Phased array imaging for damage localization using multi-narrowband Lamb waves

Highlights

• A damage imaging method using multi-narrowband Lamb waves is proposed.

• Grating lobes and sidelobes are suppressed while mainlobes are retained.

• Imaging results with fewer artifacts are achieved.

Abstract

In the conventional phased array imaging methods based on only single narrowband Lamb waves, as the scattering behavior between Lamb waves and defects is closely related to the wavelength and the defect size, the information within only a single narrowband is limited. Besides, limited by the size of elements in phased arrays, the ratio of the element spacing to the wavelength may not be able to reach a small enough value, as a result, grating lobes in some directions and high sidelobes will inevitably appear. Aimed at utilizing Lamb wave information contained in multiple frequency bands so as to improve the image quality of Lamb wave phased array imaging, a multi-narrowband fusion method is proposed. The information of multi-narrowband Lamb waves with different carrier frequencies is fused using the geometric mean. Because the positions of grating lobes and the sidelobes are related to the carrier frequency once the sensor array is fixed, the mainlobe is retained and grating lobes as well as sidelobes can be suppressed after the fusion of multiple narrowband signals with different carrier frequencies. So imaging results with fewer artifacts are achieved compared with that generated using only single narrowband signals. The results of damage localization on an aluminum plate with two defects verify the effectiveness of the proposed method.

Introduction

Lamb waves, which propagate in plate-like structures, are a useful tool for the nondestructive evaluation (NDE) as well as structural health monitoring (SHM) of thin wall structures because of some excellent characteristics of Lamb waves [1], [2]. For some cases of SHM or NDE using Lamb waves, usually an array consisting of several PZTs is permanently bonded to surfaces of the monitored structure or directly integrated into its interior to transmit and receive Lamb waves. So the positions of elements in the sensor array cannot change once the array is bonded to the structure. According to the element spacing of the sensor array, there are two types of array layouts: the sparse array and the compact array [3], [4]. In most cases, damage detection using sparse arrays requires baseline data recorded in an intact state because the scattering signals caused by defects are hard to separate directly from the original response signals. In cases of compact array based SHM or NDE systems, the baseline data are not a required option for damage localization. Both types of array layouts are widely used in different scenarios [5], [6], [7], [8], [9].

To visualize the defects on the surfaces or hidden in the interior of the monitored structure, imaging methods are proposed to generate images. There are Lamb wave based damage imaging methods that can be applied to different types of arrays. The delay-and-sum (DAS) imaging method [10], [11], [12], the sparse decomposition based imaging method [13], [14], [15], [16], [17], the minimum variance distortionless response (MVDR) imaging method (it can be seen as the DAS imaging with adaptive weights) [18], [19], [20], RAPID imaging [7], [21], [22], and wavefield imaging [23], [24] are typical representatives of these methods. Some other imaging methods, such as the multiple signal classification (MUSIC) imaging method [25], [26], the total focusing method (TFM) [27], [28], [29], and the sign coherence factor (SCF) method [30], [31], are more commonly used in compact arrays.

Among the imaging methods developed for compact arrays, there is a special category, which can be referred to as the phased array imaging. Signals can be focused on a desired point to increase the energy proportion of damage scattering signals and suppress interferences to improve imaging performances in phased array imaging. Kudela et al. proposed an electronically scanned Lamb wave phased imaging algorithm by controlling the waveforms transmitted from the elements to achieve signal focusing to desired points [32]. Because Lamb waves are dispersive, the transmitted waveforms must be carefully designed, which indicates that they must be changed when the desired focusing point changes. It is a time-consuming process to scan the examined structure under such a strategy.

Instead of directly focusing in the transmitting process, more attempts for damage imaging are investigated by post-processing algorithms. In such a way, the transmitted signals are the same and the process of signal acquisition is fast. Some signal processing techniques to achieve signal focusing have also been developed by researchers in the Lamb wave based SHM and NDE fields. Yang et al. proposed a Lamb wave phased array imaging algorithm based on the TFM and frequency response functions, in which the pre-compensation and post-compensation for dispersion are considered [28]. Lang et al. proposed the focusing phased imaging algorithm [33], in which the phase information like that used in the SCF algorithm is used for damage imaging. Sternini et al. proposed a modified MVDR based phased imaging method for guided wave beamforming [34]. Prado et al. proposed an SCF weighted TFM imaging algorithm that combines the A0 and S0 modes [35]. Considering both signal focusing and the correlations among dispersive Lamb waves, the waveform correlation based TFM and the waveform covariance based method are proposed by the authors [36]. However, all the above methods are based on single narrowband Lamb waves, which limit imaging performances because the information of single narrowband signals is not enough.

There are also studies about multi-frequency based imaging methods. Yang et al. proposed the F-MUSIC algorithm, in which Lamb waves of different frequencies are fused [37], but the signals used for imaging are still within a single narrowband. The information contained within broadband is still not fully used. Besides the limited information within a single narrowband, Giurgiutiu et al. comprehensively analyzed the requirements of a linear phased array for damage imaging and found that the magnitudes of grating lobes and sidelobes are attributed to the ratio of the wavelength to the element spacing [38]. Grating lobes will appear when the ratio of the element spacing to the wavelength cannot reach a small enough value. In application, because of the limitation of the element size, the element spacing may not meet the required conditions so grating lobes may appear. Besides the ratio of the wavelength to the size of a defect that will affect the magnitude of scattering waves and then affects imaging results, the magnitudes of grating lobes and sidelobes in the beamforming can also affect imaging results. Therefore, if broadband signals are utilized, it is expected that damage imaging performances could be improved.

Proposed here is an alternative phased imaging method based on multi-narrowband Lamb waves. Different from the above mentioned imaging methods that are based on single narrowband Lamb waves, the proposed method utilizes multi-narrowband Lamb waves of different carrier frequencies. The images generated using single narrowband Lamb waves are fused by taking their geometric mean. Besides several single narrowband Lamb waves of different carrier frequencies that can provide more information about defect scattering, beamforming analysis shows that the proposed multi-narrowband fusion method can suppress the magnitudes of grating lobes and sidelobes. As a result, images with fewer artifacts are obtained compared with that generated using only single narrowband signals.

The remainder of this paper is organized as follows. The methodology of the proposed multi-narrowband fusion method is described in detail in Section 2. Simulations and experiments on aluminum plates are implemented for validation in Sections 3 Numerical study, 4 Experimental validation, respectively. In Section 5, conclusions are drawn.