A Frequency-Correcting Method for a Vortex Flow Sensor Signal Based on a Central Tendency
Abstract
:1. Introduction
- Ideally, the output signal of vortex flow sensor is a sinusoidal wave [5,6] and its frequency is proportional to the flow velocity [7], as shown in Equation (1). Therefore, the flow velocity can be measured by measuring the signal frequency;
- The vortex signal also satisfies the characteristic that the amplitude is proportional to the frequency square [7], as shown in Equation (2), which is called the amplitude square dependence.
2. Analysis of Generalized Mode
2.1. The Background of Generalized Mode
- The mean represents the mean level of data, which can be calculated without data sorting. Compared with median and mode, it has good real-time performance. However, the mean is sensitive to each data and vulnerable to the influence of outliers [28,29]. In the case of skewed distribution, it will deviate from the overall characteristics of the data, or even become less representative.
- The median represents the level of the middle position of the data, which only considers the centre position of the data set, but does not care about the difference between value of other samples and the median. Therefore, the median is robust. In the skewed distribution, it is always between the mean and the mode. Compared with the mean, outliers have less influence on it, but its selection ignores the statistical characteristics of most data.
- The mode is the value of the data with the most frequent occurrence. It is the most direct statistic to reflect the central tendency of the data. Compared with mean and median, mode is not easily affected by outliers, while most of the statistical characteristics of data are retained. Mode adapts to the widest data distributions, which has a significant advantage in analyzing the central tendency of data.
2.2. The Definition of Generalized Mode
- Sort the data set size in ascending order: ;
- Calculate and ;
- If , will be discarded; otherwise, will be discarded. Whatever, the length of the data set and the data set is updated;
- Repeat the above steps until , then the generalized mode is calculated as Equation (9).
2.3. The Design of Generalized Mode Method
3. System Algorithm Design
4. Simulation Verification
4.1. The General Design of Simulation
4.2. Feasibility Performance
- It has the form of a sine wave, which satisfies the proportional relationship between frequency and flow as shown in Equation (10), including different frequency points in each channel;
- The amplitude shown in Equation (11) is proportional to the square of the frequency.
4.3. Anti-Interference Performance
- Including all kinds of possible interference in vortex signal, to truly restore the field measurement environment and verify the anti-interference performance of the system under complex working conditions.
- The periodic vibration noise conforms to the model shown in Equation (15), and the noise frequency and intensity can be changed by adjusting the parameters and respectively.
- The transient impact vibration noise conforms to the model shown in Equations (16) and (17), and the times of noise can be changed by signal superposition.
4.4. Real-Time Performance
5. Experimental Verification
5.1. Anti-Vibration Experiment
5.2. Calibration Experiment
6. Results Discussion
7. Conclusions
- A new central tendency analysis method called the generalized mode algorithm is proposed in this paper. Compared with the traditional mean, median, and mode, the generalized mode is insensitive to outliers. It retains most of the statistical characteristics of the data, which is more suitable for practical application. In addition to being used in the vortex flow meter signal-processing system, the idea of generalized mode can also be used for reference in other signal-processing fields, such as the electromagnetic flow meter signal-processing system.
- A new signal-processing method of vortex flow meter is designed based on the generalized mode algorithm, which avoids the conflict between frequency resolution and real-time performance existing in the FFT spectrum analysis method. Meanwhile, it solves the problem that the filter bank method needs to filter out the noise in the sub-band. Experiments show that the proposed algorithm has good measurement accuracy and anti-interference performance, especially for the interference of strong periodic vibration noise and strong transient impact vibration noise in the sub-band. Under various interference conditions, the absolute value of the relative error of vortex frequency is within 0.87%, as shown in Table 7, Table 8, Table 9 and Table 10.
- The generalized mode method is applied in the vortex flow meter system. The results of the anti-vibration experiments carried out in the 40 mm diameter liquid flow device showed that the generalized mode method performed better than the filter bank method, as shown in Figure 28. The results of the calibration experiments in the 80 mm diameter gas flow device showed that the repeatability of the vortex flow meter designed in this paper is less than 0.14%, as shown in Table 11, which indicates it has good practical application value.
