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Real-time Monitoring of Pollutant Diffusion States and Source Using Fuzzy Adaptive Kalman Filter

  • Xudong Wang
  • Daqian Zhang
  • Liying Chen
Article
  • 81 Downloads

Abstract

An inverse analysis method for the real-time monitoring of pollutant diffusion is developed based on fuzzy adaptive Kalman filter (FAKF) coupled with weighted recursive least squares algorithm (WRLSA). In the monitoring process, the discrete diffusion states equation is established first. Then, the FAKF is adopted to realize the precise monitoring of the pollution diffusion states while the WRLSA is used to monitor the pollutant source in real time. Finally, the simulations are presented to validate the effectiveness of the technique, which shows that this technique has wide applications in situations with several different kinds of sources and measurement noises. Besides, the results demonstrate the strong robustness of this method to have great monitoring performance.

Keywords

Diffusion state Fuzzy adaptive Kalman filter Inverse analysis Pollutant source Real-time monitoring 

Nomenclature

e, ec

inputs of fuzzy inference unit

f

number of measurement points

C

pollutant concentration

Dx,Dy

diffusion coefficients

EC

concentration monitoring error

ESo

pollutant source monitoring error

Lx,Ly

length and width

So

pollutant source strength

Bb

sensitive matrix of WRLSA

H

measurement matrix

I

unit matrix

K

gain matrix of Kalman filter

Kb

gain matrix of WRLSA

M

sensitive matrix of WRLSA

P

covariance of state estimation errors

Pb

error covariance of source estimation

Q

process noise covariance

R

measurement noise covariance

S

residual variance

Z

output vector

\( \overline{\boldsymbol{Z}} \)

sequence of measurement residual

Greek Symbols

γ

weighting factor

σq

standard deviation of process noises

σr

standard deviation of measurement noises

τ

time

Ф

state transition matrix

Ψ

input matrix

Superscripts

^

monitored result in equations

T

transpose of a vector or a matrix

k

the kth time step

Subscripts

exa

exact result

mon

monitored result

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and EnvironmentSoutheast UniversityNanjingPeople’s Republic of China
  2. 2.Key Laboratory of Low-Grade Energy Utilization Technologies and Systems of Ministry of Education,School of Power EngineeringChongqing UniversityChongqingPeople’s Republic of China
  3. 3.Institute of Innovation and EntrepreneurshipChengdu Technological UniversityChengduPeople’s Republic of China

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