Detection and localisation of pre-damage heat spots in CFRP panels using Lamb waves

Abstract

Undetected defects arising from the effect of heat exposure within composite panels can develop into critical cracks or delamination, potentially leading to structural failure. This study describes a novel approach to the structural health monitoring (SHM) of carbon fibre-reinforced polymer composite panels to detect and localise pre-damage levels of heat-spot effects. An appropriate heat-spot identification technique was proposed using ultrasonic Lamb-wave propagation from a surface-mounted sensor network. Preliminary tests validated the possibility of detecting heat-exposed areas and assessed the influence of temperature and excitation frequency on signal characteristics and detectability. Multiple indices were compared to detect the signal deviation due to the heat effect, and a time-shift deviation index (DI) was proposed. Consequently, the sensor-path coverage was experimentally determined for sensor-network optimisation. Heat-spot detection and localisation experiments were then conducted for three locations across a temperature severity range and using multiple excitation frequencies. The heat spot was detected and localised at all locations, regardless of severity; however, at a temperature of 35°C, accurate localisation was not always attained. The experimental results supported a correlation between localisation accuracy, excitation frequency, temperature severity and the employed DI. Higher excitation frequencies were found to generally improve localisation accuracy among various DIs. A root mean squared deviation anomaly measure taking into account the first five cycles of the signal emerged as the most effective DI, demonstrating robustness across tested frequencies, temperature severities and locations. Experimentation determined that a Lamb-wave-based SHM solution is viable to detect and localise heat spots in carbon fibre-reinforced polymer components, even at a pre-damage level.

Introduction

In the past three decades, composite materials have been used more widely as the material of choice for component manufacture. ¹ Their rapid innovation has spread from the aerospace industry towards other sectors such as information technology, photonics and renewable energy. ² Novel uses of composite materials are commonplace, with examples such as large composite wind turbines, high-value automotive products and composite bridges in the civil engineering sector. ² Their ubiquitous use and characteristic failure mechanisms require a suitable monitoring regime of such structures, where maintaining structural integrity is critical due to the potential for deterioration over time and the implications of failure.

Ultrasound-based non-destructive testing (NDT) and structural health monitoring (SHM) techniques are promising for damage detection and characterisation. ³ They encompass a variety of techniques that may be used to monitor the structural integrity of materials, components or systems without inducing damage. By selecting and applying the most appropriate method, safety assurance and the verification of composite integrity may be achieved. ⁴ Such techniques may be applied to both plate-like structures ¹ and modern engineering structures, including piping, structural welds, turbines, aircraft frames and heavy machinery. ⁵ In particular, utilising ultrasonic-guided Lamb waves (LWs) to localise damage and defects of various types and sizes has emerged as a vital technique ⁵ due to their sensitivity to both surface and embedded structural damage.^6,7 LWs can propagate over long distances within complex structures, ⁸ further enhancing their utility in damage assessment and localisation. As a significant potential user of this technique, aerospace maintenance, repair and overhaul companies face significant challenges in efficiently and effectively meeting the routine NDT inspection demand; primarily as a result of the labour-intensive and time-consuming nature of traditional inspection methods that are reliant on manual processes and discrete analysis equipment. ² There exists a pressing need within this sector and others to improve efficiency and transition towards more sustainable practices by increasing the inspection and repair rate of composite components over replacement, and for streamlining inspection processes to optimise resource utilisation and reduce costs. ²

The susceptibility of composite materials to structural and material-property alterations due to temperature fluctuations underscores the criticality of monitoring for potential heat effects. Given the widespread applications of mechanical, civil, and aerospace composite structures, exposure to unintended heating is virtually inevitable. Temperature variations induce changes in density, stress, and ultimately, the formation of damage within composite materials. ⁹ Undetected defects arising from heat damage within composite materials have the potential to develop into critical cracks, jeopardising the safety of the entire structure and potentially culminating in catastrophic failures. ¹⁰ Early detection of heat spots is therefore imperative for averting catastrophic failures in composite panels, enabling timely corrective actions to preserve structural integrity and ensure safe operation. Real-time monitoring of heat spots could facilitate proactive maintenance, prolonging the lifespan of composite panels while mitigating the risk of unforeseen breakdowns, and is crucial in managing through-life costs. A potential example is an aircraft subjected to a lightning strike; the increased Joule heating, resulting in a temperature rise at the points of lightning entry and exit, ¹¹ could precipitate damage within the composite material. ¹²

In service, composite structures are routinely exposed to a variety of thermal loads and gradients beyond lightning events, and these exposures can contribute to material degradation, localised overheating and eventual structural compromise. One such example is composite airframe components such as wing leading edges and control surfaces which experience elevated temperatures due to aerodynamic heating at high flight speeds. ¹ This aerodynamic heating is caused by viscous dissipation and frictional resistance in the boundary layer and can significantly raise local surface temperatures, especially on supersonic or high-speed aircraft. Elevated temperature fields influence thermal expansion, accelerate matrix softening and contribute to progressive microstructural damage. ¹ Moreover, components adjacent to aircraft engines and exhaust plumes are routinely exposed to high temperatures during normal operation. ¹ Gas turbine engines operate with very high internal temperatures in the combustion and turbine sections, and downstream of the turbine core, exhaust gas temperatures are sufficiently elevated to drive oxidation, creep and thermal fatigue in nearby structures and coatings. Research on turbine blades and hot-section components illustrates that these regions undergo significant thermomechanical loads, with high exhaust gas temperatures leading to microstructural changes and reduced heat resistance in alloys and coatings exposed to gas-side thermal environments. ¹ Outside of aerospace, large composite structures such as wind turbine blades routinely encounter thermal asymmetries and localised heating due to environmental factors such as solar loading, thermally driven temperature gradients and operational heating. Recent studies on wind turbine blade composites highlight the use of thermographic methods to detect defects by leveraging thermal contrasts produced by localised heating, ² demonstrating that thermal conditions and heat-related anomalies are important in maintenance and SHM in industrial settings as well as in aerospace applications. ²

Taken together, these scenarios show that localised thermal exposure is a common and consequential phenomenon in composite structures across multiple domains of engineering. These conditions can produce temperature elevations and gradients that precede or coincide with structural damage, underscoring the need for real-time monitoring of heat spots. In such cases, the ability to localise heat spots using NDT before they manifest as discernible damage spots becomes paramount. Subsequent assessment of the temperature or heat intensity at these localised spots emerges as a crucial endeavour in pre-empting potential structural compromises and ensuring operational safety. By discovering the presence of heat spots during such incidents and localising them, further inspection and investigation of the identified locations would be facilitated, easing the involved process.

