Simulation Study on the Performance of Ultrasonic Pulse-Echo Detector for Ice Thickness Identification

In-flight icing detectors are important for the flight safety of aircraft. Detectors based on ultrasonic pulse-echo can be used for detecting ice thickness. To study the influencing factors of ultrasonic pulse-echo detection performance, a simulation model of elastic wave-piezoelectric coupling was established, which was used to analyze the influence of different types of piezoelectric ceramics, matching layers with different acoustic impedances, and different substrate materials on ultrasonic pulse-echo signals. It was found that when aluminum is used as the substrate material, the ultrasonic echo signal has a higher signal-to-noise ratio. Furthermore, the influence of aluminum substrate materials with different thicknesses on ultrasonic pulse-echo was analyzed. The ice thickness can be identified by measuring the time of flight between the aluminum-ice interface echo and the ice-air interface echo. The results indicate that when the thickness of the aluminum substrate is 25mm, the upper detection limit of ice layer thickness can reach about 10mm. Therefore, the detection upper limit of ice layer thickness can be extended by appropriately increasing the thickness of the aluminum substrate material.


Introduction
In-flight icing is one of the important hidden dangers that affect flight safety and even lead to catastrophic accidents [1][2][3].According to the Flight Safety Department of the Federal Aviation Administration (FAA), there were 3230 accidents caused by weather conditions from 1990 to 2000, of which 12% were caused by icing [4,5].Aircraft icing detection is an important technical means to achieve flight icing warning and ensure flight safety [6,7].At present, there are various methods for detecting aircraft icing, such as magnetostriction ice detectors [8], infrared ice detectors [9,10], optical fiber ice detectors [11], impedance ice detectors [12,13], ultrasonic ice detectors [14,15], and other sensors.Each type of sensor has its detection advantages and disadvantages, but currently, the icing sensors used on aircraft can only determine whether ice is forming and cannot provide more ice information.Ice thickness can help pilots determine the degree of icing, and is an important indicator for activating the deicing system.Ultrasonic pulse-echo technique is widely used in many fields, such as damage detection, distance measurement, medical detection, etc.In 1988, Hansman et al. [15] proposed a surface-mounted ultrasonic system for accurately measuring ice thickness.The probe of the sensor is exposed directly to the outside and is constantly impacted by high-speed airflow, which can easily be worn and damaged.In recent years, some scholars have begun to study the propagation characteristics of ultrasonic echoes in ice layers.Mendonck et al. [16] conducted a comprehensive study on the propagation of ultrasonic waves in both liquid and ice water drops and focused on investigating the impact of porosity on ultrasonic attenuation in liquid droplets.Gu [17] introduced the ensemble empirical mode decomposition (EEMD) method into snow depth detection and conducted analysis on the time of flight (ToF) estimation of snow depth ultrasonic signals based on the echo signal model to improve measurement accuracy.Shi et al. [18] used the pulse-echo reflection method and the throughtransmission method for pore defect detection and porosity numerical evaluation of carbon fiberreinforced polymer composites.Wang et al. [19] introduced an innovative ultrasonic pulse-echo technique for the detection of freezing characteristics in water film on ice surfaces.Additionally, they devised a novel approach to measure the thickness of glaze ice.Tao [20] studied the installation of ultrasonic probes inside the wing skin for measuring ice thickness and further investigated the influence of pore structure on ultrasonic echoes.Due to the thickness of the skin being 3mm, the signal-to-noise ratio of the pulse-echo signal is small, which is not conducive to the detection of ice thickness.In addition, the ice layer used for detection is regular and flat, making it difficult to simulate real icing conditions.
This paper simulated the propagation process of ultrasonic pulse echoes in aluminum ice structures.The influence of different types of piezoelectric ceramics, different the acoustic impedances of matching layers, and different substrate materials on ultrasonic echo signals were analyzed.Furthermore, aluminum was selected as the substrate material to study the effect of different substrate thicknesses on ultrasonic echo signals.A method was proposed to identify the thickness of the ice layer by measuring the time of flight (ToF) of the aluminum-ice interface echoes and the ice-air interface echoes.This method can expand the detection upper limit of ice layer thickness by increasing the thickness of the substrate material within a certain range.

Physics and Mathematics Model
The basic principle of ultrasonic pulse-echo detection of ice thickness is to excite pulse waves via a piezoelectric transducer and identify the ice thickness by receiving the interface echo of the pulse waves between the ice layer and the air, calculating its time of flight (ToF), as shown in figure 1.The piezoelectric transducer consists of an acoustic match layer, piezoelectric elements, and a backing element.where is the material density, is the velocity, is the stiffness tensor, is the strain tensor, is the stress tensor, is a body force.The equations are applied to both isotropic and anisotropic materials.Bulk dissipation can be added by using the Damping subnode.
Piezoelectric ceramics require coupling of piezoelectric effects in addition to linear elastic waves mathematical models.The constitutive relationship of piezoelectric effect can be written as: (2) where D is the electric displacement; E is the electric field; d is the piezoelectric constants matrix, s is the material compliance contents matrix, and is the permittivity matrix.The low-reflecting boundary conditions are used on the boundary of the aluminum plate and the backing element, and all others are free boundary conditions, as shown in figure 2.

