Determination of Real-time Vortex Shedding Frequency by a DSP

Transcription

1 335~342 ( 年 ) Journal o the Chinese Society o Mechanical Engineers, Vol.27, No.3, pp.335~342(26) Determination o Real-time Vortex Shedding Frequency by a DSP Chih-Chung Hu*, Jiun-Jih Miau**and Tzu-Liang Chen*** Keywords Vortex shedding requency, DSP, ast Fourier transorm, Auto-correlation. ABSTRACT An algorithm is designed or a digital signal processor to perorm computations o ast Fourier transorm and auto-correlation to determine real-time vortex shedding requency o a 6 vortex lowmeter. In the algorithm, a digital band-pass ilter which is able to tune its center requency according to the input signal is arranged at the irst step to remove noise components rom a vortex shedding signal. Ater iltering, the vortex shedding signal is utilized to compute vortex shedding requency, which is done by the technique o auto-correlation as the vortex shedding requency estimated is less than 2 Hz or by the technique o ast Fourier transorm as the requency estimated is larger than 2 Hz. The test result shows that the maximum error o vortex shedding requency computed is less than.3 % when the vortex lowmeter measures at moderate to higher low rates. For the case in lowest low rate, the signal-to-noise ratio or the vortex shedding signal is about 1/12. Even so, the vortex shedding requency determined is about 1.1% deviated rom the true value. Furthermore, the vortex shedding requency determined by the algorithm has a time lag o.512 second rom the true vortex shedding requency as the low rate is slewing. INTRODUCTION Vortex lowmeters has been applied in many cases Paper Received June, 25. Revised October, 25, Accepted November, 25., Author or Correspondence: Chih-Chung Hu. * Assistant Proessor, Department o Electronic Engineering, Kao Yuan University o Technology, Kaohsiung, Taiwan, ROC. ** Proessor, The Institute study o sloshing-orce Aeronautics and behavior Astronautics, o luid National Cheng Kung University, Tainan, Taiwan, ROC. *** Techician, Institute o Aeronautics and Astronautics, National o industrial Cheng Kung low University, measurements. Tainan, Taiwan, ROC. It works based on the measurement principle that the Karman vortex shedding requency generated by low over a vortex shedder is linearly proportional to the low velocity. Thereore, the measurement o volumetric low rate by a vortex lowmeter reduces to a problem o obtaining a reliable vortex shedding requency. There are several methods to detect shedding vortices rom a vortex shedder. Among them, piezoelectric material is avorably used due to its simplicity and low cost. However, its drawback is that vortex shedding signals are susceptible to be contaminated by noises due to piping vibration, pulsation low, and even by low turbulence (Ogawa & Matsubara, 1985; Takahashi & Itoh, 1993; Miau et al., 2; Ghaoud & Clark, 22). When a vortex lowmeter measures at moderate low rates, the signal-to-noise ratio, denoted as SNR, o the vortex shedding signal is usually high, and the vortex shedding requency can be identiied with less diiculty. However, as the vortex lowmeter is used at lower low rates, the SNR gets poorer, which poses a challenge to obtain an accurate vortex shedding requency. Several methods have been proposed in literature to calculate vortex shedding requency. Among them, the most popular and simplest one is to measure the time length between consecutive zero-crossings o a vortex shedding signal, but this method ails as the SNR value becomes poor (Ghaoud & Clark, 22). Phase-locked loop, denoted as PLL, is also proposed or tracing vortex shedding signal. In the study o Clark & Ghaoud (23), a design o dual-pll circuit is applied to a vortex lowmeter. With the parameters o the dual-pll circuit having been careully determined, the dual-pll is able to trace vortex shedding signal well. A preilter have to be arranged prior to the dual-pll unit to remove noise components rom vortex shedding signal. I the preilter doesn t unction properly, an erroneous center requency might be obtained or the phase-locked loop and then a ake vortex shedding component would be traced. In addition, correlators have been applied to vortex lowmeters. In the study o Menz (1997), two sets o ultrasonic sensors separated by an axial distance L are -335-

2 J. CSME Vol.27, No.3 (26) used to determine the vortex shedding signals. A time-lag cross-correlation unction between the two sensors signals is reduced by a correlator in order to ind the transit time o the vortices, and hence the vortex shedding requency. It is noteworthy that the vortex shedding requency estimated rom transit time has a resolution uncertainty o t /( T s ) i the correlation result is calculated rom digital data. Herein, t is the sampling interval o the digital data and T s is the transit time o vortices estimated, i.e., vortex shedding period. As a result, the uncertainty o vortex shedding requency estimated by this method would increase with the low rate. Concerning the analysis o stationary signals, ast Fourier transorm, denoted as FFT, has been known as the most widely used mathematical tool. However, perorming ast Fourier transorm requires a large amount o computations. Due to this cause and lack o high-perormance microprocessors in the past, it was diicult to perorm ast Fourier transorm or vortex lowmeters in real-time low measurement. Fortunately, by the rapid advance in integrated-circuit technology, high speed digital signal processors are now easily obtained. As compared to traditional microprocessors, digital signal processors show much better perormance in real-time signal processing and intensive numerical calculations. Hence, perorming ast Fourier transorm in real time with the aid o a digital signal processor becomes possible. In this study, an algorithm is designed to perorm auto-correlation and ast Fourier transorm to locate vortex shedding requency o a 6 vortex lowmeter. To implement the algorithm in real time, a digital signal processor, denoted as a DSP, is employed. EXPERIMENTAL FACILITY The algorithm presented in this paper is evaluated by applying it to a T-shaped vortex lowmeter (Miau et al., 1996) whose diameter is 6 inch, seeing in Fig. 1. Vortex shedding signals are detected by a piezoelectric element rigidly embedded in the shedder, seen also in Fig. 1. The vortex lowmeter was installed onto an air low calibration system or test. The mass low rate o the calibration system is regulated by a set o choked sonic nozzles and pressure regulators upstream o the vortex lowmeter. The low rate or the calibration system is able to be controlled ranging rom 1 to m 3 /hr at ambient pressure condition. The extended uncertainty or the calibration system is.31 % certiied by National Laboratory Accreditation o Taiwan. In this study, the vortex lowmeter was tested at dierent low velocities ranging rom U = 5.44 m/s to m/s. A 32-bit digital signal processor, TMS32 C6711, made by Texas Instrument is employed to execute the algorithm designed in this study. The processor has a clock rate o 1 MHz. Fig. 1. A schematic drawing o the 6 vortex lowmeter. charge converter PZT PZT ABPF Anti-aliasing PZT sensor top view o vortex shedder DSP DBPF c ilter setting Amplitude detector I c= then s= Else i c<2hz then Auto-correlation ON Fig. 2. Block diagram o operation COMPUTATION ALGORITHM Schmitt trigger The procedure o signal processing proposed in this study is schematically shown in Fig. 2. From let to right, it is composed o three main components, i.e., a signal source rom PZT, an analog band-pass ilter and a DSP processing unit. Details o each block are given below. Signal processing prior to DSP The electric charges generated by the piezoelectric element due to vortex shedding are converted into AC voltage by a charge converter. Figure 3a shows the raw signal obtained rom the 6 vortex lowmeter at the s low rate -336-

3 C.C. Hu et al.: Determination o Real-time Vortex Shedding Frequency by a DSP. incoming low velocity o U = 5.44 m/s, about the lower limit o the present low rate measurement. The corresponding requency spectrum is shown in Fig. 4a. The vortex shedding requency is noted about Hz. As seen, the vortex shedding component is completely buried in noises. The SNR value or this case is about 1/12. The SNR is deined as P / P n (Best, 1997), where P denotes the energy residing in the vortex shedding component in a power spectrum, and P n denotes the energy o residual components. The raw signal is then iltered by an analog band-pass ilter, denoted as ABPF in Fig. 2, to avoid aliasing o data sampling beore entering the DSP processor. Since the vortex shedding requency under consideration would be in the range between 2 Hz to 4 Hz, the sampling rate o a 16-bit A/D converter or the DSP is chosen to be 1 Hz, i.e., the Nyquist requency is 5 Hz. Consequently, the band-pass or the ABPF is set between 2 Hz and 5 Hz. As an illustration, the raw signal trace originally shown in Fig. 3a is now processed by the ABPF and the result is shown in Fig. 3b. Figure 4b gives the corresponding requency spectrum. The SNR value is about 1/7 or the trace shown in Fig. 3b. Ater ABPF, the analog vortex shedding signal is then digitized by the 16-bit A/D converter or urther DSP processing. raw signal o a time length o.512 second. In Fig. 5a, the high