Previous investigations into temperature effects on ultrasonic LW propagation^13,14 have yielded significant insights, revealing notable changes in amplitude and arrival time in response to temperature variations. The influence of temperature on LWs’ time of arrival (TOA) in a composite sandwich panel was investigated by Šedková and Vích, ¹⁵ and the difference between damage-affected signals and temperature-affected signals was compared. Time-of-flight delays indicating a velocity decrease with increasing temperature were confirmed for the $A_0$ and $S_0$ modes. ¹⁵ This was further investigated by Vích and Šedková ¹⁶ In-flight measurements on an ultralight aircraft were performed to investigate the influence of temperature change on the LW signals. The difference between temperature-change effect and damage effect on the signals using changes in signal patterns, such as velocity and amplitude changes and signal reflections and scattering, was demonstrated. ¹⁶ These findings have implications for compensating for temperature effects in guided-wave damage-detection systems and offer a valuable opportunity to detect and localise heat spots within composites. However, there remains a notable gap in research, to the authors’ best knowledge, concerning the active detection and localisation of temperature fluctuations and heat spots by observing these changes.

Concurrently, a diverse array of studies has explored the efficacy of guided-wave sensor networks in detecting and localising damage within composite panels. ¹⁷ Capineri et al. ¹⁸ used a sensor network of flexible piezo-polymer transducers to detect artificial defects, in a carbon overwrapped pressured vessel, by calculating a damage index based on the distortion and amplitude of LW signals from the same sensing path in healthy and damaged conditions. Furthermore, Fakih et al. ⁸ and Mustapha et al. ¹⁹ investigated the use of LWs to detect barely visible indentation damage in carbon fibre/epoxy (CF/EP) sandwich composites. In the study by Mustapha et al., ¹⁹ a damage index was defined based on the change in the peak magnitude and time reversal method. Building on this research, this article will explore the potential for using LWs to detect pre-damage levels of temperature effect.

Consideration is needed of a range of signal processing techniques that might be applied to improve the accuracy and efficiency of ultrasonic testing using various LW modes. Wu et al. ²⁰ and Diogo et al. ²¹ focused on the application of signal processing techniques for ultrasound testing in plates. They considered the benefits of filtering and the use of Hilbert transforms and windowing techniques to improve guided-wave signal quality and enhance the ability of detection. The application of these techniques was further evaluated by Samaitis et al., ²² as the importance of mode selection and the application of a suitable frequency-thickness range was considered. Understanding and applying these signal processing techniques appropriately can significantly enhance the quality and interpretability of ultrasonic Lamb-wave data, leading to more accurate and reliable detection and characterisation of damage in materials like carbon fibre-reinforced polymer (CFRP) panels. This is necessary to assure accuracy, reliability and cost-effective NDT. ⁴

This study focuses on the conceptual SHM technique to validate whether LWs have utility in the detection and localisation of pre-damage-level heat spots within composite panels and investigates the ability to determine their severity. An anomaly measure based on the time shift (TS) of the measured signal was proposed as part of this study. An appropriate heat-spot detection technique was suggested, and an experimental investigation was conducted utilising active heat-spot detection methods employing piezoelectric elements. The study employed two CFRP composite panels, and a network of sensors facilitated the detection and localisation of any signal anomalies attributed to localised heat sources. Preliminary studies conducted on the first composite panel informed the final experiment design and optimisation of the sensor network needed for heat-spot identification. Thus, comprehensive insights into the behaviour of LWs under differing thermal conditions were acquired. The deviation index (DI) in terms of TS, proposed in this paper, was found to be effective for detecting heat spots and the most precise for their localisation.

The rest of the article is organised as follows: the second section I explains the overall methodology of the suggested framework and the experimental investigation for heat-spot detection and localisation; the third section II presents and discusses the obtained results; and the fourth section summarises the conclusions and suggests some future work.

Methodology

In this section, the methodology is explained for the experimental design and setup, preliminary experiments, data preprocessing, optimisation and heat-spot identification experiments conducted in this study.

Materials and samples

Two identical test specimens, CFRP panels with a quasi-isotropic configuration [±45/0/ $\overline{90}$ ]s, of seven layers and an overall thickness of 3 mm, referred to hereafter as panels 1 and 2, were used as the experimentally tested samples. Both CFRP panels had dimensions of 290 mm by 310 mm, as shown in Figure 1(a) and (b).

Figure 1.

(a) Piezoelectric sensor placement on panel 1, (b) piezoelectric sensor placement on panel 2, and (c) the whole experimental setup.

Experimental setup

Networks of surface-mounted sensors were arranged across the composite panels and used to detect and localise any ultrasound-signal changes, as shown in Figure 1(a) and (b). The used Lead Ziconate Titanate (PZT) elements were of type PZ27 from Ferroperm Piezoceramics A/S with a diameter of 10 and 1 mm thickness. The type was chosen as a compromise between sensitivity and temperature-dependent performance. For provisional testing, two PZT elements were placed on panel 1 at either end of the composite panel, along the centreline, as shown in Figure 1(a). A sensor network of PZTs was later optimised and distributed on panel 2 to enclose a rectangular area, as shown in Figure 1(b). Throughout testing, one PZT element operated as the actuator, while the remaining functioned as sensors, with the actuator role rotating among all PZT elements sequentially. Both panels were simply supported using foam placed under their left and right sides to ensure consistent boundary conditions and reduce signal-interfering vibrations.

The experimental setup (Figure 1(c)) consisted of a data-acquisition system, including a custom-made multiplexer ²³ which switched between the transmit-receive sensor pairs, a TiePie Engineering Handyscope-HS3 PC acting as a function generator and oscilloscope, sensors and a heat lamp. The infrared (IR) heat lamp was positioned vertically above the composite panels by a clamp stand to allow a heat spot to be imposed on the composite, as shown in Figure 1(c). The heat spot was induced using a Philips IR300CH 300 W E27 IR heat lamp (179 mm, 230/250 V) (RS Components Ltd, Birchington Road, Corby, Northants, NN17 9RS, UK) and a focusing cone.

The use of a 300-W bulb ensured a high enough temperature could be reached while minimising wait time. A simple reflective cone was constructed from aluminium and used to focus the IR light into a heat spot. The heat spot was concentrated to a diameter of 25 mm, reducing the area of the sample exposed to direct heat. Thermocouples, with digital liquide crystal display (LCD) screens, were fixed to the composite panels using heat-resistant polyimide masking tape to monitor and control the temperature variation of the heat spot. These were strategically positioned at the periphery of the heat spot on both the top and bottom of the panel. An additional thermocouple was positioned on the top of the panel, 40 mm from the centre of the spot. This allowed the detection of heat changes directly on the heated surface and the reverse side of the panel, as well as monitoring heat dispersion. The design of the experiment is inherently flexible as the heat-lamp placement and distance from the panel surface can readily be altered, allowing for the temperature and location of the heat spot to be controlled and varied. Hence, the level of severity of the heat spot inflicted upon the composite panel can be adjusted. The temperature was closely monitored and controlled by turning the lamp on and off as necessary. This was carefully tuned beforehand to ensure minimal fluctuation of temperature.

It should be noted here that the authors were not trying to mimic the dynamics of the transient heating process in real conditions. The purpose was to mimic the condition after the heating occurs, leading to the existence of a heat spot of a certain temperature and diameter in the monitored structure. The aim was to show that if such a condition occurs, the suggested technique can detect and localise the heat spot, even before any damage occurs in the structure. With this objective in mind, the designed experimental setup is considered good enough, as it allows the creation of a heat spot of a specific diameter and temperature during measurement.

