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Research and realization of ultrasonic gas flow rate measurement based on ultrasonic exponential model
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Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras 5 6
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Research and realization of ultrasonic gas flow rate measurement based on ultrasonic exponential model
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Dandan Zheng ⇑, Huirang Hou, Tao Zhang
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Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering & Automation, Tianjin University, Tianjin 300072, China
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a r t i c l e
i n f o
Article history: Received 21 August 2015 Received in revised form 5 January 2016 Accepted 7 January 2016 Available online xxxx Keywords: Ultrasonic gas flow rate measurement Energy genetic-ant colony optimization3cycles (EGACO-3cycles) Time difference method
a b s t r a c t For ultrasonic gas flow rate measurement based on ultrasonic exponential model, when the noise frequency is close to that of the desired signals (called similar-frequency noise) or the received signal amplitude is small and unstable at big flow rate, local convergence of the algorithm genetic-ant colony optimization-3cycles may appear, and measurement accuracy may be affected. Therefore, an improved method energy genetic-ant colony optimization-3cycles (EGACO-3cycles) is proposed to solve this problem. By judging the maximum energy position of signal, the initial parameter range of exponential model can be narrowed and then the local convergence can be avoided. Moreover, a DN100 flow rate measurement system with EGACO-3cycles method is established based on NI PCI-6110 and personal computer. A series of experiments are carried out for testing the new method and the measurement system. It is shown that local convergence doesn’t appear with EGACO-3cycles method when similarfrequency noises exist and flow rate is big. Then correct time of flight can be obtained. Furthermore, through flow calibration on this system, the measurement range ratio is achieved 500:1, and the measurement accuracy is 0.5% with a low transition velocity 0.3 m/s. Ó 2016 Elsevier B.V. All rights reserved.
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1. Introduction
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Ultrasonic flowmeter has been developed rapidly in recent years. Compared with traditional flowmeters, ultrasonic flowmeter has high accuracy and repeatability. Moreover, because of no moving parts, it does not create extra pressure drop and allows bi-direction measurement [1]. Thus, ultrasonic flowmeter is more and more widely applied in process monitoring, measurement and control [2]. Where, the ultrasonic flowmeter with timedifference method is the most widely used [3]. In order to obtain an impressive result of flow rate measurement, it is crucial to detect the onset of ultrasonic received signals correctly, and acquire the time-of-flight (TOF) accurately. Generally, the received signals are susceptible to noises, and the amplitude and envelope of signals are not stable due to the instability of flow field and environment. Therefore, the accuracy of flow rate measurement is affected. In order to solve these problems, much research has been done. In 2007, an absolute TOF detection algorithm based on a time and frequency domain was proposed and the Hilbert transform was applied to calculate the wrapped phase signal by Kupnik et al. [4]. It was shown that for automobile exhaust absorption flow rate measurement, all the TOF was
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⇑ Corresponding author.
detected correctly from 52 °C to 415 °C, under 18–8 dB (signal-to-noise, SNR). Furthermore, it was illustrated that the algorithm outperformed cross-correlation methods in terms of the TOF detection. However, the biggest deficiency of this algorithm is the low accuracy. In 2010, TDC-GP2 (high precision clock chip) was applied in the TOF detection and the wavelet transform was studied to process time difference between upstream and downstream by Hua et al. [5]. The results showed that wavelet de-noising algorithm could effectively improve measurement accuracy and data stability, and relative errors of ultrasonic liquid flowmeter are less than 0.5%. However, the validity of wavelet de-noising algorithm is feasible for glitch noises, not all noises. In 2011, an optimized ultrasound driven method of incorporation of amplitude modulation and phase modulation was used to stimulate the transmitter. The envelope zero-crossing was detected and an optimal TOF algorithm (time-shift superposition of ultrasonic received signals) was applied to flow rate calculations by Wang and Tang [6]. It was shown that for double-path ultrasonic gas flow rate measurement, the nominal accuracies after flow weighted mean error (FWME) adjustment were better than 0.8% in the flow range of 0–450 m3/h. The validity of the optimal TOF algorithm is based on that the largest signal peak position can be detected correctly. However, the largest signal peak position is easy to be changed by noises and the unstable flow fields. In
http://dx.doi.org/10.1016/j.ultras.2016.01.005 0041-624X/Ó 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: D. Zheng et al., Research and realization of ultrasonic gas flow rate measurement based on ultrasonic exponential model, Ultrasonics (2016), http://dx.doi.org/10.1016/j.ultras.2016.01.005
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2014, multipath ultrasonic gas flowmeter was realized based on double-threshold method using automatic gain control technology (AGC) by Chen et al. [7]. It was shown that the measurement accuracy could reach 3% in the flow range of 0–1100 m3/h. The main idea of double-threshold detection is that the available signal is identified from the instance the signal amplitude exceeds a preset threshold level (called nonzero comparing), and then the TOF is obtained from the instance the signal amplitude becomes zero (called zero comparing). The problem is that if the received signal is mingled with noises, the correct zero point of the signal may not be found by zero comparing. The error of TOF measurement will increase if the available signal is not identified by nonzero comparing (i.e. the adopted signal cycle isn’t the desired cycle, called wrong signal, WS) [6]. An algorithm genetic-ant colony optimization-3cycles (GACO-3cycles) was proposed and applied in single path ultrasonic gas flow rate measurement based on ultrasonic exponential model by authors in 2015 [8]. Simulation results showed that the measurement accuracy was high and the anti-noise ability was strong with GACO-3cycles method. Wrong signal didn’t appear until 10 dB. Besides, experimental results illustrated that the measurement accuracy of DN100 single-path gas ultrasonic flowmeter can reach 0.5% in the flow range of 14–848 m3/h. However, when the amplitude of received signal is unstable under big flow rate or the frequency of noises is close to that of the desired signals (called similar-frequency noise), wrong signal may appear and then the accuracy of flow rate measurement is affected seriously. There are some commercial ultrasonic gas flowmeters manufactured by companies. Products of these well-known companies are listed in Table 1. As shown in Table 1, for single path ultrasonic gas flowmeters, the mean relative error can’t reach 1%. The maximum measurement range ratio of products above is 50:1 (0.6–30 m/s or 0.72–36 m/s), and the maximum and the minimum measurable flow rates are 36 m/s and 0.6 m/s respectively. When the actual flow rate is lower or higher, the products are not applicable. In this paper, in order to remain the better measurement accuracy (0.5%, as shown in Ref. [8]) under new noises and extend the measurement range, an improved method of GACO-3cycles (called energy GACO-3cycles, EGACO-3cycles) is proposed for wrong signal judging and correcting. A real-time flow rate measurement system using this method is established based on data acquisition card (NI PCI6110) and personal computer (PC). In Section 2, the principle of flow rate measurement using EGACO-3cycles method is introduced. In Section 3, the established ultrasonic gas flow measurement system is described. The efficacy of EGACO-3cycles method is tested and flow calibration on this measurement system is carried out in Section 4. This is followed by the conclusions in Section 5.