Author Contributions
Funding
Conflicts of Interest
References
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Diameter (mm) | Frequency Range of Liquid (Hz) | Frequency Range of Gas (Hz) |
---|---|---|
25 | 8.75–270 | 45.00–2650 |
32 | 5.00–220 | 32.50–2200 |
40 | 2.50–180 | 22.50–1650 |
50 | 2.00–140 | 20.00–1400 |
65 | 1.75–110 | 15.00–1100 |
80 | 1.50–90 | 10.00–850 |
100 | 1.25–75 | 7.50–720 |
125 | 1.13–58 | 5.75–580 |
150 | 0.95–50 | 4.50–460 |
200 | 0.80–40 | 3.25–380 |
250 | 0.63–31 | 2.75–260 |
Index | Period (s) | Frequency (Hz) | The Relative Error (%) |
---|---|---|---|
Mean | 0.1616 | 6.19 | 4.91 |
Median | 0.1672 | 5.98 | 1.36 |
Mode | \ | \ | \ |
Generalized mode | 0.1697 | 5.89 | –0.1 |
Flow (L/s) | Frequency (Hz) | Amplitude (mV) |
---|---|---|
2.02 | 5.27 | 7.08 |
2.92 | 7.64 | 14.88 |
8.99 | 23.48 | 140.55 |
11.99 | 31.33 | 250.24 |
17.76 | 46.39 | 548.64 |
2.02 | 5.27 | 7.08 |
a1 | b2 | c3 | Degree of Fitting | Ideal Value | 4 | |
---|---|---|---|---|---|---|
Amplitude | 62.8 | 0.05249 | 0.00890 | 0.9971 | 0.0515 V | 0.00629 |
Frequency | 0.1767 | 40.83 | 3.117 | 0.9916 | 40.89 Hz | 2.20405 |
Channel | Sub-Band | Frequency (Hz) | Amplitude (V) | ||
---|---|---|---|---|---|
1 | 2–4 | 3.77 | 0.0036 | 0.0002 | 0.7653 |
2 | 4–8 | 5.90 | 0.0089 | 0.0003 | 0.7538 |
3 | 8–16 | 12.69 | 0.0411 | 0.0008 | 0.7931 |
4 | 16–140 | 24.64 | 0.1548 | 0.0025 | 1.1434 |
Frequency Point (Hz) | Channel 1 (2–4 Hz) | Channel 2 (4–8 Hz) | Channel 3 (8–16 Hz) | Channel 4 (16–140 Hz) | Selected Sub-Ban (Hz) |
---|---|---|---|---|---|
3.77 | 3.7500 | 3.7975 | 0.0000 | 0.0000 | 2–4 |
5.90 | 5.7391 | 5.8428 | 0.0000 | 0.0000 | 4–8 |
12.69 | 4.9485 | 12.2034 | 12.7946 | 12.8142 | 8–16 |
24.64 | 5.1173 | 11.8812 | 23.8914 | 24.5629 | 16–140 |
Frequency Point (Hz) | Relative Error (%) | |||
---|---|---|---|---|
[20] | [15] | [4] | Ours | |
3.77 | 0.40 | 0.27 | −0.53 | 0.31 |
5.90 | 0.34 | 0.13 | −0.97 | −0.17 |
12.69 | −0.32 | −0.18 | 0.82 | 0.15 |
24.64 | −0.14 | −0.06 | 0.31 | 0.11 |
Noise Frequency (Hz) | Noise Intensity | Relative Error (%) | |||
---|---|---|---|---|---|
[20] | [15] | [4] | Ours | ||
4 | Weak | 0.43 | –0.34 | –1.10 | –0.38 |
Strong | –0.61 | 0.79 | –3.47 | 0.85 | |
40 | Weak | –0.19 | –0.15 | –0.28 | 0.17 |
Strong | 0.58 | 0.35 | 0.44 | –0.25 |
Noise Intensity | Noise Times | Relative Error (%) | |||
---|---|---|---|---|---|
[20] | [15] | [4] | Ours | ||
Weak | 1 | 0.31 | 0.17 | –0.57 | –0.18 |
2 | –0.37 | 0.35 | 1.06 | 0.21 | |
3 | 0.46 | –0.30 | 4.91 | 0.29 | |
Strong | 1 | >100 | >100 | 2.02 | –0.38 |
2 | >100 | >100 | 3.40 | 0.65 | |
3 | >100 | >100 | 5.52 | 0.78 |
