2-D iteratively reweighted least squares lattice algorithm and its application to defect detection in textured images

In this paper, a 2-D iteratively reweighted least squares lattice algorithm, which is robust to the outliers, is introduced and is applied to defect detection problem in textured images. First, the philosophy of using different optimization functions that results in weighted least squares solution in the theory of 1-D robust regression is extended to 2-D. Then a new algorithm is derived which combines 2-D robust regression concepts with the 2-D recursive least squares lattice algorithm. With this approach, whatever the probability distribution of the prediction error may be, small weights are assigned to the outliers so that the least squares algorithm will be less sensitive to the outliers. Implementation of the proposed iteratively reweighted least squares lattice algorithm to the problem of defect detection in textured images is then considered. The performance evaluation, in terms of defect detection rate, demonstrates the importance of the proposed algorithm in reducing the effect of the outliers that generally correspond to false alarms in classification of textures as defective or nondefective

On line power spectra identification and whitening for the noise in interferometric gravitational wave detectors

In this paper we address both to the problem of identifying the noise Power Spectral Density of interferometric detectors by parametric techniques and to the problem of the whitening procedure of the sequence of data. We will concentrate the study on a Power Spectral Density like the one of the Italian-French detector VIRGO and we show that with a reasonable finite number of parameters we succeed in modeling a spectrum like the theoretical one of VIRGO, reproducing all its features. We propose also the use of adaptive techniques to identify and to whiten on line the data of interferometric detectors. We analyze the behavior of the adaptive techniques in the field of stochastic gradient and in the Least Squares ones.Comment: 28 pages, 21 figures, uses iopart.cls accepted for pubblication on Classical and Quantum Gravit

The Rank of the Covariance Matrix of an Evanescent Field

Evanescent random fields arise as a component of the 2-D Wold decomposition of homogenous random fields. Besides their theoretical importance, evanescent random fields have a number of practical applications, such as in modeling the observed signal in the space time adaptive processing (STAP) of airborne radar data. In this paper we derive an expression for the rank of the low-rank covariance matrix of a finite dimension sample from an evanescent random field. It is shown that the rank of this covariance matrix is completely determined by the evanescent field spectral support parameters, alone. Thus, the problem of estimating the rank lends itself to a solution that avoids the need to estimate the rank from the sample covariance matrix. We show that this result can be immediately applied to considerably simplify the estimation of the rank of the interference covariance matrix in the STAP problem

Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved

A fast algorithm for LR-2 factorization of Toeplitz matrices

In this paper a new order recursive algorithm for the efficient −1 factorization of Toeplitz matrices is described. The proposed algorithm can be seen as a fast modified Gram-Schmidt method which recursively computes the orthonormal columns i, i = 1,2, …,p, of , as well as the elements of R−1, of a Toeplitz matrix with dimensions L × p. The factor estimation requires 8Lp MADS (multiplications and divisions). Matrix −1 is subsequently estimated using 3p2 MADS. A faster algorithm, based on a mixed and −1 updating scheme, is also derived. It requires 7Lp + 3.5p2 MADS. The algorithm can be efficiently applied to batch least squares FIR filtering and system identification. When determination of the optimal filter is the desired task it can be utilized to compute the least squares filter in an order recursive way. The algorithm operates directly on the experimental data, overcoming the need for covariance estimates. An orthogonalized version of the proposed −1 algorithm is derived. Matlab code implementing the algorithm is also supplied

Noise parametric identification and whitening for LIGO 40-meter interferometer data

We report the analysis we made on data taken by Caltech 40-meter prototype interferometer to identify the noise power spectral density and to whiten the sequence of noise. We concentrate our study on data taken in November 1994, in particular we analyzed two frames of data: the 18nov94.2.frame and the 19nov94.2.frame. We show that it is possible to whiten these data, to a good degree of whiteness, using a high order whitening filter. Moreover we can choose to whiten only restricted band of frequencies around the region we are interested in, obtaining a higher level of whiteness.Comment: 11 pages, 15 figures, accepted for publication by Physical Review

Underdetermined-order recursive least-squares adaptive filtering: The concept and algorithms

Published versio

Non-Linear Model Predictive Control with Adaptive Time-Mesh Refinement

In this paper, we present a novel solution for real-time, Non-Linear Model Predictive Control (NMPC) exploiting a time-mesh refinement strategy. The proposed controller formulates the Optimal Control Problem (OCP) in terms of flat outputs over an adaptive lattice. In common approximated OCP solutions, the number of discretization points composing the lattice represents a critical upper bound for real-time applications. The proposed NMPC-based technique refines the initially uniform time horizon by adding time steps with a sampling criterion that aims to reduce the discretization error. This enables a higher accuracy in the initial part of the receding horizon, which is more relevant to NMPC, while keeping bounded the number of discretization points. By combining this feature with an efficient Least Square formulation, our solver is also extremely time-efficient, generating trajectories of multiple seconds within only a few milliseconds. The performance of the proposed approach has been validated in a high fidelity simulation environment, by using an UAV platform. We also released our implementation as open source C++ code.Comment: In: 2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR 2018

Lattice dynamical wavelet neural networks implemented using particle swarm optimisation for spatio-temporal system identification

Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNN), is introduced for spatiotemporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimisation (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet-neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated waveletneurons are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares (OLS) algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet-neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet-neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework