Additional information from flowmeters via signal analysis

998 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 39. NO. 6. DECEMBER 1990

Additional Information from Flowmeters via Signal Analysis

JOE E. AMADI-ECHENDU, MEMBER, IEEE, AND E. H. HIGHAM

Abstract-The need to apply modern signal processing techniques to enhance the performance of process instrumentation systems has been identified as one of the priority areas for research and development in process instrumentation and process control. This performance en- hancement can be in the form of extracting additional information from flowmeters beyond the customary requirements of measuring the flow rate. This paper demonstrates the new importance of flow measurement signals from the point of view of extracting additional information such as for condition monitoring purposes, and for diagnostic engineering management and optimization of process plant operations. The signal processing methods involve system identification techniques and the qualitative signatures which have been identified for a turbine flowmeter system have also been related to the condition of the process plant.

Enhanced transducer ................................................... :r Part of the process monitoring, control, diagnostics, engineering management and optimisation of plant

Transducer

I I operation system I :primary sensor j rewonse sinnal i I A c t

condition

Signal processing system capable of extracting as

much useful information as possible from the transduce

Change detection and

signal including a identification system

I. INTRODUCTION LOWMETERS are used to acquire information about F fluid flow, but interestingly, the information provided

by a flowmeter is customarily made available in the range of 4-20 mA dc transmission signal which is required of process instrumentation systems. From a signal processing consideration, this industry standard transmission signal has the implication that, in general, the outputs from existing flowmeters do not reflect the dynamic nature of the information at the interface between the process and the instrument. The effect of the so-called process noise on recording equipment is highly undesirable. But, with current technology, it is feasible to process the basic signal from a flow sensor not only to provide the basic measurement of flow rate, but also to provide other additional information which may depict the condition of either the instrumentation system, the process plant, or both.

In assessing the priorities for research and development in process instrumentation and process control [ l] , the need to apply modem signal processing and analysis techniques to enhance the performance of individual instru- ments or instrumentation systems has been clearly identified. Although some of the current generation of “smart” sensors [2] have incorporated some means for checking the zero and span of an instrument, because the signal which is being checked is the 4-20 mA dc standard, the methods used do not necessarily guarantee that the sensor dynamic characteristics have not changed. At least, intuition suggests that a change in either the zero or

Manuscript received February 14. 1990: revised J u n e 30. 1990. The authors are with the School of Enyineeriny and Appl~ed Science\.

IEEE Log Number 9038896. University of Sussex, Brighton. BNI 9QT. UK

real noise content. I additt!onal- I information

.................................................... ,

Fig. 1. The new framework for enhanced process instrumentation systems.

span or both could also be as a result of changes in the sensor’s dynamic characteristics. As shown in Fig. 1, the view here is that the local validation problem demands a more detailed study of the primary signal produced at the interface between the flow and the measurement system to produce three separate outputs: 1) an index associated with the quality of the measurement, 2) an assessment of the condition of the instrumentation system, and 3) other information relating to the general condition of the process plant, The new breed of process instrumentation systems being advocated may still use the current generation of sensing elements, but the conventional restrictions on the bandwidth of signal conditioning circuits must be re- laxed if the “new” transmitters are to be of any use and particularly within the framework of a unified process industry jieldbus standard.

Some recent studies including [3] and [4] have shown that the pulse signal from existing flowmeters can be pro- cessed or analyzed not only to provide the basic measurement of flow rate, but also to provide information which could indicate:

1) the condition of the flowmeter, 2) the effect of other equipment installed in a plant, 3) the general condition of the process plant.

