Space-time modeling of traffic flow

A key concern in transportation planning and traffic management is the ability to forecast traffic flows on a street network. Traffic flows forecasts can be transformed to obtain travel time estimates and then use these as input to travel demand models, dynamic route guidance and congestion management procedures. A variety of mathematical techniques have been proposed for modeling traffic flow on a street network. Briefly, the most widely used theories are: -Kinetic models based on partial differential equations that describe waves of different traffic densities, -deterministic models that use nonlinear equations for the estimation of different car routes, -large scale simulation models such as cellular automata and, -stochastic modeling of traffic density at distinct points in space. One problem with these approaches is that the traffic flow process is characterized by nonstationarities that cannot be taken into account by the vast majority of modeling strategies. However, recent advances in statistical modeling in fields such as econometrics or environmetrics enable us to overcome this problem. The aim of this work is to present how two statistical techniques, namely, vector autoregressive modeling and dynamic space-time modeling can be used to develop efficient and reliable forecasts of traffic flow. The former approach is encountered in the econometrics literature, whereas the later is mostly used in environmetrics. Recent advances in statistical methodology provide powerful tools for traffic flow description and forecasting. For a purely statistical approach to travel time prediction one may consult Rice and van Zwet (2002). In this work, the authors employ a time varying coefficients regression technique that can be easily implemented computationally, but is sensitive to nonstationarities and does not take into account traffic flow information from neighboring points in the network that can significantly improve forecasts. According to our approach, traffic flow measurements, that is count of vehicles and road occupancy obtained at constants time intervals through loop detectors located at various distinct points of a road network, form a multiple time series set. This set can be described by a vector autoregressive process that models each series as a linear combination of past observations of some (optimally selected) components of the vector; in our case the vector is comprised by the different measurement points of traffic flow. For a thorough technical discussion on vector autoregressive processes we refer to Lutkerpohl (1987), whereas a number of applications can be found in Ooms (1994). Nowadays, these models are easily implemented in commercial software like SAS or MATLAB; see for example LeSage (1999). The spatial distribution of the measurement locations and their neighboring relations cannot be incorporated in a vector autoregressive model. However, accounting for this information may optimize model fitting and provide insight into spatial correlation structures that evolve through time. This can be accomplished by applying space-time modeling techniques. The main difference of space-time models encountered in literature with the vector autoregressive ones lies in the inclusion of a weight matrix that defines the neighboring relations and places the appropriate restrictions. For some early references on space-time models, one could consult Pfeifer and Deutsch (1980 a,b); for a Bayesian approach, insensitive to nonstationarities we refer to Wikle, Berliner and Cressie (1998). In this work, we discuss how the space-time methodology can be implemented to traffic flow modeling. The aforementioned modeling strategies are applied in a subset of traffic flow measurements collected every 15 minutes through loop detectors at 74 locations in the city of Athens. A comparative study in terms of model fitting and forecasting accuracy is performed. Univariate time series models are also fitted in each measurement location in order to investigate the relation between a model's dimension and performance. References: LeSage J. P. (1999). Applied Econometrics using MATLAB. Manuscript, Dept. of Economics, University of Toronto Lutkerpohl H. (1987). Forecasting Aggregated Vector ARMA Processes. Lecture Notes in Economics and Mathematical Systems. Springer Verlag Berlin Heidelberg Ooms M. (1994). Empirical Vector Autoregressive Modeling. Springer Verlag Berlin Heidelberg Pfeifer P. E., and Deutsch S. J. (1980a). A three-stage iterative procedure for Space-Time Modeling. Technometrics, 22, 35-47 Pfeifer P. E., and Deutsch S. J. (1980b). Identification and Interpretation of First-Order Space-Time ARMA models. Technometrics, 22, 397-408 Rice J., and van Zwet E. (2002). A simple and effective method for predicting travel times on freeways. Manuscript, Dept. of Statistics, University of California at Berkeley Wikle C. K., Berliner L. M. and Cressie N. (1998). Hierarchical Bayesian space-time models. Environmental and Ecological Statistics, 5, 117-154