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2. Principle of EGACO-3cycles method for flow measurement
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Based on ultrasonic exponential model, the accurate value of TOF can be estimated by GACO-3cycles method [8]. Furthermore,
the flow rate can be obtained based on time-difference method. In view of the similar-frequency noises (frequency of noises is close to that of the desired signals) and the unstable signals under big flow rate, the improved method EGACO-3cycles is proposed.
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2.1. TOF estimation
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One of the parameters in exponential model is the desired TOF. Its accurate value can be obtained using EGACO-3cycles. Exponential model and EGACO-3cycles are stated as follows.
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2.1.1. Exponential model The exponential model of ultrasonic received signal is shown below [9]:
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Ag ðkts Þ ¼ Aðkt s Þ sin½2pf c ðkt s sÞ þ h m kts s kts s e T uðkts sÞ Aðkts Þ ¼ A0 T
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ð1Þ ð2Þ
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where A0 accounts for the signal amplitude, T and m are distinct to the specific ultrasonic sensor, s is the desired TOF, ts is the sampling period, k is the sampling point serial number, fc is the central frequency of the ultrasonic sensor, h is the initial phase, and u(ktss) is the unit step signal. Given that fc is determined by the ultrasonic sensor, and h is 0 rad, there are four independent variables: A0, T, m and s of the exponential model. The more accurate s is estimated, the better the ultrasonic flow rate measurement accuracy is.
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2.1.2. EGACO-3cycles method When there are different tightness of fixtures on ultrasonic sensors, circuit noises or errors of data acquisition, similar-frequency noises may appear. Because it may be taken as the available signals by GACO-3cycles method, the local convergence (i.e. the reconstructed signal cycle isn’t the desired cycle, wrong signal) may appear (Fig. 9). In addition, when the received signals are unstable under big flow rate, wrong signal may appear too (Fig. 10). Compared to authors’ previous studies (Ref. [8]), similarfrequency noises is a new problem that is not considered before. Besides, wrong signal may be caused by the unstable received signals under big flow rate. So the maximum measurable flow rate is only achieved 30 m/s if using GACO-3cycles method. In order to solve these problems, EGACO-3cycles method is proposed. There are five steps of EGACO-3cycles.
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(1) Judgment of zero point time after maximum signal peak
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The maximum signal peak can be found by looking for the maximum sampling voltage. Then the first zero point time after maximum signal peak can be obtained through zero comparing (Fig. 1). (2) Calculations of signal energy
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Under ideal conditions, the maximum signal peak judged by step 1 is correct. But when the signal envelope changes or there
Table 1 Comparisons of some commercial ultrasonic gas flowmeters. Company
Product model
Caliber
Path number
Measurement range
Mean relative error (%)
Repeatability (%)
E+H
Proline Prosonic Flow B 200
DN50-DN200
2
KROHNE
SeniorSonic JuniorSonic OPTISONIC 7300
DN100-DN600 DN100-DN1000 DN50-DN600
GE
Sentinel
DN100-DN250
4 1 or 2 2 1 2
3 1.5 0.3 1.5 1 2 0.5 1.0
0.5
Daniel
1–3 m/s 3–30 m/s 0.6–30 m/s 0.6–30 m/s >1 m/s 3.6–36 m/s 0.72–3.6 m/s
0.05 0.1 0.2 0.08 0.15
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Actual sampling signal Zero-comparing
Maximum peak
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Zero point after maximum peak
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Time (μs) Fig. 1. Zero point time after maximum peak.
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are noises, the correct maximum peak may not be recognized by step 1. Therefore, signal peak is replaced by signal energy. Considering the similar symmetry of the positive and negative signals, positive signals are selected to replace the whole signal. Signal energy of each cycle can be obtained by calculating the sum of all positive sampling point voltages of each cycle. As shown in Fig. 2, taking the maximum signal peak (by step 1) as the center, nine signal energies are calculated. (3) Judgment of zero point time after maximum signal energy
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Considering the position of maximum signal peak may be changed, the signal energy of several adjacent cycles is adopted to judge the position of maximum signal energy.
E3k ¼ Ek þ Ekþ1 þ Ekþ2
ð3Þ
s3k ¼ skþ1 ; k ¼ 1; 2; . . . ; 6; 7
ð4Þ
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E3k . For example, in Fig. 2, E34 is the energy sum of the 4th, 5th and 6th signals and s34 is the zero point time after the 5th signal peak. By analyzing the experimental data, for more than 97% of the received signals, the position of maximum signal energy can be judged correctly using three consecutive cycle energies. For less than 3% of the received signals, the position of maximum signal energy cannot be judged correctly (wrong signal), when the time error of zero point after maximum signal energy is close to n⁄8.3 ls (n ¼ 1; 2; 3 . . ., and the central frequency of the ultrasonic sensor is 120 kHz, 8.3 ls = 1/(120 kHz)). Based on this rule, set a time reference sp . Determination of sp :
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① Initialization. Get 10 zero point time after maximum signal energy using 10 received signals before flow rate measure-
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0.05 4
0.04
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0.03 8
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0.02 1
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Ek is the kth signal energy. E3k is the energy sum of the kth, (k + 1)th and (k + 2)th signals. sk is the zero point time after the kth signal peak. s3k is the center zero point time corresponding to
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T=5.5*8.3μs
-0.01 -0.02
τ 34
-0.03 -0.04 -0.05 380
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Time (μs) Fig. 2. Signal energy of each cycle.
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ment. Then sort these zero point time and take the 5th zero point time as the initialization of sp . ② Updating sp . When the difference between new zero point time and sp is close to n⁄8.3 ls (wrong signal), don’t update sp , otherwise, update sp using new zero point time. (4) Initial estimation of TOF
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Wrong signal can be avoided when the position of maximum signal energy is judged correctly. Then the initial estimation of TOF can be obtained by Eq. (5).
s ¼ sp T
ð5Þ
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T is the difference between the starting time of received signal and time reference. The T is a certain value, once the ultrasonic sensors and emission signal are determined specifically. In this paper, as shown in Fig. 2, T = 5.5⁄8.3 ls. s_ is initial estimation of TOF.
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(5) Narrowing TOF initial range and accurate estimation of TOF
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such as various velocity profiles in pipe, geometric deviation caused by manufacturing process and installation, hardware and software errors of measurement system and so on, the mean flow needs to be corrected by Eq. (7) (the detail described in velocity v Sections 3 and 3.2 and 3.2). Thus, the volume flow rate can be . calculated based on v
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3. Flow rate measurement system design
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The flow rate measurement system based on EGACO-3cycles method is consisted of three modules: signal emitting and receiving, data acquiring and data processing. As shown in Fig. 4, as the core control chip, the signal emitting and acquiring are controlled by MSP430F249T. Signal acquiring is realized through NI PCI-6110 programmed in LabVIEW on personal computer [10]. Signal processing is accomplished in MATLAB. The combination of MATLAB and LabVIEW is realized through MATLAB script in LabVIEW.