Experimental methodology

A sinusoidal tone burst (12 V peak-to-peak) enclosed in a Gaussian window was used as the input signal for the actuator. ¹ The signal was initially actuated as a chirp signal and then subsequently dechirped after acquisition. ¹ This improved the signal-to-noise ratio (SNR) while avoiding the use of an amplifier. By dechirping the signal, only the desired five-cycle Hann-windowed sinusoidal tone burst was used, making it easier to identify modes, calculate velocities and analyse different wavepackets. The Gaussian chirp signal was created using the number of sample points ( $S_p=2^{14}$ ), the centre excitation frequency ( $f$ ), the sampling frequency ( $F_s=10\mathrm{MHz}$ ), the number of averages ( $\mathrm{Av}=16$ ), the number of cycles ( $C_n=5$ ) and the stretch factor ( $S_f=12$ ) as input parameters. The signal input amplitude was kept constant throughout testing. Activation and acquisition of wave signals were fulfilled via a signal-generation and data-acquisition code developed using MATLAB® (1994–2026 The MathWorks, Inc.).

Several preliminary experiments were carried out on panel 1 to comprehensively understand the effect excitation frequency and heat-spot temperature have on the measured signals. These experiments were also used to determine the sensing-path coverage of the piezoelectric sensors. The experimental data from preliminary tests on panel 1 informed the suitability of different DIs and the optimisation of the sensor-network design on panel 2. Detection and localisation experiments were subsequently conducted on panel 2, aiming to determine the potential of LWs for examining heat sources within composite panels. Heat spots were identified using a well-known probability-based localisation imaging technique. ²⁴

A flowchart summarising the methodology is shown in Figure 2. These steps are further detailed in the subsequent subsections.

Figure 2.

A flowchart of the proposed methodology for heat-spot detection and localisation.

Preliminary experiments

Panel 1 was set up as detailed in ‘Experimental setup’ section and shown in Figure 1. The heat lamp was initially arranged for all preliminary tests such that a heat spot of 25 mm diameter was created along or away from the sensing path of the panel, as shown in Figure 3.

Figure 3.

The sensing path and heat spot location for (a) the frequency and temperature experiments and (b) the path-coverage experiment.

The first preliminary test (Figure 3(a)) examined the impact of different excitation frequencies on heat-spot detection. This provided an understanding of the frequency response characteristics of the composite material and aided the selection of optimal frequencies for improved detection accuracy and technique refinement. LW signals were recorded at room temperature (RT) (20°C) and at heat-spot temperatures ranging from 25 to 55°C at 5°C intervals. These results were subsequently analysed. The experiment was conducted across a range of excitation frequencies from 100 to 400 kHz at 50 kHz intervals, as well as at 120 kHz. The LW-mode identification was based on dispersion curve analysis, with further validation through existing studies on LW transmission in CFRP panels with similar properties. A limit of 55°C was imposed on the panel’s heat spot to avoid irreversible surface damage that could distort subsequent readings. This limit was deliberately set well below the possible glass-transition temperature range of the composite, 80–220°C. ²⁵

The experiment setup was then repeated (Figure 3(a)), using the same methodology as previously defined, to determine the temperature threshold at which the heat spot became distinctly discernible in the signals, and establish an optimal temperature range for further experiments. A critical temperature threshold at which irreversible damage was caused to the composite panel due to heat exposure was also investigated. This provided insights into what temperature to use for the identification experiments by examining the temperature effect on the measured signals, assessing the sensitivity of the signals to localised temperature changes along the sensing path, and therefore finding the best anomaly measures that would be sensitive to such changes. Additionally, this aimed to check if any distinctive signal features or significant changes could be observed, in the signals or the anomaly measures, when permanent damage occurs. Initially, a benchmark signal was recorded with the panel undamaged at RT (20°C). The heat spot temperature was then raised systematically in 10°C increments, with signal measurements taken at each interval until a temperature of 100°C was reached. This experiment was conducted using a range of excitation frequencies ranging from 100 to 300 kHz at 50 kHz intervals. Due to the limitations of the setup, a higher temperature, and therefore permanent damage, could not be easily reached.

The third preliminary test (Figure 3(b)), conducted across a range of excitation frequencies (100–300 kHz at 50 kHz intervals, as well as at 120 kHz), determined the sensing-path coverage, that is, identifying the point at which the heat spot becomes undetectable when moving away from the actuator-sensor PZT path (sensing path). This gave insights into the spatial sensitivity of heat-spot detection, facilitating sensor-placement optimisation. Lamb-wave readings were initially acquired without the heat spot to establish a benchmark, and subsequently with the heat spot maintained at 45°C. The heat spot was then incrementally displaced towards the panel’s edge (away from the sensing path), with readings recorded at each interval. Before the heat spot was moved, the composite panel was left to cool to RT. This process was repeated every 10 mm, starting from a displacement of 0 mm (heat spot on the path), until reaching 100 mm away from the sensing path (total of 10 steps). Each displacement step was labelled accordingly: D0 (0 mm), D1 (10 mm), D2 (20 mm), … and D10 (100 mm).

Preliminary results

The optimal excitation frequency among those tested was investigated, considering LWs’ dispersion characteristics, where velocity varies with frequency and material thickness. Utilising multiple frequencies enables targeting defects of varying sizes and types. Lower frequencies, characterised by longer wavelengths, are more sensitive to larger defects like delamination or cracks, ²⁶ while higher frequencies, with shorter wavelengths, are better suited for detecting smaller defects or localised material-property changes, such as those induced by heat exposure. ²⁶ Additionally, different LW modes, (e.g., the fundamental $A_0$ and $S_0$ modes), exhibit varying propagation characteristics, interacting differently with defects. ²⁷ Targeting different LW modes necessitates examining their strength of appearance in the measurements and their clarity, in terms of being separated from other modes and boundary reflections. Multifrequency experimentation allows the identification of the most sensitive frequency for the investigated type of damage/change, heat spots in this case. Environmental noise can influence signal clarity^28; exploring multiple frequencies also allows the identification of the frequency range offering the best SNR. ²⁸ A higher SNR enhances the signal clarity against background interference and facilitates precise assessment of damage/heat-spot presence and severity.

For identification of the modes, panel 1 was investigated at different frequencies. The resulting experimental signals were compared to the theoretical dispersion curves in Figure 4, indicating the two fundamental modes and some higher symmetric and anti-symmetric modes. The dispersion curves were determined using the Dispersion Calculator ²⁹ for a seven-layer [±45/0/( $\overline{90}$ )]s CFRP of 3 mm thickness. As shown in Figure 4, for frequencies below 350 kHz, only two LW modes exist: the fundamental anti-symmetric ( $A_0$ ) and the fundamental symmetric ( $S_0$ ) modes, with $S_0$ being identified as the fastest mode.

Figure 4.