Spectral Modelling for Transformation and Separation of Audio Signals

The Short-Time Fourier Transform is still one of the most prominent time-frequency analysis techniques in many fields, due to its intuitive nature and computationally-optimised basis functions. Nevertheless, it is far from being the ultimate solution as it is plagued with a variety of assumptions and user-specific design choices, which result in a number of compromises. Numerous attempts have been made to circumvent its inevitable internal deficiencies, which include fixed time-frequency resolutions, static sample points, and highly biased outputs. However, its most important assumption, stationarity, is yet to be dealt with effectively. A new concept is proposed, which attempts to improve the credibility of the STFT results by allowing a certain degree of deviation from stationarity to be incorporated into the analysis. This novel approach utilises an ensemble of estimates instead of a single estimation in order to investigate the short-time phase behaviour of every frequency bin. The outcome is the definition of a quality measure, phase stability, that discriminates the "structured" from the "artefact" frequency components. This quality measure is then used in the framework of source separation as a single application example where it is possible to investigate its potential on the performance of the algorithm. Specifically, it was used in the spectral peak picking step of a numerical model-based source separation algorithm. It was found that the phase stability quality measure acts as an effective data reduction tool, which qualifies it as a more appropriate thresholding technique than the conventional methods. Based on this example, it is anticipated that this new method has great potential. Its ability to discriminate between "structured" and "noise" or edge effect/"artefacts" qualifies it as a promising new tool that can be added in the arsenal of the STFT modifications and used in the development of a hybrid super-STFT

Tracking Rhythmicity in Biomedical Signals using Sequential Monte Carlo methods

Cyclical patterns are common in signals that originate from natural systems such as the human body and man-made machinery. Often these cyclical patterns are not perfectly periodic. In that case, the signals are called pseudo-periodic or quasi-periodic and can be modeled as a sum of time-varying sinusoids, whose frequencies, phases, and amplitudes change slowly over time. Each time-varying sinusoid represents an individual rhythmical component, called a partial, that can be characterized by three parameters: frequency, phase, and amplitude. Quasi-periodic signals often contain multiple partials that are harmonically related. In that case, the frequencies of other partials become exact integer multiples of that of the slowest partial. These signals are referred to as multi-harmonic signals. Examples of such signals are electrocardiogram (ECG), arterial blood pressure (ABP), and human voice. A Markov process is a mathematical model for a random system whose future and past states are independent conditional on the present state. Multi-harmonic signals can be modeled as a stochastic process with the Markov property. The Markovian representation of multi-harmonic signals enables us to use state-space tracking methods to continuously estimate the frequencies, phases, and amplitudes of the partials. Several research groups have proposed various signal analysis methods such as hidden Markov Models (HMM), short time Fourier transform (STFT), and Wigner-Ville distribution to solve this problem. Recently, a few groups of researchers have proposed Monte Carlo methods which estimate the posterior distribution of the fundamental frequency in multi-harmonic signals sequentially. However, multi-harmonic tracking is more challenging than single-frequency tracking, though the reason for this has not been well understood. The main objectives of this dissertation are to elucidate the fundamental obstacles to multi-harmonic tracking and to develop a reliable multi-harmonic tracker that can track cyclical patterns in multi-harmonic signals

Signal separation of musical instruments: simulation-based methods for musical signal decomposition and transcription

This thesis presents techniques for the modelling of musical signals, with particular regard to monophonic and polyphonic pitch estimation. Musical signals are modelled as a set of notes, each comprising of a set of harmonically-related sinusoids. An hierarchical model is presented that is very general and applicable to any signal that can be decomposed as the sum of basis functions. Parameter estimation is posed within a Bayesian framework, allowing for the incorporation of prior information about model parameters. The resulting posterior distribution is of variable dimension and so reversible jump MCMC simulation techniques are employed for the parameter estimation task. The extension of the model to time-varying signals with high posterior correlations between model parameters is described. The parameters and hyperparameters of several frames of data are estimated jointly to achieve a more robust detection. A general model for the description of time-varying homogeneous and heterogeneous multiple component signals is developed, and then applied to the analysis of musical signals. The importance of high level musical and perceptual psychological knowledge in the formulation of the model is highlighted, and attention is drawn to the limitation of pure signal processing techniques for dealing with musical signals. Gestalt psychological grouping principles motivate the hierarchical signal model, and component identifiability is considered in terms of perceptual streaming where each component establishes its own context. A major emphasis of this thesis is the practical application of MCMC techniques, which are generally deemed to be too slow for many applications. Through the design of efficient transition kernels highly optimised for harmonic models, and by careful choice of assumptions and approximations, implementations approaching the order of realtime are viable.Engineering and Physical Sciences Research Counci

