Fiber reinforced plastic (FRP) composite materials are becoming increasingly popular, particularly in the aerospace field, due to their higher mechanical benefits over metals such as low weight and high stiffness and strength (Chandrashekhar and Ganguli, 2016; Baccar and Söffker, 2017; Castro et al., 2019). However, composite components can often demonstrate fragility toward low-velocity impacts (Atobe et al., 2011; Marchi et al., 2011; Ciampa et al., 2016; Ali et al., 2017), which can considerably degrade the structural integrity and, if not detected, they can result in catastrophic failures. Acoustic emission (AE)-based structural health monitoring (SHM) systems have become an important tool to provide in-service detection and localization of low-velocity impacts, thus enhancing safety of composite components. Literature presents various AE localization methods developed over the years (Haider et al., 2018; Morse et al., 2018; Qiao et al., 2019; Qiu et al., 2019; Tian et al., 2019; Yin et al., 2019). However, only few AE source identification systems can be used in anisotropic inhomogeneous composite materials, especially if no prior knowledge of the propagating wave field and mechanical properties of the host component are provided (Tobias, 1976; Ciampa and Meo, 2010a; McLaskey, 2010), which is generally common in practical aerospace applications.

SHM algorithms for AE localization in composite materials typically rely on the time of arrival (TOA) estimation (Ciampa and Meo, 2010b; Ciampa et al., 2012; Kundu, 2012; Kundu et al., 2012; Emanuele et al., 2017; Seno et al., 2019). However, TOA-based techniques require a relatively large number of receiver transducers measuring the coherent part of the wave field (ballistic wave). Advanced signal processing methods such as peak detection (Castro et al., 2018; Das and Leung, 2018; Zhou et al., 2019), cross-correlation (Kim et al., 2015; Li et al., 2018), Hilbert (Chen et al., 2018; Kim and Yuan, 2018), and wavelet transformation (Bianchi et al., 2015; Zhu et al., 2017) have been employed to extract physical parameters from measured data in order detect AE waves. Nevertheless, the dispersive nature of guided waves, as well as boundary reflections and mode conversion in geometrically complex components can all alter the acquired signal resulting in incorrect TOA estimations (Ciampa and Meo, 2011). Ciampa and Meo (2011) recently developed a time reversal (TR) signal processing technique to compensate the dispersive behavior of guided waves and to enhance the localization (imaging) process in inhomogeneous FRP composites. TR method requires, in principle, only one receiver transducer and, unlike current TOA-based AE monitoring systems, it uses a diffusive wave field to achieve focusing of the source with high accuracy. TR process is typically divided into two steps. The first one involves training of the structure under investigation by creating a baseline grid in which each point pertains to a corresponding recorded impulse response (i.e., the experimental Green's function). The second step consists of correlating the impulsive transfer function associated to each baseline grid point against the inversion of the structural response of a new impact of unknown location. The predicted impact cell is identified as the cell with the greatest correlation. Within each cell, a more precise location can be achieved with topographic methods such as the center of gravity (CoG) technique.

TR has been tested on both isotropic plate-like and complex composite components with various experimental conditions (Ing and Quieffin, 2005; Chen and Yuan, 2010; Bas et al., 2011; Qiu et al., 2011; Chen et al., 2012a; Park et al., 2012; Remillieux et al., 2015). For example, Ciampa and Meo (2014) used TR on a composite tail rotor blade of a helicopter made of both glass and carbon fiber materials with varying thickness. Experimental results demonstrated that the calculated impact location could be achieved with a high level of accuracy at any point on the structure. The same authors (Ciampa et al., 2016) tested the effects of TR by varying the number of excitation points in the baseline grid, the number of piezoelectric sensors and by compensating temperature changes using a forward step signal stretch (FSSS) technique. Although only one sensor is required for TR, it was shown that increasing the number of sensors and taking an average from the contribution decreases the probability of localization error (Ciampa et al., 2016).