requency undulation embedded in the auto-correlation trace is noted due to noise components in Fig. 3a, which makes it impossible to reduce the vortex shedding requency by identiying the local maxima in the auto-correlation curve. In Fig. 5b, the situation o the ABPF-iltered signal trace seems better than that in Fig. 5a, but the undulation o the auto-correlation curve is still eatured with other requency components which produce undesirable local maxima. amplitude (volt.) 2E-3 1E-3 2E-3 1E-3 1E-3 5E-4 (a) (b) (c) s (Hz) Fig. 4 Frequency spectra corresponding to Fig. 3. vortex signal (volt.).4 (a) (b) (c) Fig. 3. U = 5.44 m/s, (a) raw signal, (b) ater ABPF, (c) ater DBPF. Algorithm in DSP Active Band-Pass Filter Beore introducing the algorithm in the DSP, it is noteworthy that the requency spectra in both Figs. 4a and 4b show that several noise components are comparable and even larger than the vortex shedding component. Hence, it is diicult to identiy the vortex shedding requency in a straightorward manner. On the other hand, Fig. 5 shows the auto-correlation results o the signal traces in Fig. 3. In Fig. 5, the auto-correlation unction, R VV (τ ), with respect to the time lag, τ, or τ = to.1 second, is deduced rom a Rvv(τ) (volt. 2 ) 8E-5 4E-5 (a) E-5 (b) 1E E-6 (c) N=2 τ -1E τ (s) Fig. 5. Auto-correlation unctions corresponding to Fig. 3. In order to acilitate identiying the vortex shedding requency rom either auto-correlation or ast Fourier transorm results, an additional band-pass ilter with an adjustable center requency prior to the auto-correlation or ast Fourier transorm computation is deemed necessary. Along this concern, the digital vortex shedding signal in the DSP processor is then arranged to be iltered by a inite impulse response band-pass ilter, denoted as DBPF in Fig. 2, with an order o 81. The DBPF has a band-pass whose low-requency cut-o is.7 c and high-requency cut-o is 1.3 c. c is the center requency o the DBPF, which is determined by an amplitude detector described below. Figure 3c shows the DBPF-iltered result rom -337-

4 J. CSME Vol.27, No.3 (26) the trace in Fig. 3b, or c being set as 3 Hz. As seen, the vortex shedding component in the signal trace is clearly discernable. Further, Figs. 4c and 5c are the corresponding requency spectrum and auto-correlation trace. The SNR value at this stage is improved to a level o 2.4. Thereore, the vortex shedding requency can be accurately determined rom both requency spectrum and auto-correlation results, which are 23.44Hz and 23.53Hz, respectively. Ater DBPF, the signal is routed to a D/A converter, and then to a Schmitt trigger or pulse output. Meanwhile, the signal is stored in a data buer o 512 points in size. Immediately ater the buer illed up, the 512-point data record is transer to another buer or auto-correlation or ast Fourier transorm computations. On the other hand, the original data buer keeps receiving data rom the output o DBPF. Since the sampling rate is 1 Hz, the ull length o each data record is.512 second. Hence the computation result can be updated every.512 second. Digital Vortex Signal Amplitude Detector LPF A c & Clark, 22). In this study, reerring to Fig. 6, the design o amplitude detector is simpliied to reduce the computation eorts in the DSP, which contains only an absolute unction and a low-pass ilter, denoted as LPF. In this study, the vortex shedding signal measured undulates in sinusoidal with respect to zero. The absolute unction in Fig. 6 makes all the negative parts o vortex shedding signal become positive. By urther processing with a low-pass ilter, a DC level output can be obtained. The DC level is proportional to the amplitude o vortex shedding signal. The amplitude detector behaves similarly to an analog rectiier. Figure 7 shows an illustration. In Fig. 7 the DC level, saying signal level in the ollowing, is denoted by a dashed line or a vortex shedding signal obtained at U = 7.98 m/s. The LPF in Fig. 6 actually is a inite impulse response low-pass ilter with an order o 81. It should be noted that the setting o cut-o requency or the low-pass ilter deserves careul considerations. I the cut-o requency is too high, the amplitude detector became too sensitive to the amplitude modulation o a vortex shedding signal, which might not be caused by the variation o low velocity. Inversely, i the cut-o requency is too low, the amplitude detector would not be able to ollow the amplitude variation due to low velocity slewing. In this study, the cut-o requency is set as 1 Hz. Fig. 6. Block diagram o the amplitude detector. 