Salvatore Caporale

Ultrasonic guided-waves characterization with Warped Frequency Transforms

In this work a new time-frequency procedure for the extraction of multimodal and dispersive guided waves (GWs) from a recorded time-waveform is presented. The proposed ldquoWarped Frequency Transformrdquo (WFT) is based on a time-frequency domain tiling chosen to match the spectro-temporal structure of the different propagating guided waves by selecting an appropriate warping map which generates non-linearly frequency modulated atoms. The WFT transformation is fast, invertible, covariant to group velocity-delay shifts and, in force of the more flexible tiling, presents enhanced modes extraction capabilities. An application to Lamb Waves propagating in an isotropic plate is presented to show the potential of the proposed procedure.

Fast Computation of Frequency Warping Transforms

In this paper, we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency (TF) plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped nonsmooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.

Exploiting Non-Linear Chirp and sparse deconvolution to enhance the performance of pulse-compression ultrasonic NDT

A pulse-compression procedure based on Non-Linear Chirp for Ultrasonic Non Destructive Testing is presented. Non-Linear Chirp signals can be tailored to reproduce any desired continuous spectrum. Here, such capability is exploited to take into account the features of the specific hardware set-up in use, and particularly to adapt the excitation signal to the probes. An application of the proposed procedure to Air-Coupled Ultrasound Imaging is also presented. In order to enhance the imaging resolution, L1-norm Total Variation deconvolution is exploited and compared with standard L2-norm Wiener deconvolution. Although the usage of Air-Coupled probes entails a high attenuation of the ultrasonic signals due to transmission in air and reflections at the air-sample interface, the experimental results show that the combination of Pulse Compression technique and of advanced signal processing guarantees the effectiveness of the inspection.

Analytical computation of fast frequency warping

In this work we introduce an analytical characterization of the frequency warping operator of arbitrary shaped non-smooth warping maps. The transformation matrix is decomposed in two additive terms: the first term represents its nonuniform Fourier transform approximation while the second term is imposed for aliasing suppression. The first transformation is known to be analytically characterized and fast computable by an interpolation approach. For the second transformation an analytical representation is introduced which allows a fast computation and a simple design. Finally, an example of a potential application is shown.

Frequency Warping Biorthogonal Frames

Frequency warping is theoretically designed to be a unitary operator of infinite input and output dimensions, thus performing the resolution of identity. In real implementations finite dimensions have to be considered, then perfect reconstruction cannot be fulfilled. The accuracy of reconstruction is particularly compromised in case of non-smooth warping maps, which are more useful for practical applications. In order to overcome this limitation, a new frequency warping biorthogonal frame operator for non-smooth warping maps is introduced in this work. The proposed transformation is based on a mathematical model which has been previously introduced for computational purposes. By adding some redundancy with respect to the truncation of the infinite dimensions operator, the effect of an infinite output dimension can be taken into account in a compressed way, based on an analytical factorization. In the reconstruction process, the additional redundant samples are expanded, thus guaranteeing near perfect reconstruction.

An Accurate Algorithm for Fast Frequency Warping

In this work we present a fast and accurate algorithm to compute frequency warping of arbitrary shaped maps. In contrast to the common Laguerre approach, frequency warping is represented by a matrix of truncated finite dimensions. The transformation matrix is decomposed in two additive terms: the first term represents its nonuniform Fourier transform approximation while the second term is imposed for aliasing suppression. Both matrices are approximated with a least square approach according to a suitable set of vectors. The cardinality of this set is shown to be nearly proportional to the logarithm of the matrix dimension. Finally, trade-off aspects between algorithm complexity and performance are discussed

From chirps to random-FM excitations in pulse compression ultrasound systems

Pulse compression is often practiced in ultrasound Non Destructive Testing (PDF) systems using chirps. However, chirps are inadequate for setups where multiple probes need to operate concurrently in Multiple Input Multiple Output (PDF) arrangements. Conversely, many coded excitation systems designed for PDF miss some chirp advantages (constant envelope excitation, easiness of bandwidth control, etc.) and may not be easily implemented on hardware originally conceived for chirp excitations. Here, we propose a system based on random-FM excitations, capable of enabling PDF with minimal changes with respect to a chirp-based setup. Following recent results, we show that random FM excitations retain many advantages of chirps and provide the ability to frequency-shape the excitations matching the transducers features.

A new Warped Frequency Transformation (WFT) for Guided Waves characterization

The characterization of the dispersive behaviour of stress guided waves (GWs) from a time transient measurement is generally attempted by means of time-frequency representations (TFRs). Unfortunately, any TFR is subjected to the time-frequency uncertainty principle that limits the capability of the TFR to distinguish multiple, closely spaced guided modes, over a wide frequency range. To this aim we implemented a new Warped Frequency Transform (WFT) that in force of a more flexible tiling of the time-frequency domain presents enhanced modes extraction capabilities. Such tiling, composed by non linearly modulated atoms, is built on the dispersive group velocity curve of a particular propagating mode. The resulting TFR thus emphasizes the energy content associated to that particular guided mode within the recorded time waveform. Here we propose an application of the WFT to numerically simulated Lamb Waves propagating in an aluminum plate. The results show that the proposed WFT limits interference patterns which appears with others TFRs and produces a sparse representation of the dispersive Lamb wave pattern that can be suitable for identification and characterization purposes.

Frame bounds estimation of frequency warping operators

In this work we provide an accurate analytical estimation of the frame bounds for frequency warping operators of arbitrary shaped non-smooth warping maps. We deal with both the Nonuniform Fourier Transform approximation and the aliasing suppressed form of the frequency warping operator. The estimation procedure is obtained by using an analytical model of the aliasing operators which has been previously introduced. The provided estimations can be used as design formulas for the parameters, such as degree of smoothness and redundancy, involved in the definition of the frequency warping operators.

Constant envelope pseudo orthogonal excitations for ultrasound testing

Various techniques to generate pseudo-orthogonal excitations for Ultrasonic Non Destructive Testing (UT-NDT) are discussed, with the constraint that they deliver constant-envelope waveforms and they are FM based. Pseudo-orthogonal excitations enable multiple Tx probes to be operated simultaneously so that many measurements can be taken at once. The constraints assure minimal disruption of conventional hardware arrangements and guarantee a good exploitation of the power conversion abilities of the Tx probes. The goal is to seek a progressive management of the trade-off between contrasting merit factors.