Accuracy Assessment of the 2D-FFT Method Based on Peak Detection of the Spectrum Magnitude at the Particular Frequencies Using the Lamb Wave Signals
Abstract
:1. Introduction
- (1)
- Development of an algorithm of the signal-processing method.
- (2)
- Mathematical modeling of the dispersion curve segments. The purpose is to identify the capabilities of the most accurate reconstructed segments and determine the uncertainty components associated with the model errors.
- (3)
- Experimental setup and verification of the results.
- (4)
- Determination of input and output parameters, which affect the final method accuracy. Optimization of the selected uncertainty components for uncertainty quantification in high-dispersion and non-dispersion zones of phase-velocity dispersion curves of the A0 and S0 modes.
2. The Technique of Peak Detection of the Spectrum Magnitude
- I.
- Application of the 2D-FFT method for analysis of the B-scan data. Since the 2D-FFT method is well-known, the mathematical equations are not given, but the segment of the A0 mode phase-velocity curve obtained by this method is displayed in Figure 1.
- II.
- Detection of 2D spectrum magnitude peaks includes the following steps:
- Selecting the frequency bandwidth (from f1 up to f2).
- Estimating the phase velocity of Lamb wave modes from the 2D-FFT image and applying the peak detection of 2D spectrum magnitude at maximum energy and particular frequencies (within the selected frequency bandwidth).
- The second-order polynomial approximation is applied in order to reduce the influence of scattering effects of detected peaks of phase velocity due to the presence of blurred shapes of 2D spectrum magnitude.
3. The Object Mathematical Simulation and Numerical Verification of the 2D-FFT Method
3.1. The Object Mathematical Simulation
3.2. Mathematical Verification of the Method
3.2.1. Investigation of the A0 Mode
3.2.2. Examining the S0 Mode
4. Experimental Verification
4.1. Description of the Experimental Setup
4.2. Experimental Verification of the Analyzed Method
5. Analysis of Uncertainties
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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1.68 | 3.28 | 0.12 |
Frequency, kHz | |||
---|---|---|---|
160 | 29.1 | 5.79 | 0.54 |
700 | 2.61 | 1.87 | 0.05 |
Velocity, m/s | Mean Absolute Error | Mean Relative Error | |
---|---|---|---|
A0 mode | |||
1590 | 9.85 | 1.67 | 0.62 |
S0 mode | |||
5315 | −86.84 | 34.77 | 1.61 |
Object Parameter xi | Parameter Change Δxi | Velocity Change ΔFxi, m/s | Sensitivity Coefficient Wxi |
---|---|---|---|
ρ = 2780 kg/m3 | Δρ = 556 kg/m3 | A0 mode | |
110 | |||
S0 mode | |||
640 | |||
υ = 0.3435 | Δυ = 0.0687 | A0 mode | |
14 | 200 m/s | ||
S0 mode | |||
122 | 170 m/s | ||
E = 71.787 GPa | ΔE = 14.357 GPa | A0 mode | |
105 | |||
S0 mode | |||
572 | |||
d = 2 mm | Δd = 1.6 mm | A0 mode | |
137 | |||
S0 mode | |||
3 |
Quantity | Value | Standard Uncertainty | Distribution | Sensitivity Coefficient | Uncertainty Contribution |
---|---|---|---|---|---|
9.85 m/s | 1.67 m/s | normal | 1.0 | 1.7 m/s | |
0.0 m/s | 3.28 m/s | normal | 1.0 | 3.3 m/s | |
0.0 m/s | 1.2 m/s | normal | 1.0 | 1.2 m/s | |
0.0 m | 28.9 × 10−6 m | rectangular | 600 × 103 s−1 | 17 m/s | |
0.0 m | 289 × 10−6 m | rectangular | 34 × 103 s−1 | 9.9 m/s | |
0.0 kg/m3 | 0.289 kg/m3 | rectangular | 0.06 m/s | ||
0.0 m | 28.9 × 10−6 | rectangular | 200 m/s | 5.9 × 10−3 m/s | |
0.0 GPa | 289 × 10−6 GPa | rectangular | 2.1 × 10−3 m/s | ||
1599.8 m/s | 20.3 m/s | ||||
Result value: | Expanded uncertainty: | Coverage factor: | Coverage: | ||
1600 m/s | 41 m/s | 2.00 | 95% (normal) |
Quantity | Value | Standard Uncertainty | Distribution | Sensitivity Coefficient | Uncertainty Contribution |
---|---|---|---|---|---|
−86.8 m/s | 34.8 m/s | normal | 1.0 | 35 m/s | |
0.0 m/s | 5.79 m/s | normal | 1.0 | 5.8 m/s | |
0.0 m/s | 19.1 m/s | normal | 1.0 | 19 m/s | |
0.0 m | 28.9 × 10−6 m | rectangular | 600 × 103 s−1 | 17 m/s | |
0.0 m | 289 × 10−6 m | rectangular | 7500 s−1 | 2.2 m/s | |
0.0 kg/m3 | 0.289 kg/m3 | rectangular | 0.33 m/s | ||
0.0 m | 28.9 × 10−6 | rectangular | 1700 m/s | 0.05 m/s | |
0.0 GPa | 289 × 10−6 GPa | rectangular | 0.01 m/s | ||
5315.2 m/s | 43.7 m/s | ||||
Result value: | Expanded uncertainty: | Coverage factor: | Coverage: | ||
5315 m/s | 87 m/s | 2.00 | 95% (normal) |
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Draudvilienė, L.; Meškuotienė, A.; Raišutis, R.; Tumšys, O.; Surgautė, L. Accuracy Assessment of the 2D-FFT Method Based on Peak Detection of the Spectrum Magnitude at the Particular Frequencies Using the Lamb Wave Signals. Sensors 2022, 22, 6750. https://doi.org/10.3390/s22186750
Draudvilienė L, Meškuotienė A, Raišutis R, Tumšys O, Surgautė L. Accuracy Assessment of the 2D-FFT Method Based on Peak Detection of the Spectrum Magnitude at the Particular Frequencies Using the Lamb Wave Signals. Sensors. 2022; 22(18):6750. https://doi.org/10.3390/s22186750
Chicago/Turabian StyleDraudvilienė, Lina, Asta Meškuotienė, Renaldas Raišutis, Olgirdas Tumšys, and Lina Surgautė. 2022. "Accuracy Assessment of the 2D-FFT Method Based on Peak Detection of the Spectrum Magnitude at the Particular Frequencies Using the Lamb Wave Signals" Sensors 22, no. 18: 6750. https://doi.org/10.3390/s22186750
APA StyleDraudvilienė, L., Meškuotienė, A., Raišutis, R., Tumšys, O., & Surgautė, L. (2022). Accuracy Assessment of the 2D-FFT Method Based on Peak Detection of the Spectrum Magnitude at the Particular Frequencies Using the Lamb Wave Signals. Sensors, 22(18), 6750. https://doi.org/10.3390/s22186750