4 experimental data approximated curve vortex signal (volt.) vortex shedding signal amplitude variation c (Hz) Fig. 7. Signal level o a vortex signal trace. Amplitude Detector In order to determine the center requency o the DBPF, an amplitude detector is arranged in the algorithm as shown in Fig. 2. Since the strength o vortex shedding is known proportional to the density o luid and square o low velocity, it is possible to make a rough estimation o the vortex shedding requency rom the strength o a vortex shedding signal (Takahashi & Itoh, 1993; Ghaoud & Clark, 22), which can be measured by an amplitude detector. An amplitude detector usually comprises an absolute unction, peak-detector, and a low-pass ilter (Ghaoud..4.8 A.5 (volt..5 ) Fig. 8. Shedding requency ( c ) versus signal amplitude (A). The approximated curve is described as.5 = A 6.7. c + The amplitude detector in this study provides a rough estimation on vortex shedding requency, and this estimated requency, saying c, is then orwarded to the DBPF to tune its center requency. To do so, the relation between vortex shedding requency and signal level shall be built beorehand. In this study, the -338-

5 C.C. Hu et al.: Determination o Real-time Vortex Shedding Frequency by a DSP. lowmeter was installed at the location where ully-developed pipe low condition is reached (Corpron, G. P., 1987a,b). Following the result o Fig. 7, the average signal level at dierent low rates can be obtained. Figure 8 shows the relation between vortex shedding requency and averaged signal level or U = 5.44 m/s to m/s. As seen, the vortex shedding requency shows a trend linearly proportional to the root o the signal amplitude detected, which can be.5 described as c = A c denotes the vortex shedding requency reduced rom this relation and A is the amplitude o vortex shedding signal in voltage. The maximum deviation between the linear curve itted and the experimental data is occurred at the lower limit o the range, which amounts to 3%. At higher low rates, the discrepancies are less than 1%. With this relation, once the signal level is obtained, the center requency or the DPBF is determined accordingly. Frequency Computation Unit Conventionally, when reducing vortex shedding requency by auto-correlation or cross-correlation techniques, only the irst local maximum o correlation unction is utilized to estimate the time delay or the transit time so-called (Menz, 1997). A drawback o this method is that the uncertainty o vortex shedding requency estimated gets large as the vortex shedding period gets shorter. In this study, to minimize the uncertainty due to this concern o time resolution, the auto-correlation unction, R VV (τ ), o the vortex shedding signal is computed or τ = to.1 second. Ater the completion o the computation, the numbers o local maxima in the correlation curve are counted, denoted as N, and the time delay corresponding to the last local maximum is identiied as τ. Subsequently, the vortex shedding requency is deduced rom N / τ. See Fig. 5c or an illustration, where N = 2 and τ =.85 second. Hence, the uncertainty o vortex shedding requency due to time resolution is reduced to a level o t / τ, i.e.,.1/.1 or this study, and it keep almost a constant value as the vortex shedding period gets shorter. The computation o ast Fourier transorm in this study has a requency resolution o 1.95 Hz, i.e., (1/.512) Hz. I the vortex shedding requency is greater than 2 Hz, the uncertainty o requency resolution by ast Fourier transorm becomes lower than that by autocorrelation unction. PERFORMANCE VERIFICATION The algorithm is veriied with some artiicial signals. The artiicial signals are made up rom true vortex shedding signals, but the component o vortex shedding requency is replaced artiicially. This is made or the sake that one could reer to a known requency, thereore evaluate the tracing ability o the vortex shedding requency. In the paper o Ghaoud & Clark(22), a model was built or simulating the real vortex shedding signals. The simulated shedding signal primarily comprised a sinusoidal component at a given vortex shedding requency and an additive band-limited noise. In this study, instead o employing the simulated model by Ghaoud & Clark (22), a simple and more direct procedure is adopted. The raw signal acquired rom the real pipe low measurement is processed by a band-stop ilter to remove the vortex shedding component, but the noise components, n(t), is kept. Subsequently, a sinusoidal component with its amplitude and requency comparable to the removed vortex shedding component is added to n(t). Hence, the simulated signal with a known vortex shedding requency and real noise components is obtained. Figures 9a and 9b present two simulated vortex shedding signals