Numerical problems are usually solved using heuristic algorithms, due to their simplicity and easy understanding. Nevertheless, most of these methods have calibration parameters that do not count with selection premises oriented to obtain the best performance for the algorithm. This paper introduces an iterative technique that deals with this problem, searching for the calibration parameters that improve the Differential Evolution (DE) algorithm. The application of the proposed technique is illustrated on a real burst location problem in a pipeline prototype. The obtained results show the good performance of the methodology proposed for the burst location task, including the mapping of the calibration parameters that ameliorate the searching process.

References

References
1.
Holland
,
J. H.
,
1970
, “
Robust Algorithms for Adaptation Set in a General Formal Framework
,”
IEEE
Symposium on Adaptive Processes Decision and Control
, Austin, TX, Dec. 7–9, p.
175
.
2.
Schwefel
,
H.
,
1965
, “
Kybernetische Evolution Als Strategie Der Experimentellen Forschung in Die Strömungstechnik
,” Diplomarbeit 233, TU Berlin, Technical Universite of Berlin, Germany.
3.
Das
,
S.
, and
Suganthan
,
P. N.
,
2011
, “
Differential Evolution: A Survey of the State-of-the-Art
,”
IEEE Trans. Evol. Comput.
,
15
(
1
), pp.
4
31
.
4.
Liu
,
Y.
,
2017
, “
Adaptive Just-in-Time and Relevant Vector Machine Based Soft-Sensors With Adaptive Differential Evolution Algorithms for Parameter Optimization
,”
Chem. Eng. Sci.
,
172
, pp.
571
584
.
5.
Fanelli
,
M.
, and
Cabrera
,
E.
,
2015
, “
Detection of Abrupt Flow Discontinuities in Open-Surface Channels by Transient Analysis
,”
J. Hydraul. Eng.
,
142
(
1
), p.
04015037
.
6.
Pérez-González
,
A.
,
Begovich
,
O.
, and
Ruiz-León
,
J.
,
2014
, “
Modeling of a Greenhouse Prototype Using PSO Algorithm Based on a LabView TM Application
,”
11th International Conference on Electrical Engineering, Computing Science and Automatic Control
(
CCE
), Campeche, Mexico, Sept. 29–Oct. 3, pp.
1
6
.
7.
Clerc
,
M.
, and
Kennedy
,
J.
,
2002
, “
The Particle Swarm-Explosion, Stability, and Convergence in a Multidimensional Complex Space
,”
IEEE Trans. Evol. Comput.
,
6
(
1
), pp.
58
73
.
8.
Trelea
,
I. C.
,
2003
, “
The Particle Swarm Optimization Algorithm: Convergence Analysis and Parameter Selection
,”
Inf. Process. Lett.
,
85
(
6
), pp.
317
325
.
9.
Adedeji
,
K. B.
,
Hamam
,
Y.
,
Abe
,
B. T.
, and
Abu-Mahfouz
,
A. M.
,
2017
, “
Burst Leakage-Pressure Dependency in Water Piping Networks: Its Impact on Leak Openings
,”
IEEE AFRICON
,
Cape Town, South Africa
, Sept. 18–20, pp.
1502
1507
.
10.
Ye
,
G.
, and
Fenner
,
R. A.
,
2010
, “
Kalman Filtering of Hydraulic Measurements for Burst Detection in Water Distribution Systems
,”
J. Pipeline Syst. Eng. Pract.
,
2
(
1
), pp.
14
22
.
11.
Misiunas
,
D.
,
Lambert
,
M.
,
Simpson
,
A.
, and
Olsson
,
G.
,
2005
, “
Burst Detection and Location in Water Distribution Networks
,”
Water Sci. Technol.: Water Supply
,
5
(
3-4
), pp.
71
80
.
12.
Kowalczuk
,
Z.
, and
Gunawickrama
,
K.
,
2004
, “
Detecting and Locating Leaks in Transmission Pipelines
,”
Fault Diagnosis
,
Springer
, Berlin, pp.
821
864
.
13.
Eiswirth
,
M.
, and
Burn
,
L.
,
2001
, “
New Methods for Defect Diagnosis of Water Pipelines
,”
Fourth International Conference in Water Pipeline Systems
, York, UK, Mar. 28–30, pp.
137
150
.
14.
Chaudhry
,
M. H.
,
2014
,
Applied Hydraulic Transients
,
Springer Science & Business Media
, New York.
15.
Delgado
,
M.
, and
Begovich
,
O.
,
2017
, “
A Comparison Between Leak Location Methods Based on the Negative Pressure Wave
,”
14th International Conference on Electrical Engineering, Computing Science and Automatic Control
(
CCE
), Mexico City, Mexico, Oct. 20–22, pp.
