Sparse signal model for ultrasonic nondestructive evaluation of CFRP composite plates

Abstract

Signal processing has been proven to be an useful tool to characterize damaged materials under ultrasonic nondestructive evaluation. In this work, we hypothesize that the transfer function of multilayered materials for a through-transmission configuration can be represented as a classical all-pole model with sparse coefficients. To test this hypothesis, we propose an analysis-by-synthesis scheme which, by assuming an underlying sparse digital signal model of the specimen, infers the order and extent of the model parameters corresponding to a certain impact damage level. Then, we exploit the sparse structure of the obtained digital filter for practical NDE applications, with emphasis on impact damage identification of carbon-fiber reinforced polymer plates.

A sparse digital signal model for ultrasonic nondestructive evaluation of layered materials

“…. a 2K T ; k Á k 0 is the l 0 -norm, and K cor- intuitive results described in [30,31]. As can be observed, 533 Goupillaud-type structures are a particular case of our formalism, 534 for which the gain G a i ¼ 1 and the sample delay m i ¼ 1; 8i ¼ 1; Table 1 Overview of the obtained multilayered specimens.…”

“…Such an exci-575 tation is here preferred over spike since it has shown better perfor-576 mance in our setup[30,31,33]. This could be explained by the 577 cancelation and elimination of some nonlinear and relaxation com-578 ponents as a result of the waveform symmetry (positive and nega-579 tive parts) of the excitation signal.…”

“…In this paper, we introduce a novel digital signal model for ultrasonic 30 NDE of multilayered materials. This model borrows concepts from lattice filter theory, and bridges them 31 to the physics involved in the wave-material interactions. In particular, the proposed theoretical frame-32 work shows that any multilayered material can be characterized by a transfer function with sparse coef-33 ficients.…”

Fast algorithms for high-order sparse linear prediction with applications to speech processing

“…In particular, while reintroducing well-known methods to seek a short-term predictor that produces a residual that is sparse rather than minimum variance (e.g., [16,25]), the idea of employing high-order SpLP (HOSpLP) to model the cascade of short-term and long-term predictors was also introduced [26,27]. The application of HOSpLP was originally introduced for speech processing purposes, however its formulation is intimately related to the regularization of ill-conditioned problems and to the precise modeling of long-term redundancies, thus it quickly found applications in diverse fields, such as radar [28], geology [29], video packet-loss concealment [30], and general signal representations [31,32].…”

Computational analysis of a fast algorithm for high-order sparse linear prediction

“…SLP has proved to be an interesting alternative to classic LP by allowing better statistical models and more meaningful signal representation finding its way in various applications ranging from timefrequency representation [12] and filter design [13] to more application specific tasks, like, e.g., speech dereverberation [14], video processing [15], geology [16], and radar imaging [17]. The compact representation that linear prediction provides reveals a model for the process, called the autoregressive (AR) model.…”