Study of Parameter Configuration on an Embedded System Used for Acoustic Leak Localization in Metallic Pipelines
Abstract
:1. Introduction
2. Materials and Methods
- Step 1: The acoustic signals acquired by the two sensors are segmented into a number of NF equally sized spectral bands, via FIR filters.
- Step 2: The signal in each spectral band is fragmented into NT temporal portions.
- Step 3: Each portion of each spectral band from Sensor 1 is cross-correlated with its corresponding portion from Sensor 2. At the end of this step, NT values for the time lag Δn (expressed in samples) between the signals from the two sensors are produced in each spectral band. The time lag Δn (Δn = FS∙Δt), along with the value of the propagation velocity of the vibroacoustic waves, are crucial for the successful estimation of the leak position.
- Step 4: The Δn values considered as outliers are rejected and then from the ones that remain, the dominant Δn value (i.e., the most frequently appeared) in each spectral band is selected. This can be expressed mathematically as follows:
- Step 5: The final value of the leak position (x) is calculated as a weighted mean of the position estimates (i.e., the xi’s) from all the spectral bands, by using the following equation:
- WF: the width of the spectral bands (in Hz).
- WT: the width of the temporal portions (in samples).
- Dur: the duration of the leak measurements (in samples).
- FS: the sampling frequency (in Hz).
- Bits: the number of bits in the representation of the sample values.
- Taps: the number of taps of the designed FIR filters.
3. Results
- For WT: 32,768 samples, 65,536 samples, 131,072 samples, and 262,144 samples.
- For WF: 800 Hz and 1600 Hz.
- For Dur: 131,072 samples, 262,144 samples, and 524,288 samples.
- For FS: 12.8 kHz and 25.6 kHz.
- For Bits: 10, 16, and 24.
- For Taps: 47 and 63.
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Parameter Values | Leak | Execution Time | Estimated Leak Position | Localization Error | |
---|---|---|---|---|---|
WT = 65,536 Samp. WF = 800 Hz Bits = 24 FS = 25.6 kHz Dur = 262,144 Samp. Taps = 47 | 3 mm-B | 16 s | 19.29 m | 1.6% | Average error: 3.1% Average execution time: 16 s Memory: 1.5 MB |
3 mm-C | 16 s | 21.56 m | 0.5% | ||
5 mm-A | 16 s | 19.27 m | 6.1% | ||
5 mm-B | 16 s | 18.30 m | 0.1% | ||
5 mm-C | 16 s | 20.44 m | 1.2% | ||
7 mm-A | 16 s | 16.26 m | 1.6% | ||
7 mm-B | 16 s | 25.00 m | 10.2% | ||
7 mm-C | 16 s | 23.54 m | 3.5% |
Parameter Values | Leak | Execution Time | Estimated Leak Position | Localization Error | |
---|---|---|---|---|---|
WT = 32,768 Samp. WF = 800 Hz Bits = 24 FS = 12.8 kHz Dur = 262,144 Samp. Taps = 63 | 3 mm-B | 6 s | 21.24 m | 4.6% | Average error: 6.4% Execution time: 6 s Memory: 1.5 MB |
3 mm-C | 6 s | 17.21 m | 6.0% | ||
5 mm-A | 6 s | 15.20 m | 0.0% | ||
5 mm-B | 6 s | 23.17 m | 7.4% | ||
5 mm-C | 6 s | 22.18 m | 1.5% | ||
7 mm-A | 6 s | 19.63 m | 6.6% | ||
7 mm-B | 6 s | 27.12 m | 13.3% | ||
7 mm-C | 6 s | 29.05 m | 11.7% |
Parameter Values | Leak | Execution Time | Estimated Leak Position | Localization Error | |
---|---|---|---|---|---|
WT = 65,536 Samp. WF = 800 Hz Bits = 16 FS = 25.6 kHz Dur = 262,144 Samp. Taps = 47 | 3 mm-B | 16 s | 19.50 m | 1.9% | Average error: 3.6% Execution time: 16 s Memory: 1 MB |