Vortex Signal | Noise Signal | Cycle Number | Relative Error (%) | ||
---|---|---|---|---|---|
[20] | [15] | Ours | |||
Low flow | Out of the sub-band | 40 | 0.00 | 0.00 | 0.00 |
20 | 0.00 | 0.00 | 0.00 | ||
10 | 0.00 | 0.02 | 0.00 | ||
5 | 0.11 | −0.15 | 0.00 | ||
3 | −1.69 | −2.04 | −0.23 | ||
Low flow | In the sub-band | 40 | 0.00 | 0.00 | 0.00 |
20 | 0.00 | 0.00 | 0.01 | ||
10 | 0.00 | −0.03 | −0.12 | ||
5 | 0.64 | 0.96 | 0.52 | ||
3 | 4.78 | 5.21 | −0.72 | ||
High flow | Out of the sub-band | 40 | 0.00 | 0.00 | 0.00 |
20 | 0.00 | 0.00 | 0.00 | ||
10 | 0.01 | 0.00 | 0.02 | ||
5 | −0.15 | −0.19 | −0.08 | ||
3 | 0.25 | 0.37 | −0.10 | ||
High flow | In the sub-band | 40 | 0.00 | 0.00 | 0.00 |
20 | 0.00 | 0.00 | 0.00 | ||
10 | −0.01 | −0.05 | 0.01 | ||
5 | 0.98 | 0.31 | −0.20 | ||
3 | −3.01 | −4.49 | 0.87 |
Location of the Flow Detection (m3/h) | Testing Time (s) | Total Pulse (Pulse) | Mean Frequency (Hz) | Standard Values (m3/h) | K Factor 1 (1/L) | Mean Coefficient (1/L) | Repeatability Error (%) |
---|---|---|---|---|---|---|---|
63 | 60.000 | 2412 | 40.200 | 63.457 | 2.2806 | 2.2772 | 0.13 |
59.000 | 2366 | 40.102 | 63.457 | 2.2749 | |||
59.000 | 2367 | 40.119 | 63.457 | 2.2761 | |||
143 | 59.000 | 5338 | 90.475 | 143.191 | 2.2749 | 2.2763 | 0.09 |
60.000 | 5438 | 90.633 | 143.194 | 2.2786 | |||
59.000 | 5340 | 90.508 | 143.189 | 2.2753 | |||
302 | 60.000 | 11420 | 190.333 | 301.992 | 2.2689 | 2.2712 | 0.14 |
59.000 | 11260 | 190.847 | 301.992 | 2.2750 | |||
60.000 | 11424 | 190.400 | 301.985 | 2.2698 | |||
548 | 59.000 | 20375 | 345.339 | 547.679 | 2.2699 | 2.2676 | 0.11 |
59.000 | 20355 | 345.000 | 547.679 | 2.2678 | |||
59.000 | 20331 | 344.593 | 547.676 | 2.2651 | |||
695 | 59.000 | 25665 | 435.000 | 694.701 | 2.2542 | 2.2570 | 0.12 |
60.000 | 25704 | 428.400 | 694.722 | 2.2576 | |||
59.000 | 26160 | 443.390 | 694.723 | 2.2593 |
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Li, B.; Wang, C.; Chen, J. A Frequency-Correcting Method for a Vortex Flow Sensor Signal Based on a Central Tendency. Sensors 2020, 20, 5379. https://doi.org/10.3390/s20185379
Li B, Wang C, Chen J. A Frequency-Correcting Method for a Vortex Flow Sensor Signal Based on a Central Tendency. Sensors. 2020; 20(18):5379. https://doi.org/10.3390/s20185379
Chicago/Turabian StyleLi, Bin, Chengyi Wang, and Jie Chen. 2020. "A Frequency-Correcting Method for a Vortex Flow Sensor Signal Based on a Central Tendency" Sensors 20, no. 18: 5379. https://doi.org/10.3390/s20185379
APA StyleLi, B., Wang, C., & Chen, J. (2020). A Frequency-Correcting Method for a Vortex Flow Sensor Signal Based on a Central Tendency. Sensors, 20(18), 5379. https://doi.org/10.3390/s20185379