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Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System

Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System. T. Escobet R.M. Huber A. Nebot F.E. Cellier Dept ESAII IRI Dept. LSI ECE Dept. UPC UPC/CSIC UPC UofA. Introduction.

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Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System

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  1. Enhanced Equal Frequency Partition Method for the Identification of a Water Demand System T. Escobet R.M. Huber A. Nebot F.E. Cellier Dept ESAII IRI Dept. LSI ECE Dept. UPC UPC/CSIC UPC UofA

  2. 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.

  3. 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.

  4. Enhanced EFP method • The 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.

  5. FIR fuzzification process • Then applies EFP to the remaining set of significantly different patterns to decide on a meaningful set of landmarks.

  6. Water demand application • The system to be modeled is the water distribution network of the city of Sintra in Portugal.

  7. 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 modelof the water demand system.

  8. Discretization of system variables • Demand 1 (Mabrao reservoir) α=10% δ=1%

  9. Discretization of system variables • Second valve α=10% δ=1%

  10. 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.

  11. Discretization of system variables • Pressure-flow at node 4 α=10% δ=1%

  12. Pressure-flow models errors

  13. Prediction of the pressure-flow at node 4 FIR prediction with EFP (upper) and EEFP (lower)

  14. 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 networkis 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.

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