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Proceedings ArticleDOI

A methodology for modeling HVAC components using evolving fuzzy rules

01 Jan 2000-Vol. 1, pp 247-252
TL;DR: A methodology for the evolutionary construction of fuzzy rule-based (FRB) models is proposed and a new encoding mechanism is used that allows the fuzzy model rule base structure and parameters to be estimated from training data without establishing the complete rule list.
Abstract: A methodology for the evolutionary construction of fuzzy rule-based (FRB) models is proposed in the paper. The resulting models are transparent and existing expert knowledge could easily be incorporated into the model. An additional advantage of the model is represented by the economy in computational effort in generating the model output. A new encoding mechanism is used that allows the fuzzy model rule base structure and parameters to be estimated from training data without establishing the complete rule list. It uses rule indices and therefore significantly reduces the computational load. The rules are extracted from the data without using a priori information about the inherent model structure. It makes FRB models as flexible as other types of 'black-box' models (neural networks, polynomial models etc.) and in the same time significantly more transparent, especially when only small subset of all possible rules is considered. This approach is applied to modelling of components of heating ventilating and air-conditioning (HVAC) systems. The FRB models have potential applications in simulation, control and fault detection and diagnosis.

Summary (1 min read)

Introduction

  • This approach is applied to modelling of components of heating ventilating and air-conditioning (HVAC) systems.
  • In [3] and [13] they are used for adjustment of parameters of membership functions only (parameter identification).
  • It significantly minimises the length of the chromosome, which is also due to the use of realcoded GA.

IV. EVOULTIONARY SEARCH PROCEDURE

  • Numerical solution of both parameter and structural identification problems is sought by an evolutionary search procedure.
  • Child chromosomes are produced using modified recombination, mutation and selection operation.
  • While the application of overlapping Gaussian membership functions can minimise the effect on the model, gaps in the coverage of the model are still undesirable.
  • In addition, if the number of rules required is too small to ensure complete coverage of the input/output space by the FLT, the penalty function will still allow feasible solutions to be derived, but will favour the solutions with the least number of holes.

V. MODELLING A BOILER

  • A first principles based model of a nominally rated 300kW, natural gas fired boiler was used to generate training data that covered a typical range of operation.
  • From the data, two models were generated.
  • In the scheme in Figure 1, the load model (FP: Load) is given by, ,retrumflowww TTCpmq and the fuel consumption (FP: En. Con.) model is given by, , gross fuel q Q where q is the load across the boiler, wm and wCp are the mass flow rate and specific heat capacity of water.
  • The training and validation results for both the efficiency and the flow temperature models are depicted in Figures 2 and 3.
  • The term “Root MSE” noted on each plot refers to the root-mean-square-error between the data and model predictions.

VI. CONCLUSION

  • A methodology for the evolutionary construction of fuzzy rule-based (EFRB) models is proposed in the paper.
  • A new encoding mechanism is used that allows the fuzzy model rule base structure and parameters to be estimated from training data without establishing the complete rule list.
  • It makes EFRB models as flexible as other types of 'black-box' models (neural networks, polynomial models etc.) and in the same time significantly more transparent, especially when only small subset of all possible rules is considered.
  • Practical building services engineering problem is considered in order to illustrate the applicability of the approach.
  • The EFRB models have potential applications in simulation, control and fault detection and diagnosis.

