The concept of “energy efficiency” has many interpretations, but if to express the most typical, it obviously will be the degree or measure of efficient use of any energy resource that is brought to the object that is the consumer of these resources.
One of the quantitative definitions of energy efficiency of a building can be the Energy conversion efficiency,
According to the authors of the review [1], energy efficiency involves the elimination of unnecessary energy waste and increases its efficiency in all energy processes that take place in the house.
The maximum energy efficiency will have those buildings in which at the same rate of the energy conversion efficiency, the amount of total investment in the installation of thermal insulation and engineering systems to ensure optimal indoor climate will have a minimum value at their maximum durability. Significant energy consumption to maintain the thermal comfort of the premises does not increase the energy efficiency of buildings.
In modern scientific research solving, the problem of decision-making in uncertainty conditions where the choice of alternatives requires the analysis of complex information of different physical nature in search of the best solution is called a methodology of systems analysis. The essence of system analysis is multicriteria (decision) analysis (MCDA). That is why, when designing energy-efficient buildings, there is a need for a systematic analysis of the factors that affect the multicriteria (as usual) value of the objective function. With the help of system analysis, it is possible to substantiate the optimal design solution to reduce energy costs for the construction and operation of the building as a single energy and environmental system.
The concept of “reliability” is used very often in various branches of technics. In the material of this paper, the authors consider the term “reliability” as an integral indicator that numerically expresses the probability of providing several guaranteed thermophysical, physic-mechanical and durability characteristics in the design of thermal insulation products.
The author [2] believes that the urgency of the problem of ensuring the reliability of technical facilities, including buildings, structures and building structures is obvious because no one needs unreliable equipment, structures, materials, failure of which can lead to material and social losses.
Ensuring the reliability of the thermal insulation shell guarantees the maintenance of optimal microclimatic conditions of the premises at the actual consumption of thermal energy for heating. When substantiating the need for construction of low-rise buildings using multilayered thermal insulation products made of straw, there is a need to assess the reliability of their energy efficiency, by taking into account both quantitative and qualitative parameters of impact.
The scarcity of fossil energy reserves, especially oil, natural gas and coal, leads to a significant increase in their value. This requires the implementation of advanced up to dated technologies aimed at reducing energy consumption to ensure the affordable thermal regime of buildings [3].
The authors of the study [4] have confirmed that increasing the energy efficiency of buildings is impossible without improving the thermal insulation capacity of envelopes. The authors propose a method of modelling the mechanism of energy-saving management in substantiating the choice of ecological and economic feasibility of materials for thermal modernization of the thermal insulation of buildings.
The materials are recommended for the installation of thermal insulation shell by the Ukrainian Code of thermal insulation [5], do not fully justify the decision-making in the design and technological implementation of multilayered opaque structures from presented in Code thermal insulation materials of organic origin, for instance as [6, 7, 8, 9, 10]. This is also confirmed by studies presented in [11, 12, 13].
In paper [14] the mathematical apparatus of probability theory was used to determine the variability probability of thermophysical parameters of enclosing structures. The variability of physic-mechanical characteristics of building materials in general [15], [16] and materials of natural origin in particular [8] presupposes the use of a probabilistic approach to determine their main thermal performance parameters. That is why in the paper [14] it is proposed to operate with such a concept as reliability. The authors of [14] proposed criterion of “thermal failure”. This criterion is numerically equal to the probability of moisture condensation on the inner surfaces of enclosing structures in the room, with a decrease in local temperatures of the inner surfaces of the insulating shell to the temperature of steam [14].
In the researches [11, 12, 17, 18], the methodological basis for ensuring energy efficiency of buildings and thermal reliability in terms of heat-accumulating ability [19, 20] of enclosing structures. A methodology for analyzing the energy efficiency of buildings taking into account the level of thermal comfort in the premises is also proposed.
The conducted analysis of literature sources [22], [23] has shown that major reasons for the insignificant use of straw products as cheap value, natural and ecologically friendly by-product material, particularly in Ukraine, are the lack of practical experience in assessment of its real thermal performance characteristic, bias to the material in guaranteeing of the comfortable living conditions, etc.