3 mm-C | 16 s | 20.56 m | 1.0% | ||
5 mm-A | 16 s | 19.27 m | 6.1% | ||
5 mm-B | 16 s | 18.30 m | 0.1% | ||
5 mm-C | 16 s | 19.65 m | 2.3% | ||
7 mm-A | 16 s | 16.26 m | 1.6% | ||
7 mm-B | 16 s | 26.36 m | 12.2% | ||
7 mm-C | 16 s | 23.54 m | 3.5% |
Parameter Values | Leak | Execution Time | Estimated Leak Position | Localization Error | |
---|---|---|---|---|---|
WT = 65,536 Samp. WF = 1600 Hz Bits = 10 FS = 25.6 kHz Dur = 524,288 Samp. Taps = 47 | 3 mm-B | 16 s | 17.09 m | 1.7% | Average error: 5.8% Execution time: 16 s Memory: 1.25 MB |
3 mm-C | 16 s | 20.46 m | 1.1% | ||
5 mm-A | 16 s | 22.06 m | 10.3% | ||
5 mm-B | 16 s | 15.89 m | 3.5% | ||
5 mm-C | 16 s | 21.09 m | 0.2% | ||
7 mm-A | 16 s | 15.89 m | 1.0% | ||
7 mm-B | 16 s | 28.24 m | 15.0% | ||
7 mm-C | 16 s | 30.50 m | 13.9% |
Parameter Values | Leak | Execution Time | Estimated Leak Position | Localization Error | |
---|---|---|---|---|---|
WT = 131,072 Samp. WF = 800 Hz Bits = 24 FS = 25.6 kHz Dur = 524,288 Samp. Taps = 47 | 3 mm-B | 57 s | 16.39 m | 2.7% | Average error: 2.5% Execution time: 57 s Memory: 3 MB |
3 mm-C | 57 s | 21.23 m | 0.0% | ||
5 mm-A | 57 s | 16.41 m | 1.8% | ||
5 mm-B | 57 s | 19.11 m | 1.4% | ||
5 mm-C | 57 s | 22.88 m | 2.5% | ||
7 mm-A | 57 s | 13.45 m | 2.6% | ||
7 mm-B | 57 s | 22.88 m | 7.0% | ||
7 mm-C | 57 s | 22.61 m | 2.1% |
Parameter Values | Leak | Execution Time | Estimated Leak Position | Localization Error | |
---|---|---|---|---|---|
WT = 131,072 Samp. WF = 800 Hz Bits = 24 FS = 25.6 kHz Dur = 262,144 Samp. Taps = 63 | 3 mm-B | 29 s | 15.49 m | 4.1% | Average error: 4.6% Execution time: 29 s Memory: 1.5 MB |
3 mm-C | 29 s | 20.40 m | 1.2% | ||
5 mm-A | 29 s | 21.37 m | 9.2% | ||
5 mm-B | 29 s | 19.72 m | 2.3% | ||
5 mm-C | 29 s | 22.34 m | 1.7% | ||
7 mm-A | 29 s | 17.65 m | 3.7% | ||
7 mm-B | 29 s | 24.98 m | 10.1% | ||
7 mm-C | 29 s | 24.11 m | 4.3% |
Parameter Values | Leak | Execution Time | Estimated Leak Position | Localization Error | |
---|---|---|---|---|---|
WT = 65,536 Samp. WF = 800 Hz Bits = 16 FS = 12.8 kHz Dur = 262,144 Samp. Taps = 63 | 3 mm-B | 8 s | 18.83 m | 0.9% | Average error: 1.9% Execution time: 8 s Memory: 1 MB |
3 mm-C | 8 s | 21.44 m | 0.4% | ||
5 mm-A | 8 s | 17.00 m | 2.7% | ||
5 mm-B | 8 s | 19.43 m | 1.8% | ||
5 mm-C | 8 s | 20.99 m | 0.3% | ||
7 mm-A | 8 s | 18.83 m | 5.4% | ||
7 mm-B | 8 s | 17.33 m | 1.3% | ||
7 mm-C | 8 s | 19.44 m | 2.6% |
Parameter Values | Leak | Execution Time | Estimated Leak Position | Localization Error | |
---|---|---|---|---|---|
WT = 131,072 Samp. WF = 800 Hz Bits = 10 FS = 25.6 kHz Dur = 262,144 Samp. Taps = 47 | 3 mm-B | 28 s | 21.62 m | 5.1% | Average error: 4.0% Execution time: 28 s Memory: 640 KB |
3 mm-C | 28 s | 18.02 m | 4.8% | ||
5 mm-A | 28 s | 15.49 m | 0.4% | ||
5 mm-B | 28 s | 21.61 m | 5.1% | ||
5 mm-C | 28 s | 20.97 m | 0.4% | ||
7 mm-A | 28 s | 20.97 m | 8.6% | ||
7 mm-B | 28 s | 22.19 m | 6.0% | ||
7 mm-C | 28 s | 20.07 m | 1.7% |
Parameter Values | Leak | Execution Time | Estimated Leak Position | Localization Error | |
---|---|---|---|---|---|
WT = 65,536 Samp. WF = 800 Hz Bits = 10 FS = 12.8 kHz Dur = 262,144 Samp. Taps = 63 | 3 mm-B | 8 s | 19.46 m | 1.9% | Average error: 2.9% Execution time: 8 s Memory: 640 KB |
