Enhanced Equal Frequency Partition Method for the Identification

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

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

Introduction • The Equal Frequency Partition is one of the simplest unsupervised partitioning methods.

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.

Introduction • The first goal is to present an enhancement to the EFP method

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.

Enhanced EFP method ¬The EEFP method eliminates multiple observations of the same behavioral pattern.

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.

FIR fuzzification process Then applies EFP to the remaining set of significantly different patterns

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

Water demand application • The system to be modeled is the water distribution network

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

Water demand application • The water demands for each reservoir are measured data stemming

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.

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

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

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

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

Discretization of system variables • The last input variable is the state of the

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.

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

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

Pressure-flow models errors

Pressure-flow models errors

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

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

Conclusions • In this paper an enhancement to the classical Equal Frequency Partition method

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.