condition for real-time measurement of power of unsteady ......3/21/2018 kazushi sanada 6....

3/21/2018Kazushi SANADA

Kazushi SANADAYokohama National University, Japan

Condition for Real-time Measurement of Power of Unsteady Fluid Flow in a Pipe by Kalman Filter

1

pup pmid pdown

Bpd

Apd

1s c

+ -

g

++

++

pmid

x

cf

qmid

Pmid

L1 L2

1

2

3

4

5

6


Introduction

Kalman filter theory

Off-line estimation of unsteady flow rate by Kalman filter

Plant model of Kalman filter: Pipeline dynamics model

Real-time implementation of Kalman filter

Conclusion

2


1. Introduction

3

Electromagnetic flowmeter

○Direct measurement in real-time

×sensor may disturb flow×sensor is influenced by velocity distribution×time-special distribution is not obtained

Coriolis flow meter

Laser Doppler flow velocimeter

http://www.kanomax.co.jp/fsmart.html

http://www.keyence.co.jp/atsuryoku/ryuryou/fd_s/

http://www.keyence.co.jp/atsuryoku/ryuryou/fd_m/

http://www.fujielectric.co.jp/products/instruments/products/flow_ultra/FSV.html

Ultrasonic flowmeterConductivity

U-shape tube

Velocity distribution Pin-point Velocity


1. Introduction

• Kalman filter is proposed to estimate unsteady fluid flow in a pipe using a model of pipeline dynamics.

• The merit of this method is to use only three pressure sensors without flow sensor which may disturb flow in a pipe.

• The aim of this research is to develop a real-time indirect measurement system of unsteady flow rate and fluid power in a pipe.

4


2. Kalman filter theory

5

Kalman filter estimates the optimal state variables of a system which is disturbed by noise.

1 1

1 , and

.

1 1 , andPriori estimation

Posteriori estimation

Kalman gain

Riccati equation

Variances

,

, and .


2. Kalman filter theory

6

A measurement system using a Kalman filter


3. Pipeline mode; Optimized finite element modelof pipeline dynamics

7

pin pout

qin qoutx

p , q

ρ,A, c0)(

qp

xpA

tq

f

02

xq

Ac

tp

Equation of motion

Continuity equation

Interlacing grid system and linear shape function

0 fppFqBq

ofemofemAA

t dd

0 qEp ofemAc

t

2

dd

TDNU ,qq,,qq 11 q TNppp 21,p

Finite element approximation

State variables at grid points


3. Pipeline model; Optimized finite element modelof pipeline dynamics

8

The interlacing grid spacing is optimized to minimize the error function of model’s eigenvalues compared with theoretical ones.

321

1

2

3

1

2

2

1

2

1121 1)1(2

1)12(

12

),,(k

i n

ik

i n

ik

i n

iN iii

lllJ

Uniform Optimized

Lc

n 2

ni2

ni )12(

ni )1(2


3. Pipeline model; Optimized finite element model of pipeline dynamics

9

Optimized finite element model can be used by a state space block of MATLAB/Simulink.

GUI for automatic calculation of state space representation


4. Off-line estimation of unsteady flow rate by the Kalman filter

10

A test circuit of measuring unsteady flow rate

0

0.5

1

0

0.5

1

0

0.5

1

0

0.5

1

0 50 100 150 200 2500

0.5

1

f [Hz]

|q| [

l/min

]|q

| [l/m

in]

|q| [

l/min

]|q

| [l/m

in]

|q| [

l/min

]

Drive frequency of servo valve : 100Hz

Drive frequency of servo valve : 75hz




FFT analysis of unsteady flow rate estimated by the Kalman filter

5 5.01 5.02 5.0325

26

27

28

29

30

t [s]

q [l/

min

]

Kalman Filter MOC Flow Sensor


5. Real-time implementation of Kalman filter

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Kalman filter is installed in a real-time computing system.

Target pipe simulator

Kalman filter



12

21μs100μs >



13

5 6 7 8 9 100

50

100

SlaveMaster

N

Turn

arou

nd T

ime

(

s)

Turnaround time for various numbers of elements N(Sampling time: 100μs for N=9 or less, 1000μs for N=10)

CPU elapsed time depends on the number of finite elements of pipeline model.

(Kalman filter)


6. Conclusion

• Real-time implementation of the Kalman filter is proposed to measure incompressible unsteady laminar flow rate and power of fluid flow in a pipe.

• A steady-state Kalman filter is implemented in a real-time computing system.• It successfully works with a sampling time of 100 μs.

Future works• to reduce computational task• to reduce the order of the pipeline model by order-reduction theory, etc.• to select suitable number of finite elements

Acknowledgment• This work is supported by Grant-in-Aid for Scientific Research (C) (JSPS KAKENHI

Grant Number JP17K06226).

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Thank you for your attention!

Contact:

3/21/2018Kazushi SANADA 15

• Kazushi SANADA• Yokohama National University• E-mail: [email protected]

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condition for real-time measurement of power of unsteady ......3/21/2018 kazushi sanada 6....

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