Ultrasonic Guided Wave Health Monitoring of High-Temperature Aircraft Structures Based on Variational Mode Decomposition and Fuzzy Entropy

Abstract

This paper presents an innovative approach to high-temperature health monitoring of aircraft structures utilizing an ultrasonic guided wave transmission and reception system integrated with a zirconia heat buffer layer. Aiming to address the challenges posed by environmental thermal noise and the installation of heat buffers, which can introduce structural nonlinearities into guided wave signals, a composite guided wave consisting of longitudinal and Lamb waves was proposed for online damage detection within thermal protection systems. To effectively analyze these complex signals, a hybrid damage monitoring technique combining variational mode decomposition (VMD) and fuzzy entropy (FEN) was introduced. The VMD was employed to isolate the principal components of the guided wave signals, while the fuzzy entropy of these components served as a quantitative damage factor, characterizing the extent of the structural damage. Furthermore, this study validated the feasibility of piezoelectric probes equipped with heat buffer layers for both exciting and receiving ultrasonic guided wave signals in a dual heat buffer layer, a one-transmit-one-receive configuration. The experimental results demonstrated the efficacy of the proposed VMD-FEN damage factor for real-time monitoring of damage in aircraft thermal protection systems, both at ambient and elevated temperatures (up to 150 °C), showcasing its potential for enhancing the safety and reliability of aerospace structures operating under extreme thermal conditions.

1. Introduction

Hypersonic vehicles are highly regarded for their exceptional speed and maneuverability, but they endure more severe loads and temperature environments than conventional aircraft during their missions [1]. Therefore, their design must consider the thermal damage that these vehicles’ structures might suffer, as well as the diagnostic assessment schemes for structural damage under high-temperature conditions. However, traditional contact non-destructive testing (NDT) techniques require the aircraft to be grounded and disassembled for inspection, which is not only inefficient but also often fails to reach all areas that need to be inspected, and in some cases, may even introduce new damage. Thus, achieving online damage detection of the thermal protection structure of the aircraft has become an urgent challenge to be overcome in the field of hypersonic vehicle research [2,3].

Ultrasonic guided wave technology, with its advantages of online scanning, long-range coverage, global accessibility, and rapid response, offers the possibility of online inspection for large-scale equipment structures [4,5,6]. The general process of the structural ultrasonic guided wave damage diagnostic method is to use the piezoelectric crystal sensor network bonded on the surface of the structure to stimulate and receive ultrasonic guided waves. The location and severity of the damage can be identified by extracting the signal factors related to the damage characteristics in the guided wave signal, and then the health assessment and life prediction of the structure can be carried out [7,8,9]. In ultrasonic guided wave damage monitoring technology, piezoelectric active crystal sensors (PWASs) have the characteristics of simple networking and low power consumption, and can be installed on the structure without affecting the structural integrity, so they have become a common sensing technology [10,11].

In the high temperature environment faced by thermal protection structure damage monitoring technology, the general ultrasonic guided wave monitoring process will face the risk of high temperature depolarization of piezoelectric chip sensors. Prof. Zhanjun Wu [12] investigated the change process of the performance of a sensor pasted on the surface of a structure at different temperatures and found that the excitation ability of the sensor gradually decreased with the change of temperature, and a sharp decline occurred at 100 °C. Prof. Fu-kuo Chang [13] proposed two methods of analytical model and numerical simulation to compensate for the influence of temperature on the response of a piezoelectric sensor. Parametric studies showed that surface-mounted piezoelectric transducers established a linear functional relationship between a change in sensor signals and a specific combination of material properties within a certain temperature range; however, over a certain temperature range, the sensor depolarization resulted in a loss of damage diagnostic ability of the monitoring system.

In response to this challenge, the method of welding a waveguide rod on a metal pipe was adopted in the field of high-temperature pipeline damage detection. The waveguide rod plays the role of heat dissipation and ultrasonic waveguide at the same time [14,15,16,17]. Se-beom’s [18] research showed that the waveguide rod-based damage diagnostic system had a stable operation in temperature cycles up to 150 °C for 3300 h. Referring to aircraft structure assembly specifications, we used zirconia ceramic columns with stable high-temperature performance as the heat buffer layer, installed the piezoelectric sensors at the top of the buffer layer, and permanently installed them on the cold side of the thermal protection structure through high-temperature adhesive. This method can continuously measure changes in structural damage in real time by exciting ultrasonic guided wave energy and improves the efficiency of damage monitoring through a distributed sensor network. In order to solve the nonlinear effect caused by the interface of the bonded waveguide, it is necessary to extract the principal component from the complex nonlinear and non-stationary signals by means of modal decomposition signal processing technology. At the same time, in view of the complex signal environment, it is necessary to propose strong robust signal features as damage factors.