LW dispersion curves of the quasi-isotropic CFRP panels: seven layers, panel thickness 3 mm, [±45/0/( $\overline{90}$ )]s. ²⁹ LW: Lamb wave; CFRP: carbon fibre-reinforced polymer.

For frequencies exceeding 350 kHz, higher symmetric and anti-symmetric modes may appear in the signal. As there are inadequate results at such frequencies, frequencies greater than or equal to 350 kHz will be disregarded in the subsequent sections to avoid interference from unwanted modes. For the other frequencies investigated (100–300 kHz), the $S_0$ was assumed to be the first arriving transmission in the received signals and subsequently used for all analyses; this was confirmed by calculating the mode’s group velocity. The group velocity and amplitude of the second peak of the first wavepacket were plotted against the excitation frequency, as shown in Figure 5(a) and (b), respectively. At the tested excitation frequencies, the group velocity ranged between 5670 and 6060 m/s, as depicted in Figure 5(a), which is consistent with the $S_0$ mode in the theoretical dispersion curve (Figure 4) and other studies. ³⁰

Figure 5.

(a) Group velocity and (b) amplitude of the second peak of the $S_0$ mode versus the central excitation frequency–first preliminary experiment.

The signal strength of the S₀ mode was assessed for each test frequency (see Figure 5(b)). Higher signal amplitudes were observed at 200 and 250 kHz, reaching 1.78 and 1.76 V, respectively, which might be indicative of greater inspection accuracy and being less prone to noise effects. However, 100, 120 and 150 kHz frequencies exhibited clearer signals. At these frequencies, better mode separation between the first arrivals of the $S_0$ and $A_0$ modes was observed as there is a substantial difference in group velocity between the two modes (Figure 4). As higher frequencies have shorter periods, the modes span over a shorter time and thus can be more separated. However, sometimes, the boundary reflection of the $S_0$ mode can arrive between these two modes, contaminating the end of the $S_0$ mode and part of the $A_0$ mode, depending on the travelled distance and the PZT positions with respect to the panel edges. This was seen at 200 and 250 kHz which contained numerous reflections, making mode distinction challenging. Noise levels were also considered, with 250 kHz exhibiting significant background noise. Based on the above analysis, the frequencies chosen for panel 2 tests were 120, 200 and 300 kHz. The 120 kHz frequency was selected for its clear signal with minimal electromagnetic interference and a high SNR that facilitated straightforward interpretation; the 200 kHz for its highest second peak amplitude indicating its potential accuracy; and the 300 kHz for its clear signal and relatively high second peak amplitude. Panel 2 testing at multiple frequencies aimed at obtaining a diverse range of signal readings for a comprehensive analysis.

The absolute second peak values of the $S_0$ mode were selected to analyse the TS and amplitude variation (AV) (Figure 6), compared to the benchmark signal (RT ≈ 20°C), as the localised temperature was elevated in the second preliminary experiment (temperature range: 25–55°C in steps of 5°C).

Figure 6.

The extracted S₀ mode for a heat spot of 20°C (red) and 55°C (blue) with TS and AV labelled; 120-kHz central excitation frequency. TS: time shift; AV: amplitude variation.

The results of the 120 kHz central excitation frequency are depicted in Figure 7. As the temperature of the heat spot increases linearly, a clear increase in both the TS and AV from the benchmark signal is observed in Figure 7(a) and (b), respectively. This alteration in the signal pattern serves as a clear indication of the sensitivity of LW measurements to the presence of heat spots. The plots also show a strong direct correlation between the two studied signal features (TS and AV) and the localised temperature level. Based on both plots, it can be concluded that a heat spot with a temperature greater than or equal to 25°C (5°C elevation from the benchmark temperature) can be detected using the $S_0$ mode, which therefore renders it suitable for further investigations. In addition, there is a large increase in the TS between 20 and 30°C (Figure 7(a)) and in the peak signal amplitude between 25 and 35°C (Figure 7(b)), after which they both increase in a nearly linear fashion with the increase in temperature. This means there might be high confidence in heat-spot detection for temperatures of 35°C or higher. Hence, 35–55°C was chosen as an optimal temperature range for the localisation experiments, as this temperature range shows an obvious shift in time and a clear change in peak amplitude in a predictable monotonic trend.

Figure 7.

The change in the S₀ second peak’s (a) arrival time and (b) amplitude, due to the increase in the localised heat-spot temperature—second preliminary experiment; 120-kHz central excitation frequency.

The sensors’ direct range of detection was analysed using the results of the third preliminary test. Similarly, the absolute second peak of the $S_0$ mode was selected for analysis. The AV for all the damage cases was normalised based on the highest value of AV (in this case D0 at the centre of the sensing path) such that the highest AV was equated to 1. The absolute TS and normalised AV for each damage case (D0–D10) were compared to the healthy benchmark signal and plotted, as shown in Figure 8 for 120 kHz. The heat spot at a 0 mm displacement from the sensor path (D0) shows a clear TS (Figure 8(a)) and AV (Figure 8(b)), indicating a clear presence of the heat spot. The clear indication of the heat spot (in both TS and AV) continues up to a 50 mm displacement from the sensing path (D5); this is particularly prominent in Figure 8(a) and shown by the clustering of corresponding data points in Figure 8(b). For both graphs, there is less effect from the heat spot when displaced more than 50 mm from the sensing path, suggesting that for displacements of 60–100 mm, the heat spot was outside the direct range of the sensors (sensing path) and could not be reliably detected. This coincides with an 85% decrease in AV, illustrated by the dashed line at 15% in Figure 10(b). This trend was seen across all the analysed excitation frequencies.

Figure 8.

The change in the S₀ second peak’s (a) TS and (b) AV due to the increase in the heat spot displacement away from the sensing path—third preliminary experiment; 120-kHz central excitation frequency. TS: time shift; AV: amplitude variation.

Based on the above results, the sensing-path coverage was fixed at 50 mm; this was applied to both the sensor-network optimisation and the heat-spot-imaging algorithm.

In order to determine whether the 50 mm sensing path coverage is valid for excitation frequencies of 200 and 300 kHz, the absolute TS and normalised AV for each defect case (D0–D9) were compared to the healthy benchmark signal and plotted, as shown in Figure 9 (f = 200 kHz) and Figure 10 ( $f$  = 300 kHz).

Figure 9.

The change in the S₀ s peak’s (a) TS and (b) AV due to the increase in heat spot displacement—third preliminary experiment; 200-kHz central excitation frequency. TS: time shift; AV: amplitude variation.

Figure 10.

The change in the S₀ s peak’s (a) TS and (b) AV due to the increase in heat spot displacement—third preliminary experiment; 300-kHz central excitation frequency. TS: time shift; AV: amplitude variation.

