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

Instationary modal Analysis for Impulse-type stimulated structures

In order to determine modal parameters, classical experimental modal analysis can be used in engineering application. This method finds a system frequency response function using fast Fourier Transform (FFT). The Fourier Transform is one type of global data analysis method. The frequency resolution is equal to the reciprocal of the total sample time. So applying the FFT is not suitable for any transient signal to reveal local characteristics. However, in modern manufacturing industries, processing forces are rapidly changing. The dynamic behavior may vary rapidly in a short time due to variations in the machining parameters and changes in boundary conditions. These nonlinear and non-stationary dynamic parameters are not constant during machining operations identification using FFT. In this research, an innovative transient signal analysis approach has been developed, which is based on an application of the least squares estimation. The proposed method provides transient information with high resolution and to identify the time-varying modal parameters during machining. Least squares estimation can be augmented with a sliding-window operation (SWLSE) to reveal the actual system dynamic behavior at any moment. The accuracy of this method depends on the window size, the noise ratio and the sampling rate etc. The estimation accuracy of modal parameters is discussed in this work. To examine the efficiency of the SWLSE method experimental tests are performed on a laboratory beam system and the results are compared with the classical experimental modal analysis (CEMA) method. The laboratory beam system is designed and assembled that the stiffness and damping ratio of the structure can be adjusted. Additionally, the proposed method is applied to the identification of the actual modal parameters of machine tools during machining operations. In another application, the proposed method provides also the process varied damping information in a process monitoring

Caractérisation de l'amortissement des structures complexes par la méthode de corrélation

Abstract : The thesis presents inverse correlation techniques able to measure accurately the damping loss factor of complex plane structures. In the first chapter, the state of the art gathering numerous local and global characterization methods is presented. In the second part of the chapter, various topics of direct interest to the thesis such as classical damping loss factor measurement techniques and the analytical solution based on the discrete general laminate model (GLM) are briefly discussed. In the second chapter, the inhomogeneous wave correlation (IWC) method based on the maximization of the correlation between an inhomogeneous wave and the measured displacement field as a function of the wave heading angle is revisited. A new variant that considers the exponential decay with distance from the excitation point in the inhomogeneous wave formulation is introduced. The purpose of introducing this variant is to improve the estimation of the damping loss factor. The validity of the proposed method is investigated numerically on flat thin structures and sandwich damped structures. The performance of the method related to the excitation point location and the size of the observation window are also investigated. A new Green's function-based model correlation (GFC) method able to estimate the equivalent elastic parameters of complex structures at different propagation angles is detailed in the third chapter. Contrary to the IWC method, the measured displacement field is correlated with a Green's function-based model. This approach is more adapted to describe the field near the excitation point and offers more stability in estimating the damping loss factor compared to previous methods. Several results, with simulated and measured data, are compared with an analytical discrete laminate model and show the accuracy of this technique to recover the damping loss factor of complex structures as function of the frequency and the heading angle. In the second part of the chapter, the impact of different excitation location on the estimation of the wavenumber and the damping loss factor is investigated. A spatial angular filter to rectify the estimation of the damping loss factor is introduced. In the fourth chapter, the image source method with an objective of improving the previous GFC method in the low frequency range and for lightly damped structures is introduced. The proposed method takes into account the reflection at boundaries which is ignored in the free field Green's function used in the previous chapter. The performance of the method is investigated for two types of boundary conditions: simply supported and free edges. The identified parameters of the numerical simulations are compared to the previous GFC method and to the analytical discrete laminate model.Le travail de thèse porte sur la caractérisation de l'amortissement des structures complexes par la méthode de corrélation. Dans le premier chapitre, un état de l'art rassemblant de nombreuses méthodes de caractérisations locales et globales est présenté. Dans la deuxième partie du chapitre, les méthodes de mesures expérimentales de l'amortissement et un modèle analytique de référence sont abordés. Dans le deuxième chapitre, la methode Inhomogeneous Wave Correlation (IWC) qui calcule la corrélation entre le champ de déplacement mesuré et une onde plane inhomogène est revisitée. Une nouvelle variante qui considère la décroissance exponentielle avec la distance du point d'excitation dans la formulation d'onde inhomogène est introduite. L'introduction de cette variante a pour but d'améliorer l'estimation de l'amortissement. La validité de la méthode proposée est étudiée numériquement sur des structures planes avec différents degrés de complexité. Les performances de la méthode en fonction la position du point d'excitation et de la taille de la fenêtre d'observation sont également étudiées. Un nouveau modèle de corrélation basé sur la fonction de Green permettant d'estimer les paramètres élastiques équivalents des structures complexes en fonction de l'angle de propagation est détaillé dans le troisième chapitre. Contrairement à la méthode IWC mentionnée ci-dessus, le champ de déplacement mesuré est désormais corrélé avec un modèle basé sur la fonction de Green. Cette dernière est plus adaptée pour décrire le champ proche du point d'excitation et offre plus de stabilité sur l'estimation de l'amortissement comparée aux méthodes précédentes. Plusieurs résultats, avec des données simulées et mesurées, sont comparés au modèle analytique et montrent la précision de cette technique pour estimer précisément l'amortissement des structures complexes en fonction de la fréquence et de l'angle de propagation des ondes. Dans la deuxième partie du chapitre, la performance de la méthode sur l'estimation de l'amortissement en fonction des différents points d'excitation est également étudiée et un filtre angulaire spatial est introduit pour améliorer le résultat. Dans le quatrième chapitre, la méthode des sources images qui a pour objectif d'améliorer l'estimation de l'amortissement en basses fréquences des structures faiblement amorties est introduite. Cette approche prend en compte les réflexions des ondes de flexion aux frontières. La performance de la méthode est étudiée sur deux types de conditions limites : bords simplement appuyés et bords libres. Le résultat est comparé à la méthode introduite dans le troisième chapitre ainsi qu'au modèle analytique GLM

Modal identification using optimization approach.