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A Methodology for Modeling HVAC Components using
Evolving Fuzzy Rules
P. P. Angelov, V. I. Hanby, R. A. Buswell and J. A. Wright
Abstract--A methodology for the evolutionary
construction of fuzzy rule-based (EFRB) models
is proposed in the paper. The resulting models
are transparent and existing expert knowledge
could easily be incorporated into the model (both
at initialisation stages and during its generation).
An additional advantage of the model is
represented by the economy in computational
effort in generating the model output. A new
encoding mechanism is used that allows the fuzzy
model rule base structure and parameters to be
estimated from training data without
establishing the complete rule list. It uses rule
indices and therefore significantly reduces the
computational load. The rules are extracted from
the data without using a priori information about
the inherent model structure. It makes EFRB
models as flexible as other types of 'black-box'
models (neural networks, polynomial models
etc.) and in the same time significantly more
transparent, especially when only small subset of
all possible rules is considered. This approach is
applied to modelling of components of heating
ventilating and air-conditioning (HVAC)
systems. The EFRB models have potential
applications in simulation, control and fault
detection and diagnosis.
KeywordsFuzzy Logic, Modelling, Genetic
Algorithms, HVAC, Component Modelling.
I.INTRODUCTION
The computational demands of combined HVAC
systems and building simulations can be
considerable as these are often used for energy
predictions over annual operational cycles. Fuzzy
rule-based models as with other black-box
approaches have the potential to reduce the
computational demand of the simulation by
mapping the inputs and outputs of the system
components directly. In reality, processes associated
with some typical components, such as boilers or
compressors, can be too complex to be readily
described by analytical methods and polynomial
representations and recently neural networks [2]
based on test data are employed. One disadvantage
of black-box methods is the lack of transparency.
Models using fuzzy rules can offer a high degree of
transparency, but traditionally require the
incorporation of a priori knowledge and subjective
estimation to establish the rule base, i.e. the model
structure. In many cases it is a complex and
ambiguous process [6].
Recently genetic algorithms (GA) and neural
networks have been used to extract an appropriate
rule base from data [1], [3]-[5], [9], [12]-[13]. In [3]
and [13] they are used for adjustment of parameters
of membership functions only (parameter
identification). In another group of papers the
linguistic labels are assigned at the end of the
identification process only [4]-[5], which makes
these models quite close to neural networks,
including the limited interpretability.
The limitation of these approaches has been that the
exhaustive list of fuzzy rules is usually considered
[9],[12]. The length of the chromosome there is
determined on the basis of all possible combinations
of linguistic variables, which hampers solving
problems with realistic dimensions and makes
models practically not interpretable.
An effective encoding approach [1] is used in this
paper. It significantly minimises the length of the
chromosome, which is also due to the use of real-
coded GA. This permits simultaneous parameter and
structure identification as well as the application of
the approach to problems with realistic dimensions.
Unlike most of the black-box models and some of
the fuzzy rule-based approaches, the knowledge
extracted from the data is fully interpretable and
could help for better understanding of the nature of
the process being modelled. Expert knowledge
could be added both at the initialisation step and
during the identification process. Hybrid types of
models composed of both fuzzy rules and crisp
equations or inequalities could also be considered.
The approach is applied to the modelling of axial
fans as a components of an air conditioning system.
II. EVOLVING FUZZY RULES

