Surface Rust Detection Using Ultrasonic Waves in a Cylindrical Geometry by Finite Element Simulation
2. Finite Element Simulation
2.1. Intact Steel Rod Model
2.2. Corroded Steel Rod Models
3. Research Hypotheses and Approach
3.1. Hypotheses of Ultrasonic Wave Propagation in Intact and Corroded Rod Models
- In the intact steel rod model, the time domain radial displacement is collected at R. The first ultrasonic wave packet is the one propagating along the path at a velocity of and arriving at time . The second ultrasonic wave packet propagates along the path and arrives at time with a velocity of . Both the first and the second wave packets are surface waves (fundamental mode of Rayleigh waves). These surface waves were chosen for surface rust detection, rather than bulk waves  and guided waves , because bulk waves attenuate much faster than surface waves, and guided waves require multiple sensors to be in place.
- In the corroded steel rod models (CM1~CM5), the ultrasonic waves propagating along the path are affected by the presence of surface rust. As shown in Figure 3c, some of the ultrasonic waves propagate through the surface rust and arrive at time (i.e., > , since the ultrasonic wave velocity is slower in rust than it is in steel).
- Some of the ultrasonic waves are scattered from the surface rust and propagate along the path . Time is the total time of flight (TOF) of the scattered ultrasonic wave propagating along path (). The propagation velocities of ultrasonic waves on path and path are respectively and .
- In Figure 3d, path is the path of ultrasonic waves diffracted by the surface rust (). TOF of these ultrasonic waves is (i.e., ).
- Higher frequencies are affected more than lower frequencies by the presence of surface rust. This is because the effective depth of each frequency is approximately its wavelength . With a ‘shallow’ effective depth, higher frequencies interact with the surface rust more than lower frequencies.
3.2. Damage Detection Algorithm
3.2.1. Damage Detection
- Generate/introduce ultrasonic waves at transmitter T of model IM.
- Collect the time domain radial displacement at receiver R.
- Apply STFT to in order to convert it to its spectrogram .
- In the spectrogram , show the half-power contour at −3 dB from the maximum amplitude of the first wave packet.
- Determine the centroid of the half-power contour for the first wave packet by finding its coordinates in the spectrogram .
- The centroid frequency of this FE simulation is thus found. For the intact model (IM), .
- Repeat the steps for an artificially corroded model. For corroded models, .
3.2.2. Damage Localization
3.2.3. Damage Quantification
4. Simulation Results
4.1. Time Domain Response
4.2. Time-Frequency Domain Response
4.3. Surface Rust Detection
4.4. Surface Rust Localization
4.5. Surface Rust Quantification
- The presence of surface rust can be detected by the reduction of centroid frequency of the first wave packet in the STFT spectrogram of corroded steel rod models.
- The location of surface rust is estimated by finding the difference in arrival time (TOF) between helically propagating ultrasonic waves and scattered ultrasonic waves (due to surface rust).
- The length of surface rust can be predicted by calculating the difference in TOF between longitudinally propagating ultrasonic waves of intact and corroded steel rod models. This difference in TOF is related to the longitudinal dimension (length) of surface rust.
- The width of surface rust can be determined by calculating the difference in TOF of the first wave packet between intact and corroded steel rods in the STFT spectrogram at a fixed frequency (e.g., 1 MHz in this paper).
- The thickness of surface rust can be estimated by utilizing the second-order derivative of the first wave packet of corroded steel rod models.
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|Material||Density (kg/m)||Young’s Modulus (MPa)||Poisson’s Ratio|
|Model||Surface Rust Location|
|Surface Rust Length|
|Surface Rust Width|
|Surface Rust Thickness|
|Model||Predicted (mm)||Actual (mm)||Error (%)|
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Tang, Q.; Du, C.; Hu, J.; Wang, X.; Yu, T. Surface Rust Detection Using Ultrasonic Waves in a Cylindrical Geometry by Finite Element Simulation. Infrastructures 2018, 3, 29. https://doi.org/10.3390/infrastructures3030029
Tang Q, Du C, Hu J, Wang X, Yu T. Surface Rust Detection Using Ultrasonic Waves in a Cylindrical Geometry by Finite Element Simulation. Infrastructures. 2018; 3(3):29. https://doi.org/10.3390/infrastructures3030029Chicago/Turabian Style
Tang, Qixiang, Cong Du, Jie Hu, Xingwei Wang, and Tzuyang Yu. 2018. "Surface Rust Detection Using Ultrasonic Waves in a Cylindrical Geometry by Finite Element Simulation" Infrastructures 3, no. 3: 29. https://doi.org/10.3390/infrastructures3030029