Optimal Design and Modeling of Sustainable Buildings Based on Multivariate Fuzzy Logic

Recently, the concept of green buildings approach has gained massive evolution on account of the beneficial impacts posed by these sustainable structures. A green building is one that is optimally designed with minimal operational cost and exploitation of energy harvesting techniques to derive the large-scale ambient energy from the natural environment. The significant advantages offered by this sustainable development perception modeling include energy conservation, lower water consumption, recycling of construction materials, waste minimization, preservation of natural resources, etc. The sustainable construction and maintenance of buildings is aimed at meeting the needs of the present without compromising the potential of future generations.

Environment conducive construction and operation practices are typically deployed in the design of the green performance-efficient buildings. Moreover, from the perspective of user communities residing in these buildings, user satisfaction issues regarding the health and comfort of residents is also a consequential concern. Economical green system design techniques have currently drawn considerable attention to address the key challenges for the sustainable development of green buildings. Nevertheless, with global rising awareness for the climate change due to emission of harmful greenhouse gases from conventional energy sources, the presented energy harvesting system using the naturally replenished ambient energy as green sustainable energy sources is appealing as a relatively novel and promising solution. The green buildings framework aims to achieve the energy-proficient solutions for globally efficient systems from the environmental impacts and the quality-of-experience (QoE) prospectives of end-users. The recent emphasis is on green systems design and management to contribute significantly to reducing the global warming effects by minimizing the demand on non-renewable resources.

The proposed ecologically-feasible model relies on environmental friendly techniques to generate energy from the renewable resources that do not cause carbon dioxide emissions, e.g., solar cells, wind turbines, electromagnetic waves, thermal energy, etc. This can subsequently alleviate the energy costs and potentially hazardous effects of harmful gas emissions caused on the environment. In addition, the energy should be accumulated in such a way that the stored energy can be effectively used under the conditions that there is always energy available when needed. The green setup paradigm for the sustainable development of effectively automated smart buildings can essentially facilitate mitigation of the greenhouse effect and reduced operational expenditure. The optimized sustainable building architecture pertaining to energy limitations and environmental considerations is aimed at minimizing the global warming impact by reducing the radiations caused by greenhouse gas emissions. These gases usually generated in various industrial applications can be potentially mitigated through the ascending dependence on renewable energy sources as the emerging green sources of clean energy.

Multi-dimensional decision-making framework pursued with the flexible fuzzy logic concept has recently attracted considerable research interest. Green building practices among the traditional construction procedures are implemented predicated on the global rising concerns of climate change and resource limitations in energy sectors, in addition to the improved quality of life requirements. In this work, we consider multiple factors affecting the sustainable development of green building design through the implementation of fuzzy logic technique. These imprecise and uncertain characteristics influencing the robust and persistent building structure can be optimally modeled by multi-attribute decision-making scheme based on fuzzy logic. Different input attributes contemplated in the proposed fuzzy-based sustainable building model comprise of (1) the on-site renewable energy consumption, (2) indoor environmental air quality, (3) water conservation, (4) services accessibility with public facilities, (5) reused material content employed in construction practices, and (6) greenhouse gas emissions. Moreover, the performance of these buildings is assessed through various heterogeneous criteria that serve as different fuzzy outputs. These performance parameters incorporate the energy efficiency, user satisfaction, resources optimization and environment quality factors associated with the adaptive design of sustainable infrastructure.

