Time reversal active sensing for health monitoring of a composite plate

Abstract

The applicability of a time reversal concept in modern acoustics to structural health monitoring was investigated. The time reversal method has been adapted to guided-wave propagation to improve the detectability of local defects in composite plate structures. Specifically, a wavelet-based signal processing technique has been developed to enhance the time reversibility of Lamb wave in thin composite plates. The validity of the proposed method is demonstrated through experimental studies in which input signals exerted at piezoelectric (PZT) patches on a quasi-isotropic composite plate are successfully reconstructed by using the time reversal method. The ultimate goal of this study is to develop a reference-free damage diagnosis technique based on the time reversal process so that defects can be identified without relying on any past baseline data.

Introduction

There has been a significant increase in the use of solid composites in load-carrying structural components, particularly in the aircraft and automobile industries. With the advances in sensor and hardware technologies that can generate and detect Lamb waves, many studies have been proposed to use Lamb waves for detecting defects in composite structures [1], [2], [3], [4]. In particular, many researchers have recognized the potential use of piezoelectric (PZT) actuators/sensors for Lamb-wave-based structural health monitoring [2], [4], [5].

Lamb waves are mechanical waves whose wavelength is in the same order of magnitude as the thickness of the plate. The analysis and interpretation of Lamb waves can be complicated due to their dispersive and multimodal natures. The various frequency components of Lamb waves travel at different speeds and the shapes of wave packets change as they propagate through a solid medium. Multiple symmetric and anti-symmetric wave modes are generated as the driving frequency for wave generation increases.

Recently, attention has been paid to the time reversal method developed in modern acoustics to compensate the dispersion of Lamb waves and to improve the signal-to-noise ratio of propagating waves [6], [7], [8], [9]. For instance, a pulse-echo time reversal method, that is, the time reversal method working in pulse-echo mode has been employed to identify the location and size of defects in a plate [7], [8], [9]. However, if there exist multiple defects in a plate, this iterative pulse-echo process tends to detect only the most distinct defect, requiring more sophisticated techniques to detect multiple defects. Furthermore, the pulse-echo process seems impractical for structural health monitoring applications, because a dense array of sensors is required to cover the entire boundary of the plate being investigated.

In the time reversal method, an input signal can be reconstructed at an excitation point (point A) if an output signal recorded at another point (point B) is reemitted to the original source point (point A) after being reversed in a time domain as illustrated in Fig. 1. This time reversibility (TR) of waves is based on the spatial reciprocity and time reversal invariance of linear wave equations [10], [11]. The specific goal of the research described in this paper is to reconstruct the known excitation signal at the original input location through the time reversal process of Lamb waves. In this study, an enhanced time reversal method is proposed so that the reconstruction of the input signal can be achieved for Lamb wave propagation. The ultimate goal is to use this TR of Lamb waves for damage diagnosis.

Although the application of the time reversal concept to Lamb waves is not a new idea [8], [12], the full reconstruction of the input signal has not been attempted before for Lamb waves. To achieve this goal, a specific narrowband input waveform and a wavelet-based signal filtering technique are employed to enhance the TR of Lamb waves. The complete reconstruction of the input signal cannot be achieved when a broad-band excitation is employed for Lamb wave propagations. Due to the frequency dependence of the time reversal process of Lamb waves, different frequency components of the broad-band excitation are scaled differently during the time reversal process and the original input signal cannot be fully restored. This is the primary reason for using a narrowband excitation. Once this TR is enforced for Lamb waves, our vision is to detect certain types of defects by examining the deviation of the reconstructed signal from the original input signal without relying on any past baseline data.

Often damage detection problems are cast in the context of statistical pattern comparison in which a damage state of the system is inferred by comparing test data with baseline data. However, the dependency of damage diagnosis on the prior baseline data makes the field deployment of current damage detection technologies extremely difficult. For instance, subtle signal changes due to damage could often be masked by larger operational and environmental variations of the in-service structure. In addition, the test data corresponding to a case where there may be damage are often collected long after the baseline data were recorded when the structure was in pristine condition. Therefore, the development of this baseline-free damage diagnosis technique can address the issue of minimizing false-positive indications of damage due to varying operational and environmental conditions. The validity of the proposed method is demonstrated through experimental studies of a quasi-isotropic composite plate, in which input signals exerted at PZT patches are successfully reconstructed during the time reversal process. Its application to actual damage diagnosis is reported elsewhere.

This paper is organized as follows: first, an analysis of Lamb waves using the Mindlin plate theory is described in Section 2; in Section 3, the TR of Lamb waves is investigated by introducing a time reversal operator in a frequency domain; the wavelet-based signal processing techniques to enhance the TR of Lamb waves are discussed in Section 4; numerical examples and experimental investigations are presented in Section 5 to demonstrate the validity of the enhanced time reversal method; and finally, this paper is concluded in Section 6 with a brief summary and discussions.