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3.1. Hardware design
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3.1.1. Emission For piezoelectric ultrasonic transducers, when emission frequency is equal to the resonance frequency of ultrasonic transducer, the efficiency of piezoelectric conversion is the best. In this paper, the resonance frequency of ultrasonic sensor is 120 kHz. Therefore, the emission frequency is set to 120 kHz. The emission module is shown in Fig. 5. In consideration of serious attenuation of ultrasonic wave in air, a high stimulation voltage is designed in order to get a good received signal. As shown in Fig. 5, two square wave sequences are emitted by MSP430F249T. Because of weak driving ability of the signal emitted by MSP430F249T, power drive (through TC4426EOA) circuit is needed. In order to stimulate ultrasonic transducer better and get a good received signal, alternating current signal (AC signal) with 30 V (peak-to-peak voltage) is generated by push–pull circuit. Then the low voltage is boosted. In this paper, the voltage booster ratio is 1:20. Therefore, the final stimulating voltage to emitting sensor is 600 V (peak-to-peak voltage).
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3.1.2. Receiving and sampling The measurement accuracy of flow rate can be affected by the error of data sampling. The sampling accuracy involves both voltage and time accuracy. In this paper, multi-function data acquisition card NI PCI-6110 with 0:2— 42 V programmable input voltage range is applied in data sampling. Voltage resolution ratio of PCI-6110 is 12 bits. The maximum sampling rate can reach 5 MHz. As shown in Fig. 6, PCI-6110 can be programmed in LabVIEW [10]. ① Choose sampling channel. ② Considering the amplitude of actual received signal is within 0:2 V, sampling voltage range is set to 0:2 V. Therefore, the sampling accuracy is 0.0977 mV
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For DN100 single-path ultrasonic gas flowmeter with 45° path angle, the difference between upstream TOF and downstream TOF is about 87 ls under 50 m/s flow velocity. Therefore, the initial range of TOF in exponential model must be set at least 87 ls. However, large parameter range isn’t conducive to the convergence of GACO-3cycles method, and wrong signal is easy to appear. For EGACO-3cycles method, the initial estimation of TOF can be obtained by step 4. Based on this, the initial range of TOF can be narrowed to [s_ t; s_ þ t]. It is considered that the errors of time reference sp and initial estimation of TOF s_ are less than a signal period (8.3 ls) by step 3 and 4, so t is set to 8.3/2 ls. Due to the small parameter range, wrong signal can be avoided in big flow rate or under similar-frequency noises. Besides, it is conducive to fasten iteration of GACO-3cycles method. Finally, the accurate value of TOF can be obtained through GACO-3cycles [8].
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2.2. Flow rate measurement
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For a single-path ultrasonic flowmeter based on the timedifference method, a schematic diagram of the experimental test can be calculated setup is shown in Fig. 3 and the flow velocity v using Eqs. (6) and (7).
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v¼ 257 258 259 260 261 262
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L 2cos/
v ¼ f ðv Þ
1
sa
1
sb
ð6Þ ð7Þ
D is diameter of the pipe. L is length of acoustic path, connecting upstream transducer to downstream transducer. / is path angle between the acoustic path and the pipe axis. In this paper, D = 100 mm, L = 141 mm and / ¼ 45 . sa and sb are transit times of ultrasound propagation downstream and upstream respectively. v is average flow velocity along the path. Considering some factors,
Fig. 3. Schematic diagram of the experimental test setup.
Fig. 4. Ultrasonic flow measurement system based on EGACO-3cycles method.
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Fig. 5. Emission module.
Fig. 6. Sampling setting in LabVIEW.
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(0.4/212 V). ③ In order to guarantee long-term stability of sampling, set the actual sampling rate to 4 MHz (not the maximum sampling rate). ④ Set the sampling number 2500 to guarantee the received signal be sampled in large flow rate range. It should be noted that the sampling number 2500 is just for one received signal. Lots of received signals can be got by multi-trigger. ⑤ Set digital edge triggering as triggering mode, and this is controlled by MSP430F249T.
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3.2. Software design
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EGACO-3cycles method is realized through MATLAB program embedded in LabVIEW. In consideration of measurement system error, velocity profile and nonlinearity of ultrasonic flow rate measurement, measurement data processing and flow rate correction are necessary in order to improve measurement accuracy. So the first-order lag filter and median filter are applied in flow velocity processing and the flow velocity is corrected through the leastsquares curve fitting. The data processing block is shown in Fig. 7. At a certain flow rate point, get 300 flow velocity values. Take every 100 values as a group. Then apply the first-order lag filter and median filter in each group and get corresponding filtered velocities. Moreover, take the average value of these three velocities as the final result for this flow rate point. In the same way, 10 flow velocity values at 10 flow rate points can be obtained from 0 m/s to 50 m/s. So build an array a[1,2,3. . .,10] for the ten values. Meanwhile, store the standard flow velocity values in array b[1,2,3,. . .,10]. Finally, the
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Fig. 7. Data processing.
relationship between array a and b can be obtained through leastsquares curve fitting (fourth power, Eq. (8)).
b ¼ P 1 a4 þ P2 a3 þ P3 a2 þ P4 a þ P5
ð8Þ
P1, P2, P3, P4, P5 are fitting coefficients. With Eq. (8), the error of flow velocity measurement can be reduced and the measurement accuracy can be improved. In this paper, P1, P2, P3, P4, P5 are 0.000000535, 0.000067356, 0.006134263, 1.038518045, 0.011481229 respectively, determined by experiments.
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4. Experiment analysis and results
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In order to verify the validity of EGACO-3cycles method for wrong signal judgment and correction, a series of experiments are carried out. Moreover, the calibration experiment is done to test the established measurement system. All experiments are conducted in Tianjing key laboratory of process measurement and control. The experimental system is shown in Fig. 8.
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4.1. Judgment and correction of wrong signal
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For similar-frequency noises caused by different tightness of fixtures on ultrasonic sensors, circuit noises or errors of data acquisition, wrong signal can be avoided by using EGACO-3cycles method. As shown in Fig. 9. Signals are sampled at 0 m/s. Fig. 9a is ideal signal under ideal conditions (signal amplitude is stable and the SNR is high). Fig. 9b and c are actual signals under similarfrequency noises. EGACO-3cycles method is applied to reconstruct signal of Fig. 9b. In contrast, and GACO-3cycles method is used to reconstruct signal of Fig. 9c. Fig. 9d–f are the magnified graphs of Fig. 9a–c. It is shown that the similar-frequency noises are taken as the desired signal with GACO-3cycles method (Fig. 9f), thus the obtained TOF is less a signal cycle than the actual TOF. In con-
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4.2. Calibration experiments
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The problem of wrong signal can be solved and the flow rate measurement range can be broadened when using EGACO-3cycles method. Through analyzing the actual received signals, the amplitudes of received signals are within the range [0.01, 0.05] V from 0.1 m/s to 50 m/s. The setting parameters m and T are within the ranges [3.4, 3.8] and [12.3, 12.7]. So the initial parameter values of exponential model are set in the intervals A0 [0.01, 0.05] V, m [3.4, 3.8], T [12.3, 12.7], s [s_ 4:15, s_ þ 4:15] us (s_ is initial estimation of TOF) respectively, which are suitable for various actual received signals. Ten flow rate points are calibrated from 0.1 m/s to 50 m/s. For the flow velocity measurement, the mean relative error (E) and repeatability (Er) are presented in this paper. The calibration results are shown in Table 2.
