ÓÄÊ 004.896
Estimation
of the correction coefficient value to the fuel consumption rate for machines
using methods of fuzzy logic
1 Goryaev V.M., 2 Dzhakhnaeva
E.N., 3 Sangadjieva E.,
1 Kalmyk State University named after B.B.Gorodovikov,
Elista, e-mail: goryaeff@yandex.ru; 2 Kalmyk State University named after B.B.Gorodovikov, Elista, e-mail: dzhakhnaeva-en@yandex.ru ;3 Kalmyk State University named after B.B.Gorodovikov, Elista, e-mail: sangel96@mail.ru
This article
is devoted to one of the actual tasks of planning the work at the harvesting
stage. this is the task of estimating the correction factor for fuel costs for combine
harvesters. Its urgency is due to the fact that the fuel cost norms are set for
new machines without taking into account the increase in their service life and
operating conditions, therefore the values of the projected costs can
significantly differ from the actual ones. The most significant factors
affecting fuel costs are the following: the lifetime of the combine, the crop
yield and the length of the field race.
Keywords: fuzzy logic method, fuel, evaluation, correction factor, method of mean center
One of the most difficult to manage and the most
costly step in the production of grain crops is the stage of harvesting. In
order to harvest the crop at the optimal time and efficiently, the agricultural
enterprises use a large number of technical means, the management of which is a
rather difficult task. This is due to the fact that in order to make effective
decisions it is necessary to analyze a significant amount of information about
the properties and characteristics of technical resources involved in
harvesting and transport operations and the environment for their operation. To
solve this problem, as a rule, economic-mathematical methods [1], queueing
theory [2], simulation modeling [3], and logistical methods [4] are used. However,
these approaches do not allow to fully take into account such features of the
technological process of harvesting and transport operations as nonstationarity
and stochastic behavior, non-reproducibility of experiments, lack of
information on the characteristics of the process. These features of the
technological process can be taken into account when solving problems of
planning and operational management of agricultural work due to the application
of methods of the theory of fuzzy sets and fuzzy logic.
One of the urgent tasks at the planning stage of
harvesting is the task of forecasting fuel costs for combine harvesters. Its
urgency is due to the fact that the norms of fuel costs are set for new
machines without taking into account the increase in their service life and
operating conditions, therefore the values of the estimated costs can
significantly differ from the actual ones.
The most significant factors affecting fuel costs
are the following [5]: the lifetime of the combine, the crop yield and the length
of the rutting field. However, information on these indicators may be
incomplete or inaccurate, therefore it is rational to apply fuzzy logic methods
to calculate the correction factor to the fuel consumption rate.
Formulation
of the problem
to develop a method of predicting a value of the
correction factor to the rate of fuel consumption for combine harvesters on the
basis of methods of fuzzy logic, which allows to consider the impact of the
timing of equipment maintenance and technological conditions of its operation
on the fuel consumption.
The
solution of the problem
Due to the fact that the information necessary to
build the base of fuzzy rules is quantitative, and not linguistic, the base of
fuzzy rules will be formed using the universal method of constructing the base
of fuzzy rules based on numerical data [6, 7].
Let us consider the main stages of building fuzzy
rule base.
1) Separation of the space of input and output
data into regions. Based on the statistical data taken from the source
[5], we will form a set of training data, consisting of vectors:
(1)
where 
- number of training vector; 
- crop yield, ö/ãà; 
- the length of field, m; 
- service life of the combine, year; 
- the value
of the correction factor to the rate of fuel consumption.
Together with this, we fix the minimum and
maximum values of input and output variables: 
,
,
, 
. Each of these domains defines the separation
variables that characterize incoming and outgoing variables. All variables set
in the form of triangular membership functions.
2) Synthesis of fuzzy rules based on training
data. To form a fuzzy rule, it is necessary to determine the maximum
degree of belonging of each component of the learning vector to the given
segments. If one of the components of the learning vector has the greatest
degree of belonging to a certain fuzzy set given on one of the segments, this
fuzzy set is included in the rule. We introduce the fuzzy rules in the
following general form:
(2)
where 
- number
of the rule, 
- fuzzy set,
characterizing crop yield, 
- fuzzy set,
characterizing the length of the rutting field, 
- fuzzy
set characterizing the service life of the combine, 
- a fuzzy
set specifying the correction factor to the fuel consumption rate for combine
harvesters.
3) The definition of the degree of truth for
each rule. The goal of this stage is to solve the problem of
conflicting rules, and, as a consequence, to reduce the number of rules. At
this stage, rules that have the same conditions and different conclusions are
processed. Each rule is given a certain degree of truth, followed by a choice
of the contradictory rules of the rule, in which the degree of truth is the
greatest. For the rule 
degree of the truth 
is determined by the formula:
(3)
where 
- the value
of the element's membership function to the fuzzy set , 
- the
value of the membership function of the element to the fuzzy set , 
- the
value of the membership function of the element to the fuzzy set 
, 
- the value of the membership function of the
element 
to the fuzzy set 
.
4) Creating a base of fuzzy rules. The base of
fuzzy rules can be represented in the form of a three-dimensional matrix, in
cells of which there are fuzzy sets 
. The dimensions of the matrix correspond to the
values
, for
example, fuzzy sets 
are given on the axis. 
. In the base of fuzzy rules we will introduce 27
rules.
Based on the constructed base of fuzzy rules, you
can determine the quantitative value of the output variable 
for certain incoming signals 
. Calculation of the output variable is carried
out using the method of defuzzification in the middle center on the basis of
the formula:
(4)
where 
- the degree of activity 
-ãî the degree of activity of the rule, determined by the
rule:
(5)
Conclusions
The application of the developed fuzzy model for
estimating the correction factor to the fuel consumption rate makes it possible
to obtain an adequate result for combine harvesters with different operating
resources, depending on the characteristics of the fields on which harvesting
is carried out.
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