In this vein, this paper presents the analysis of the pulse output from a turbine flowmeter using a system identification approach. The flowmeter has been defined as a sin-

0018-9456/90/1200-0998$01 .OO 0 1990 IEEE

AMADI-ECHENDU AND HIGHAM: FLOWMETERS VIA SIGNAL ANALYSIS 999

gle-input, single-output system and some useful signa- general finer

% v(r) Y p i I y , . tures have been obtained for different process plant

measuring the time interval between corresponding edges of the pulse train from a turbine flowmeter as described in detail in [3].

observer mechanism ekment configurations. The method of data acquisition involves -+

I m(r)

Fig 2 Block diagram representation of the flowmeter system

11. THE FLOWMETER SYSTEM A. Dejnition of the Flowmeter System

From a systems consideration, a flowmeter may be described by the single-input, single-output system (SISO) shown in the block diagram of Fig. 2. At steady state, it can be assumed that the input to the system is the gravi- tational flow velocity of the fluid U ( t ) . This signal can be derived from the well-known time-invariant Nuvier- Stokes momentum balance equation which represents the ideal, steady, and uniform motion of the process fluid. The operation of a positive-displacement pump installed in a plant produces a dominating axial flow velocity component within the flow channel. Thus an expression for the flow velocity can be derived from the three-dimen- sional time-varying Nuvier-Stokes equation, or visualized simply as

u ( r ) = u(r)e’$‘‘’u(t) ( 1 )

(2)

where

a ( t ) = A [ 1 + m ~ , , ~ ( t ) ] .

m is the modulation index, $ ( t ) and s ( r ) ( r and 0 are cylindrical coordinates ) both describe the generally ran- dom phase and amplitude perturbation effects imposed by the operation of the pump and other equipment installed in the plant along the flow channel; for example, valves and bends which introduce additional turbulence, swirl, and other assymetric flow profiles.

These effects which are imposed on the fluid flow are characteristic of the installation and manifest as trends and periodicities in v ( t ) . However, v ( t ) is also modified by the transformation function associated with the sensing mechanism. This means that the information made available at the interface between the flow and the sensing element can be represented by

( 3 )

The proportionality variable K is a function of the sensing mechanism and flowmeters are usually described by the type of sensing mechanism employed.

Inherently, the sensing element in a flowmeter is a transducingjfilter since the signal it produces from the information available in the flow is limited by the sensor bandwidth. Thus the electrical signal produced by the sensor can be represented by

y ( t ) = h ( t ) * f i ( t ) . (4) In (3) and (4), the sensing mechanism and element em-

ployed in a flowmeter have been respectively represented

by K ( t ) and h ( r ) to account for changes in the flowmeter characteristics. It is apparent that these changes, as well as the trends and periodicities due to the operation of other equipment in the plant, affect the quality of the signal produced by a flow sensor. Hence, most flow measurement systems make use of signal conditioning circuits or transmitters designed to “cut off” or “clean up” the signal prior to measurement. Nevertheless, it is pertinent to pre- sent a brief description of the turbine flowmeter system within the framework advocated here for devising methods which take advantage of these noise effects.

B. The Turbine Flowmeter The sensor mechanism employed in a turbine flowmeter

typically consists of a multibladed free spinning rotor which is made to rotate by the rate of change of momentum or the force of the fluid impinging on the blades. Hence, the information made available at the sensor element interface is related to the angular rotational velocity of the rotor blades which is also directly proportional to the flow velocity or volumetric flow rate. The signal produced by the sensor may be represented by the expression

y ( t ) = h ( t ) * N D ( t ) ( 5 )

where

h sensing element (i.e., magnetic pickup and as-

K fluid kinematic and turbine mechanical proper-

N number of blades on the turbine rotor, U ( t ) axial flow velocity component, d effective diameter at the sensing interface.

The signal produced by the turbine meter is inherently periodic in nature and the effects due to plant operation manifest as perturbations about this turbine blade periodicity. It has been demonstrated in [3] and [4] that the strong periodicity apparent in the signal from a turbine flowmeter can be used to assess the condition of the instrument.

sociated electronics) response function,

ties see (3),

111. SIGNAL PROCESSING A N D SIGNATURES A. Data Acquisition and Experiments

From the definition of the flow measurement system given in Section 11, it is evident that the measured signal can be viewed as a flow signal time series y,, which has been generated by the unobserved “exogenous” excita- tion of a realizable filter as depicted in Fig. 2. With the pulse train option provided by many manufacturers for