The guided wave excitation mode based on a thermal buffer layer has the problem of strong noise interference and mode aliasing, and the traditional signal analysis method finds it difficult to effectively characterize the structural damage [19]. VMD is commonly used in the diagnosis of guided wave damage in low SNR ultrasound [20,21,22]. This method can be used to separate useful signals from noise signals by non-recursive variational decomposition and is suitable for the noise reduction of received signals in complex environments. The fault detection algorithm based on fuzzy entropy is robust to strong noise environments and is an objective fault detection algorithm in low SNR environments [23].

This paper used an ultrasonic guided wave transmission and reception system for high-temperature damage identification based on a zirconia heat buffer layer and proposed an online monitoring method for damage in the thermal protection system based on a composite guided wave of longitudinal waves and Lamb waves. In response to the structural nonlinear interference of guided wave signals caused by environmental thermal noise and the installation method of the heat buffer layer, this paper proposed a damage monitoring technique combining VMD with fuzzy entropy. The VMD was used to extract the main components of the guided wave signal, and its fuzzy entropy was used as a damage factor to characterize the severity of the damage. Finally, based on the dual heat buffer layer one-transmit-one-receive mode, the feasibility of piezoelectric probes with heat buffer layers for exciting and receiving ultrasonic guided wave signals was verified, as well as the feasibility of the VMD-FEN damage factor for online monitoring of aircraft thermal protection system damage at room temperature and high temperatures (150 °C).

2. High-Temperature Structural Damage Diagnostic Method Based on a Sensor Network with a Thermal Buffer Layer

2.1. Principle of Online Damage Monitoring

Structural overload and impact can lead to changes in physical properties and geometric boundaries, which is referred to as service-induced damage in structures. When ultrasonic guided waves propagate through a damaged structure, they may experience changes in wave structure due to parameter degradation or transformation in dispersion characteristics and propagation modes due to geometric changes. Therefore, by comparing and analyzing the changes in the characteristics of the benchmark signals and the monitoring signals (such as the amplitude, phase, and energy of the signals), the structural damage condition can be characterized and reconstructed. However, extreme environments can cause sensor failure and signal distortion, making it impossible to accurately characterize the structural damage based on the signal features [12,24].

The ceramic heat buffer layer is considered as a rod structure, and the vibration generated by the sensor d33 is equivalent to striking one end of the rod. At this time, energy mainly propagates in the form of longitudinal waves along the length direction of the rod structure. To address the issue of sensor failure in structural damage monitoring under high-temperature conditions, ultrasonic guided wave probes with thermal buffering capabilities were designed to excite and receive guided wave-longitudinal wave composite waves. The thermal buffer layer of the probe serves both to maintain the sensor temperature and to transmit guided wave signals, as shown in Figure 1a. Longitudinal waves are excited within the buffer layer by the actuator installed on the cold side, and then transmitted to the structure in the form of in-plane and out-of-plane displacements through the bonding interface. After modulation by the upper and lower surfaces, ultrasonic guided waves are formed within the structure, and at the receiving sensor position, a guided wave-longitudinal wave transformation is executed to form the received signal with the sensor array shown in Figure 1b. The size and installation position of the probe’s thermal buffer layer are shown in

Table 1. The size and installation position of the probe.

No.	1#	2#	3#	4#	5#	6#
X (mm)	100	100	100	300	300	300
Y (mm)	100	200	300	100	200	300
The thickness of buffer layer (cm)	1	2	3	1	2	3

.

Figure 1a illustrates the appearance of the online monitoring device for damage in the thermal protection system of high-temperature aircraft based on composite guided waves. The tetragonal zirconia ceramic thermal buffer layer is a smooth white column with a density of 6 g/cm³, a Young’s modulus of 205 GPa at room temperature, and a thermal conductivity of 2.2 W/mK.

The measurement principle of the dual thermal buffer layer one-transmit-one-receive mode for measuring damage in the thermal protection system of high-temperature aircraft is shown in Figure 2. The measurement signal is emitted by the excitation sensor, propagates along the thermal buffer layer in the form of a longitudinal wave, enters the thermal protection system of the high-temperature aircraft, propagates within the plate in the form of Lamb waves, and is then collected by the receiving sensor after passing through the thermal buffer layer.