1
6
.
16.
Allen
,
M.
,
Prels
,
A.
,
Lqbal
,
M.
,
Srirangarajan
,
S.
,
Llm
,
H. B.
,
Glrod
,
L.
, and
Whittle
,
A. J.
,
2011
, “
Real-Time in-Network Distribution System Monitoring to Improve Operational Efficiency
,”
J.-Am. Water Works Assoc.
,
103
(
7
), pp.
63
75
.
17.
Martins
,
J. C.
, and
Seleghim
,
P.
, Jr
,
2010
, “
Assessment of the Performance of Acoustic and Mass Balance Methods for Leak Detection in Pipelines for Transporting Liquids
,”
ASME J. Fluids Eng.
,
132
(
1
), p.
011401
.
18.
Delgado-Aguiñaga
,
J.
,
Besancon
,
G.
,
Begovich
,
O.
, and
Carvajal
,
J.
,
2016
, “
Multi-Leak Diagnosis in Pipelines Based on Extended Kalman Filter
,”
Control Eng. Pract.
,
49
, pp.
139
148
.
19.
Verde
,
C.
,
2005
, “
Accommodation of Multi-Leak Location in a Pipeline
,”
Control Eng. Pract.
,
13
(
8
), pp.
1071
1078
.
20.
Verde
,
C.
, and
Torres
,
L.
,
2017
,
Modeling and Monitoring of Pipelines and Networks: Advanced Tools for Automatic Monitoring and Supervision of Pipelines
, Vol.
7
,
Springer
, Cham, Switzerland.
21.
Wylie
,
E. B.
,
Streeter
,
V. L.
, and
Suo
,
L.
,
1993
,
Fluid Transients in Systems
, Vol.
1
,
Prentice Hall
,
Englewood Cliffs, NJ
.
22.
Meniconi
,
S.
,
Brunone
,
B.
,
Ferrante
,
M.
,
Capponi
,
C.
,
Carrettini
,
C.
,
Chiesa
,
C.
,
Segalini
,
D.
, and
Lanfranchi
,
E.
,
2015
, “
Anomaly Pre-Localization in Distribution–Transmission Mains by Pump Trip: Preliminary Field Tests in the Milan Pipe System
,”
J. Hydroinformatics
,
17
(
3
), pp.
377
389
.
23.
Soares
,
A. K.
,
Covas
,
D. I.
, and
Reis
,
L. F.
,
2008
, “
Analysis of PVC Pipe-Wall Viscoelasticity During Water Hammer
,”
J. Hydraul. Eng.
,
134
(
9
), pp.
1389
1394
.
24.
Meniconi
,
S.
,
Duan
,
H.
,
Brunone
,
B.
,
Ghidaoui
,
M. S.
,
Lee
,
P.
, and
Ferrante
,
M.
,
2014
, “
Further Developments in Rapidly Decelerating Turbulent Pipe Flow Modeling
,”
J. Hydraul. Eng.
,
140
(
7
), p.
04014028
.
25.
Axworthy
,
D. H.
,
Ghidaoui
,
M. S.
, and
McInnis
,
D. A.
,
2000
, “
Extended Thermodynamics Derivation of Energy Dissipation in Unsteady Pipe Flow
,”
J. Hydraul. Eng.
,
126
(
4
), pp.
276
287
.
26.
Brunone
,
B.
,
Golia
,
U.
, and
Greco
,
M.
,
1995
, “
Effects of Two-Dimensionality on Pipe Transients Modeling
,”
J. Hydraul. Eng.
,
121
(
12
), pp.
906
912
.
27.
Vardy
,
A. E.
, and
Brown
,
J. M.
,
1995
, “
Transient, Turbulent, Smooth Pipe Friction
,”
J. Hydraul. Res.
,
33
(
4
), pp.
435
456
.
28.
Prashanth Reddy
,
H.
,
Silva-Araya
,
W. F.
, and
Hanif Chaudhry
,
M.
,
2011
, “
Estimation of Decay Coefficients for Unsteady Friction for Instantaneous, Acceleration-Based Models
,”
J. Hydraul. Eng.
,
138
(
3
), pp.
260
271
.
29.
Zhao
,
M.
, and
Ghidaoui
,
M.
,
2004
, “
Review and Analysis of 1-D and 2-D Energy Dissipation Models for Transient Flows
,”
International Conference on Pressure Surges
, Chester, UK, Mar. 24–26, pp. 477–492.
30.
Duan
,
H.
,
Meniconi
,
S.
,
Lee
,
P.
,
Brunone
,
B.
, and
Ghidaoui
,
M. S.
,
2017
, “
Local and Integral Energy-Based Evaluation for the Unsteady Friction Relevance in Transient Pipe Flows
,”
J. Hydraul. Eng.
,
143
(
7
), p.