Generally, fuzzy rule-based models consists of a
number of rules of the following type, called
Mamdani type [6]:
IF(x
1
is X
1
)AND...AND(x
n
is X
n
)THEN(y is Y) (1)
where x
i
is a fuzzy linguistic input variable;
y is the output variable;
Y is the fuzzy linguistic term of y;
Y{Y
1
,Y
2
,...,Y
m0
};
X
i
is the fuzzy linguistic term or label of the
i-th input variable; X
i
{X
1
i
, X
2
i
,...,X
mi
i
}
A fuzzy set and its membership function define
each linguistic label. Different types of membership
functions are possible: Gaussian, triangular,
trapezoidal, etc. [6].
For a specified number of linguistic variables and
labels it is possible to determine the number of all
possible fuzzy rules (R), which could be formulated
out of them. Even if only combinations, in which
each variable is participating are considered, this
number could be extremely high for real problems,
because of the so called curse of dimensionality
[6],[9],[12]:
R =
1n
1j
j
m
(2)
where m
j
is the number of linguistic terms of the j-th
linguistic variable.
It would be impossible to interpret such a model,
even if it is generated automatically. Practically,
significantly smaller number of rules (r) could be
used, because of information redundancy [6]:
r << R (3)
Extraction of a set of rules has been made,
generally, by the following two approaches: using
neural networks or by GA. We explore the second
one.
GA could be considered as a driven
stochastic search technique which imitate
the process of natural selection. They are
specifically appropriate for the problem
we have to solve [7], because of their
robustness, model structure independence,
capacity to escape local minima.
The GA probes a set of trial points at every
iteration. The trial set, called population, consists of
several chromosomes, which comprises a number of
genes. Each problem variable is coded into a gene.
The modified version of the original binary GA [7],
called real-coded GA or evolutionary algorithms
[10] makes problem definition more compact by
representing each variable by a single gene:
TABLE I
REAL-VALUED CHROMOMOME
i
x
1
i
x
2
i
n
x
where i=1,2,...P; P denotes the population size.
Part of the chromosomes from the current epoch is
selected for reproduction. There is two operations,
which are usually applied for producing new
chromosomes: crossover and mutation. Mutation is
a triggering from 0 to 1 and vice versa for the
standard binary-coded GA [7]. Different schemes
for mutation exist for real-coded GA [10].
III. FUZZY RULES ENCODING
Application of evolutionary technique for extraction
of the fuzzy model requires an appropriate encoding
of the fuzzy rules and their parameters. Encoding of
all possible fuzzy rules into the chromosome as in
[9],[12] is time consuming and can become an non-
solvable problem for problems with realistic
dimension (>5 inputs and 7-9 linguistic labels). We
propose to consider encoding of the indices of rules,
which participate into the fuzzy model only. Their
number is significantly smaller: normally some tens
of rules are used and could be interpreted. Different
encoding schemes could be used. The basic
requirement is non-ambiguity (uniqueness) in
coding and decoding. We introduce a simple
encoding procedure, which assigns an index to
every possible rule. A positive integer number
represents each fuzzy rule. The genotype of the
chromosome considered in our approach consists of
two parts: indices of rules, which participate into the
fuzzy model and their parameters:
TABLE II
GENOTYPE: LEFT PART REPRESENTS INDICIES OF RULES;
RIGHT ONE MEMBERSHIP FUNCTIONS PARAMETERS
I
1
I
2
I
K
p
11
p
12
p
1nm
i
A two-stage coding scheme is adopted in this paper:
first, we translate each linguistic label into a L -
based number (where
1
1
)max(
n
i
i
mL
is the
maximal number of labels in all linguistic
variables). 0 is assigned to the one marginal
linguistic label, 1 to the next etc. As second stage,
we transform the set of L-based numbers (codes of
labels) into decimal integer positive number. They
represent the index of the considered fuzzy rule:
I =
10
n
L
2
L
1
L
)t, ... , t,(t
+1 (4)

