230 research outputs found
Nonlinear system identification using wavelet based SDP models
System identification has played an increasingly dominant role in a wide range of engineering applications. While linear system's theory is mature, nonlinear system identification remains an open research area in recent years. This thesis develops a new, efficient and systematic approach to the identification of nonlinear dynamic systems using wavelet based State Dependent Parameter (SDP) models, from structure determination to parameter estimation. In this approach, the system's nonlinearities are analysed and effectively represented by a SDP model structure in the form of wavelets. This provides a computationally efficient tool to open up the `black-box', offering valuable insights into the system's dynamics. In this thesis, 1-dimensional (1-D) approach is first developed based on a conventional SDP model structure which relies on a single state variable dependency. It is then extended into a multi-dimensional approach in order to solve the identification problem of systems with significant multi-variable dependence nonlinear dynamics. Here, parametrically efficient nonlinear model is obtained by the application of an effective model structure selection algorithm based on the Predicted Residual Sums of Squares (PRESS) criterion in conjunction with Orthogonal Decomposition (OD) to avoid any ill-conditioning problems associated with the parameter estimation. This thesis also investigates the aspects of noise, stability and other engineering application of the proposed approaches. More specifically, this includes: (1) nonlinear identification in the presence of noise, (2) development of bounded characteristics of the estimated models and (3) application studies where the developed approaches have been used in various engineering applications. Particularly, the modelling and forecast of daily peak power demand in the state of Victoria, Australia have been effectively studied using the proposed approaches. This strongly motivates a great deal of potential future research to be carried out in the area of power system modelling
Determining The Value-at-risk In The Shadow Of The Power Law: The Case Of The SP-500 Index
In extant financial market models, including the Black-Scholesâ contruct, the dramatic events of October 1987 and August 2007 are totally unexpected, because these models are based on the assumptions of âindependent price fluctuationsâ and the existence of some âfixed-point equilibriumâ. This paper argues that the convolution of a generalized fractional Brownian motion (into an array in frequency or time domain) and their corresponding amplitude spectra describes the surface of the attractor driving the evolution of prices. This more realistic approach shows that the SP-500 Index is characterized by a high long term Hurst exponent and hence by a âblack noiseâ with a power spectrum proportional to f-b (b > 2). In that set up, the above dramatic events are expected and their frequencies are determined. The paper also constructs an exhaustive frequency-variation relationship which can be used as practical guide to assess the âvalue at riskâ.Market Collapse; Fractional Brownian Motion; Fractal Attractors; Maximum Hausdorff Dimension of Markets and Affine Profiles; Hurst Exponent; Power Spectrum Exponent; Value at Risk
Applied Harmonic Analysis and Sparse Approximation
Efficiently analyzing functions, in particular multivariate functions, is a key problem in applied mathematics. The area of applied harmonic analysis has a significant impact on this problem by providing methodologies both for theoretical questions and for a wide range of applications in technology and science, such as image processing. Approximation theory, in particular the branch of the theory of sparse approximations, is closely intertwined with this area with a lot of recent exciting developments in the intersection of both. Research topics typically also involve related areas such as convex optimization, probability theory, and Banach space geometry. The workshop was the continuation of a first event in 2012 and intended to bring together world leading experts in these areas, to report on recent developments, and to foster new developments and collaborations
Recognition and matching in the presence of deformation and lighting change
Natural images of objects and scenes show a fascinating amount of
variability due to different factors like lighting and viewpoint change,
occlusion, articulation and non-rigid deformation. There are certain cases
like recognition of specular objects and images with arbitrary deformations
where existing techniques do not perform well. For image deformation, we
propose a method for faster keypoint matching with histogram descriptors and a
completely deformation invariant representation. We also propose a method for
improving specular object recognition.
Histograms are a powerful statistical representation for keypoint matching
and content based image retrieval. The earth mover's distance (EMD) is an
important perceptually meaningful metric for comparing histograms, but it
suffers from high (O(n3 log n)) computational complexity. We
propose a novel linear time algorithm for approximating EMD with the
weighted L1 norm of the wavelet transform of the difference
histogram. We prove that the resulting wavelet EMD metric is equivalent to
EMD. We experimentally show that wavelet EMD is a good approximation to EMD,
has similar performance, but requires much less computation. We also give a
fast algorithm for the best partial EMD match between two histograms.
Images of non-planar object can undergo a large non-linear deformation due
to a viewpoint change. Complex deformations occur in images of non-rigid
objects, for example, in medical image sequences. We propose using the
contour tree as a novel framework invariant to arbitrary deformations for
representing and comparing images. It represents all the deformation invariant
information in an image.
Lighting changes greatly affect the appearance of specular objects and
make recognition difficult much more than for Lambertian objects. In model
based recognition of specular objects, an important constraint is that the
estimated lighting should be non-negative everywhere. We propose a new method
to enforce this constraint and explore its usefulness in specular object
recognition, using the spherical harmonic representation of lighting. The new
method is faster as well as more accurate than previous methods. Experiments
on both synthetic and real data indicate that the constraint can improve
recognition of specular objects by better separating the correct and incorrect
models
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
- âŠ