1.1 Related work

In this section, a literature review has been conducted specifying the relevant studies in the area of sustainable design architecture of performance-oriented green buildings. A multi-objective building design model is developed by Yao [1] for prospective sustainable construction and global economic growth. This model is aimed at the prediction of the operation period with improved energy efficiency and environmental performance, without consideration of the recycled material content and users’ perspective criteria. Ahn et al. [2] formulated an integrated construction process to facilitate cooperation among decision-makers and stakeholders for developing resilient buildings at the early stages of sustained configuration. Abualrejal et al. [3] introduced the awareness about green building methods dealing with the energy efficiency issues. This paper employed the inductive and qualitative analysis technique to retrieve the constructive sustainability and material conservation criteria. It focused on the optimal performance of energy, without taking into account the resource efficiency and environmental protection issues. Ho and So [4] developed a self-sustainable city model for resource management and household waste reduction. This structural model applied various environment constructs for analyzing the adjusted R-squared and t-values of community based culture-constrained attributes. Singh [5] investigated the impact of various materials on the design and development of sustainable buildings which cause reduced environmental degradation and concurrently with the lower operating costs. Recycling and reuse principles are adopted together with the selection of natural green resources for achieving optimal green building objectives. Blanco et al. [6] evaluated the performance of green buildings envelope through the multiple linear regression technique. It aimed at alleviating the external surface temperature and enhancing the energy proficiency of buildings to realize environment sustainability by validation over the experimental data. The green rating systems are studied by Oberti and Plantamura [7] to account for the development of naturally feasible environment. The most effective indoor and outdoor elements are considered in the proposed mechanism in an effort to design energy conserving sustainable sites with the occupants’ well-being as the primary concern. However, compared with our approach, this work [7] did not consider the recyclability and efficient water consumption techniques for enhanced sustainable performance of green building design. Patnaik et al. [8] assessed the significance of indoor environment quality factor in the design of green buildings. The impact of this parameter is computed by measuring the prevailing degrees of user satisfaction, climate profile and emissions of volatile organic compounds from the conventional building materials. As opposed to this, we effectuate the energy conservation, resource management, and client satisfaction objectives, along with the improved environment characteristics through the multiple-input multiple-output (MIMO) fuzzy design. Li et al. [9] employed the isolated forest algorithm and average value interpolation techniques to achieve the energy preservation goal in green building operations.

Recently, an extensive review of information and communications technology architecture to effectuate the concept of green buildings in existing construction enterprises is performed by Martins et al. [10]. This framework considered the emphasis of environmental stability and user-centered convenience for accomplishing the sustainable operation of various design applications. Bhatt et al. [11] employed several natural phenomena of rainwater harvesting, solar energy generation, standard illumination, etc. to facilitate the development of energy- and cost-effective buildings. Singh et al. [12] introduced the GRIHA rating system for assessing the green building schemes and administering the future sustainable construction. Various aspects of acquiring sustainability are examined with their associated rating points in this employed strategy, while mutually providing incentives for the economical growth. Borissova [13] presented combinatorial optimization model for determining the green building principles based on utility function associated with the experts’ knowledge. In this model, multiple criteria affecting the modern building projects weighted by appropriate coefficients are contemplated to retrieve the aggregate group decision estimations. Rajagopal and Karuppiah [14] employed numerical analysis technique of response surface methodology for utilization of recycled waste materials in manufacturing industry. The proposed framework evaluated cost-effective and sustainable development of built up infrastructure projects with improved environment quality. Petrova et al. [15] employed data mining and semantic modeling techniques for predicting the performance of sustainable building design. This is accomplished by retrieving patterns in the large volumes of existing data utilized by the building architects. Relationship analysis among various parameters influencing the adoption of green building conventions is performed by Saleh et al. [16]. For this, they used the partial least squares approach to structural equation modeling for synchronic estimation of multiple decision variables. Contrary to these recently proposed sustainable building models existing in literature, we employ the artificial intelligence strategy of fuzzy problem-solving reasoning algorithm for the adaptive setting and assessment of multiple attributes effecting the planning, operation and maintenance of sustainable building architectures.

1.2 Contribution

Despite the aforementioned previous works, in this paper, we have proposed a novel fuzzy logic-based sustainable building model which examines the uncertain impact of different parameters affecting the intelligent development of green buildings. To the best of the author’s knowledge, no prior work has applied the computationally intelligent fuzzy reasoning methodology for implementation of the sustainable building planning and operation. In this paper, we have scrutinized multiple performance indicators for attaining optimal design and construction practices of green buildings including the energy efficiency, user satisfaction, resources optimization, and environment quality. These diverse attributes typically possess disparate range of values and varying units. Therefore, the fuzzy logic system evidently appears as the potential and effective method for retrieving the multidimensional system optimization. In contrast, the earlier works have employed only one or two of these objectives for the design optimization of sustainable building. The performance of the proposed model is captured from a multidimensional scope using the fuzzy control approach. Measuring the feasibility performance of sustainable building design from the perspective of adaptive fuzzy control system which models different attributes associated with the resource efficiency and environment quality is a scarce methodology on literature review. Because of the imprecise and ambiguous data coupled with the optimal design and operation of green buildings, fuzzy reasoning mechanism apparently constitutes a convenient tool for the initial design stages of sustainable and smart buildings. The advantages of the deployed MIMO fuzzy system is the coherent and analytical modeling of the developed sustainable structure, contemplating various dimensions influencing the performance of green building design. Moreover, it facilitates the decision-making implementation that emulates the human reasoning paradigm. This multivariable Mamdani-type fuzzy logic controller determines the set of optimal output parameters assessing the performance analysis of autonomous sustainable development. The nonlinear MIMO fuzzy control process operates in a self-organizing decentralized way for exploiting the fuzzy rule base and making corresponding inferences.

