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

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.
• d range of similar observations.
• a 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 model of the water demand
  system.

8
Discretization of system variables

• Demand 1 (Mabrao reservoir)

a10 d1
9
Discretization of system variables

• Second valve

a10 d1
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

a10 d1
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
  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.