There is also no methodology in Ukrainian Building Codes for assessment of their energy efficiency, during the erecting of the thermal insulation shell. All of the abovementioned encouraged the authors to dedicate the present research to the developing of a mathematical model for assessing the reliability of energy efficiency of thermal insulation construction products made of straw using a fuzzy knowledge base.
To do this, the authors propose to solve the following problems:
Construction of a hierarchical classification of quantitative and qualitative factors influencing the reliability of energy efficiency of thermal insulation building materials from straw using an expert fuzzy knowledge base.
Development of a mathematical model for complex assessment of the reliability of thermal insulation building materials made of straw, based on linguistic variables by fuzzy rules and fuzzy logical operations.
In assessing the reliability the concept of the structural-probabilistic model was used [24]. This model requires a huge amount of statistical samples and reliable data about the distribution law of reliability indicators. To analyze the types, consequences and intensity of failures as an indicator of reliability the following methods could be applied [24, 25, 26]:
– uniform distribution of reliability;
– weights;
– indefinite Lagrange multipliers;
– matrix method of reliability calculation;
– Delphi method;
– method of statistical modelling, etc.
The reliability assessment method’s selection is based on the following criteria: the object life cycle, the failure criteria, etc.
The reliability of the efficiency ensuring of the thermal insulation construction products can be determined by the probability of their complex parameters failure-free during the life cycle of the building by the formula [25]
where
Evaluation of the objective function – the reliability of energy efficiency of thermal insulation construction products from straw using equation (1) requires a significant database of experimental data. Besides, the objective function contains both quantitative and qualitative factors. One of the mathematical devices that allow operating with such data is the device of fuzzy logic [27].
According to this mathematical apparatus, the fuzzy set by which the term
where (
The logical conclusion between cause and effect is described by a system of fuzzy logical statements, respectively:
For the MIN operation
For the MAX operation
Fuzzy logical operations
The rule of distribution of belonging degrees according to the normalization (μ1 + μ2 +…
where
The degree of membership
By the known line elements of the matrix (8), elements of all other lines are calculated. The arbitrary element a
In this matrix (8), in each cell, expert assessments of the benefits of one of the factors of influence over the other have been evaluated by means of a 9-point Saati scale [28].
In the research [29] the hierarchical classification of quantitative as well as qualitative influence factors which characterizes the reliability of efficiency of heat-insulating building products from a straw for envelope multilayered designs has been proposed.
Taking into account the results of research [29], Fig. 1 presents a structural model of hierarchical relationships in the form of a logical inference tree for linguistic variables that describe, thermo-physical, physic-mechanical and durability indicators as factors of influence respectively.
The root of the logical inference tree corresponds to the value of the objective function – the assessment of the reliability of energy efficiency of thermal insulation products made of straw, and hanging tops – quantitative and qualitative thermo-physical, physicmechanical parameters as well durability indicators as linguistic variables, respectively.
According to the principle of linguistic variables, the causal relationships between the influencing factors of the model are described using fuzzy terms [4], [27]. The qualitative fuzzy term as a linguistic variable is defined by a word that characterizes the quantitative expressions “Low” (L), “Below average” (BA), “Average” (A), “Above average” (AA) and “High” (H). Proposed fuzzy terms create expert fuzzy knowledge bases that characterize the relationships between input and output variables.
Reliability of efficiency of heat-insulating building products from a straw for envelope designs according to researches [29] and the inference tree (Fig. 1) as linguistic variable
where
The meaningful interpretation of the factors influencing the reliability of ensuring the energy efficiency of heat-insulating construction products made of straw and the corresponding set of linguistic evaluations is described by relations (10), (11), (12).
A linguistic variable describing the thermo-physical factors influencing the reliability of the energy efficiency of heat-insulating construction products made of straw can be represented by the ratio
where
T(
where
The dimensionless indicator of thermal inertia
A linguistic variable describing the physic-mechanical factors influencing the reliability of the efficiency of the heat-insulating building materials from a straw can be represented by the ratio (12)
where
The linguistic variable that describes the durability indicators as factors influencing the reliability of the energy efficiency of heat-insulating materials made of straw can be represented by the equation (13)
where
The knowledge matrix for the approximation of dependence (9) using fuzzy rules of type “IF-THEN” by taking into account the accepted gradations of terms is given in Table 1.