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v i v si Ei ¼ v si
ð8Þ
Pl
i¼1 Ei
E¼
0.05
ð9Þ
l
v i is average flow velocity of ultrasonic flowmeter obtained in the ith calibration. v si is the average standard flow velocity in the
Fig. 8. Ultrasonic gas flow rate experimental system.
Actual sampling signal Reconstructed signal
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Amplitude (V)
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Time (μs)
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Amplitude (V)
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Amplitude (V)
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Amplitude (V)
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trast, when EGACO-3cycles method is adopted, wrong signal is avoided and correct TOF is obtained (Fig. 9e). For gas ultrasonic flow measurement, acoustic signals attenuate seriously at big flow rate, and the signal envelope trends to be flat. Thus the small received signals may be submerged in noises, which leads to wrong signal appear. Some signals at 50 m/s are sampled and analyzed. Similar to Fig. 9, in Fig. 10a, there is no wrong signal under ideal conditions. In Fig. 10c, wrong signal appears with GACO-3cycles method. In Fig. 10b, wrong signal is avoided using EGACO3cycles method. Fig. 10d–f is the magnified graphs of Fig. 10a–c. From Fig. 10f, it is shown that when the starting cycle of the desired signal is submerged in noises, the starting cycle may be taken as noise with GACO-3cycles method, and then the obtained TOF is larger a signal cycle than the actual TOF. In contrast, from Fig. 10e, the small starting cycle can be reconstructed by EGACO3cycles method and correct TOF is obtained.
500
550
0.02
f
0 -0.02 400
420
440
460
Time (μs)
Fig. 9. Judgment and correction of wrong signal caused by similar-frequency noises.
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Fig. 10. Judgment of wrong signal at big flow rate.
Table 2 Results of calibration.
v si
(ms1)
0.1 0.2 0.3 0.8 5 15 25 35 45 50
401 402 403 404 405
406
408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425
E (%)
Er (%)
0.06 0.12 0.04 0.44 0.02 0.29 0.03 0.37 0.41 0.029
0.35 0.039 0.09 0.035 0.14 0.08 0.015 0.15 0.037 0.035
ith calibration. Ei is the relative error of the ith calibration. l is the calibration number of each flow rate point under the same condition, l = 3. The time of each calibration is 30 s. E is the mean relative error. The smaller E is, the better the measurement accuracy of the velocity is.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pl 2 i¼1 ðEi EÞ Er ¼ l1
ð10Þ
Er is repeatability. According to ‘Verification Regulation of Ultrasonic Flowmeters, JJG 1030-2007’ [11], the definition of repeatability is from Bessel equation. Differ from the mean relative error (E), repeatability expresses the precision of measurement not the accuracy. The smaller Er is, the better the stability of velocity measurement is. As shown in Table 2, except the flow rate points 0.8 m/s and 50 m/s, the errors of velocities higher than 30 m/s are bigger than that lower than 30 m/s. It might be caused by heavy turbulence fluctuation at high flow rate, especially when flow velocity is higher than 30 m/s. Besides, the data fitting method might influence the error distribution. The least-squares curve fitting is selected in this paper, which assure global optimization of measurement data. Therefore, although the mean relative error fluctuates at flow rate range 0.1–50 m/s, all errors are less than 0.5%, and the repeatability is better than 0.2% from 0.2 m/s to 50 m/s. The measurement range ratio is wide (500:1).
According to JJG 1030-2007 [11], the accuracy of ultrasonic flowmeter is defined as the worst accuracy of velocities higher than transition velocity. Meanwhile, the accuracy of velocities lower than the transition velocity cannot be more than twice the accuracy above it. For the flow measurement system established in this paper, if 0.3 m/s is selected as the transition velocity, the measurement accuracy (i.e. mean relative error) is better than 0.5% with EGACO-3cycles method.
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5. Conclusions
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For ultrasonic gas flow rate measurement, because of the different tightness of fixtures on ultrasonic sensors, circuit noises and errors of data acquisition, similar-frequency noises may appear. In addition, when flow velocity is high, the small starting cycle of signal may be submerged in noises because of severe attenuation of ultrasound propagation. Both situations may lead to wrong signal of measurement with GACO-3cycles method, which affect the measurement accuracy. In order to improve this method, energy GACO-3cycles (EGACO-3cycles) method is proposed. In consideration of the changeless maximum energy position of received signals, transit time of ultrasound propagation at the zero point after maximum energy position can be determined. In this way, wrong signal can be avoided. Moreover, a real-time flow rate measurement system with EGACO-3cycles method is established. It is mainly realized based on the control chip MSP430F249T and data acquisition card NI PCI-6110. The main conclusions are stated as below.
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(a) The problem of wrong signal caused by similar-frequency noises and the unstable signals at big flow rate is solved by the proposed method EGACO-3cycles. (b) A flow rate measurement system is established based on personal computer. Real-time data processing is realized through MATLAB nested in LabVIEW by the MATLAB Script. It is shown that for DN100 single path ultrasonic gas flow rate measurement, the accuracy is better than 0.5% from 0.1 m/s to 50 m/s. Besides, the transition velocity (0.3 m/s) is low and the measurement range ratio is achieved 500:1.
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Acknowledgments
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This work is supported by the National Natural Science Foundation of China (Grant No. 61101227) and the Natural Science Foundation of Tianjin (Grant No. 13JCQNJC03300).
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References
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[1] L.C. Lynnworth, Y. Liu, Ultrasonic flowmeters: half-century progress report 1955–2005, Ultrasonics 44 (2006) e1371–e1378. [2] American Gas Association, Measurement of Gas by Multipath Ultrasonic Meters AGA Report 9, 1998 [3] J.T. Walsh, A report of acoustic transit time accuracy field work performed in North America, in: 5th International Conference on Hydraulic Efficiency Measurements, Lucerne, Switzerland, July 2004. [4] Mario Kupnik, Edwin Krasser, Martin Gröschl, Absolute transit time detection for ultrasonic gas flowmeters based on time and phase domain characteristics, IEEE Ultrason. Symp. (2007) 142–145.