Final Research Report on Auto-Tagging of Music

The deliverable D4.7 concerns the work achieved by IRCAM until M36 for the “auto-tagging of music”. The deliverable is a research report. The software libraries resulting from the research have been integrated into Fincons/HearDis! Music Library Manager or are used by TU Berlin. The final software libraries are described in D4.5. The research work on auto-tagging has concentrated on four aspects: 1) Further improving IRCAM’s machine-learning system ircamclass. This has been done by developing the new MASSS audio features, including audio augmentation and audio segmentation into ircamclass. The system has then been applied to train HearDis! “soft” features (Vocals-1, Vocals-2, Pop-Appeal, Intensity, Instrumentation, Timbre, Genre, Style). This is described in Part 3. 2) Developing two sets of “hard” features (i.e. related to musical or musicological concepts) as specified by HearDis! (for integration into Fincons/HearDis! Music Library Manager) and TU Berlin (as input for the prediction model of the GMBI attributes). Such features are either derived from previously estimated higher-level concepts (such as structure, key or succession of chords) or by developing new signal processing algorithm (such as HPSS) or main melody estimation. This is described in Part 4. 3) Developing audio features to characterize the audio quality of a music track. The goal is to describe the quality of the audio independently of its apparent encoding. This is then used to estimate audio degradation or music decade. This is to be used to ensure that playlists contain tracks with similar audio quality. This is described in Part 5. 4) Developing innovative algorithms to extract specific audio features to improve music mixes. So far, innovative techniques (based on various Blind Audio Source Separation algorithms and Convolutional Neural Network) have been developed for singing voice separation, singing voice segmentation, music structure boundaries estimation, and DJ cue-region estimation. This is described in Part 6.EC/H2020/688122/EU/Artist-to-Business-to-Business-to-Consumer Audio Branding System/ABC D

Inpainting of Missing Audio Signal Samples

V oblasti zpracování signálů se v současné době čím dál více využívají tzv. řídké reprezentace signálů, tzn. že daný signál je možné vyjádřit přesně či velmi dobře aproximovat lineární kombinací velmi malého počtu vektorů ze zvoleného reprezentačního systému. Tato práce se zabývá využitím řídkých reprezentací pro rekonstrukci poškozených zvukových záznamů, ať už historických nebo nově vzniklých. Především historické zvukové nahrávky trpí zarušením jako praskání nebo šum. Krátkodobé poškození zvukových nahrávek bylo doposud řešeno interpolačními technikami, zejména pomocí autoregresního modelování. V nedávné době byl představen algoritmus s názvem Audio Inpainting, který řeší doplňování chybějících vzorků ve zvukovém signálu pomocí řídkých reprezentací. Zmíněný algoritmus využívá tzv. hladové algoritmy pro řešení optimalizačních úloh. Cílem této práce je porovnání dosavadních interpolačních metod s technikou Audio Inpaintingu. Navíc, k řešení optimalizačních úloh jsou využívány algoritmy založené na l1-relaxaci, a to jak ve formě analyzujícího, tak i syntetizujícího modelu. Především se jedná o proximální algoritmy. Tyto algoritmy pracují jak s jednotlivými koeficienty samostatně, tak s koeficienty v závislosti na jejich okolí, tzv. strukturovaná řídkost. Strukturovaná řídkost je dále využita taky pro odšumování zvukových nahrávek. Jednotlivé algoritmy jsou v praktické části zhodnoceny z hlediska nastavení parametrů pro optimální poměr rekonstrukce vs. výpočetní čas. Všechny algoritmy popsané v práci jsou na praktických příkladech porovnány pomocí objektivních metod odstupu signálu od šumu (SNR) a PEMO-Q. Na závěr je úspěšnost rekonstrukce poškozených zvukových signálů vyhodnocena.Recently, sparse representations of signals became very popular in the field of signal processing. Sparse representation mean that the signal is represented exactly or very well approximated by a linear combination of only a few vectors from the specific representation system. This thesis deals with the utilization of sparse representations of signals for the process of audio restoration, either historical or recent records. Primarily old audio recordings suffer from defects like crackles or noise. Until now, short gaps in audio signals were repaired by interpolation techniques, especially autoregressive modeling. Few years ago, an algorithm termed the Audio Inpainting was introduced. This algorithm solves the missing audio signal samples inpainting using sparse representations through the greedy algorithm for sparse approximation. This thesis aims to compare the state-of-the-art interpolation methods with the Audio Inpainting. Besides this, l1-relaxation methods are utilized for sparse approximation, while both analysis and synthesis models are incorporated. Algorithms used for the sparse approximation are called the proximal algorithms. These algorithms treat the coefficients either separately or with relations to their neighbourhood (structured sparsity). Further, structured sparsity is used for audio denoising. In the experimental part of the thesis, parameters of each algorithm are evaluated in terms of optimal restoration efficiency vs. processing time efficiency. All of the algorithms described in the thesis are compared using objective evaluation methods Signal-to-Noise ratio (SNR) and PEMO-Q. Finally, the overall conclusion and discussion on the restoration results is presented.