IO00 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT. VOL. 39. NO. 6. DECEMBER 1990

PD meter is not in circuit; fmean = 102 Hz 1.02- I Vortex flowmeter 1

to l I

ti Turbine Water Differeniial pressure

coupling Q meter zter orifice plate 0.99 t

From Central I 0 0.5 1 1.5 2 2.5 3 3 5 4 4.5 5

lank heating pump 0 98

Fig. 3 . Schematic outline of experimental flow rig showing layout of in- struments.

fiscal measurement purposes, perturbations which manifest in the flowmeter output are observed as variations in the period of the pulse train. Therefore, meaningful data relating to the dynamic nature of the flow process and the effects of instrument operation can be obtained by measuring either the pulse zero-crossing instants or the pulse periods. The data presented in this paper have been obtained via the latter “pulse period measurement” method because the duty cycle of the pulse train is usually fixed by the signal conditioning circuit and moreover, the de- sign of flow transmitters is such that the frequency of the output signal (and not the pulse zero-crossing instant) is proportional to flow rate.

Several records of data were obtained by measuring the periods of the pulse train from a 38. l-mm ( 1.5-in. ) turbine flowmeter installed in the experimental plant illus- trated by the schematic outline shown in Fig. 3. For the results presented in this paper, the experiments were con- ducted at a flow rate of 50 liters per minute. A minimum of three data records were taken for each installation condition with each record consisting of 2 100 measurements of consecutive pulse periods. The signal processing was carried out using records consisting of a minimum of 250 measurements and the results obtained for all the data sets were identical with respect to each installation condition. In the first condition, a rotary piston positive displacement (RPPD) flowmeter or water meter was installed at 20 diameters downstream of the turbine flowmeter, and in the second condition, the water meter was removed.

B. Signal Analysis The typical time series records of the turbine pulse pe-

riod data obtained from these experiments are shown in Fig. 4. In both experimental cases, the fine structure in the plots depict the dominating periodicity attributable to the ( N = 6 ) blades of the turbine sensing mechanism, that is, the rotor. In Fig. 4(a), low frequency trends are evident for the case where the water meter was not installed, and this effect can be attributed to the perturbations caused by the operation of the pump. For the case where the water meter was installed, as shown in Fig. 4(b), it is apparent

(a)

PD meter in circuit; fmean = 80 Hz 102, I

I , ’ , I I 2 3 4 5 6 7

0.98 ‘ time(secs):: Flow rate @ 50 Vmin

(b) Fig. 4 . Typical pulse period time series from a turbine flowmeter showing

(a) the effect of the pump and (b) the combined effects of the pump and the water meter.

periods whereas in Fig. 5(b), the “amplitude-modulation” effect of the water meter causes the very significant peak at 6.7 periods. With the mean pulse frequency at 80 Hz, it can be deduced that the water meter induces perturbations in the flow in the region of 9.3 Hz. When the turbine blade periodicity is deemphasized, the periodogram plot of Fig. 5(c) clearly shows the shift in periodicity to 6.7 periods. Based on a comparison with identical results obtained from the analysis of several data sets, it was evident that if any of the blades of the turbine flowmeter had been damaged, the effect of the water meter would have appeared at a different blade periodicity.

Statistical analyses of the period data [4] show that the pulse signal arising from the turbine flowmeter can be decomposed or resolved into the following “structural” components:

Yl = S(PLt9 Pr, trr, 7 1 3 e l ) (6) where

pl corresponds to the mean signal level relating to the

p f is contributed by the turbine blade structure, rrl corresponds to trends arising from other modula-

tion effects including sensor element parameter variations,

q, corresponds to general stochastic perturbation components due to assymetric flow noise and electronic noise,

mean flow velocity,

e, is due to measurement errors.

that the resistive effect of the water meter superimposes a low frequency envelope on the turbine blade periodicity and even obscures the trend effect of pump operation as observed in Fig. 4(a).