The developed system model employing fuzzy decision-making with multiple attributes is based on two key steps. The first step is the identification of multiple qualitative parameters for evaluating the sustainability performance of environmentally optimal buildings. In this step, the notion of expert knowledge is utilized to capture the implicit uncertainties of various attributes that facilitates the decision-making phenomenon via the fuzzy logic concept. The key attributes influencing the efficient layout and deployment of such environment conducive buildings including renewable energy consumption, indoor air quality factor, water conservation, services accessibility, recycled material, and greenhouse gas emissions are contemplated as the input variables to the formulated fuzzy inference methodology. The presented fuzzy design model combines these heterogeneous parameters by employing the membership functions and fuzzification interfaces. In the second step, the fuzzy inference system captures the expert knowledge through the prespecified fuzzy rules database. The simultaneous impact of multiple decision criteria incorporated in the fuzzy logic controller is considered for assessment of the feasibility performance factor. The developed fuzzy inference system with several input criteria is implemented using Fuzzy Logic Toolbox in Matlab simulation tool. Besides, we evaluate the validation performance of the proposed model by estimating the system error measurements including mean absolute error and logarithmic quotient error for assessing the viability prediction of various output parameters for a particular sample dataset.

1.3 Organization of the paper

The remainder of this paper is organized as follows. In section 2, we introduce some elementary knowledge of the fuzzy logic concept. The proposed fuzzy logic-based sustainable buildings model is discussed in section 3. In section 4, we provide the detailed simulation analysis and the model validation results for the developed fuzzy system. Finally, the whole work is concluded in section 5, with practicable future research directions.

The basic architecture of the proposed fuzzy model for sustainable buildings design is demonstrated in Figure 1. This structured framework with heuristic fuzzy computing employs six input and four output attributes relevant to the optimal formulation of the green sustainable buildings. The first input of renewable energy consumption is focused on the utilization of renewable energy sources such as wind power generation, solar photovoltaic system, geothermal power, etc. to accomplish the sustainable development of buildings. Healthful interior environment of building standards associated with the occupants’ comfort, hygiene, and minimal exposure to the pollutants is ensured by the second attribute of indoor air quality metric. With the increasing global demand for water, water use mitigation and rain water harvesting through water conservation technologies is apprehended as the third input to the presented fuzzy design model. Delivering services with the upgraded facilities to meet the ever changing provisions of clients is concretized through the fourth input parameter of services accessibility. The fifth input characterizes the incorporation of the recycled and alternative material content for the design and construction of green eco-friendly building architectures. In addition, combating the greenhouse gas emissions through the sustainable building development and operation implementations is the auxiliary setup goal. Furthermore, the fundamental performance indicators of energy efficiency, user satisfaction, resources optimization and environment quality correlated with the lifecycle and maintenance of sustainable buildings are envisaged as the four outputs of the fuzzy inference system. The considerable significance of these distinctive input and output attributes is contemplated by employing the MIMO fuzzy control discipline. The relationship between the multiple diverse input and output variables is illustrated in Table 1. For instance, the fuzzy output energy efficiency is determined by the input attributes of renewable energy consumption and recycled material content. Each of these inputs are characterized by the Low, Average and High fuzzy linguistic terms. Thus, the energy efficiency output requires a total of (3²)=9 fuzzy rules. The second fuzzy output of user satisfaction is specified using the fuzzy input variables of indoor air quality, services accessibility, recycled material and greenhouse gas emissions identified with 2,2,3 and 2 linguistic variables. This contributes to 24 fuzzy rules. Likewise, the third fuzzy output resources optimization depends on the input variables of renewable energy consumption, water conservation and recycled material content, comprehensively requiring (3³)=27 fuzzy rules. The fourth output variable of environment quality factor determined by the input parameters of renewable energy consumption, indoor air quality, recycled material, and greenhouse gas emissions, is designated by (3*2*3*2)=36 fuzzy rules. The commonly applied triangular, trapezoidal, Gaussian, Gaussian combination and generalized bell-shaped membership functions are utilized to represent these various fuzzy inputs and outputs as illustrated in Figures 2 and 3. Here, the x-axis represents the designated range of the specific input/output dimension, and the y-axis denotes the corresponding degree of membership for that particular variable. Table 2 lists the different linguistic terms corresponding to the fuzzy inputs and outputs, together with their implemented membership functions and the associated fuzzy numbers. Mathematically, these characteristic functions are illustrated in the generalized Eqns. (1)-(4). Here, ω is the vector of numerical input values that are evaluated using the specific membership function. Triangular and trapezoidal fuzzy sets identified by linear membership functions and non-smooth crossover points are defined using three and four parameters, respectively. Also, the non-linear generalized bell-shaped membership function defined in Eq. (3) is described in terms of the width , the center , and the parameter  regulating the slope of the membership curve. Similarly, the non-linear Gaussian (or Gaussian combination) membership function outlined in Eq. (4) is specified in terms of the center , and the width  of the membership curve. For both the generic bell-shaped and Gaussian membership functions, these various parameters determine the smoothness of the non-linear function around the transitions. Accordingly, the fuzzy rule base in our proposed optimization model comprises of the overall  inference rules as demonstrated in Table 3.