By utilizing a network of distributed ultrasonic guided wave probes for signal transmission and reception, benchmark signals are collected when the structure is in a healthy state, and monitoring signals are collected when there is a suspicion of structural damage. The correlation between signal characteristics and the extent of damage is referred to as the “damage factor”, which has different expressions for different energy transfer modes.

2.2. VMD-FEN Damage Index

The damage factor represents the correlation between the severity of structural damage within the signal path control area and the changes in guided wave signal characteristics. By monitoring the trend of damage factor changes, it is possible to identify the occurrence of damage and quantitatively analyze the damage propagation rules. Damage to the thermal protection system can be simplified into the loss of structural damping, changes in structural geometry, and changes in structural thermal performance, all of which affect the mode and amplitude of ultrasonic guided waves. In plate and shell structures, the propagation mode of Lamb wave signals is relatively regular, and damage will cause changes in signal characteristics such as the amplitude, phase, and spectral distribution. Traditional ultrasonic guided wave damage diagnostic methods often use the signal energy under different conditions or the correlation coefficient between the damage signal and the benchmark signal to represent the severity of structural damage within the signal path control range.

In this paper, composite ultrasonic guided waves were used to characterize the damage. In this case, the thermal buffer layer–structure interface is connected by adhesive, which needs to face more complex guided wave propagation characteristics, more boundary reflections in the signal, and more serious signal aliasing. Under high-temperature conditions, the connection interface produces a breathing effect, introducing nonlinear thermal noise into the ultrasonic guided wave signal, making the signal more complex. Therefore, this paper needed to propose a damage factor that can accurately standardize the signal changes caused by damage in a complex environment and extract the main components of the signal without noise as much as possible.

Due to the non-stationary characteristics of Lamb wave signals, traditional noise reduction methods have certain limitations. The VMD method can effectively handle nonlinear and non-stationary signals and is suitable for analyzing Lamb wave damage signals. This method can adaptively analyze the damage signal and decompose it into different sub-components, effectively separating the useful signal from the background noise [25]. The use of the variational mode decomposition (VMD) method to analyze ultrasonic guided wave signals and extract the main modal components involves constructing and solving a variational problem to achieve effective signal decomposition.

Firstly, the signal f(t) collected by the receiving sensor is initialized:

$$f\left(t\right)={\sum }_{j=1}^K{u}_j\left(t\right)$$

(1)

Next, we determine the number of modes K for VMD decomposition, as well as the initial central frequency ${\mathsf{\omega }}_{\mathrm{j}}(\mathrm{j}=\mathrm{1,2},\dots ,K)$ for each mode:

$$u_j=A_j\left(t\right)\mathrm{c}\mathrm{o}\mathrm{s}({\mathsf{\omega }}_{\mathrm{j}}t+{\theta }_j\left(t\right))$$

(2)

where $A_j\left(t\right)$ is the amplitude of the mode, ${\mathsf{\omega }}_{\mathrm{j}}t$is the central frequency of the mode, and ${\theta }_j\left(t\right)$ represents the modal phase.

Then, we define the energy function $\mathrm{E}(\mathrm{U},\mathsf{\Omega })$, where $\mathrm{U}$ is the collection of modal components and $\mathsf{\Omega }$ is the collection of central frequencies. The energy function typically consists of two parts: one is the error between the modal components and the original signal, and the other is the smoothness constraint of the modal components.

Next, we solve for the minimum of the energy function using an optimization algorithm (such as the alternating direction method of multipliers (ADMM)), thereby obtaining the central frequency and modal function of each modal component. The detailed steps of this part are described in many literatures sources.

Finally, we calculate the spectral energy of each modal component and select the modal component with the greatest energy as the main modal component.

The VMD method effectively extracts the main modal components from ultrasonic guided wave signals by adaptively decomposing the signal into a series of modal components with specific central frequencies and limited bandwidths. This approach is of significant importance for analyzing and identifying defects or other features within ultrasonic guided wave signals. By extracting the main modal components, signal analysis and interpretation can be conducted more accurately [26].