The time-domain periodogram plots shown in Fig. 5 also depict these effects as well. In Fig. 5(a), the periodogram is dominated by the turbine blade structure at 6

It may be misleading to presume that these structural components are purely additive or multiplicative. Hence, it is difficult to guarantee that the spectrum of the period data will contain distinctive frequencies representing the attributes of the respective components. This is evident from the time series shown in Fig. 4(b), where the signal contains the effects of both the pump and the water meter.

- 1

AMADI-ECHENDU A N D HIGHAM: FLOWMETERS VIA SIGNAL ANALYSIS

2.838 l I1 RCF I1

B

1.185

-2 xie

I (U)

B

7,367

-2 XlB

I (U)

52 24 12 4 Period 2

(a)

51 24 12 4 Period 2

(b)

B 52 24 12 4 Pericd 2

(C)

Fig. 5 . Periodogram of pulse period series showing: (a) Turbine periodicity (turbine: flowrate at SO l /min with no PD meter in circuit; periodogram peaks at 125, 41.7, 19.2, 11.9, 10.9, 6.0, and 3.0). (b) Shift due to water meter effect (turbine: flowrate at 50 I /min with PD meter in circuit; periodogram peaks at 6.8, 6.0. 3.3, and 3.0). (c) Relative strength of the water meter effect (turbine: flowrate at 50 1 /min with PD meter in circuit; seasonal differences; periodogram peaks at 16.7, 8.6, 7.5, 6.7, and 3.3).

For brevity, it should be considered that the preceding time-domain signatures have been obtained from a signal processing blackbox whose input is the pulse period time series arising from the turbine flowmeter. Within an ex- pert systems approach, it is very desirable to represent the time-domain signatures in a parametric format. Thus one technique [4] for processing the pulse period data involves the identification of autoregressive integrated moving average (ARIMA) or time series models for representing the turbine flowmeter system. The justification for

B

PllCF ' 1 Kf ' 1

B

1 j

-,I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -1 , / , 1 , ( , , , , , ~ , 1 , , , ~ , 1 , 1 , ~ , , , 1 , ~ 1 , , , , ~ , , , 1 , / 1 1 1 1 1 ) 1

(C)

Fig. 6 . Statistical inference using acf's and pacf's: (a) water meter off- line (turbine: flowrate at 50 l /min with no PD meter in circuit). (b) Water meter on-line (turbine: flowrate at 50 l /min with PD meter in circuit). (c) Emphasizing water meter effect (turbine: flowrate at 50 1 /min with PD meter in circuits: seasonal differences).

this ARIMA model approach may be apparent from the behavior of the autocorrelation and partial autocorrelation functions of the period data as shown in Fig. 6(a)- (c). The acf's and pacf's not only depict the turbine blade periodicity and the effect of the water meter, but more importantly, they indicate that the pulse signal from the turbine flowmeter may have been generated by a combi- nation of autoregressive (AR) and moving average (MA) processes. Hence, it is possible to deduce the following model representation after di'erencing has been applied to the pulse period time series:

6 6

f k = - c a1fk-I + ek + c C1ek-l. (7) I = I I = I

- T ' 1

1002 IEEE TRANSACTIONS ON INSTRUMENTATION A N D MEASUREMENT. VOL. 39. NO. 6, DECEMBER 1990

10-2 lo' : 10."

10-17

10' 102 103 104 10.20' ' ' " " " ' ' ' " " " ' ' ' " " " ' ' ' " . . f i J

100

104

' I lo-"

10-12 ' ' " " " ' ' ' " " " ' ' " * " " ' ' ' """' ' ' " ""

103 10-1 100 101 102

frequency (Hz)

(b) Fig. 7 . Transfer function signatures, broken curves for water meter on-

line. (a) ARIMA transfer function estimate. (b) FFT transfer function estimate.