In all TR tests performed to date on composite components, receiver piezoelectric (PZT) transducers have all been surface mounted (e.g., Ing and Quieffin, 2005; Chen and Yuan, 2010; Bas et al., 2011). However, in real operating conditions, external exposure of the sensor can lead to failure due to environmental factors such as moisture and corrosion (Birman, 1996). As a result, it is often desirable to embed transducers, thus creating “smart” FRP composite structures. The novelty of this paper is to evaluate, for the first time, the performance of TR for impact localization on smart composite structures with embedded receiver PZT sensors. For the electrical insulation of PZTs into carbon/epoxy composites, a new manufacturing process developed by Andreades et al. (2018, 2019) was used. It consists of using thin E-glass fiber fabric patches as insulating interlayers for PZT sensors, which provide enhanced adhesion with the surrounding epoxy matrix against standard insulation techniques adopting Kapton and Teflon patches (Huang and Nemat-Nasser, 2007; Clausen et al., 2013; Andreades et al., 2018). Another innovative aspect of this paper is to further enhance the reliability and accuracy of the TR imaging process by proposing a new topological algorithm for impact localization, here named as minimum average (MA), and comparing its performance against the CoG technique. Various case studies were analyzed to simulate real operational conditions, including changes of the training (baseline) signals and double impacts, for which the alteration to AE responses are less predictable. The outline of this research work is as follows: in section Time Reversal Theory, the time reversal impact localization algorithm is introduced. The new topological MA approach and the traditional CoG method are described in section Topological Approaches for Impact Localization. Section Experimental Set-Up shows the set-up used to perform experimental tests, whilst in section Impact Localisation Results are illustrated. Conclusions are reported in section Conclusion.

The TR method is conventionally split into two steps: a “forward” and a “backward” propagation step (Chen et al., 2012b; Ciampa and Meo, 2012, 2014; De Simone et al., 2018). It also used for guided waves applications (Wang et al., 2004; Huang et al., 2019) but, in this work, the time reversal process is applied as a step of a new passive impact localization technique. According to (De Simone et al., 2018), during the “forward” step the structure is divided into a grid containing M excitation points. Each point is, in turn, excited by an impulsive waveform such as that caused by a low velocity impact. N passive sensors record the local response for each of the M impacts, resulting in a data set of size M × N. Using the hypothesis of free unbounded space, assuming the wave field Ψ(r,t) can be measured at any point over the structure and all deformations are linearly elastic, the general solution of the elastodynamic wave equation can be simplified to

where r = x1î + x2ĵ + x3k^  in Lagrangian coordinates, t represents time, G(r, t₀; r₀) is the Green space-time function, showing the wave field produced at r at time t by an impulsive impact located at r₀ excited at time t₀. The symbol ⊗t represents the convolution over time, Ω is the solid volume and e(r₀, t) is the excitation function indicating an impulsive force (Ciampa and Meo, 2014). Due to the impacts behaving as impulse responses, it is reasonable to treat the excitation function as a Dirac delta function. In this case the Green space-time function is called “impulse response” and is equal to the measured wave field (De Simone et al., 2018). The excitation points are used to convert the surface of the structure into a discrete domain with M points at various locations r_m, meaning the spatial integral in Equation (1) becomes a sum of convoluted components,

The “backward” propagation step involves the correlation of the waveform emitted at an unknown location r_m0 with the impulse responses of each excitation point. It can be shown (Ciampa and Meo, 2014; De Simone et al., 2018) that

is maximum when r_m = r_m0, where τ is the time lag and R_TR is the TR operator equal to the cross-correlation between the baseline impulse response and the impulse response of the new impact of unknown location. The Cauchy-Schwarz inequality (Aldaz et al., 2015) proves that