From the graphs in Figures 9 and 10, there is a clear increase in both TS and AV due to the heat spot at a 0 mm displacement from the sensor path (D0), compared to the benchmark signal. This indicates a clear presence of the heat spot. This pronounced indication of the heat spot is present up to a 50 mm displacement from the sensing path (D4). As seen in both Figures 9 and 10, there is reduced effect from the heat spot when displaced more than 50 mm from the sensing path. This suggests that the heat spot was outside the range of the sensors for displacements of 60–100 mm. As was the case at 120 kHz, this coincides with an 85% decrease in amplitude shift at both 200 and 300 kHz, shown by the dashed line at 15% in Figures 9(b) and 10(b). This confirms the suitability of a 50 mm sensing path for excitation frequencies of 200 and 300 kHz.

Heat-spot localisation experiments

The results of the preliminary experiments were used to optimise a sensor network for heat-spot identification, as later outlined in ‘Optimisation’ section. The optimised sensor network was then tested to assess its ability to detect and localise heat spots of varying severity at various excitation frequencies. These experiments were carried out using panel 2. The heat lamp was arranged so a 25 mm diameter heat spot was created at three distinct locations (tested one at a time) detailed in Figure 11(a). A coordinate system was employed, where the lower left corner of the plate was set to be the origin, and the monitoring area is spanned by the horizontal x and vertical y axes, as shown in Figure 11(a).

Figure 11.

(a) Panel 2 with the employed optimised sensor network of eight surface-mounted PZTs and the coordinates of the three tested heat-spot locations; and (b) all the sensing paths and the actual heat-spot locations used for heat-spot imaging.

Thermocouples were positioned for each location of the heat spot as previously described in ‘Experimental setup’ section. To investigate varying degrees of heat severity, three different temperatures (35, 45 and 55°C) were used. Three excitation frequencies (120, 200 and 300 kHz) were used to explore the influence of frequency variation on heat-spot identification performance at each distinct temperature. The temperatures and frequencies were chosen based on the results of the preliminary experiments. Data were collected from the sensor network before (benchmark readings) and after applying any localised heat changes for all sensing paths (Figure 11(b)). This experimental protocol was replicated across the three distinct heat spot locations, location 1, location 2 and location 3 (Figure 11(a)).

Data processing

Signal pre-processing

After data acquisition, pre-processing was performed for all the measured signals. Although the fundamental antisymmetric $A_0$ mode is often reported to be sensitive to surface heating effects and debondings, its applicability was evaluated to assess its suitability in the present study. The preliminary analyses performed assessed the feasibility of using the $A_0$ mode for heat-spot interrogation; however, it was found that, for the frequency range considered in preliminary experiment 1 (100–400 kHz), the $A_0$ mode could not be reliably isolated. As illustrated in Figure 12, at tested excitation frequencies (in this case 120 and 300 kHz), wave packets arriving after the fundamental $S_0$ mode is affected by superposition with other propagating modes as well as by boundary reflections. This results in complex, overlapping signal components that are difficult to interpret consistently and unsuitable for quantitative comparison. In contrast, the $S_0$ mode arrives first, exhibits limited modal interference and can be more robustly extracted from the measured response. Consequently, while the $A_0$ mode was considered, its strong susceptibility to mode superposition and reflections in the examined configuration led to its exclusion from further analysis in favour of the $S_0$ mode.

Figure 12.

Transmit signal for wave excitation (black) and the captured response (blue) for the case of (a) 25°C heat spot and 120 kHz excitation frequency; and (b) 25°C heat spot and 300 kHz excitation frequency.

The fundamental symmetric $S_0$ mode was found by other researchers to be highly sensitive to debonding and small-scale surface damage, ¹⁹ as well as being the fastest mode present for the frequencies analysed.^19,31 This was also confirmed in this study by evaluating the dispersion curves of the examined CFRP panels (‘Preliminary results’ section). Being the first arriving transmission, this mode contains fewer reflections compared to other parts of the signal, meaning it is easier to isolate. In addition, this first wavepacket showed a better trend in the performed experiments; therefore, it was selected to interrogate the structure under study. Figure 13(a) shows a typically captured signal at 120 kHz, and Figure 13(b) a zoomed-in portion of the response showing the $S_0$ mode used for this investigation. In both figures, the transmit signal was scaled to fit within the same range as the captured signal, for plotting and visualisation purposes.

Figure 13.

(a) Transmit signal for wave excitation (black) and the captured response (blue) and (b) the extracted S₀ mode.

As part of data preprocessing, the direct current (DC) offset (vertical shift in the amplitude of the signals) was removed and adjusted to zero. A low-pass filter was also applied to remove the high-frequency noise and allow a clearer analysis of the lower-frequency LW information. ²¹ As it is the fastest mode existing at the excited frequencies, the $S_0$ mode was identified as the first transmitted wave packet. According to its known group velocity, a starting point was chosen in each signal based on the expected position of the $S_0$ mode. ³¹ The electromagnetic noise, seen overlapping with the transmit signal in Figure 13(a), was removed and the $S_0$ mode separated from the whole signal. The data points falling between the first five wave peaks, located after the chosen starting point, were only kept. The cutting and cleaning process was semi-automated; it had to include some manual interference to ensure it was performed without any errors while maintaining accuracy. The signals underwent resampling before the DI was calculated due to the small AVs and TSs that are sometimes not captured during analysis because of the insufficient sampling rate.

Anomaly measures

As part of this study, it is important to investigate and assess the impact of localised-heat effects on the measured signals using quantifiable metrics. This necessitates adopting/suggesting several anomaly measures to examine their sensitivity and find the most suitable DI. In recent applications, ²⁴ the root mean squared deviation (RMSD) has emerged as a valuable DI. RMSD operates within the time domain, offering a comprehensive approach to signal analysis. ²⁴ Its efficacy in Lamb-wave anomaly detection stems from its capacity to account for both AV and TS between two signals. AV was the second anomaly measure considered; the amplitude of a wave can quantitatively reflect the energy carried by the signal. ³² Damage located at the propagation path leads to reflection and scattering of LWs, causing a reduction of signal energy. ³² In terms of this study, a change in amplitude could occur, assuming the localised heat is expected to locally affect the material properties. Hence, the ratio of the peak amplitude in the heat-affected signal to that of the benchmark signal can be used as an indicator to depict the presence of a heat spot. The third anomaly measure, proposed for this study, was in terms of TS. Localised heat could be presumed to induce dimensional changes, such as localised expansion. These alterations, in conjunction with material changes, could affect the time of flight (ToF) of the interrogated mode, $S_0$ . ³²

The RMSD DI was calculated by measuring the amplitude deviation of all the data points compared to the corresponding data points in the benchmark signal, as shown in Equation (1), ²⁴

$$\mathrm{RMSD}=\sqrt{\frac{{\sum }_{i=0}^{N-1}(S_d\left(i\right)-S_b\left(i\right){)}^2}{{\sum }_{i=0}^{N-1}{S}_b(i{)}^2}}$$

(1)

where the index $i$ corresponds to the $i$ th data point of the signal, and $S_b$ and $S_d$ are the signals measured before (benchmark) and after introducing the heat spot, respectively. This was applied to both the whole signal and the first five peaks of the $S_0$ mode.