This equation can be expressed as an equivalent digital filter of the form

6

1 + c Cj2-I

1 + c a,2-;

i = I A(z) = 6

i = I

The complete ARIMA model includes the integration of the differencing operator as follows:

empirical transfer function estimates for the turbine flowmeter system can also be obtained using spectral or Fou- rier techniques. Again, for brevity, consider that the frequencies contained in y , can be decomposed via Fourier series, then an estimate of the transfer function describing the operational status of the turbine flowmeter within the process plant environment can be obtained from

N y~ - J Z * ( J / N ) k

@ j w ) = ; = I , i , k , r = l , 2 ; . * , N c Rl,(r)e-J2r(i/NJr

r = I

(10)

where R,, is the estimated covariance of U , . In practice, R,, is unknown, hence empirical methods employing the fast Fourier transform J FFT ) and spectral windows have been used to compute H ( j w ) .

Fig. 7(b) shows the smoothed empirical estimates of the transfer function describing the turbine flowmeter. The broken curves represent the signatures when the water meter was installed in series with the flowmeter. The rip- ples at higher frequencies arise due to the effects of non- uniform time interval in the measurement of the pulse periods. A resonance effect is apparent in the transfer function estimates shown in Fig. 7 for the case when water meter was installed in the plant. In comparison to other experiments carried out and the identical results obtained, it is evident that the pulse signal from a turbine flowmeter can be used to distinguish the difference between the operation of the water meter from that of the pump acting alone.

IV. DISCUSSIONS The analysis previously presented may not be exhaus-

tive because of the limited range of experiments. Never- theless, signatures have been identified which suggest that there is sufficient information in the signal produced from a turbine flowmeter which can be used to identify the condition of both the flowmeter and a water meter simulta- neously installed in series in a process plant. Evidently, each signature or dynamic model contains attributes which indicate the operational status of the plant as depicted by the instrument.

The dynamic models demonstrated can be very useful for the purposes of validating the operational mode of the flowmeter, for checking whether or not the zero and span of the transmitter have changed, and/or for other purposes relating to condition monitoring and failure diagnosis using the flowmeter. In this vein, it must be emphasized that the new generation of process instrumentation transmitters should be designed to qualitatively harness as much information as possible from the primary signal from a sensor.

It is apparent that the techniques suggested here could either make dedicated diagnostic sensors redundant or un- necessary, or they could be used to augment information

(9)

from which an estimate of the transfer function f i ( z = e'") of the turbine system can be computed. The ARIMA model transfer function signatures obtained for the two process conditions indicated are shown in Fig. 7(a).

Although the derivation of ARIMA model transfer function signatures is trivial from the presentation above,

H ( 4 H ( 2 ) = ~

1 - 2 - d

AMADI-ECHENDU A N D HIGHAM: FLOWMETERS VIA SIGNAL ANALYSIS

available for failure diagnosis particularly where dedicated diagnostic sensors are absolutelv necessary. The

Io03

REFERENCES -

ideas discussed here have wide ranging ramifications to- [ I ] E. H . Higham. “An assessment of the priorities for research and development in process instrumentation and process control,” The I n s / .

wards intelligent flowmetering, control, and supervision Chetn. E n x , . 1987, O f the operation of process plants. In the broadest per- 121 J . M . Favennec. “Smart sensors in industry.“ J. Phw. E: Scientific

Insrruments, vol. 20. pp. 1087- 1090. 1987.

signatures using the flow measurement signal,” IEEE Trans. Insrrum. Meas . . vol. 39. D D . 416-420. Am. 1990.

’pective’ the raised in this paper cenainly justify 131 J . E. Amadi-Echendu and p, J . Humen. “Identification of process p l a n t investments for research in this area, and such ef- forts should be directed towards methods which Drovide .. 1

for increased safety, reduced maintenance, and the e]im- ination Of the human ‘perator from dangerous process plant environments. 1989, pp. 154-158.

141 J . E. Amadi-Echendu er a l . . “Plant health monitoring using a turbine flowmeter,” in Proc. of 1 s t Inr. Congress on Condition Monitoring and Diagnostic Engineering Management. Birmingham, U . K . , Sept.

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Additional information from flowmeters via signal analysis