In the analysis of ultrasonic guided wave signals, fuzzy entropy (FEN) is an indicator used to measure the complexity and irregularity of a signal. It combines the concepts of fuzzy set theory and entropy to quantify the uncertainty and chaotic characteristics of a signal [27]. When the structure is intact, the propagation characteristics of the ultrasonic guided wave signals are relatively stable, resulting in a lower fuzzy entropy. After damage occurs, the propagation path and characteristics of the ultrasonic guided wave signals change, leading to an increase in signal uncertainty and a corresponding rise in fuzzy entropy. By comparing the fuzzy entropy values before and after damage, the severity of the damage can be assessed. The greater the change in fuzzy entropy, the greater the impact of the damage on the signal, indicating more severe damage. Using the change in fuzzy entropy before and after damage to measure the severity of the damage is an effective signal analysis method. By quantitatively analyzing the uncertainty and chaotic characteristics of the signal, valuable information can be provided for structural health monitoring and damage assessment.

First, the main mode component of the ultrasonic guided wave signal is divided into several equal length segments, where each segment is regarded as a local feature. Then, the fuzzy set is obtained by applying fuzzy processing to each local feature, and the uncertainty of the signal is quantified by using a membership function. For each local feature, the entropy of its membership function is calculated. The higher the entropy, the greater the uncertainty of the signal. The entropy values of all local features are averaged or aggregated in other forms to obtain the global fuzzy entropy, as shown below:

$$H_F\left(U_{k-max}\right)=-k{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}\mu \left(x\right)\mathrm{l}\mathrm{n}\left(\mu \left(x\right)\right)dx$$

(3)

The fuzzy entropy of the main mode component of the guided wave signal under different damage states is defined as the damage factor, and the damage expansion trend is characterized by monitoring the change of different damage factors:

$${DI}_{VMD-FEN}^i=H_F\left(U_{k-max}^i\right)$$

(4)

3. Experiment Setup

3.1. Experimental Platform

The experiments in this paper utilized the HS-GWDS hot spot ultrasonic guided wave detection software and hardware system. The typical failure process of the aircraft’s thermal protection structure was simplified by heating the bottom of a flat plate to simulate aerodynamic heating and drilling holes on the surface of the structure to simulate damage and failure. The structure was simplified to an aluminum alloy flat plate with dimensions of 500 mm × 500 mm × 3 mm. The heat source is a graphite constant temperature heating plate with an effective heating area of 600mm × 400 mm and a temperature control accuracy of ±1 °C.

The online monitoring device for damage in the thermal protection system based on a composite of longitudinal waves and Lamb waves is shown in Figure 3. The device consists of a thermal buffer layer, excitation piezoelectric transducers, reception piezoelectric transducers, high-temperature adhesive, and an aluminum alloy specimen simulating the aircraft structure.

3.2. Sensor System

The sensors selected are PZT-5A type lead zirconate titanate (PZT) d31 piezoelectric ceramic sensors, with a diameter of 8 mm and a thickness of 0.25 mm. The optimal excitation frequency for the S0 mode Lamb wave is between 250 kHz and 300 kHz. The thermal buffer layer needs to have excellent heat insulation capabilities and maintain its elastic modulus and thermal stability at high temperatures. Therefore, zirconia ceramic, which has the lowest thermal conductivity and the best high-temperature stability among common ceramic materials, was chosen as the thermal buffer layer.

To investigate the heat insulation effect of thermal buffer layers of different sizes, the ultrasonic guided wave signal transmission and reception capabilities of the insulated probes at different temperatures, and the effectiveness of the proposed sensor probe system for damage detection at different temperatures, an insulated probe array with a thermal buffer layer was designed. This array consists of three pairs of insulated probes of different sizes, with each pair forming a signal path. Considering the excitation and reception factors of the longitudinal wave, a frequency sweeping method was used in this paper to find the optimal excitation and reception frequency. The excitation signal was a 5-cycle sine pulse modulated by a Hann window, with a central excitation frequency ranging from 150 to 500 kHz and a frequency sweep step of 50 kHz.

