Frontmatter

Independent component analysis (ICA) is a well-known technique for blind source separation (BSS) based on higher-order statistics. Assuming the sources are independent, the fact that the sources can be uniquely recovered is a consequence of the unicity the canonical polyadic decomposition (CPD), a decomposition of a tensor in rank-one terms. Contrary to matrix decompositions, tensor decompositions can be unique without imposing additional constraints such as orthogonality or nonnegativity. Block component analysis (BCA) is an entirely new technique for BSS and factor analysis which also exploits the unicity of tensor decompositions, but does not make the assumption that the sources should be statistically independent. In this poster, we explain how BCA works and how to compute the associated block term decompositions (BTD). The latter is a generalization of the CPD and multilinear SVD (MLSVD), which are in turn the two most prominent generalizations of the matrix SVD to tensors. Block term decompositions can be formulated as nonlinear optimization problems in which the objective function is not analytic in its complex variables. We generalized several well-known unconstrained optimization methods such as (L-)BFGS, NCG and nonlinear least squares methods such as Levenberg-Marquardt to this class of problems and applied them to compute a certain type of BTD. In the nonlinear least squares methods, we exploited the problem's structure, which resulted in some of the most efficient algorithms for BTDs to date.status: publishe

Simulation study of the localization of a near-surface crack using an air-coupled ultrasonic sensor array

The importance of Non-Destructive Testing (NDT) to check the integrity of materials in different fields of industry has increased significantly in recent years. Actually, industry demands NDT methods that allow fast (preferably non-contact) detection and localization of early-stage defects with easy-to-interpret results, so that even a non-expert field worker can carry out the testing. The main challenge is to combine as many of these requirements in one single technique. The concept of acoustic cameras, developed for low frequency NDT, meets most of the above mentioned requirements. These cameras make use of an array of microphones to visualize noise sources by estimating the Direction Of Arrival (DOA) of the impinging sound waves. Until now, however, because of limitations in frequency range and lack of integrated nonlinear post-processing, acoustic camera systems have never been used for the localization of incipient damage. The goal of the current paper is to numerically investigate the capabilities of locating incipient damage by measuring the nonlinear airborne emission of the defect using a non-contact ultrasonic sensor array. We will consider a simple case of a sample with a single near-surface crack and prove that after efficient excitation of the defect sample, the nonlinear defect responses can be detected by a uniform linear sensor array. These responses are then used to determine the location of the defect by means of three different DOA algorithms. The results obtained in this study can be considered as a first step towards the development of a nonlinear ultrasonic camera system, comprising the ultrasonic sensor array as hardware and nonlinear post-processing and source localization software.status: publishe