whose shedding requencies are given as 23Hz and 315Hz, respectively. The signals are then employed or examining the requency tracing ability o the algorithm. It is noted that the signal trace in Fig. 9a has a noise level comparable to that in Fig. 3b. Figures 1a and 1b show the test results correspondingly. In Fig. 1, the dashed line indicates the reerence vortex shedding requency, and the triangular and the circular symbols denote the requencies obtained by auto-correlation unction and ast Fourier transorm with respect to time, respectively. In Fig. 1a, the deviations o the triangular and circular symbols rom the dashed line are about 1.1%, and 1.9%, respectively. The result shows that vortex shedding requency estimated by auto-correlation has a smaller error then that by ast Fourier transorm in the low requency range. It is noted that the time interval between two neighboring symbols is.512 second. On the other hand, in Fig. 1b the deviations o triangular and circular symbols rom the dashed line are about.5% and.17%, respectively, inerring that at high requency the results reduced by ast Fourier transorm are more accurate than those reduced by auto-correlation. As a result, a combined strategy o autocorrelation and ast Fourier transorm is proposed, i.e., auto-correlation is employed or c less than 2 Hz, while ast Fourier transorm is or c larger than 2 Hz

6 J. CSME Vol.27, No.3 (26) signal (volt.) signal (volt.) s (Hz) s (Hz) (b) (a) Fig. 9. Simulated vortex shedding signals, (a) s = 23 Hz, (b) s = 315 Hz (b) (a) Fig. 1. Vortex requency estimation or the signals in Fig reerence requency requency estimated Fig. 11. Algorithm tracing ability on vortex shedding requency : reerence : by autocorrelation Ο: by FFT Fig. 12. Vortex shedding signal corresponding to the slewing low in Fig. 11. This strategy is urther veriied by examining its dynamic response. Figure 11 shows the result obtained. It is seen that the low starts with a constant vortex shedding requency o 177 Hz and then accelerates to a higher low rate or s = 224 Hz. The slew rate o this case, expressed in terms o the rate o change o requency, is 18.3 Hz/s. Figure 12 shows the artiicial signal corresponding to the time period o t = 5 to 7 second in Fig. 11. As the low rate reached s = 271 Hz, the low is slowed down with a rate o -3.1 Hz/s and inally reached a low rate o s = 4 Hz. As seen, the vortex shedding requency estimated by the algorithm, denoted by the triangular symbols, shows highly consistent with the reerence requency, indicated by the dashed line, during the periods o constant low rate. Speciically, the maximum deviation is less than.3%. However, during the slewing periods, the estimated requency has a lag o.512 second reerring to the reerence requency, which is due to that the data record is processed every.512 second. For reerence, the time lag o the conventional algorithms, reported by Ghaoud & Clark (22), is about 1 to 3 second. DISCUSSION By comparing the present algorithm with conventional methods or computing the vortex shedding requency, several comments can be made as below. 1. In this study, both ast Fourier transorm and auto-correlation are employed to determine the vortex shedding requency. Since the length o a data record or computation is.512 second, the time length could be more then ten or even hundreds o vortex shedding periods, depending on the low rate. Consequently, it is supposed to be more reliable then the zero-crossing technique, which employs only one wave period o the signal or computation. For reerence, the accuracy o a zero-crossing technique ound in the study o Clark & Ghaoud (23) is between.5 to 2.9% within a low range rom 3 to.25 l/s. 2. In the study o Menz (1997), only the irst local maximum o the correlation curve was used to estimate the vortex shedding requency. The accuracy by this approach is about 1% to 2% (Menz, 1997). One o the drawbacks concerning this approach is that the requency resolution became poorer as vortex shedding requency gets higher. In this study, all the local maxima on the auto-correlation curve are collected or estimating the vortex shedding requency, and hence improves -34-

