4th International Conference on Acoustics and Vibration

Huajiang Ouyang received BEng in Engineering Mechanics in 1982, MSc (MEng) in Solid Mechanics in 1985, and PhD in Structural Engineering in 1989, from Dalian University of Technology, China. He is now a Professor of Structural Dynamics and Control in the School of Engineering, University of Liverpool, and also School Director of Postgraduate Research.
Prof Ouyang is a Royal Academy of Engineering and Leverhulme Trust Senior Research Fellow in 2009-2010. He is a Fellow of the Institute of Physics and was Chair of the Applied Mechanics Group. He is also a Subject Editor of Journal of Sound and Vibration and European Region Editor of International Journal of Vehicle Noise and Vibration.
His current interests are structural dynamics and vibration control, moving-load dynamics, structural identification, friction-induced vibration such as brake squeal or in bolt joints, and uncertainty analysis.

Machines and structures suffer degradation and even damage during services. As a result, their geometric and/or material properties may deviate from their initial designed values. It is very useful to be able to modify a machine/structure to restore its original health or acquire new desirable properties. Structural modifications for good dynamic performance have been studied by many researchers and are a topic of this talk.
Structural modifications are a subject of inverse analysis and difficult to implement on real structures. The Dynamics and Control Research Group at the University of Liverpool has developed various methods for structural modifications. One methodology is based on measured receptances for assigning frequencies and modes. The method does not rely on or need the theoretical model of the machine/structure under investigation and thus avoids the inherent modelling errors of the machine/structure. Receptance values at only a few locations are needed. The method is first validated on a five-degree-of-freedom lumped-parameter laboratory structure and then applied to a real structure (a linear feeder used in food processing industry). Both desirable frequencies and modes are realised satisfactorily.
It is well known that although structural modifications can successfully assign some frequencies and modes, they also cause other unassigned frequencies and modes to change. This phenomenon is called spill-over and is often undesirable. A new method is developed to make partial assignment of frequencies (leaving other frequencies unchanged). It is also capable of maintaining the configuration of the original structure, that is, the structure of the mass and stiffness matrices remains unchanged after the modifications. It is believed that this is the first time that structural modifications for partial frequency assignment have been achieved in theory. Numerical examples are presented to demonstrate its effectiveness.

Ali Mohammad-Djafari received the B.Sc. degree in electrical engineering from Polytechnic of Teheran, in 1975, the diploma degree (M.Sc.) from Ecole Supérieure d'Electricit(SUPELEC), Gif sur Yvette, France, in 1977, the "Docteur-Ingénieur" (Ph.D.) degree and "Doctorat d'Etat" in Physics, from the University of Paris Sud 11 (UPS), Orsay, France, respectively in 1981 and 1987. He was Assistant Professor at UPS for two years (1981-1983). Since 1984, he has a permanent position at "Centre National de la Recherche Scientifique (CNRS)" and works at "Laboratoire des signaux et systèmes (L2S)" at SUPELEC. He was a visiting Associate Professor at University of Notre Dame, Indiana, USA during 1997-1998. From 1998 to 2002, he has been at the head of Signal and Image Processing division at this laboratory. Presently, he is "Directeur de recherche" and his main scientific interests are in developing new probabilistic methods based on Bayesian inference, Information Theory and Maximum Entropy approaches for Inverse Problems in general in all aspects of data processing, and more specifically in imaging and vision: image reconstruction, signal and image deconvolution, blind source separation, sources localization, data fusion, multi and hyper spectral image segmentation. The main application domains of his interests are Computed Tomography (X rays, PET, SPECT, MRI, microwave, ultrasound and eddy current imaging) either for medical imaging or for non destructive testing (NDT) in industry, multivariate and multi dimensional data, signal and image processing, data mining, clustering, classification and machine learning methods for biological or medical applications.
He has supervised more than 20 Ph.D. Thesis, more than 10 Post-doc research activities and more than 50 M.Sc. Student research projects. In 2013, he was supervising 6 Ph.D. Thesis where four graduated successfully. He has more than 40 full journal papers and more than 200 papers in national and international conferences. He has organized or coorganized about 10 international workshops and conferences. He has been expert for a great number of French national and international projects. Since 1988 he has many teaching activities in M.Sc. and Ph.D. Level in SUPELEC, University of Paris sud, ENSTA and Ecole centrale de Paris.
He also participated and managed many industrial contracts with many French national industries such as EDF, RENAULT and THALES and great research institutions such as CEA, INSERM, INRIA as well as the regional (such as Digiteo), national (such as ANR) and European projects (such as ERASYSBIO).
For an overview and acces to more details of his activities and publications, please see his web page:
http://djafari.free.fr for general, http://djafari.free.fr/news.htm
for news and activities and
http://publicationslist.org/djafarie for the list of publications.

In this tutorial, first the problem of source localization is considered as an inverse problem of spatially varying deconvolution and different methods of regularization are investigated. In particular the Least Squares (LS) methods subject to the minimum L0 or L1-norm are presented. Then, to push further the limitations of the deterministic methods which need, for example the prior knowledge of the number of sources or the regularization parameter, the Bayesian estimation approach is presented.

An important step in the Bayesian approach is the assignment of the prior laws to noise and to the desired solution of the inverse problem. When this step is done appropriately, the expression of the posterior law can be obtained and used to do inference about the unknowns. Two point estimators are commonly used: the Maximum A Posteriori (MAP) and the Expected A Posteriori (EAP). In this tutorial, two classes of heavy tailed prior laws are considered: Generalized Gaussian (GG) and the Student-t or Cauchy distributions. The corresponding Bayesian methods are implemented and compared to the classical Beam-Forming (BF), CLEAN, Minimum Norm (MN) LS or Quadratic Regularization (Tikhonov) or Sparsity enforcing based methods.

Between the advantages of the Bayesian framework, we can mention the possibility to account for the approximation errors. As an example, we will see how the near-field propagation model which is a spatially variant Point Spread Function (PSF) convolution can be approximated by a far field model which is a fixed PSF convolution which can be computed via Fast Fourier Transform (FFT). However, this approximation generate errors on the predicted data which is spatially variant and this has to be accounted for during the inversion method. We will see how the Bayesian framework can handle this with a non stationary Gaussian
model for these errors where we need to estimate the spatially variant variances simultaneously. Inverse Gamma priors are assigned to these unknown variances which are conjugate priors for the Gaussian probability laws.

At the end, we give some details of a Bayesian method which accounts for the spatial variability of the observation predicting errors via a non stationarity Gaussian probability model and for the sparsity of the acoustic sources spatial distribution. This last property is modeled via a Student-t probability law which can be modeled in a hierarchical way through its Infinite Gaussian Mixture (IGM) equivalence.
Finally, to propose a non supervised inversion and source localization method a Variational Bayesian Approximation (VBA) computational method is presented and its performances are compared to more classical deterministic or Bayesian methods.