where |•| is the absolute value. Equation (4) can be rewritten as

As the Euclidean norm and signal energy, respectively, are defined as

(De Simone et al., 2018). Hence, Equation (5) can be written as

The TR correlation coefficient, C_TR, defined as

can be used as a measure of similarity between two signals (De Simone et al., 2018). Comparing Equations (8) and (9), it is clear that the following inequality is satisfied, 0 ≤ C_TR ≤ 1, where a C_TR value near to one represents strong signal similarity and identifies the impact location. The C_TR value is calculated for all baseline excitation points and those points nearest to the impact have the highest values. As reported in the Introduction section, although only one sensor is required for the imaging process, it has been shown that using multiple sensors and, then, averaging the C_TR values associated to each baseline point given by the readings from each sensor, allows for the compensation of incoherent measurement noise due to electronics, environmental, and operational conditions (Ciampa et al., 2016; Castro et al., 2019).

In order to improve the accuracy of the impact location, a new topological approach, here named as the MA method is proposed, which resembles the traditional CoG technique. The effectiveness of this new method is discussed in the following sections. For all impact cases, the absolute error of the calculated impact locations was used, and it was defined as the Euclidian distance between the calculated and the real impact position:

where x and y are the calculated coordinate positions and x₀ and y₀ are the actual impact coordinates.

All tests described in this paper were conducted on a single CFRP plate with dimensions of 200 × 200 × 3 mm and a layup sequence of [90/0]3s. As can be seen in Figure 1, the plate contained four embedded PZT sensors of 6.5 mm diameter and 0.3 mm thickness, which were located between the fourth and fifth layers from the top, covered with thin 10 × 10 mm woven E-glass fiber fabric patches. The manufacturing process for the electrical insulation of PZT transducers was described in Andreades et al. (2018). Each sensor (labeled A–D) was positioned 20 mm from the edges in the four corners of the plate. A baseline grid of hundred 15 × 15 mm cells were marked onto the plate as shown in Figures 2A,B. Impacts were generated by dropping a pencil from a consistent height of 85 mm. To accurately impact desired positions on the plate, while releasing the pencil from the same height, a tube held by a retort stand and clamp was used. This set-up is shown in Figure 2A.

The plate was suspended with four foam squares, to prevent interactions and reflections with the table. The impact signal responses from PZT sensors were acquired using a four channel PicoScope, with 8 bits of resolution, at a sampling rate of 2 MHz and an acquisition time of 50 ms. A single threshold trigger was used with a 5% pre-trigger time set to ensure the whole impulse response was captured.

To validate the robustness of the proposed work, practical experimental conditions were applied on each impact test in order to alter AE responses. These included a refining of the baseline grid (please see section Pencil Drop test and Grid Refinement) and the presence of material damage and double impacts, both causing variation of the baseline signals (please see section Double Bounce Impact and Baseline Variation With Damage).

Impact localization results are divided into two sub-sections. In the first one, the effectiveness of TR for impact localization with the new MA approach and embedded piezoelectric sensors were evaluated on the composite plate. Both the original and the refined grid were considered. In the second sub-section, impact localization results with double bouncing and damage test were reported.

This study investigated the performance of time reversal for the localization of the impact sources on a fiber reinforced plastic composite with embedded piezoelectric sensors. A topologic approach was proposed in order to enhance the accuracy of time reversal in retrieving impact location. Experimental tests were accomplished to assess the effectiveness of time reversal against many practical issues in real conditions, such as material imperfections and double bouncing, which were not consider during the initial training process. Based on the results presented, it can be concluded that the time reversal applied on a composite with embedded piezoelectric sensors proved to be an effective impact localization methodology where alterations of acoustic emission in the baseline signals are less predictable, once the impacts will be possibly distributed equally over the surface of the structure. In addition, the minimum average approach proved to be an alternative for systems that require less data to perform the impact localization. Future work will focus on the on reproducibility. This will include the use of multiple baselines and weighting functions for an improved selection of the cell under consideration for impact localization.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation, to any qualified researcher.

AC and BC run the time reversal experiments. FB supported the development of ultrasound testing. CA manufactured the composite plate with embedded transducers. MM supported the development of time reversal theory. FC supported the development of time reversal for impact localization and led the research team.