7 C.C. Hu et al.: Determination o Real-time Vortex Shedding Frequency by a DSP. the problems mentioned. 3. PLL provides an alternative way to lock vortex shedding requency. Clark & Ghaoud (23) designed a dual-pll circuit with an active preilter to trace vortex shedding signal. However, tuning the parameters o PLL is usually troublesome. According to the study o Clark & Ghaoud (23), the accuracy or the dual-pll circuit is about.5 to 3.% within a low range rom 3 to.25 l/s, while or the lower low rate down to.1 l/s, the accuracy is 6.5%. 4. Regardless o zero-crossing, PLL, correlation unction and the present algorithm, the accuracy o vortex shedding requency estimation is strongly dependent upon the perormance o preilters. Usually a smart ilter with its center requency as a variable is desirable. I the center requency reduced by the amplitude detector are too ar rom the true vortex shedding requency, an erroneous requency might have been locked or computed by zero-crossing, PLL, correlation unction or the present algorithm. This situation could be happened as the piezoelectric sensor decays with time or the gain or signal ampliication is changed inadvertently. In this case, the requencyamplitude relation might break down. Hence, a more reliable pre-ilter with more intelligent capability seems necessary. CONCLUSIONS In this study, an algorithm is designed to estimate real-time vortex shedding requency o a vortex lowmeter. The algorithm mainly comprises two parts, one o which is the active band-pass ilter with an adjustable center requency determined by an amplitude detector, and the other is the computation subroutine or determining vortex shedding requency, which is composed o auto-correlation and ast Fourier transorm. Due to the concern o the requency resolution, the auto-correlation technique is implemented i the vortex shedding requency is less than 2 Hz, whereas the ast Fourier transorm is or the vortex shedding requency larger than 2 Hz. The test results o the algorithm demonstrate a tracing ability characterized by a time lag o.512 second on vortex shedding requency or the low rate varying with time. For constant low rate at moderate and higher vortex shedding requencies, the estimated error on vortex shedding requency is less than.3%. For the lowest low rate or which the SNR value is about 1/12, the vortex shedding requency estimated is about 1.1% deviated rom the true value. In summary, the combination o auto-correlation and ast Fourier transorm computation in the present algorithm can provide reliable vortex requency estimation. ACKNOWLEDGMENT The authors would like to acknowledge the support rom National Science Council or this work, under the contract number o NSC E-6-8. REFERENCES Best, R. E., Phase-locked loops, McGraw-Hill, New York, Clark, D. W., Designing phase-locked loops or instrumentation applications, Flow Measurement and Instrumentation 32, pp (22). Clark, D. W. and Ghaoud, T., A dual phase-locked loop or vortex low metering, Flow Measurement and Instrumentation 14, pp (23). Corpron, G. P., Vortex Flowmeter Perormance Characteristics Part A: The Eect o Installation Conditions on the Perormance o a T-Cross Section Vortex Flowmeter, ASME Fluids Engineering Division, FED-Vol. 58, pp. 1-9 (1987a). Corpron, G. P., Vortex Flowmeter Perormance Characteristics Part B: Comparison o Several Vortex Flowmeters Calibrated in Water, Low Pressure Air and High Pressure Air, ASME Fluids Engineering Division, FED-Vol. 58, pp (1987b). Ghaoud, T. and Clark, D. W., Modeling and tracking a vortex lowmeter signal, Flow Measurement and Instrumentation 13, pp (22). Menz, B., Vortex lowmeter with enhanced accuracy and reliability by means o sensors usion and sel-validation, Measurement 22, pp (1997). Miau, J. J., Li, Y. P., Chou, J. H., Huang, Y. C., and Yang, C. C., Integration o Vortex Shedder and Sensor or a Vortex Flowmeter, FLOMEKO 96, Proceedings o the 8 th International Conerence on Flow Measurement, Standard Press o China, Beijing, China, pp (1996). Miau, J. J., Hu, C. C., and Chou, J. H., Response o a vortex Flowmeter to impulsive vibrations, Flow Measurement and Instrumentation 11, pp (2). Ogawa Y. and Matsubara, N., New type o vortex shedding lowmeter, FLUCOME 85, -341-

8 J. CSME Vol.27, No.3 (26) Proceedings o the International Symposium, Tokyo, Japan, pp (1985). Takahashi, S. and Itoh, I., Intelligent vortex lowmeter, FLOMEKO 93, Proceedings o the 6 th International Conerence on Flow Measurement, Korea, pp (1993). NOMENCLATURE A: signal level o vortex shedding ABPF: analog band-pass ilter DBPF: digital band-pass ilter c : center requency o DBPF s : vortex shedding requency reduced P : energy residing in the vortex shedding P n : energy o noise components PLL: phase-locked loop R vv : autocorrelation unction SNR: signal to noise ratio deined as P / P n T s : vortex shedding period t : time in second t: sampling interval U : pipe low velocity in m/s τ : time delay or autocorrelation unction τ :time length o the inal maximum o R vv 流流量 率 易 良 流 理 流 率 數 理 (TI TMS32 C6711) 行 流流量 理 數 濾 率 數 濾 率 流 度 濾 (SNR) 1/12 流 數 濾 理 2.4 數 濾 率 率 立葉 降 率 度 流 率 2Hz 利 來 流 率 流 率 2Hz 利 立葉 理 流 流 率.3% 流 1/12 流 率 1.1% 流 流 率 力