The AV DI was a direct comparison between the amplitude of the $S_0$ mode before and after a heat spot was created. The AV DI was defined as in Equation (2), ²⁴

$$\mathrm{AV}=|1-\frac{A_{\mathrm{peak}}\left(S_d\right)}{A_{\mathrm{peak}}\left(S_b\right)}|$$

(2)

where $A_{\mathrm{peak}}$ is the amplitude of the chosen peak of the $S_0$ mode. Equation (2) was applied to the second peak of the $S_0$ mode, as this peak is less prone to boundary reflections and is of a large-enough amplitude to avoid measurement-noise effects.

The TS DI is proposed in this study as the ratio of the absolute time difference between corresponding peaks in the benchmark and heat-affected signals, with respect to the period of the wave at the excitation frequency ( $f$ ), as shown in Equation (3),

$$\mathrm{TS}=\left|\frac{t_d-t_b}{T}\right|$$

(3)

where $t_b$ represents the time location of a peak in the healthy benchmark signal, $t_d$ represents the time location of the corresponding peak in the heat-affected signal, and $T$ is the period of the wave at the excited centre frequency (calculated as $T=1/f$ ). The larger the difference between the locations of the corresponding peaks, the greater the DI, indicating a greater TS between the signals. Similarly, Equation (3) was applied to the second peak of the $S_0$ mode.

The three used DIs include an absolute value or a square in their equations, making them suitable for amplitude and TSs in both positive and negative directions. As going from lower to higher temperatures at the heat spot produced a TS forward (slower TOF), this means that going from higher to lower temperatures has the opposite effect (similarly regarding amplitude changes). This fact was confirmed in the literature by authors such as Šedková and Vích, ¹⁵ and is related to thermal expansion in the material at elevated temperatures, which reduces density/stiffness and slows the speed of the ultrasonic wave. Since time and AVs in any direction can be sensed, the proposed DIs are expected to remain effective even when capturing cooling effects.

The three distinct DIs yield varying anomaly measures for each respective sensing path, necessitating normalisation before comparison. To achieve this, a normalisation method was proposed, where the anomaly values of all sensing paths were normalised with respect to the path with the highest DI. ²⁴ Each DI was thus normalised across all sensing paths, resulting in a standardised range between 0 and 1. Based on this definition, DI = 0 indicates the absence of any heat spot, while a non-zero value indicates the presence of a heat spot, with DI = 1 indicating the most affected path within the sensor network. By normalising, the comparability of the DI values is ensured, reflecting the relative affected levels across all paths.

Localisation imaging technique

Fifty-six sensing paths were available from the optimised network of eight PZT sensors placed on panel 2. Overlapping sensing paths connecting sensors on the same edges (e.g., paths 1–2, 2–1 and 1–3) were neglected to prevent a high intersection of sensing paths, as this could potentially skew and reduce the accuracy of the image reconstruction. The configuration of the remaining 32 sensing paths is shown in Figure 11(b). Using a data fusion technique, anomaly measures obtained for the paths were utilised to construct the localisation image. The heat spot is expected to be located around the intersection of the paths with the highest anomaly measures. ²⁴

The image ( $I$ ) was constructed by dividing the monitored area into uniform 1 mm² grid points. The presence of a heat spot at each grid point was evaluated from all sensing paths by merging the anomaly measure perceptions. The probability of a heat spot at a grid point $(x,y)$ in the observed area is given by Equation (4), ²⁴

$$I(x,y)=\sum _{j=1}^J{P}_j(x,y)=\sum _{j=1}^J{\mathrm{DI}}_j{y}_j(z)$$

(4)

where $P_j(x,y)$ is the probability of a heat spot at a grid point $(x,y)$ obtained from the anomaly measure of the jth path, ${\mathrm{DI}}_j$ is the anomaly measure (or DI) for the jth path, and $y_j(z)$ is the normal distribution function for the jth path (see Equation (5)). To address potential heat spot presence near paths, the anomaly measure’s impact was modelled as a normal distribution within the path coverage, with maximum influence at the path. The normal distribution function is shown in Equation (5), ²⁴

$$y\left(z\right)=\frac{1}{\sigma \sqrt{2\pi }}{\mathrm{e}}^{\frac{-(z-\mu {)}^2}{2{\sigma }^2}}\mathrm{for}-\infty <z<+\infty$$

(5)

where $\sigma$ is the standard deviation and $\mu$ is the mean of the normal distribution model. $\mu$ was set equal to zero as the effect of a heat spot located on the sensing path is stronger than a heat spot further from the sensing path. In turn, $z$ defines a rectangular affected zone for each sensing path by equating the same effect for all the grid points that are equidistant from the path; $z$ is the normal distance from the grid point to the sensing path. The fusing process assigned a uniform heat-spot sensation to grid points with the same value of $z$ . ²⁴ The preliminary investigation in ‘Preliminary experiments’ section determined the value of $\sigma$ for the CFRP panels. The study concluded that the effect of a heat spot further than 50 mm from the sensing path is negligible; hence, $\sigma$ was set to 50 mm.

Results and discussion

In this section, the experimental results are shown for the heat-spot detection and localisation, respectively, and a discussion is provided about the inference and evaluation of the results. Further, refinement and optimisation of the experimental approach are considered for heat-spot detection and localisation. The results and the efficacy of the proposed approach is discussed, reflecting on its potential for the continuing development of SHM and NDT.

Anomaly-measure selection

It is important to investigate the sensitivity of each of the anomaly measures, suggested in ‘Anomaly measures’ section, to localised temperature variation and explore the influence of excitation frequencies on this sensitivity. Using the experimental data from the second preliminary test on panel 1, graphs were generated using the sensing paths 1–2. The frequencies chosen for the localisation tests, 120, 200 and 300 kHz, were analysed across all DIs. The change in the DI value with respect to temperature was plotted for each respective DI and compared across frequencies, as shown in Figure 14.

Figure 14.

Change in the DI values with respect to the heat-spot temperature for central excitation frequencies of (a) 120 kHz, (b) 200 kHz and (c) 300 kHz. DI: deviation index.

The presence of a linear trend for a DI suggests suitability for severity assessment of the heat spot. In Figure 14(a), it is seen that the RMSD DI and RMSD (full signal) DI demonstrate linear behaviour at 120 kHz. Therefore, these two DIs could be considered the most appropriate for this frequency, with the RMSD (full signal) DI yielding the most consistent result. The AV DI does not show a positive linear trend at this frequency, implying that it may not be a suitable DI for lower excitation frequencies. For Figure 14(b) and (c), all DIs begin to display positive trends. The general trend in Figure 14 suggests that the value of each DI increases with heat spot temperature. The consistency in trend across DIs generally increases at higher frequencies compared to 120 kHz, implying that higher excitation frequencies, in the range of 200–300 kHz, are better suited to severity assessment. Based on the results of this section, all the suggested DIs were employed in the heat-spot identification tests.