Results and Discussion
Piezoelectric ceramics not only need to excite pulse waves, but also need to be used to receive echoes.It can be found that PZT-4 and PZT-8 have strong reception voltage signals by comparing different types of piezoelectric ceramics, as shown in figure 3. Therefore, PZT-4 and PZT-8 are more suitable as transducer elements.The piezoelectric ceramic of the ultrasonic transducer adopts PZT-4, and the echo signals (interface echoes of ice and air) under different ice layer thicknesses can be observed, as shown in figure 4. As shown in figure 5, the echo signal in this simulation case is relatively weak and the signal-to-noise ratio is low, due to the existence of different interface attenuation (ice layer and substrate material, substrate material and matching layer, matching layer, and piezoelectric ceramic).In this case, the substrate material is acrylic plastic.Therefore, the following will compare the influence of different matching layers, substrate materials, and substrate thickness on ultrasonic echoes.The thickness of the matching layer is generally not greater than one-fourth of the wavelength.Acoustic impedance is defined as the product of density and sound velocity.The echo signals of matching layers with different impedances are compared by the simulation method.As shown in figure 6, if the impedance is too large or too small, it will cause signal distortion and reduce the signal-to-noise ratio.The reason is that the greater the difference in acoustic impedance, the more energy is reflected at the boundary of the two media.Therefore, there is an optimal impedance that can be calculated using the following equation: (3) 0.0E+0   Next, the effects of different substrate materials, namely polystyrene and aluminum, on the echo signal were compared.By analyzing the simulation results, it was found that aluminum exhibited the least amount of echo attenuation and the highest signal-to-noise ratio.This can be observed in Figure 7 and Figure 8.The impedance of aluminum differs greatly from that of the ice layer, resulting in a distinct aluminum-ice interface echo. Figure 9 shows that multiple ice-air echo signals will clearly appear within the detection range, which is beneficial for identifying the thickness of the ice layer.Therefore, the time of flight (ToF) between the aluminum-ice interface echo and the ice-air interface echo can be extracted to identify the thickness of the ice layer.
Based on the above analysis, in order to successfully identify the thickness of the ice layer, the relationship between the upper detection limit of the ice layer thickness and the substrate material needs to be met as follows: (4) where and represent the sound velocity of the substrate material and the sound velocity of the ice layer, respectively.represent the thickness of the substrate material.represents the thickness upper limit value of ice detection.For example, when the upper limit of ice thickness detection is set to 10mm, the thickness of the aluminum substrate material is not less than 20mm.For example, when the substrate thickness is 15mm, the upper detection limit for ice layer thickness is around 7.5mm; When the base thickness is 25mm, the upper detection limit for ice layer thickness is about 12mm.Similarly, when the thickness of the aluminum substrate material is set to 15mm, the upper detection limit of the ice layer thickness does not exceed 7.5mm.
The results indicate that by increasing the thickness of the aluminum substrate, the detection range for ice thickness can be extended.Specifically, in figure 8, where the thickness of the aluminum substrate is 15mm, and in figure 9, where the thickness of the aluminum substrate is 25mm.
The wavelength of a 5MHz ultrasonic pressure waves in an aluminum plate is approximately 1mm.Therefore, the propagation process of ultrasonic pulse echoes in three different thicknesses of aluminum substrates, 1mm, 0.5mm, and 0.1mm, was simulated and calculated.It can be found that the signal-tonoise ratio of ultrasonic pulse echo in the aluminum plate with a thickness of 0.1mm (one tenth of the wavelength) is relatively higher by analyzing the received voltage signal of the ultrasonic echo sensor, as shown in figure 10.However, it is difficult to be applied due to the thin thickness of the aluminum plate.Therefore, increasing the thickness of the aluminum substrate within an appropriate range to identify the thickness of the ice layer is a feasible method.

Conclusion
(1) Different types of piezoelectric ceramics were compared.The results show that PZT-4 and PZT-8 were selected as excitation and reception components with stronger reception signals.
(2) The influence of matching layers with different acoustic impedances on the signal was studied.The greater the deviation of acoustic impedance from the optimal impedance, especially when the acoustic impedance is too small, the greater the distortion of the ultrasonic echo signal.(3) Comparing the propagation characteristics of ultrasonic echoes in different substrate materials, it was found that when aluminum is used as the substrate material, the received pulse echo signal has a high signal-to-noise ratio.Therefore, aluminum is more suitable as a substrate material.(4) The ice thickness can be identified by measuring the time of flight (ToF) between the echoes from the aluminum-ice interface and the ice-air interface.When the aluminum substrate thickness is increased to 25mm, the maximum detectable ice layer thickness can reach approximately 10mm.

Reflection of ice-air interface
The second reflection waves of ice-air interface

Ice thickness
The upper detection limite of ice thickness is 12.5mm 0.0E+0 Hence, by increasing the thickness of the aluminum substrate material appropriately, the upper limit of ice layer thickness detection can be extended.

Figure 1 .
Figure 1.Schematic diagram of ultrasonic pulse-echo simulation.The velocity-strain mathematic model of linear elastic waves can be written as:

Figure 2 .
Figure 2. The boundary conditions of ultrasonic pulse-echo simulation.

Figure 3 .
Figure 3.The receive signal of different types of piezoelectric ceramics.

Figure 4 .
Figure 4.The ice-air interface echoes signal of different thickness ice layers.

Figure 5 .
Figure 5.The propagation process of ultrasonic waves.

Figure 6 .
Figure 6.Comparison of echo signals of matching layers with different impedance.

Figure 7 .
Figure 7.The effect of polystyrene substrate material on echo signal.

Figure 8 .
Figure 8.The effect of aluminum substrate material on echo signal.

Figure 9 .
Figure 9. Echo signal when the thickness of the aluminum substrate is 25mm.

Figure 10 .
Figure 10.The effect of different aluminum substrate thickness on ultrasonic echo signal.