04017015
.
31.
Bergant
,
A.
,
Ross Simpson
,
A.
, and
Vìtkovsk
,
J.
,
2001
, “
Developments in Unsteady Pipe Flow Friction Modelling
,”
J. Hydraul. Res.
,
39
(
3
), pp.
249
257
.
32.
Pezzinga
,
G.
,
2009
, “
Local Balance Unsteady Friction Model
,”
J. Hydraul. Eng.
,
135
(
1
), pp.
45
56
.
33.
Vítkovsky`
,
J. P.
,
Bergant
,
A.
,
Simpson
,
A. R.
, and
Lambert
,
M. F.
,
2006
, “
Systematic Evaluation of One-Dimensional Unsteady Friction Models in Simple Pipelines
,”
J. Hydraul. Eng.
,
132
(
7
), pp.
696
708
.
34.
Vardy
,
A.
, and
Brown
,
J.
,
2004
, “
Transient Turbulent Friction in Fully Rough Pipe Flows
,”
J. Sound Vib.
,
270
(
1–2
), pp.
233
257
.
35.
Vítkovsky`
,
J.
,
Stephens
,
M.
,
Bergant
,
A.
,
Simpson
,
A.
, and
Lambert
,
M.
,
2006
, “
Numerical Error in Weighting Function-Based Unsteady Friction Models for Pipe Transients
,”
J. Hydraul. Eng.
,
132
(
7
), pp.
709
721
.
36.
Zarzycki
,
Z.
,
2000
, “
On Weighting Function for Wall Shear Stress During Unsteady Turbulent Pipe Flow
,”
Eighth International Conference on Pressure Surges
, The Hague, The Netherlands, pp.
529
543
.
37.
Dulhoste
,
J.-F.
,
Besançon
,
G.
,
Torres
,
L.
,
Begovich
,
O.
, and
Navarro
,
A.
,
2011
, “
About Friction Modeling for Observer-Based Leak Estimation in Pipelines
,”
50th IEEE Conference on Decision and Control and European Control Conference
(
CDC-ECC
), Orlando, FL, Dec. 12–15, pp.
4413
4418
.
38.
Dulhoste
,
J. F.
,
Guillén
,
M.
,
Besançon
,
G.
, and
Santos
,
R.
,
2017
, “
One-Dimensional Modeling of Pipeline Transients
,”
Modeling and Monitoring of Pipelines and Networks
,
Springer
, Cham, Switzerland, pp.
63
81
.
39.
Sotelo Avila
,
G.
,
1991
,
Hidráulica General; Fundamentos
,
Limusa
, Mexico city, Mexico.
40.
Besançon
,
G.
,
2017
, “
Observer Tools for Pipeline Monitoring
,”
Modeling and Monitoring of Pipelines and Networks
,
Springer
, Cham, Switzerland, pp.
83
97
.
41.
Navarro
,
A.
,
Begovich
,
O.
,
Sánchez
,
J.
, and
Besancon
,
G.
,
2017
, “
Real-Time Leak Isolation Based on State Estimation With Fitting Loss Coefficient Calibration in a Plastic Pipeline
,”
Asian J. Control
,
19
(
1
), pp.
255
265
.
42.
Delgado-Aguiñaga
,
J.
,
Besançon
,
G.
, and
Begovich
,
O.
,
2015
, “
Leak Isolation Based on Extended Kalman Filter in a Plastic Pipeline Under Temperature Variations With Real-Data Validation
,”
23th Mediterranean Conference on Control and Automation
(
MED
), Torremolinos, Spain, June 16–19, pp.
316
321
.
43.
Badillo-Olvera
,
A.
,
Begovich
,
O.
, and
Peréz-González
,
A.
,
2017
, “
Leak Isolation in Pressurized Pipelines Using an Interpolation Function to Approximate the Fitting Losses
,”
Journal of Physics: Conference Series
, Lille, France, p.
012012
.
44.
Storn
,
R.
, and
Price
,
K.
,
1997
, “
Differential Evolution—A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces
,”
J. Global Optim.
,
11
(
4
), pp.
341
359
.
45.
Price
,
K.
,
Storn
,
R. M.
, and
Lampinen
,
J. A.
,
2006
,
Differential Evolution: A Practical Approach to Global Optimization
,
Springer Science & Business Media
, Berlin.
46.
Pérez-González
,
A.
,
Begovich
,
O.
, and
Ruiz-León
,
J.
,
2016
, “
Evolutive Extension: A Biological Approach to Heuristic Algorithms
,”
Latin American Conference on Automatic Control (XVII CLCA)
, Medellín, Colombia, pp.
373
378
.
You do not currently have access to this content.