3.3. Thermal Buffer Layer Insulation Performance

To simulate the hot and cold surfaces of a hypersonic structure, a controllable heating plate was used to heat one side of an aluminum alloy plate as the hot side, with the other side serving as the cold side. Sensors with thermal buffer layers and insulation probes were installed. The insulation principle of the thermal buffer layer is to reach a thermal equilibrium between its own heat dissipation and the heat conduction from the bottom. To investigate the insulation effect of thermal buffer layers of different sizes, this paper measured the top temperatures of 1 cm, 2 cm, and 3 cm thermal buffer layers after heating at the bottom for one hour at different temperatures. Considering the potential non-uniformity of the temperature field at different positions, this paper sampled and took the average of multiple locations. As showed in Figure 4, that in an environment of 100 °C, the average top temperature of the 1 cm probe was 88.25 °C, the top temperature of the 2 cm probe was 67.35 °C, and the top temperature of the 3 cm probe was 46.75 °C; in an environment of 150 °C, the average top temperature of the 1 cm probe was 118.75 °C, the top temperature of the 2 cm probe was 92.5 °C, and the top temperature of the 3 cm probe was 66.25 °C. The results indicated that after the heat conduction and air convection dissipation reach thermal equilibrium, under the bottom temperature condition of 100 °C, the insulation efficiency of the zirconia thermal buffer layer was 20 °C/cm, and under the bottom temperature condition of 150 °C, the insulation efficiency was 26 °C/cm. According to the experimental operation experience, the survival time of the sensor at an environmental temperature of 120 °C was less than 60 min, so a 2–3 cm insulation layer can effectively provide insulation, while a 1 cm insulation layer can only achieve a temperature reduction of about −30 °C under the bottom temperature condition of 150 °C, and there is still a risk of depolarization of lead zirconate titanate piezoelectric ceramic sensors working long-term within this temperature range.

4. Results and Discussion

To investigate the feasibility of heat-insulated high-temperature probes transmitting guided wave signals, analyze the impact of different temperatures on composite ultrasonic guided wave signals, and select the sensor excitation method with the highest reliability and maximum signal energy as the goal, composite ultrasonic guided wave propagation experiments were conducted under different temperatures (30 °C to 200 °C) with different probes.

The excitation signal selected is a five-cycle sine signal modulated by a Hann window, with a signal amplitude of 50 V and a gain of 30 dB, sweeping the signal excitation in the frequency domain from 150 to 500 kHz with a step size of 50 kHz. Representative signals are shown in Figure 5.

As shown in Figure 5, under room temperature conditions, the heat-insulated probe equipped with a thermal buffer layer can effectively excite signals; as the temperature rises, the sensor can still effectively propagate ultrasonic guided waves; consistent with the previous test results, due to the depolarization phenomenon of the sensor, when the temperature exceeds 150 °C, the signal of the 1 cm probe decays to zero.

A hole with a diameter of 2 cm is a typical damage size that many researchers have used as a starting point for damage identification [19,28]. To simulate different degrees of structural damage, a blind hole with a diameter of 2 cm was drilled on the direct signal path, and after monitoring, it was expanded into a through hole with a diameter of 2 cm. During the experiment, first, under the undamaged state, three sets of probes were used to form three paths to collect composite guided wave signals at different temperatures (30 °C, 50 °C, 80 °C, 100 °C, 120 °C, and 150 °C) as benchmark signals; then, after processing the blind hole damage, collect composite guided wave signals at different temperatures as the damaged state; and finally, after processing the through hole damage, collect composite guided wave signals at different temperatures as the damage expansion state.

In the widely applied ultrasonic guided wave damage diagnostic method, the signal differences under different damage conditions are used as the damage factor representing the degree of structural damage. This paper first examined the distribution trend of the damage factor of signal energy or the correlation coefficient between the signal and the benchmark under different damage conditions.

Signal Energy Damage Factor: This involves assessing the state change of the structure along the signal path by utilizing the change in the energy of the structural response signal under different conditions.

$$E_{Damage-i}={\int }_{t1}^{t2}{\left|{Sa}_{damage-i}\left(t\right)\right|}^{2}dt$$

(5)

$$E_{base}={\int }_{t1}^{t2}{\left|{Sa}_{base}\left(t\right)\right|}^{2}dt$$

(6)

$${DI}_{Condition-i}=E_{Condition-i}$$

(7)

where ${Sa}_{damage-i}$ represents the monitoring signal for the type i damage condition, $E_{damage-i}$ represents the signal energy in the i type damage condition, ${Sa}_{base}$ represents the monitoring signal in the baseline state, $E_{base}$ represents the signal energy in the reference state, and $E_{Condition-i}$ represents the signal energy in the current condition.

Signal Correlation Coefficient Damage Factor: This method uses the Pearson correlation coefficient of the structural response signals under different conditions to characterize the condition of the structure. The correlation coefficient measures the linear relationship between the signals, with higher values indicating a stronger relationship and potentially less damage, while lower values suggest a weaker relationship and potentially more damage.

$${DI}_{Condition-i}=corr({Sa}_{base},{Sa}_{damage-i})$$

(8)

where $corr({Sa}_{base},{Sa}_{damage-i})$ is the Pearson correlation coefficient between the current damage signal and the healthy signal.

