeen percentage points), but only on the condition that the variant of the model is well adapted to the tested music material. Lastly, the key change model has only a negligible influence on the system performance. In the final part of this thesis, a couple of extensions to the formerly presented system are proposed and assessed. First, the global mean chord duration is replaced by key-chord specific values, which has a positive effect on the key estimation performance. Next, the HMM system is modified such that the prior chord duration distribution is no longer a geometric distribution but one that better approximates the observed durations in an appropriate data set. This modification leads to a small improvement of the chord estimation performance, but of course, it requires the availability of a suitable data set with chord notations from which to retrieve a target durational distribution. A final experiment demonstrates that increasing the scope of the contextual model only leads to statistically insignificant improvements. On top of that, the required computational load increases greatly