where I denotes the index of the fuzzy rule;
t
j
, j=1,2,...,n+1 is code of the label t
j
[0;m
i
-1]
As an example the encoding of the following rule
could be considered:
IF (LV
1
is High) AND (LV
2
is Very Low) AND
(LV
3
is Low)) THEN (LV
4
is Medium) (5)
In this rule there are 4 linguistic variables (3 input
and an output), n=3. Let the first input and the
output have 3 linguistic terms (Low, Medium and
High) and all other variables have 5 linguistic terms
(Very Low, Low, Medium, High and Very High).
First, the codes of the used linguistic terms are
determined:
L=max(3,5,5,3)=5;
1
5
a
=2;
2
5
a
=0;
3
5
a
=1;
4
5
a
=1 (6)
Index of the fuzzy rule (5) is determined as a
transformation to the integer with a decimal base
according to (4):
I=(2
5
0
5
1
5
1
5
)
10
+1=2*5
3
+1*5
1
+1*5
0
+1=257 (7)
Decoding process is an inverse of the coding one.
First, the codes of linguistic labels are determined
from the index of the rule as residuals in division by
L:
[(257-1)/5]=51, Res((257-1),3)=1; (8)
[51/5]=10, Res(51,3)=1;
[10/5]=2; Res(10,5)=0;
[2/5]=0; Res(2,5)=2;
where Res(.) denotes residual in division of integers;
[.] denotes integer result in division of
integers.
Residual values determine in a unique way the fuzzy
rule (5) from the index 257.
This effective encoding mechanism makes it
possible to treat parameters of fuzzy membership
functions as unknowns as well. Real-valued GA also
minimises the chromosome representation and
contributes to the compactness. Encoding of fuzzy
rule parameters together with their structure into the
same chromosome reveals a possibility for fine-
tuning of the fuzzy rule-based models generated. It
makes identification process more flexible and more
independent on the subjectivity in structure
determination. In the same time, certain degree of
influence on the model structure is also possible. It
could be realised by definition of parameters like the
number of linguistic terms (m), the maximal number
of fuzzy rules considered (K), the pre-defined level
of correlation (r) and the type of the membership
functions as well as using a priori knowledge in the
initialisation. The number of fuzzy rules in the
model could be finally smaller than K due to
possible coincidence of some indices as well as due
to appearance of zeros as rules indices (zero is left
as an 'empty' index). Therefore K defines the upper
bound of k - the number of used fuzzy rules. In the
same time K could be significantly smaller than R,
which defines the number of all possible rules.
Practically, some tens of rules are enough for
reaching a pre-defined level of correlation and such
number of rules is still interpretable. The number of
linguistic labels considered (m) is recommended to
be 72 (5,7 or 9) as closer to the human perception
[6]. Values of correlation higher than 0.95 are seen
as acceptable level of closeness between
experimental and model outputs.
IV. EVOULTIONARY SEARCH
PROCEDURE
Numerical solution of both parameter and structural
identification problems is sought by an evolutionary
search procedure. The identification problem could
be formulated as
To determine the fuzzy rules (represented by
their indices) and their parameters such that to
minimise the deviation between the model and the
experimental outputs (represented by correlation):
r max (9)
subject to (1)
1 I
i
R; i=1,2,...,K
(j-1) p
lj
(j+1); l=1,2,…,n+1; j=1,2,…m
l
where =
1
l
m
LVLV
l
LV
is the lower bound of the l-th linguistic
variable;
l
LV
is its upper bound .
It is important to note that fuzzy model (1) is
considered as one of the constraints.
Evolutionary algorithm, which is applied for
numerical solution of this problem, matches better
the specifics of the considered problem:
Vector of unknowns consists of integer (indices
of fuzzy rules) and real (parameters of the
membership functions) values , not binary ones;
Real-valued GA supposes shorter chromosome,
which allows simultaneous parameter and
structure identification as well as solving
problems with realistic dimensions.
The basic algorithm applied to our problem could be
represented by the following pseudo-code.
Begin
Epoch = 0;