The distribution chart of traditional signal damage indicators for blind hole and through hole damages under different temperatures is shown in the figure below.

In the Figure 6, different bars represent different damage conditions. The results show that due to the complexity of the composite ultrasonic guided wave signals, the signal energy and signal correlation coefficient damage factors commonly used in room temperature plate and shell structure damage monitoring do not exhibit a regular distribution under different damage conditions and cannot serve as damage identification factors.

Next, the distribution trend of the damage factors obtained by directly taking the fuzzy entropy of the original signals under different damage conditions was examined.

In the fuzzy entropy signal damage indicator distribution graph at different temperatures, it can be seen that the ultrasonic guided wave signal has a lower fuzzy entropy in the undamaged structure, and the propagation characteristics of the ultrasonic guided wave signal are relatively stable. After damage occurs, the uncertainty of the ultrasonic guided wave signal increases, and the fuzzy entropy correspondingly rises. By comparing the fuzzy entropy values before and after damage, the severity of the damage can be assessed. However, due to severe signal aliasing, the signal fuzzy entropy does not exhibit a corresponding pattern under different sizes of damage conditions. Therefore, the fuzzy entropy of the original signal can serve as an early warning indicator of damage occurrence, but it cannot represent the damage expansion process.

Thus, this paper proposed a signal main component extraction method based on the VMD method to preprocess the signal and obtain the damage characteristics from the aliased signals. First, taking the room temperature undamaged signal of the 3–6 path as an example:

As showed in Figure 7 and Figure 8, using the VMD method, the guided wave signal was decomposed, as shown in Figure 9. The preset number of decompositions K was set to 9. From the figure, it can be seen that the time-domain aliased ultrasonic guided wave signal is successfully decomposed into several intrinsic mode functions (IMFs). Among the IMFs, the energy of IMF8 far exceeds that of the other signals.

Based on IMF8 as the main signal component of the signal, a comparison with the original signal is shown in Figure 10.

Signal VMD–fuzzy entropy damage index distributions at different temperatures are shown as Figure 11. The distribution chart of ${DI}_{VMD-FEN}^i$ for the undamaged structure, 2 cm blind hole, and through hole damages under different temperatures is shown in the figure below. Here, ${DI}_{VMD-FEN}^i$ represents the damage index based on the fuzzy entropy derived from the variational mode decomposition (VMD) method, and the subscript ii denotes the different damage conditions being assessed (1 for undamaged, 2 for blind hole, and 3 for through hole).

As can be seen from the figure, by monitoring the variation of the ${DI}_{VMD-FEN}^i$ damage index for the 2 cm and 3 cm probes within the temperature range of 30–150 °C, it is possible to clearly distinguish the occurrence and type of different damages. Due to the limitation of signal validity, the 1 cm probe can only operate below 100 °C. Within the range of 30–100 °C, monitoring the variation of the ${DI}_{VMD-FEN}^i$ also achieves monitoring of the healthy condition.

5. Conclusions

This paper proposed a high-temperature online monitoring method for aircraft structural damage based on a thermal buffer probe composite ultrasonic guided wave. First, a thermal buffer layer made of zirconia ceramic with low thermal conductivity was used to provide both insulation and guided wave transmission, maintaining the sensor at an appropriate working temperature while ensuring energy transfer efficiency. High-temperature tests for room temperature and signal propagation verified the effectiveness of the thermal buffer layer for insulation and guided wave transmission.

Based on the signal’s repeatability and energy efficiency, an evaluation index for selecting the excitation mode of the ultrasonic guided wave probe at different temperatures was proposed, and the frequency selection was made based on this. The impact of the damage on the propagation characteristics of ultrasonic guided waves was analyzed, and a damage measurement factor combining VMD and fuzzy entropy was proposed to achieve damage identification and monitoring.

The experimental results showed that:

The sensor’s thermal buffer layer can effectively facilitate energy transfer, and thermal buffer probes with a zirconia ceramic thickness of 2 cm or more can maintain the sensor temperature within a usable range in high-temperature environments up to 150 °C;

The fuzzy entropy of the original signal can serve as an early warning indicator of damage occurrence but cannot represent the damage expansion process;

The damage factor combining VMD and fuzzy entropy, denoted as ${DI}_{VMD-FEN}^i$, can achieve identification and monitoring of damage under different temperature conditions.