In this thesis, the modal identification problem is pursued using two different optimization approaches. The first approach is a deterministic optimization approach that minimizes the output model error in the time domain between a direct solution using the modal model and the measured response. Examples of single-input single-output identification are used to illustrate this method; it has been shown this approach is robust against noise and can be used to fine-tune the modal parameter, especially for the damping. The second approach is based on probabilistic optimization; the objective function is defined as the a posteriori probabilistic density of the parameters given observations/measurements. The conditional probability density is computed using the Bayesian theory of minimum-mean-square-error estimation. Examples of single-output under ambient excitation are simulated to demonstrate this approach. This methodology allows one to obtain not only the estimated parameters in the form of probabilistic mean but also the uncertainties in the form of covariance. The optimization approaches works though the minimization of an objective function which can be calculated from given set of modal/model parameters. Since there is no gradient or Hessian available for the objective functions defined in this thesis, two direct optimization methods: Nelder-Mead simplex and the Genetic Algorithm are adopted to search the minimum of defined objective functions and thus find the structural parameters. (Abstract shortened by UMI.)Dept. of Civil and Environmental Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .L52. Source: Masters Abstracts International, Volume: 44-03, page: 1437. Thesis (M.A.Sc.)--University of Windsor (Canada), 2005

High-resolution sinusoidal analysis for resolving harmonic collisions in music audio signal processing

Many music signals can largely be considered an additive combination of multiple sources, such as musical instruments or voice. If the musical sources are pitched instruments, the spectra they produce are predominantly harmonic, and are thus well suited to an additive sinusoidal model. However, due to resolution limits inherent in time-frequency analyses, when the harmonics of multiple sources occupy equivalent time-frequency regions, their individual properties are additively combined in the time-frequency representation of the mixed signal. Any such time-frequency point in a mixture where multiple harmonics overlap produces a single observation from which the contributions owed to each of the individual harmonics cannot be trivially deduced. These overlaps are referred to as overlapping partials or harmonic collisions. If one wishes to infer some information about individual sources in music mixtures, the information carried in regions where collided harmonics exist becomes unreliable due to interference from other sources. This interference has ramifications in a variety of music signal processing applications such as multiple fundamental frequency estimation, source separation, and instrumentation identification. This thesis addresses harmonic collisions in music signal processing applications. As a solution to the harmonic collision problem, a class of signal subspace-based high-resolution sinusoidal parameter estimators is explored. Specifically, the direct matrix pencil method, or equivalently, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) method, is used with the goal of producing estimates of the salient parameters of individual harmonics that occupy equivalent time-frequency regions. This estimation method is adapted here to be applicable to time-varying signals such as musical audio. While high-resolution methods have been previously explored in the context of music signal processing, previous work has not addressed whether or not such methods truly produce high-resolution sinusoidal parameter estimates in real-world music audio signals. Therefore, this thesis answers the question of whether high-resolution sinusoidal parameter estimators are really high-resolution for real music signals. This work directly explores the capabilities of this form of sinusoidal parameter estimation to resolve collided harmonics. The capabilities of this analysis method are also explored in the context of music signal processing applications. Potential benefits of high-resolution sinusoidal analysis are examined in experiments involving multiple fundamental frequency estimation and audio source separation. This work shows that there are indeed benefits to high-resolution sinusoidal analysis in music signal processing applications, especially when compared to methods that produce sinusoidal parameter estimates based on more traditional time-frequency representations. The benefits of this form of sinusoidal analysis are made most evident in multiple fundamental frequency estimation applications, where substantial performance gains are seen. High-resolution analysis in the context of computational auditory scene analysis-based source separation shows similar performance to existing comparable methods

Identification of natural frequency components of articulated flexible structures

M.S.Wayne J. Boo

Methodology for Correlating Experimental and Finite Element Modal Analyses on Valve Trains

The widespread use of finite element models in assessing system dynamics for noise, vibration, and harshness (NVH) evaluation has led to recognition of the need for improved procedures for correlating models to experimental results. This study develops and applies a methodology to correlate an experimental modal analysis with a finite element modal analysis of valve trains in IC-engines. A pre-test analysis procedure is employed to guide the execution of tests used in the correlation process. This approach improves the efficiency of the test process, ensuring that the test article is neither under nor over-instrumented. The test-analysis model (TAM) that results from the pre-test simulation provides a means to compare the test and the model both during the experimental approach and during the model updating process. The validity of the correlation methodology is demonstrated through its application on the valve train of a single overhead cam (SOHC) engine