Modelling Instrumental Gestures and Techniques: A Case Study of Piano Pedalling

PhD ThesisIn this thesis we propose a bottom-up approach for modelling instrumental gestures and techniques, using piano pedalling as a case study. Pedalling gestures play a vital role in expressive piano performance. They can be categorised into di erent pedalling techniques. We propose several methods for the indirect acquisition of sustain-pedal techniques using audio signal analyses, complemented by the direct measurement of gestures with sensors. A novel measurement system is rst developed to synchronously collect pedalling gestures and piano sound. Recognition of pedalling techniques starts by using the gesture data. This yields high accuracy and facilitates the construction of a ground truth dataset for evaluating the audio-based pedalling detection algorithms. Studies in the audio domain rely on the knowledge of piano acoustics and physics. New audio features are designed through the analysis of isolated notes with di erent pedal e ects. The features associated with a measure of sympathetic resonance are used together with a machine learning classi er to detect the presence of legato-pedal onset in the recordings from a speci c piano. To generalise the detection, deep learning methods are proposed and investigated. Deep Neural Networks are trained using a large synthesised dataset obtained through a physical-modelling synthesiser for feature learning. Trained models serve as feature extractors for frame-wise sustain-pedal detection from acoustic piano recordings in a proposed transfer learning framework. Overall, this thesis demonstrates that recognising sustain-pedal techniques is possible to a high degree of accuracy using sensors and also from audio recordings alone. As the rst study that undertakes pedalling technique detection in real-world piano performance, it complements piano transcription methods. Moreover, the underlying relations between pedalling gestures, piano acoustics and audio features are identi ed. The varying e ectiveness of the presented features and models can also be explained by di erences in pedal use between composers and musical eras

A Parametric Sound Object Model for Sound Texture Synthesis

This thesis deals with the analysis and synthesis of sound textures based on parametric sound objects. An overview is provided about the acoustic and perceptual principles of textural acoustic scenes, and technical challenges for analysis and synthesis are considered. Four essential processing steps for sound texture analysis are identifi ed, and existing sound texture systems are reviewed, using the four-step model as a guideline. A theoretical framework for analysis and synthesis is proposed. A parametric sound object synthesis (PSOS) model is introduced, which is able to describe individual recorded sounds through a fi xed set of parameters. The model, which applies to harmonic and noisy sounds, is an extension of spectral modeling and uses spline curves to approximate spectral envelopes, as well as the evolution of parameters over time. In contrast to standard spectral modeling techniques, this representation uses the concept of objects instead of concatenated frames, and it provides a direct mapping between sounds of diff erent length. Methods for automatic and manual conversion are shown. An evaluation is presented in which the ability of the model to encode a wide range of di fferent sounds has been examined. Although there are aspects of sounds that the model cannot accurately capture, such as polyphony and certain types of fast modulation, the results indicate that high quality synthesis can be achieved for many different acoustic phenomena, including instruments and animal vocalizations. In contrast to many other forms of sound encoding, the parametric model facilitates various techniques of machine learning and intelligent processing, including sound clustering and principal component analysis. Strengths and weaknesses of the proposed method are reviewed, and possibilities for future development are discussed

Separation of musical sources and structure from single-channel polyphonic recordings

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