[5] Meng Hua, Wang Hui, Li Mingwei, High-precision flow measurement for an ultrasonic transit time flowmeter, in: International Conference on Intelligent System Design and Engineering Application, 2010, pp. 1823–1826. [6] X.F. Wang, Z.A. Tang, Ultrasonic gas flowmeter based on optimized time-offlight algorithms, Rev. Sci. Instrum. 82 (2011) 046109. [7] Qiang Chen, Weihua Li, Wu Jiangtao, Realization of a multipath ultrasonic gas flowmeter based on transit-time technique, Ultrasonics 54 (2014) 285–290. [8] Huirang Hou, Dandan Zheng, Laixiao Nie, Gas ultrasonic flow rate measurement through genetic-ant colony optimization based on the ultrasonic pulse received signal model, Meas. Sci. Technol. 26 (2015) 045005. [9] A.M. Sabatini, Correlation receivers using Laguerre filter banks for modelling narrowband ultrasonic echoes and estimating their time-of-flights, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44 (1997) 1253–1263. [10] Asan Gani, M.J.E. Salami, A LabVIEW based data acquisition system for vibration monitoring and analysis, in: Student Conference on Research and Development Proceedings, 2002, pp. 62–65. [11] C. Wang, F. Qiu, Y. Miao, Verification regulation of ultrasonic flowmeters Chinese standard JJG 1030-200, 2007.
Please cite this article in press as: D. Zheng et al., Research and realization of ultrasonic gas flow rate measurement based on ultrasonic exponential model, Ultrasonics (2016), http://dx.doi.org/10.1016/j.ultras.2016.01.005
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Contents lists available at ScienceDirect
Ultrasonics journal homepage: www.elsevier.com/locate/ultras 5 6
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Research and realization of ultrasonic gas flow rate measurement based on ultrasonic exponential model
7
Dandan Zheng ⇑, Huirang Hou, Tao Zhang
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Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering & Automation, Tianjin University, Tianjin 300072, China
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9 10 1 2 2 4 13 14 15 16 17 18 19 20 21 22 23
a r t i c l e
i n f o
Article history: Received 21 August 2015 Received in revised form 5 January 2016 Accepted 7 January 2016 Available online xxxx Keywords: Ultrasonic gas flow rate measurement Energy genetic-ant colony optimization3cycles (EGACO-3cycles) Time difference method
a b s t r a c t For ultrasonic gas flow rate measurement based on ultrasonic exponential model, when the noise frequency is close to that of the desired signals (called similar-frequency noise) or the received signal amplitude is small and unstable at big flow rate, local convergence of the algorithm genetic-ant colony optimization-3cycles may appear, and measurement accuracy may be affected. Therefore, an improved method energy genetic-ant colony optimization-3cycles (EGACO-3cycles) is proposed to solve this problem. By judging the maximum energy position of signal, the initial parameter range of exponential model can be narrowed and then the local convergence can be avoided. Moreover, a DN100 flow rate measurement system with EGACO-3cycles method is established based on NI PCI-6110 and personal computer. A series of experiments are carried out for testing the new method and the measurement system. It is shown that local convergence doesn’t appear with EGACO-3cycles method when similarfrequency noises exist and flow rate is big. Then correct time of flight can be obtained. Furthermore, through flow calibration on this system, the measurement range ratio is achieved 500:1, and the measurement accuracy is 0.5% with a low transition velocity 0.3 m/s. Ó 2016 Elsevier B.V. All rights reserved.
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1. Introduction
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Ultrasonic flowmeter has been developed rapidly in recent years. Compared with traditional flowmeters, ultrasonic flowmeter has high accuracy and repeatability. Moreover, because of no moving parts, it does not create extra pressure drop and allows bi-direction measurement [1]. Thus, ultrasonic flowmeter is more and more widely applied in process monitoring, measurement and control [2]. Where, the ultrasonic flowmeter with timedifference method is the most widely used [3]. In order to obtain an impressive result of flow rate measurement, it is crucial to detect the onset of ultrasonic received signals correctly, and acquire the time-of-flight (TOF) accurately. Generally, the received signals are susceptible to noises, and the amplitude and envelope of signals are not stable due to the instability of flow field and environment. Therefore, the accuracy of flow rate measurement is affected. In order to solve these problems, much research has been done. In 2007, an absolute TOF detection algorithm based on a time and frequency domain was proposed and the Hilbert transform was applied to calculate the wrapped phase signal by Kupnik et al. [4]. It was shown that for automobile exhaust absorption flow rate measurement, all the TOF was
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⇑ Corresponding author.
detected correctly from 52 °C to 415 °C, under 18–8 dB (signal-to-noise, SNR). Furthermore, it was illustrated that the algorithm outperformed cross-correlation methods in terms of the TOF detection. However, the biggest deficiency of this algorithm is the low accuracy. In 2010, TDC-GP2 (high precision clock chip) was applied in the TOF detection and the wavelet transform was studied to process time difference between upstream and downstream by Hua et al. [5]. The results showed that wavelet de-noising algorithm could effectively improve measurement accuracy and data stability, and relative errors of ultrasonic liquid flowmeter are less than 0.5%. However, the validity of wavelet de-noising algorithm is feasible for glitch noises, not all noises. In 2011, an optimized ultrasound driven method of incorporation of amplitude modulation and phase modulation was used to stimulate the transmitter. The envelope zero-crossing was detected and an optimal TOF algorithm (time-shift superposition of ultrasonic received signals) was applied to flow rate calculations by Wang and Tang [6]. It was shown that for double-path ultrasonic gas flow rate measurement, the nominal accuracies after flow weighted mean error (FWME) adjustment were better than 0.8% in the flow range of 0–450 m3/h. The validity of the optimal TOF algorithm is based on that the largest signal peak position can be detected correctly. However, the largest signal peak position is easy to be changed by noises and the unstable flow fields. In
http://dx.doi.org/10.1016/j.ultras.2016.01.005 0041-624X/Ó 2016 Elsevier B.V. All rights reserved.