Initialise (randomly or using a
priori information) a
population of chromosomes
(Table 2);
While (Fitness<r)
Decode fuzzy model by rules
indices as in (8);
Calculate outputs y
similarly to (1);
Evaluate Fitness as in (9)
Perform crossover and
mutation;
Perform selection and
reproduction using Fitness
Epoch := epoch + 1;
end
End.
where
r is a pre-defined desired correlation value;
Epoch denotes number of epochs.
The algorithm is initialised by a set of chromosomes
(population), which is randomly seeded or defined
on the base of a priori expert knowledge and
previous experience (if such exists). Child
chromosomes are produced using modified
recombination, mutation and selection operation.
They are performed separately for both parts (Table
2) because of the specific of the problem: a part of
chromosomes represents indices of the rules and
consists of integer values while the other part
represents the parameters of fuzzy sets and consists
of real values. Mutation over first part of the
chromosomes, which contains the integer values, is
performed with size of mutation step [11] equal to 1
such that to produce an integer number again. The
selection is performed for the whole chromosomes
because both parts contribute to the fitness value.
It has been demonstrated to the authors that when
the number of rules is restricted, it is possible that
not all the FLT are represented, and hence “holes”
in the input/output space can be evident. While the
application of overlapping Gaussian membership
functions can minimise the effect on the model,
gaps in the coverage of the model are still
undesirable. To reduce the likelihood of holes being
present a penalty function has been introduced that
checks the population of solutions penalises these
proportionally to the number of holes present. The
penalty function is implemented in the fitness
function by,
,--)y
ˆ
-(y-exp
n
1i
2
ii
f
where
is the number of holes and
is given by,
)}y
ˆ
-(ymin-)y
ˆ
-(ymaxmax{
ii
n
1i
ii
n
1i
In the example used in this paper the function
ensured that the model gave complete coverage of
the data, without the function, one or more holes
were usually present in the optimal solution. In
addition, if the number of rules required is too small
to ensure complete coverage of the input/output
space by the FLT, the penalty function will still
allow feasible solutions to be derived, but will
favour the solutions with the least number of holes.
V. MODELLING A BOILER
A practical problem of modelling of small
boiler that could be used to supply medium
temperature hot water to a heating system is
considered.
A first principles based model of a nominally rated
300kW, natural gas fired boiler was used to generate
training data that covered a typical range of
operation. The boiler was assumed to operate at a
constant water mass flow rate and a flow and return
water temperature difference of 15K. Control of
boiler operation is typically based on the return
water temperature, thus the firing rate and return
water temperature were excited to generate the input
data. For use in HVAC system simulation, the
model inputs were considered to vary between the
maximum firing rate down to 10% of that rate, and
for return water temperatures between 20C and
100C. The resulting FRB model is therefore
suitable when the boiler is firing, the water mass
flow rate through the boiler is a constant 3.8kgS
-1
and for normal operating conditions as well as
start-up operation with the heating fluid at
ambient temperatures.
From the data, two models were generated. The first
predicted the gross efficiency of the boiler, taking
the boiler load and return water temperature as
inputs. The second modelled the flow temperature
as the output as a function of the return water
temperature and the control signal (percent of the
maximum firing rate) to the boiler. The latter model
allows the incorporation of the component into a
subsystem performance simulation, while the former
model can be used in conjunction with this to
generate predictions of fuel consumption for energy
analysis, such as annual energy cost predictions.
Figure 1 demonstrates this hybrid approach the
problem solution. “FP” refers to “First Principles”
meaning here, a directly calculable algebraic
relationship based on the physical relationship of the
variables.

Citations
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TL;DR: In this article, the role of fuzzy modeling in heating, ventilating and air conditioning (HVAC) and control models is discussed and a review of recent advances on the specific areas of conceptual design and control involving synthesis of HVAC components is presented.
Abstract: Paper presents role of fuzzy modeling in heating, ventilating and air conditioning (HVAC) and control models. HVAC design professionals are required to evaluate numerous design alternatives and properly justify their final conceptual selection through modeling. This trend, coupled with the knowledge of experienced designers, increasing complexity of the systems, unwillingness to commit additional funds to the design phase itself, can only be satisfied by approaching the conceptual design process in more scientific, comprehensive and rational manner as against the current empirical and often adhoc approach. Fuzzy logic offers a promising solution to this conceptual design through fuzzy modeling. Numerous fuzzy logic studies are available in the non- mechanical engineering field and allied areas such as diagnostics, energy consumption analysis, maintenance, operation and its control. Relatively little exists in using fuzzy logic based systems for mechanical engineering and very little for HVAC conceptual design and control. This review appraises recent advances on the specific areas of conceptual design and control involving synthesis of HVAC components.

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Q1. What contributions have the authors mentioned in the paper "A methodology for modeling hvac components using evolving fuzzy rules" ?

In this paper, a methodology for the evolutionary construction of fuzzy rule-based ( EFRB ) models is proposed and the resulting models are transparent and existing expert knowledge could be incorporated into the model ( both at initialisation stages and during its generation ).