Fuzzy Modeling Library (FMLib)
ele1-2-495: Estimation of the Low Voltage Electrical Line Length in Rural Towns

Description

Sometimes, there is a need to measure the amount of electricity lines that an electric company owns. This measurement may be useful for several aspects such us the estimation of the maintenance costs of the network, which was the main goal of the problem presented here in Spain. High and medium voltage lines can be easily measured, but low voltage line is contained in cities and villages, and it would be very expensive to measure it. This kind of line used to be very convoluted and, in some cases, one company may serve more than 10,000 small nuclei. An indirect method for determining the length of line is needed.

The problem involves finding a model that relates the total length of low voltage line installed in a rural town with the number of inhabitants in the town and themean of the distances from the center of the town to the three furthest clients in it. This model will be used to estimate the total length of line being maintained.

In this problem, it would be preferable that the solutions obtained verify the following requirement: they have not only to be numerically accurate in the problem-solving, but must be able to explain how a specific value is computed for a certain village. That is, it is interesting that these solutions are interpretable by human beings to some degree. Therefore, the use of gray-box techniques such as fuzzy modeling is recommended.

In this problem, five or seven linguistic terms are usually considered for each variable in linguistic fuzzy modeling.

Data Sets

The original data set of 495 examples has been randomly divided into 5 different subsets of 99 examples each of them. Joining 4 of these subsets in a training data set and keeping the fifth subset as test data set it is possible to build 5 different partitions of the original data set at 80%-20%, i.e., a 5-fold cross-validation. Some papers only consider a data set partition, in this case, the first partition is used.

The existing dependency of the two input variables with the output variable in the first training and test data sets is shown below.

(X1,Y) in ele1-2-495-1.tra	(X1,Y) in ele1-2-495-1.tst
(X2,Y) in ele1-2-495-1.tra	(X2,Y) in ele1-2-495-1.tst

Results

Linguistic Fuzzy Modeling: Learning/Tuning also the Data Base
Reference	Method	Learning	Tuning	MF param.	Granularity	Context	#Rules	#Labels	Training	Test	Exp. type
[CHS99]	MOGUL-D	—			—	—	19	21	150,559	166,669	1 partition
[CHV01]	Gr+MF		—			—	25	21	149,832	152,724	1 partition
[CHMV01]	Gr+MF+Context		—				19	24	163,249	147,062	1 partition
[CHMV01]	Gr+MF+Context		—				7	18	171,137	155,589	1 partition

Linguistic Fuzzy Modeling: Extending the Model Structure
Reference	Method	2 consequents	Hierarchical KB	#Rules	#Labels	Training	Test	Experiment type
[CH00]	ALM		—	13	15	178,571	180,848	1 partition
[CH00]	ALM		—	35	21	154,470	167,061	1 partition
[CHZ01]	HSLR	—		12	24	178,950	167,318	1 partition

References

Fuzzy Modeling Library (FMLib)

© Jorge Casillas