3 mm-C | 8 s | 22.07 m | 1.3% | ||
5 mm-A | 8 s | 19.46 m | 6.4% | ||
5 mm-B | 8 s | 20.06 m | 2.8% | ||
5 mm-C | 8 s | 20.53 m | 1.0% | ||
7 mm-A | 8 s | 19.46 m | 6.4% | ||
7 mm-B | 8 s | 17.00 m | 1.8% | ||
7 mm-C | 8 s | 20.08 m | 1.7% |
Parameter Values | Leak | Execution Time | Estimated Leak Position | Localization Error | |
---|---|---|---|---|---|
WT = 262,144 Samp. WF = 800 Hz Bits = 24 FS = 25.6 kHz Dur = 262,144 Samp. Taps = 63 | 3 mm-B | 31 s | 12.37 m | 8.7% | Average error: 4.7% Execution time: 31 s Memory: 1.5 MB |
3 mm-C | 31 s | 20.19 m | 1.5% | ||
5 mm-A | 31 s | 20.74 m | 8.3% | ||
5 mm-B | 31 s | 20.55 m | 3.5% | ||
5 mm-C | 31 s | 20.67 m | 0.8% | ||
7 mm-A | 31 s | 14.48 m | 1.5% | ||
7 mm-B | 31 s | 25.01 m | 10.2% | ||
7 mm-C | 31 s | 23.09 m | 2.8% |
Combination Name | Score | Combination Name | Score |
---|---|---|---|
Parameter combination 1 | Fev = 0.92 | Parameter combination 6 | Fev = 0.89 |
Parameter combination 2 | Fev = 0.89 | Parameter combination 7 | Fev = 0.95 |
Parameter combination 3 | Fev = 0.92 | Parameter combination 8 | Fev = 0.92 |
Parameter combination 4 | Fev = 0.89 | Parameter combination 9 | Fev = 0.94 |
Parameter combination 5 | Fev = 0.87 | Parameter combination 10 | Fev = 0.89 |
Combination Name | Score | Combination Name | Score |
---|---|---|---|
Parameter combination 1 | Fev = 0.92 | Parameter combination 6 | Fev = 0.88 |
Parameter combination 2 | Fev = 0.93 | Parameter combination 7 | Fev = 0.95 |
Parameter combination 3 | Fev = 0.92 | Parameter combination 8 | Fev = 0.90 |
Parameter combination 4 | Fev = 0.91 | Parameter combination 9 | Fev = 0.95 |
Parameter combination 5 | Fev = 0.80 | Parameter combination 10 | Fev = 0.88 |
Combination Name | Score | Combination Name | Score |
---|---|---|---|
Parameter combination 1 | Fev = 0.87 | Parameter combination 6 | Fev = 0.86 |
Parameter combination 2 | Fev = 0.87 | Parameter combination 7 | Fev = 0.92 |
Parameter combination 3 | Fev = 0.90 | Parameter combination 8 | Fev = 0.93 |
Parameter combination 4 | Fev = 0.88 | Parameter combination 9 | Fev = 0.94 |
Parameter combination 5 | Fev = 0.76 | Parameter combination 10 | Fev = 0.86 |
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Kousiopoulos, G.-P.; Nikolaidis, S. Study of Parameter Configuration on an Embedded System Used for Acoustic Leak Localization in Metallic Pipelines. Electronics 2023, 12, 1793. https://doi.org/10.3390/electronics12081793
Kousiopoulos G-P, Nikolaidis S. Study of Parameter Configuration on an Embedded System Used for Acoustic Leak Localization in Metallic Pipelines. Electronics. 2023; 12(8):1793. https://doi.org/10.3390/electronics12081793
Chicago/Turabian StyleKousiopoulos, Georgios-Panagiotis, and Spiros Nikolaidis. 2023. "Study of Parameter Configuration on an Embedded System Used for Acoustic Leak Localization in Metallic Pipelines" Electronics 12, no. 8: 1793. https://doi.org/10.3390/electronics12081793
APA StyleKousiopoulos, G.-P., & Nikolaidis, S. (2023). Study of Parameter Configuration on an Embedded System Used for Acoustic Leak Localization in Metallic Pipelines. Electronics, 12(8), 1793. https://doi.org/10.3390/electronics12081793