Download - Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System
![Page 1: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/1.jpg)
Enhanced Equal Frequency Partition Method for the Identification of a
Water Demand System
T. Escobet R.M. Huber A. Nebot F.E. CellierDept ESAII IRI Dept. LSI ECE Dept.
UPC UPC/CSIC UPC UofA
![Page 2: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/2.jpg)
Introduction
• The Equal Frequency Partition is one of the simplest unsupervised partitioning methods.
• However, EFP is sensitive to data distribution.
• A good partitioning is obtained if all possible behaviors of the system are represented with a comparable number of occurrences.
![Page 3: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/3.jpg)
Introduction
• The first goal is to present an enhancement to the EFP method to be used within the FIR methodology that allows to reduce, to some extent, the data distribution dependency.
• The second goal is to use the EEFP method within the discretization step of FIR for the identification of a model of a water demand system.
![Page 4: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/4.jpg)
Enhanced EFP methodThe EEFP method eliminates multiple
observations of the same behavioral pattern. δ = range of similar observations. α = minimum number of occurrences to assume
that this behavioral pattern is over-represented.
![Page 5: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/5.jpg)
FIR fuzzification processThen applies EFP to the remaining set of
significantly different patterns to decide on a meaningful set of landmarks.
![Page 6: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/6.jpg)
Water demand application• The system to be modeled is the water
distribution network of the city of Sintra in Portugal.
![Page 7: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/7.jpg)
Water demand application
• The water demands for each reservoir are measured data stemming from the water network.
• The other input variables are obtained from the simulation of a control model of the water demand system.
![Page 8: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/8.jpg)
Discretization of system variables• Demand 1 (Mabrao reservoir)
α=10% δ=1%
![Page 9: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/9.jpg)
Discretization of system variables• Second valve
α=10% δ=1%
![Page 10: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/10.jpg)
Discretization of system variables• The last input variable is the state of the
pumps. • Each pump is composed of two motors, that
can either be both stopped, both pumping, or one stopped and one pumping.
![Page 11: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/11.jpg)
Discretization of system variables
• Pressure-flow at node 4
α=10% δ=1%
![Page 12: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/12.jpg)
Pressure-flow models errors
![Page 13: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/13.jpg)
Prediction of the pressure-flow at node 4FIR prediction with EFP (upper) and EEFP (lower)
![Page 14: Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System](https://reader035.vdocuments.us/reader035/viewer/2022062816/568156de550346895dc48515/html5/thumbnails/14.jpg)
Conclusions• In this paper an enhancement to the classical Equal
Frequency Partition method is presented.
• The EEFP method allows to obtain a better distribution of the data into classes.
• A real application i.e. water distribution network is studied.
• The prediction errors obtained when the EEFP method is used in the fuzzification process are lower than the ones obtained when the classical EFP method is used.