Fuzzy knowledge matrix for equation (9)
IF | THEN | ||
---|---|---|---|
L | L | L | L |
L | L | BA | |
L | BA | L | |
BA | L | L | |
L | BA | BA | BA |
BA | L | BA | |
BA | BA | L | |
BA | BA | BA | |
A | A | A | A |
BA | A | A | |
A | BA | A | |
A | A | BA | |
AA | AA | AA | AA |
AA | AA | A | |
AA | A | AA | |
A | AA | AA | |
AA | H | H | H |
H | H | H | |
H | AA | H | |
H | H | AA |
Linguistic expressions, given in the knowledge matrix for the approximation of the dependence (9) in Table 1 corresponds to the system of the fuzzy logic equations, which characterize the membership surface of the linguistic variable, which is objective function – the reliability of ensuring the energy efficiency of heat-insulating construction products made of straw by the corresponding qualitative term (formulae 14–18):
According to the mathematical apparatus of fuzzy logic [27], the influence of quantitative and qualitative factors on the objective function is taken into account by the membership function.
The membership function is a set of values of μ (μ
In this paper, the algorithm of the membership function’s calculation is explained in the example of the influence factor
The linguistic evaluation used the term set
According to the matrix (19), the calculation of the individual memberships
According to the abovementioned method of finding the membership degree to the term “Low”, matrices of pairwise comparisons for the terms “Below the Average”, “Average”, “Above the average” and “High” and the individual membership degrees are calculated respectively.
To facilitate the comparison of all membership degrees, their normalization by dividing to the maximum value is performed as shown below in formula (20)
Thus, the normalized values of the terms “Low”, “Below the Average”, “Average”, “Above the Average” and “High” calculated by formulas (18), (19) for the linguistic variable “density” are given below. The numerator shows the normalized values of membership functions
Graphic representation of membership functions for linguistic variable
The considered technique allows constructing graphic dependences for the other factors of influence resulting in the inference tree (see Fig. 1). Graphical interpretation of the obtained dependences will allow estimating the influence of each factor – thermophysical, physic-mechanical and durability parameters.
From Fig. 2, it can be considered, that obtained membership functions for the linguistic variables “Density”, are only the first step in an approximation of an objective function. Further researches should be conducted and they could be dedicated to fine-tuning this previous model data, with that, obtained from the results of the real field research and further analysis.
It is obvious, that proposed hierarchical model of the inference tree (see Fig. 1) for the objective function could be widened and supplemented by other, significant influence factors. Due to the lack of real, field data, the determination of the reliability ensuring the energy efficiency of heat-insulating materials made of straw is still an ambiguous challenge.
In the authors’ opinion, the more real data could be collected, the more objective and comprehensive will be an assessment of the energy efficiency reliability ensuring in the terms of abovementioned influence factors.
With the aid of apparatus of the fuzzy logic and linguistic variables, a hierarchical model in the form of a logical inference tree is proposed, which contains the main quantitative and qualitative factors influencing the objective function – reliability of energy efficiency of heat-insulating building materials made of straw.
The calculation of the parameters of the mathematical model for evaluating the reliability of ensuring the energy efficiency of heat-insulating building materials made of straw on the example of the linguistic variable “Density” is conducted. Numerical values of its fuzzy set with a graphic interpretation of results are calculated. Further researches in this field should be conducted and could be dedicated to a real assessment of the reliability and fine-tuning of this previous model data, with that, obtained from the results of the real field research.
According to the authors’ opinion, the proposed fuzzy-probabilistic approach can be used as an additional tool in Building Energy Modeling (BEM) as well in the decision-making process to estimate the construction and operation cost of buildings.
This will allow evaluating, and, if necessary, increasing the reliability of energy efficiency of multilayered thermal insulation envelope structures of any type of materials, including straw.