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2014, multipath ultrasonic gas flowmeter was realized based on double-threshold method using automatic gain control technology (AGC) by Chen et al. [7]. It was shown that the measurement accuracy could reach 3% in the flow range of 0–1100 m3/h. The main idea of double-threshold detection is that the available signal is identified from the instance the signal amplitude exceeds a preset threshold level (called nonzero comparing), and then the TOF is obtained from the instance the signal amplitude becomes zero (called zero comparing). The problem is that if the received signal is mingled with noises, the correct zero point of the signal may not be found by zero comparing. The error of TOF measurement will increase if the available signal is not identified by nonzero comparing (i.e. the adopted signal cycle isn’t the desired cycle, called wrong signal, WS) [6]. An algorithm genetic-ant colony optimization-3cycles (GACO-3cycles) was proposed and applied in single path ultrasonic gas flow rate measurement based on ultrasonic exponential model by authors in 2015 [8]. Simulation results showed that the measurement accuracy was high and the anti-noise ability was strong with GACO-3cycles method. Wrong signal didn’t appear until 10 dB. Besides, experimental results illustrated that the measurement accuracy of DN100 single-path gas ultrasonic flowmeter can reach 0.5% in the flow range of 14–848 m3/h. However, when the amplitude of received signal is unstable under big flow rate or the frequency of noises is close to that of the desired signals (called similar-frequency noise), wrong signal may appear and then the accuracy of flow rate measurement is affected seriously. There are some commercial ultrasonic gas flowmeters manufactured by companies. Products of these well-known companies are listed in Table 1. As shown in Table 1, for single path ultrasonic gas flowmeters, the mean relative error can’t reach 1%. The maximum measurement range ratio of products above is 50:1 (0.6–30 m/s or 0.72–36 m/s), and the maximum and the minimum measurable flow rates are 36 m/s and 0.6 m/s respectively. When the actual flow rate is lower or higher, the products are not applicable. In this paper, in order to remain the better measurement accuracy (0.5%, as shown in Ref. [8]) under new noises and extend the measurement range, an improved method of GACO-3cycles (called energy GACO-3cycles, EGACO-3cycles) is proposed for wrong signal judging and correcting. A real-time flow rate measurement system using this method is established based on data acquisition card (NI PCI6110) and personal computer (PC). In Section 2, the principle of flow rate measurement using EGACO-3cycles method is introduced. In Section 3, the established ultrasonic gas flow measurement system is described. The efficacy of EGACO-3cycles method is tested and flow calibration on this measurement system is carried out in Section 4. This is followed by the conclusions in Section 5.
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2. Principle of EGACO-3cycles method for flow measurement
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Based on ultrasonic exponential model, the accurate value of TOF can be estimated by GACO-3cycles method [8]. Furthermore,
the flow rate can be obtained based on time-difference method. In view of the similar-frequency noises (frequency of noises is close to that of the desired signals) and the unstable signals under big flow rate, the improved method EGACO-3cycles is proposed.
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2.1. TOF estimation
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One of the parameters in exponential model is the desired TOF. Its accurate value can be obtained using EGACO-3cycles. Exponential model and EGACO-3cycles are stated as follows.
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2.1.1. Exponential model The exponential model of ultrasonic received signal is shown below [9]:
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Ag ðkts Þ ¼ Aðkt s Þ sin½2pf c ðkt s sÞ þ h m kts s kts s e T uðkts sÞ Aðkts Þ ¼ A0 T
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ð1Þ ð2Þ
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where A0 accounts for the signal amplitude, T and m are distinct to the specific ultrasonic sensor, s is the desired TOF, ts is the sampling period, k is the sampling point serial number, fc is the central frequency of the ultrasonic sensor, h is the initial phase, and u(ktss) is the unit step signal. Given that fc is determined by the ultrasonic sensor, and h is 0 rad, there are four independent variables: A0, T, m and s of the exponential model. The more accurate s is estimated, the better the ultrasonic flow rate measurement accuracy is.
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2.1.2. EGACO-3cycles method When there are different tightness of fixtures on ultrasonic sensors, circuit noises or errors of data acquisition, similar-frequency noises may appear. Because it may be taken as the available signals by GACO-3cycles method, the local convergence (i.e. the reconstructed signal cycle isn’t the desired cycle, wrong signal) may appear (Fig. 9). In addition, when the received signals are unstable under big flow rate, wrong signal may appear too (Fig. 10). Compared to authors’ previous studies (Ref. [8]), similarfrequency noises is a new problem that is not considered before. Besides, wrong signal may be caused by the unstable received signals under big flow rate. So the maximum measurable flow rate is only achieved 30 m/s if using GACO-3cycles method. In order to solve these problems, EGACO-3cycles method is proposed. There are five steps of EGACO-3cycles.
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(1) Judgment of zero point time after maximum signal peak
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The maximum signal peak can be found by looking for the maximum sampling voltage. Then the first zero point time after maximum signal peak can be obtained through zero comparing (Fig. 1). (2) Calculations of signal energy
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Under ideal conditions, the maximum signal peak judged by step 1 is correct. But when the signal envelope changes or there
Table 1 Comparisons of some commercial ultrasonic gas flowmeters. Company
Product model
Caliber
Path number
Measurement range
Mean relative error (%)
Repeatability (%)
E+H
Proline Prosonic Flow B 200
DN50-DN200
2
KROHNE
SeniorSonic JuniorSonic OPTISONIC 7300
DN100-DN600 DN100-DN1000 DN50-DN600
GE
Sentinel
DN100-DN250
4 1 or 2 2 1 2
3 1.5 0.3 1.5 1 2 0.5 1.0
0.5
Daniel
1–3 m/s 3–30 m/s 0.6–30 m/s 0.6–30 m/s >1 m/s 3.6–36 m/s 0.72–3.6 m/s
0.05 0.1 0.2 0.08 0.15
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Actual sampling signal Zero-comparing
Maximum peak
0.03
Amplitude (V)
0.02 0.01 0 -0.01 -0.02 -0.03
Zero point after maximum peak
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Time (μs) Fig. 1. Zero point time after maximum peak.
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are noises, the correct maximum peak may not be recognized by step 1. Therefore, signal peak is replaced by signal energy. Considering the similar symmetry of the positive and negative signals, positive signals are selected to replace the whole signal. Signal energy of each cycle can be obtained by calculating the sum of all positive sampling point voltages of each cycle. As shown in Fig. 2, taking the maximum signal peak (by step 1) as the center, nine signal energies are calculated. (3) Judgment of zero point time after maximum signal energy
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Considering the position of maximum signal peak may be changed, the signal energy of several adjacent cycles is adopted to judge the position of maximum signal energy.
E3k ¼ Ek þ Ekþ1 þ Ekþ2
ð3Þ
s3k ¼ skþ1 ; k ¼ 1; 2; . . . ; 6; 7
ð4Þ
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E3k . For example, in Fig. 2, E34 is the energy sum of the 4th, 5th and 6th signals and s34 is the zero point time after the 5th signal peak. By analyzing the experimental data, for more than 97% of the received signals, the position of maximum signal energy can be judged correctly using three consecutive cycle energies. For less than 3% of the received signals, the position of maximum signal energy cannot be judged correctly (wrong signal), when the time error of zero point after maximum signal energy is close to n⁄8.3 ls (n ¼ 1; 2; 3 . . ., and the central frequency of the ultrasonic sensor is 120 kHz, 8.3 ls = 1/(120 kHz)). Based on this rule, set a time reference sp . Determination of sp :
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① Initialization. Get 10 zero point time after maximum signal energy using 10 received signals before flow rate measure-
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0.05 4
0.04
3 E4
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0.03 8
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0.02 1
Amplitude (V)
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Ek is the kth signal energy. E3k is the energy sum of the kth, (k + 1)th and (k + 2)th signals. sk is the zero point time after the kth signal peak. s3k is the center zero point time corresponding to
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0.01 0
T=5.5*8.3μs
-0.01 -0.02
τ 34
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Time (μs) Fig. 2. Signal energy of each cycle.