Optimisation

An experimental study was conducted on panel 2 to both detect and localise heat spots in the carbon-fibre composite sample. For this purpose, a network of sensors was placed around the edges of the panel. Optimisation of the sensor network was carried out on SenOpT MATLAB-based software, ³³ leveraging parameters derived from the preliminary experiments. The optimisation aimed to maximise the coverage of a grid of control points while minimising the number of PZTs used to still attain the required coverage level and percentage. Readers may refer to the study by Ismail et al. ³³ for full details of the optimisation methodology and a link for the software.

For optimisation, the path coverage was set to 50 mm, determined from the third preliminary experiment, while the maximum propagation distance was fixed at 600 mm (not a parameter of concern considering the small size of the panel). The preliminary configuration was set by specifying the minimum and maximum number of PZTs to be 6 and 14, respectively, and the PZTs to be uniformly distributed on the outer boundaries of the panel (before optimising their positions if needed). The number of control points was specified as 182 to provide a uniform grid for coverage calculation, with the level of coverage set to ensure each control point is covered by at least three sensing paths. The minimum percentage of coverage specified was 90%, mitigating the risk of blind spots and noncovered areas that could compromise the accuracy of the sensor network. Figure 15 shows the graphical user interface of SenOpt, ³³ including the used input parameters and the resulting optimised configuration of sensors. The optimised configuration includes the needed number of PZT transducers, their locations, the obtained coverage and the relative level of importance of each PZT (the impact on the coverage in the case the PZT is lost or broken).

Figure 15.

The graphical user interface of SenOpt ³³ including the used input parameters and the obtained optimised solution (number of PZT transducers, their locations and their relative level of importance).

A coordinate system, like the one described in the ‘Heat-spot localisation experiments’ section, was employed. Optimisation of the sensor network was required to maximise the efficiency and accuracy of the sensing layout, as well as to establish the minimum number of sensors required to achieve the desired level of coverage. The analysis revealed that a minimum of eight PZTs was necessary, achieving an optimised coverage of 97.8%. The optimised and the preliminary solutions were very similar, both uniformly distributed along the edges of panel 2. This is because the panel has no material discontinuities or geometrical complexities; hence, the used preliminary solution was near optimum in this case.

Heat-spot localisation results

The data for each heat spot location were analysed for the three chosen excitation frequencies using the DIs defined in the ‘Anomaly measures’ section. An example of the image reconstruction is shown in Figure 16 using the RMSD DI (five cycles) after inflicting a heat spot of 55°C at location 1. The actual and the predicted heat spot locations are represented by a cross and a square, respectively. Using their x–y coordinates, the error between the predicted and actual heat spot locations was calculated as the Euclidean distance ( $L^2\mathrm{norm})$ between the two positions. An average error was then taken for the three tested heat-spot locations to facilitate the visualisation of the results for each heat-spot temperature, excitation frequency and DI, as shown in Figure 17. When multiple spots are detected (with ≥ 95% probability), the average error of all the detected spots is reported (see examples in the Appendix A).

Figure 16.

Image reconstruction using the RMSD DI (five cycles) and various excitation frequencies for a heat spot of 55°C at location 1: (a) 120 kHz, (b) 200 kHz and (c) 300 kHz. RMSD: root mean squared deviation; DI: deviation index.

Figure 17.

Distance between the predicted and actual heat-spot locations (averaged over the three tested locations) for excitation frequencies of 120, 200 and 300 kHz, heat-spot temperatures of 35, 45 and 55°C, and all the DIs. DI: deviation index.

At location 1, using an excitation frequency of 120 kHz and the RMSD DI (five cycles), the error between the actual and predicted heat-spot locations is 37.48 mm, while at 300 kHz, the results improve, giving an error of 27.2 mm, as shown in Figure 16. Observations made for the 35 and 45°C heat spots gave a similar result. Analysis of the images and Figure 17 reveals that the accuracy of heat-spot localisation is dependent on the excitation frequency, with higher frequencies generally more consistent in producing more accurate results among various DIs. Nevertheless, the 120 kHz still shows very accurate localisations for the TS DI (third peak) and both RMSD DIs. Notably, RMSD DI (full signal) tends to give less accurate results with higher excitation frequencies.

Moreover, the results shown in Figure 17 suggest that as the temperature increases, so does the accuracy of the predicted heat-spot location, with a temperature of 55°C producing the most accurate predicted heat-spot location for image reconstruction. As an example (see Figure 18), for the case of location 2, using an excitation frequency of 300 kHz and the RMSD DI (five cycles), the error between the actual and predicted location of a heat spot of temperature of 35°C is 33.73 mm, while heating to 55°C leads to a significant decrease of the error to 11.70 mm.

Figure 18.

Image reconstruction using the RMSD DI (five cycles) and 300 kHz excitation frequency for a heat spot at location 2 of temperature of: (a) 35°C, (b) 45°C and (c) 55°C. RMSD: root mean squared deviation; DI: deviation index.

In most cases, accuracy increasing with temperature is seen to repeat for each DI and excitation frequency, especially when going from 35°C to the two higher temperatures. Based on the results from the various excitation frequencies and DIs, it can be concluded that a heat spot of 35°C can be easily detected; however, this temperature level is sometimes insufficient for a very precise localisation using some of the DIs.

Initially, the TS DI was proposed to detect time deviations due to temperature changes, the AV DI to capture only amplitude deviations, and the RMSD DI to account for both. All three DIs appeared valid and consistent during anomaly selection, ‘Anomaly-measure selection’ section. However, significant differences became evident when evaluating localisation performance. To evaluate the effect of the peak choice on the localisation performance of single-peak DIs, that is, AV DI and TS DI, the results of using the second peak and third peak of the first wave packet were both reported in Figure 17. While both peaks generally led to similar trends, significant discrepancies were noticed in several cases, with no clear superiority of either choice. In fact, the dependency of these two DIs on the values (time or amplitude) of single specific peaks has led to a poor localisation performance when compared to the RMSD DI, as evident from Figure 17 and shown in the example of Figure 19, while the RMSD DI (five cycles) was found to be the most accurate at localising the heat spots. Although the single-peak DIs are highly sensitive to localised changes, they only compare anomalies at one selected peak, making them susceptible to minor variations in amplitude or TS along any given sensing path. Such variations may sometimes arise from noise, slight coupling differences or path-dependent propagation effects rather than from the presence of a heat spot. Consequently, any small inconsistency at that single peak can disproportionately influence the DI value, leading to misleading localisation patterns. On the other hand, the RMSD DI (five cycles) evaluates cumulative differences in amplitude and phase over the entire five-cycle waveform, thereby capturing both TSs and AVs associated with thermal perturbations while averaging out random variations. This holistic consideration of the signal makes the metric more robust and less path-dependent, resulting in more consistent anomaly trends across all sensing paths. Consistency in the calculated anomalies directly improves the stability of the imaging algorithm and leads to more accurate heat-spot localisation compared to the single-peak DIs.

Figure 19.

Image reconstruction at location 1 using an excitation frequency of 300 kHz, a heat-spot temperature of 55°C, and various DIs: (a) TS (second peak), (b) TS (third peak), (c) RMSD (five cycles), (d) RMSD (full signal), (e) AV (seocnd peak) and (f) AV (third peak). DI: deviation index; TS: time shift; RMSD: root mean squared deviation; AV: amplitude variation.

