Evaluation of Non-Uniqueness in Contaminant Evaluation of Non-Uniqueness in Contaminant Source Characterization based on Sensors with Source Characterization based on Sensors with

Event Detection MethodsEvent Detection Methods

Jitendra Kumar1, E. M. Zechman1, E. D. Brill1, G. Mahinthakumar1, S. Ranjithan1, J. Uber2

1North Carolina State University, Raleigh, NC

2University of Cincinnati, Cincinnati, OH

Outline

• Introduction

• Objective

• Methodology

• Case Study

• Observations

• Ongoing/future work

Introduction

• Water distribution systems are vulnerable to accidental or intentional contamination

• Contaminant can spread very fast and threaten public health

• Accurate characterisation of source is required for taking any control measures

• Source characterization methods typically assume ideal sensor information

• Quality of information depends on the sensor– E.g., sensitivity, specificity, reliability

• Filtered sensor information – Event detection based on water quality parameters

(chlorine, pH, etc.)– Binary contamination signal based on measurement

sensitivity

• Affects quality of sensor information available for source characterization

Objectives of the study

• Effect of filtered sensor information on source characterization– Accuracy of predictions

– Degree of non-uniqueness

EPANET

SE

NS

OR

BinaryObservation

OPTIMIZATION FRAMEWORK

Simulation Model

Filtering of information

Simulation-optimization approach

Mathematical Formulation

• Find

– Source location [L(x,y)]

– Contaminant loading profile [Mt, Ts]

• Minimize prediction error

*

1 1

( ( , ), , ) ( ( , ), , )STN

t tk t S k t S

k t

S L x y M T S L x y M T

Optimization Procedure

• Niched-coevolution-based evolutionary algorithm

• Uses multiple subpopulations– One subpopulation identifies the solution that best fits the observations– Other subpopulations identify different (non-unique) solutions, if any

Reference: Zechman, Emily M., and Ranjithan, S., (2004), “An Evolutionary Algorithm to Generate Alternatives (EAGA) for Engineering Optimization Problems.” Engineering Optimization, 36(5), pp. 539-553.

Example network

• 97 nodes• 117 pipes• Hydraulic simulations at 1 hour• Quality simulations at 5 minutes• Network simulated for 24 hours

Example network included in EPANET distribution

Assumptions

• Contaminant specific sensor

• Threshold-based sensor with binary output signal

• Placement of sensors in the network was based on experience with the network

• Only non-reactive conservative pollutants are considered

True Source

Trial contamination source

Ideal observations at the sensors

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centr

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g/l)

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Con

centr

atio

n (m

g/l)

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• What’s the actual information available from a binary sensor ?

• Ideal information at a sensor

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centr

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g/l)

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Actual Concentration (mg/l)

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cent

rati

on (

mg/

l)

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Sensor sensitivity value = 0.01 mg/l

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centr

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2

Binary Sensor Signal Actual Concentration (mg/l)

0.01 mg/l

0.1 mg/l

0.2 mg/l

Effect of sensor sensitivity on quality of observation

0.5 mg/l

Observations

• Filtered information might be available from the sensors

• Sensitivity of sensor has major effect on the quality of filtered data

True/ Predicted Sensor Observations

0

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47

Time Step (10 min)

Sen

sor

Sig

nal

.

Predicted Observation

True Sensor Observation

Sensors with a sensitivity of 0.5 mg/l

Predicted Source

True/ Predicted Sensor Observations

0

1

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47

Time Step (10 min)

Sen

sor

Sig

nal

.

Predicted Observation

True Sensor Observation

contd…

Predicted Source

Sensors with a sensitivity of 0.1 mg/l

3 non-unique solutions

Predicted Source

Predicted Source

Sensors with a sensitivity of 0.01 mg/l

Contaminant loading

0500

1000150020002500300035004000

1 3 5 7 9 11 13 15 17

Time (10 min steps)

Mas

s L

oadi

ng ( m

g/m

in )

.

Perfectly matched the sensor signals at all sensors during simulation time

Observations

• More than one solutions possible at same location

• Different non-unique sources can match the observations

• Non-uniqueness increases with decrease in sensor sensitivity

Different scenarios of contaminant loading

• Several different contamination loading profiles were studied

– Constant, increasing, decreasing, intermittent

• A sensor sensitivity of 0.1 mg/l was used in this analysis

Predicted Source

Contaminant loading

0

500

1000

1500

2000

2500

3000

3500

1 3 5 7 9 11 13 15 17

Time (10 min steps)

Mas

s L

oadi

ng ( m

g/m

in )

.

Decreasing mass loading of contaminant

Contaminant loading

0

500

1000

1500

2000

2500

3000

3500

1 3 5 7 9 11 13 15 17

Time (10 min steps)

Mas

s L

oadi

ng (

mg/

min

)

.

The true source and two other possible sources were identified

The true source and two other possible sources were identified

Increasing mass loading of contaminant

Contaminant loading

0

500

1000

1500

2000

2500

3000

3500

1 3 5 7 9 11 13 15 17

Time (10 min steps)

Mas

s L

oadi

ng (

mg/

min

)

.The true source and two other possible sources were identified

Intermittent mass loading of contaminants

Predicted Source

Contaminant loading

0

500

1000

1500

2000

2500

3000

3500

1 3 5 7 9 11 13 15 17

Time (10 min steps)

Mas

s L

oadi

ng ( m

g/m

in )

.

Both solutions were predicted at true source location

Intermittent mass loading of contaminants

Predicted Source

Contaminant loading

0

500

1000

1500

2000

2500

3000

3500

1 3 5 7 9 11 13 15 17

Time (10 min steps)

Mas

s L

oadi

ng ( m

g/m

in )

.

The true source and one other possible source was identified

Intermittent mass loading of contaminants

Predicted Source

Observations

• Identified the correct and the non-unique solutions for different scenarios of contaminant loadings

• Varying degree of non-uniqueness in different scenarios

Noise in observation data

• Measurement and machine errors– Error in the concentration measurement at the probes

– Error in the trigger mechanism

• Random noise introduced

– Normal distribution

– ± 10 %, ± 50 % errorlevel

• Error level = 10 %– 2 non-unique solutions

• Error level = 50 %– 1 solution

• Higher prediction errors due to low quality data

Predicted Source

Summary

• Effects of sensor sensitivity on contaminant source characterization was studied– Accuracy of predictions– Uncertainty of predictions

• Applicability of the contaminant source characterization method for different scenarios was illustrated

• Efficient scalable simulation-optimization framework– Parallel EPANET (using MPI) for UNIX environment– Grid enabled– Presented results were obtained using 4 processors on Neptune

(Opteron cluster)

Ongoing work

• Extend study to include– Additional sensor types

– Event detection procedures

• Multiple indicators

• Effects of measurement errors in sensors with filtered output signals

Acknowledgements

This work is supported by National Science Foundation (NSF) under Grant No. CMS-0540316 under the DDDAS program.

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