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ment. Then sort these zero point time and take the 5th zero point time as the initialization of sp . ② Updating sp . When the difference between new zero point time and sp is close to n⁄8.3 ls (wrong signal), don’t update sp , otherwise, update sp using new zero point time. (4) Initial estimation of TOF
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Wrong signal can be avoided when the position of maximum signal energy is judged correctly. Then the initial estimation of TOF can be obtained by Eq. (5).
s ¼ sp T
ð5Þ
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T is the difference between the starting time of received signal and time reference. The T is a certain value, once the ultrasonic sensors and emission signal are determined specifically. In this paper, as shown in Fig. 2, T = 5.5⁄8.3 ls. s_ is initial estimation of TOF.
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(5) Narrowing TOF initial range and accurate estimation of TOF
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such as various velocity profiles in pipe, geometric deviation caused by manufacturing process and installation, hardware and software errors of measurement system and so on, the mean flow needs to be corrected by Eq. (7) (the detail described in velocity v Sections 3 and 3.2 and 3.2). Thus, the volume flow rate can be . calculated based on v
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3. Flow rate measurement system design
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The flow rate measurement system based on EGACO-3cycles method is consisted of three modules: signal emitting and receiving, data acquiring and data processing. As shown in Fig. 4, as the core control chip, the signal emitting and acquiring are controlled by MSP430F249T. Signal acquiring is realized through NI PCI-6110 programmed in LabVIEW on personal computer [10]. Signal processing is accomplished in MATLAB. The combination of MATLAB and LabVIEW is realized through MATLAB script in LabVIEW.
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3.1. Hardware design
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3.1.1. Emission For piezoelectric ultrasonic transducers, when emission frequency is equal to the resonance frequency of ultrasonic transducer, the efficiency of piezoelectric conversion is the best. In this paper, the resonance frequency of ultrasonic sensor is 120 kHz. Therefore, the emission frequency is set to 120 kHz. The emission module is shown in Fig. 5. In consideration of serious attenuation of ultrasonic wave in air, a high stimulation voltage is designed in order to get a good received signal. As shown in Fig. 5, two square wave sequences are emitted by MSP430F249T. Because of weak driving ability of the signal emitted by MSP430F249T, power drive (through TC4426EOA) circuit is needed. In order to stimulate ultrasonic transducer better and get a good received signal, alternating current signal (AC signal) with 30 V (peak-to-peak voltage) is generated by push–pull circuit. Then the low voltage is boosted. In this paper, the voltage booster ratio is 1:20. Therefore, the final stimulating voltage to emitting sensor is 600 V (peak-to-peak voltage).
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3.1.2. Receiving and sampling The measurement accuracy of flow rate can be affected by the error of data sampling. The sampling accuracy involves both voltage and time accuracy. In this paper, multi-function data acquisition card NI PCI-6110 with 0:2— 42 V programmable input voltage range is applied in data sampling. Voltage resolution ratio of PCI-6110 is 12 bits. The maximum sampling rate can reach 5 MHz. As shown in Fig. 6, PCI-6110 can be programmed in LabVIEW [10]. ① Choose sampling channel. ② Considering the amplitude of actual received signal is within 0:2 V, sampling voltage range is set to 0:2 V. Therefore, the sampling accuracy is 0.0977 mV
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For DN100 single-path ultrasonic gas flowmeter with 45° path angle, the difference between upstream TOF and downstream TOF is about 87 ls under 50 m/s flow velocity. Therefore, the initial range of TOF in exponential model must be set at least 87 ls. However, large parameter range isn’t conducive to the convergence of GACO-3cycles method, and wrong signal is easy to appear. For EGACO-3cycles method, the initial estimation of TOF can be obtained by step 4. Based on this, the initial range of TOF can be narrowed to [s_ t; s_ þ t]. It is considered that the errors of time reference sp and initial estimation of TOF s_ are less than a signal period (8.3 ls) by step 3 and 4, so t is set to 8.3/2 ls. Due to the small parameter range, wrong signal can be avoided in big flow rate or under similar-frequency noises. Besides, it is conducive to fasten iteration of GACO-3cycles method. Finally, the accurate value of TOF can be obtained through GACO-3cycles [8].
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2.2. Flow rate measurement
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For a single-path ultrasonic flowmeter based on the timedifference method, a schematic diagram of the experimental test can be calculated setup is shown in Fig. 3 and the flow velocity v using Eqs. (6) and (7).
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v¼ 257 258 259 260 261 262
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L 2cos/
v ¼ f ðv Þ
1
sa
1
sb
ð6Þ ð7Þ
D is diameter of the pipe. L is length of acoustic path, connecting upstream transducer to downstream transducer. / is path angle between the acoustic path and the pipe axis. In this paper, D = 100 mm, L = 141 mm and / ¼ 45 . sa and sb are transit times of ultrasound propagation downstream and upstream respectively. v is average flow velocity along the path. Considering some factors,
Fig. 3. Schematic diagram of the experimental test setup.
Fig. 4. Ultrasonic flow measurement system based on EGACO-3cycles method.
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Fig. 5. Emission module.
Fig. 6. Sampling setting in LabVIEW.
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(0.4/212 V). ③ In order to guarantee long-term stability of sampling, set the actual sampling rate to 4 MHz (not the maximum sampling rate). ④ Set the sampling number 2500 to guarantee the received signal be sampled in large flow rate range. It should be noted that the sampling number 2500 is just for one received signal. Lots of received signals can be got by multi-trigger. ⑤ Set digital edge triggering as triggering mode, and this is controlled by MSP430F249T.
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3.2. Software design
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EGACO-3cycles method is realized through MATLAB program embedded in LabVIEW. In consideration of measurement system error, velocity profile and nonlinearity of ultrasonic flow rate measurement, measurement data processing and flow rate correction are necessary in order to improve measurement accuracy. So the first-order lag filter and median filter are applied in flow velocity processing and the flow velocity is corrected through the leastsquares curve fitting. The data processing block is shown in Fig. 7. At a certain flow rate point, get 300 flow velocity values. Take every 100 values as a group. Then apply the first-order lag filter and median filter in each group and get corresponding filtered velocities. Moreover, take the average value of these three velocities as the final result for this flow rate point. In the same way, 10 flow velocity values at 10 flow rate points can be obtained from 0 m/s to 50 m/s. So build an array a[1,2,3. . .,10] for the ten values. Meanwhile, store the standard flow velocity values in array b[1,2,3,. . .,10]. Finally, the
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Fig. 7. Data processing.
relationship between array a and b can be obtained through leastsquares curve fitting (fourth power, Eq. (8)).
b ¼ P 1 a4 þ P2 a3 þ P3 a2 þ P4 a þ P5
ð8Þ
P1, P2, P3, P4, P5 are fitting coefficients. With Eq. (8), the error of flow velocity measurement can be reduced and the measurement accuracy can be improved. In this paper, P1, P2, P3, P4, P5 are 0.000000535, 0.000067356, 0.006134263, 1.038518045, 0.011481229 respectively, determined by experiments.