Moreover, the RMSD DI (five cycles) is consistently more accurate than the RMSD DI (full signals). This could be due to the full signal in RMSD DI (Figure 19(c)) incorporating signal reflections and superpositions in the calculation, potentially compromising anomaly-measurement accuracy by distorting time and AVs at specific peaks. ³⁴ This can be problematic in LW-based damage characterisation, where multiple reflections can interfere with the measurement. Additionally, the incorporation of multiple modes might complicate DI calculation, hindering the isolation of specific features corresponding to heat spots. Further, signal shape and amplitude can vary across multiple sensor paths, potentially resulting in the RMSD (full signal) value having incomparable ranges between different paths. This would strongly affect the efficacy of the used imaging approach. This was unlikely the case for the RMSD DI (five cycles), as the shape of the first mode is typically consistent along different sensing paths.

Additional image reconstructions, using an excitation frequency of 200 kHz and a heat spot temperature of 45°C, for locations 2 and 3 are provided in Appendix A, presenting the same DIs as discussed in this section. These supplementary figures exhibit trends consistent with those observed in the main results shown in this section.

Further considerations

Potential for heat-level assessment

The potential of the utilised DIs for quantitative or semi-quantitative assessment of the heat levels was also investigated. Figure 20 shows the maximum, average and average of the top 20% RMSD DI among all the utilised sensing paths (without any normalisation) for different heat-spot locations, temperatures and excitation frequencies. While 120 kHz does not always show consistent results, it can be clearly seen from the plots of the 200 and 300 kHz excitation frequencies that all three metrics have a positive correlation with the temperature level of the heat spot. This means that the level of anomaly measured in the sensing paths has the potential to be utilised for estimating the temperature variation/level and hence enable preliminary assessment of potential damage levels. An accurate assessment, however, requires an in-depth study to investigate how to map the available anomaly levels to the exact heat level of single or multiple potentially available heat spots within the structure. Figure 21 shows similar results for the TS DI (second peak) and AV DI (second peak) at an excitation frequency of 300 kHz. It is evident that AV DI shows a similar potential at this frequency, while this is not as clear in the case of TS DI. The reason could be that the TS DI does not provide continuous values by nature since it is limited by the resolution of the time vector (sampling frequency) in the measured signals. This might sometimes lead to similar TS DI values between different temperatures when the change in the TOA is not captured in the time step of data acquisition. To overcome discrepancies from multiple excitation frequencies or different DIs, a possible solution could be through fusing information across various frequencies and DIs or using ML to predict the heat level from all these various inputs. ²⁴ This can be the subject of a future study.

Figure 20.

Maximum, average and average of the top 20% RMSD DI (five cycles) among all the utilised sensing paths for different heat-spot locations, temperatures and excitation frequencies: (a) 120 kHz; RMSD DI; maximum; (b) 120 kHz; RMSD DI; average of all; (c) 120 kHz; RMSD DI; average of top 20%; (d) 200 kHz; RMSD; maximum; (e) 200 kHz; RMSD; average of all; (f) 200 kHz; RMSD; average of top 20%; (a) 300 kHz; RMSD; maximum; (b) 300 kHz; RMSD; average of all; and (c) 300 kHz; RMSD; average of top 20%. RMSD: root mean squared deviation; DI: deviation index.

Figure 21.

Maximum, average and average of the top 20% TS DI (second peak) and AV DI (second peak) among all the utilised sensing paths for different heat-spot locations, temperatures and excitation frequencies: (a) 300 kHz; TS DI; maximum; (b) 300 kHz; TS DI; average of all; (c) 300 kHz; TS DI; average of top 20%; (d) 300 kHz; AV DI; maximum; (e) 300 kHz; AV DI; average of all; and (f) 300 kHz; AV DI; average of top 20%. AV: amplitude variation; TS: time shift; DI: deviation index.

Distinguishing heat-spot from other defects

Šedková and Vích ¹⁵ found that an increase in ambient temperature causes a time delay that increases with signal length, since more propagation in a material with reduced ultrasonic velocity builds up a delay in space and time. On the contrary, the authors also found that defects would cause only a localised modification within the signal, providing an easy tool to differentiate between defects and temperature changes and avoid false alarms. ¹⁵ This can be explained by the single/minimal passage of the wave through a localised defect region compared to the rest of the propagation in pristine material before reaching the sensing point. In the context of a sensor network, when the change in temperature is global, the TS would also be observed in all the actuator-sensor paths, in contrast to the effects seen only in the defect-affected paths in the case of a local defect. ¹⁵

However, this is quite different in the case discussed in the current paper, when trying to deal with localised heat spots/effects. The temperature change in Šedková and Vích’s ¹⁵ work was not local; it was a change in the operating temperature of the whole structure. On the other hand, since this work is targeting localised heat effects, this makes the problem similar to the localised defect effects on the signal. The only difference here is the time-dependence factor; the localised heat effects only exist during an extraordinary/unexpected event causing a localised heat spot (e.g., a lightning strike). When the event ceases to exist, and if no damage was incurred, the heat dissipates, and the signal goes back to its normal condition. If the heating causes any permanent damage or plastic deformation, some deviation would continue to exist within the signals even after the heating event ends.

Hence, real-time monitoring can help differentiate between event-based alarms (which could be related to heat spots) and continuous alarms (which would signify the existence of a defect—can be caused by the heating event itself). A suggested future work is to investigate the capability of different DIs in differentiating the continuity of the heating event versus permanent material damage/degradation caused by the excessive heating during the event.

Conclusion

This study investigated the suitability of using ultrasonic LWs to detect and localise heat spots of varying locations and temperatures within CFRP panels. An appropriate heat-spot detection technique was proposed, and an experiment was designed. LW measurements were collected using surface-mounted piezoceramic sensor networks. Preliminary tests proved the concept, demonstrated the effects of excitation frequency and temperature on the signals produced and determined the sensing-path coverage of the sensors. The localisation experiments were conducted with a range of temperature severity. Image reconstruction using various DIs was used to visualise the error between the actual and predicted heat-spot locations and determine the accuracy of multiple techniques and excitation frequencies. The heat spot was detected in all three tested locations and three levels of heat spot severity. Furthermore, a TS anomaly measure was suggested to quantify the deviation between pristine and heat-affected signals, as well as an AV, and RMSD DI. The RMSD DI was shown to be the most suitable among other DIs that rely on single-peak variations (in time or amplitude). It was generally concluded that higher temperatures led to a more accurate localisation, with 35°C sometimes being insufficient for very precise localisation using some of the tested DIs. The proposed LW-based methodology shows high sensitivity in detecting pre-damage heat spots, within the investigated composite material, and demonstrates proficiency in localising them. Future work may include examining the potential of non-linear LW features in localising the heat spots of lower heat levels. Ways of detecting and localising heat-induced damage after the heat spot cools down would also be examined.