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4. Experiment analysis and results
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In order to verify the validity of EGACO-3cycles method for wrong signal judgment and correction, a series of experiments are carried out. Moreover, the calibration experiment is done to test the established measurement system. All experiments are conducted in Tianjing key laboratory of process measurement and control. The experimental system is shown in Fig. 8.
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4.1. Judgment and correction of wrong signal
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For similar-frequency noises caused by different tightness of fixtures on ultrasonic sensors, circuit noises or errors of data acquisition, wrong signal can be avoided by using EGACO-3cycles method. As shown in Fig. 9. Signals are sampled at 0 m/s. Fig. 9a is ideal signal under ideal conditions (signal amplitude is stable and the SNR is high). Fig. 9b and c are actual signals under similarfrequency noises. EGACO-3cycles method is applied to reconstruct signal of Fig. 9b. In contrast, and GACO-3cycles method is used to reconstruct signal of Fig. 9c. Fig. 9d–f are the magnified graphs of Fig. 9a–c. It is shown that the similar-frequency noises are taken as the desired signal with GACO-3cycles method (Fig. 9f), thus the obtained TOF is less a signal cycle than the actual TOF. In con-
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4.2. Calibration experiments
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The problem of wrong signal can be solved and the flow rate measurement range can be broadened when using EGACO-3cycles method. Through analyzing the actual received signals, the amplitudes of received signals are within the range [0.01, 0.05] V from 0.1 m/s to 50 m/s. The setting parameters m and T are within the ranges [3.4, 3.8] and [12.3, 12.7]. So the initial parameter values of exponential model are set in the intervals A0 [0.01, 0.05] V, m [3.4, 3.8], T [12.3, 12.7], s [s_ 4:15, s_ þ 4:15] us (s_ is initial estimation of TOF) respectively, which are suitable for various actual received signals. Ten flow rate points are calibrated from 0.1 m/s to 50 m/s. For the flow velocity measurement, the mean relative error (E) and repeatability (Er) are presented in this paper. The calibration results are shown in Table 2.
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v i v si Ei ¼ v si
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Fig. 8. Ultrasonic gas flow rate experimental system.
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trast, when EGACO-3cycles method is adopted, wrong signal is avoided and correct TOF is obtained (Fig. 9e). For gas ultrasonic flow measurement, acoustic signals attenuate seriously at big flow rate, and the signal envelope trends to be flat. Thus the small received signals may be submerged in noises, which leads to wrong signal appear. Some signals at 50 m/s are sampled and analyzed. Similar to Fig. 9, in Fig. 10a, there is no wrong signal under ideal conditions. In Fig. 10c, wrong signal appears with GACO-3cycles method. In Fig. 10b, wrong signal is avoided using EGACO3cycles method. Fig. 10d–f is the magnified graphs of Fig. 10a–c. From Fig. 10f, it is shown that when the starting cycle of the desired signal is submerged in noises, the starting cycle may be taken as noise with GACO-3cycles method, and then the obtained TOF is larger a signal cycle than the actual TOF. In contrast, from Fig. 10e, the small starting cycle can be reconstructed by EGACO3cycles method and correct TOF is obtained.
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Fig. 9. Judgment and correction of wrong signal caused by similar-frequency noises.
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Table 2 Results of calibration.
v si
(ms1)
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Er (%)
0.06 0.12 0.04 0.44 0.02 0.29 0.03 0.37 0.41 0.029
0.35 0.039 0.09 0.035 0.14 0.08 0.015 0.15 0.037 0.035
ith calibration. Ei is the relative error of the ith calibration. l is the calibration number of each flow rate point under the same condition, l = 3. The time of each calibration is 30 s. E is the mean relative error. The smaller E is, the better the measurement accuracy of the velocity is.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pl 2 i¼1 ðEi EÞ Er ¼ l1
ð10Þ
Er is repeatability. According to ‘Verification Regulation of Ultrasonic Flowmeters, JJG 1030-2007’ [11], the definition of repeatability is from Bessel equation. Differ from the mean relative error (E), repeatability expresses the precision of measurement not the accuracy. The smaller Er is, the better the stability of velocity measurement is. As shown in Table 2, except the flow rate points 0.8 m/s and 50 m/s, the errors of velocities higher than 30 m/s are bigger than that lower than 30 m/s. It might be caused by heavy turbulence fluctuation at high flow rate, especially when flow velocity is higher than 30 m/s. Besides, the data fitting method might influence the error distribution. The least-squares curve fitting is selected in this paper, which assure global optimization of measurement data. Therefore, although the mean relative error fluctuates at flow rate range 0.1–50 m/s, all errors are less than 0.5%, and the repeatability is better than 0.2% from 0.2 m/s to 50 m/s. The measurement range ratio is wide (500:1).
According to JJG 1030-2007 [11], the accuracy of ultrasonic flowmeter is defined as the worst accuracy of velocities higher than transition velocity. Meanwhile, the accuracy of velocities lower than the transition velocity cannot be more than twice the accuracy above it. For the flow measurement system established in this paper, if 0.3 m/s is selected as the transition velocity, the measurement accuracy (i.e. mean relative error) is better than 0.5% with EGACO-3cycles method.
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For ultrasonic gas flow rate measurement, because of the different tightness of fixtures on ultrasonic sensors, circuit noises and errors of data acquisition, similar-frequency noises may appear. In addition, when flow velocity is high, the small starting cycle of signal may be submerged in noises because of severe attenuation of ultrasound propagation. Both situations may lead to wrong signal of measurement with GACO-3cycles method, which affect the measurement accuracy. In order to improve this method, energy GACO-3cycles (EGACO-3cycles) method is proposed. In consideration of the changeless maximum energy position of received signals, transit time of ultrasound propagation at the zero point after maximum energy position can be determined. In this way, wrong signal can be avoided. Moreover, a real-time flow rate measurement system with EGACO-3cycles method is established. It is mainly realized based on the control chip MSP430F249T and data acquisition card NI PCI-6110. The main conclusions are stated as below.
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(a) The problem of wrong signal caused by similar-frequency noises and the unstable signals at big flow rate is solved by the proposed method EGACO-3cycles. (b) A flow rate measurement system is established based on personal computer. Real-time data processing is realized through MATLAB nested in LabVIEW by the MATLAB Script. It is shown that for DN100 single path ultrasonic gas flow rate measurement, the accuracy is better than 0.5% from 0.1 m/s to 50 m/s. Besides, the transition velocity (0.3 m/s) is low and the measurement range ratio is achieved 500:1.
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This work is supported by the National Natural Science Foundation of China (Grant No. 61101227) and the Natural Science Foundation of Tianjin (Grant No. 13JCQNJC03300).
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References
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Please cite this article in press as: D. Zheng et al., Research and realization of ultrasonic gas flow rate measurement based on ultrasonic exponential model, Ultrasonics (2016), http://dx.doi.org/10.1016/j.ultras.2016.01.005
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