$f\left(\omega ; x_{1}, x_{2}, x_{3}\right)$

$=\left\{\begin{array}{cc}0 & \omega \leq x_{1} \\ \left(\omega-x_{1}\right) /\left(x_{2}-x_{1}\right) & x_{1} \leq \omega \leq x_{2} \\ \left(x_{3}-\omega\right) /\left(x_{3}-x_{2}\right) & x_{2} \leq \omega \leq x_{3} \\ 0 & x_{3} \leq \omega\end{array}\right\}$       (1)

$f\left(\omega ; x_{1}, x_{2}, x_{3}, x_{4}\right)=\left\{\begin{array}{lr}0 & \quad \omega \leq x_{1} \\ \left(\omega-x_{1}\right) /\left(x_{2}-x_{1}\right) & x_{1} \leq \omega \leq x_{2} \\ 1 & x_{2} \leq \omega \leq x_{3} \\ \left(x_{4}-\omega\right) /\left(x_{4}-x_{3}\right) & x_{3} \leq \omega \leq x_{4} \\ 0 & x_{4} \leq \omega\end{array}\right\}$       (2)

$f\left(\omega ; x_{1}, x_{2}, x_{3}\right)=\frac{1}{1+\left|\frac{\omega-x_{3}}{x_{1}}\right|^{2 x_{2}}}$      (3)

$f\left(\omega ; x_{1}, x_{2}\right)=e^{\frac{-\left(\omega-x_{1}\right)^{2}}{2 x_{2}^{2}}}$      (4)

1.png

Figure 1. Basic structure of the proposed fuzzy based sustainable buildings model

Table 1. Relationship between input and output variables

Output Variable	Input Variable
Energy Efficiency	Renewable Energy Consumption, Recycled Material
User Satisfaction	Indoor Air Quality Factor, Services Accessibility, Recycled Material, Greenhouse Gas Emissions
Resources Optimization	Renewable Energy Consumption, Water Conservation, Recycled Material
Environment Quality	Renewable Energy Consumption, Indoor Air Quality Factor, Recycled Material, Greenhouse Gas Emissions

Furthermore, our model uses the widely employed center of gravity or centroid method of defuzzification, in which the defuzzified value  is calculated as follows:

$\Psi=\frac{\int_{\Psi \min }^{\Psi \max } f(\Psi) * \Psi d \Psi}{\int_{\Psi \min }^{\Psi \max } f(\Psi) d \Psi}$      (5)

This defuzzified value is the abscissa of the center of gravity of the fuzzy set  defined over the universe of discourse  of the output variables. Here, the denominator  denotes the area of the region bounded by the membership curve over the interval The fuzzy inference method deployed in this analysis paradigm is the Mamdani method. This inference technique involves decision-making with respect to input categorization and concurrent intelligent computing. In the Mamdani inference system, the output variables are represented by fuzzy sets, which subsequently require defuzzification to convert these fuzzy output variables back into the space of corresponding crisp output variables.

Table 2. Fuzzy linguistic terms and their corresponding membership functions and fuzzy numbers for different input and output variables

Variable	Linguistic Term	Membership Function	Fuzzy Numbers
	Low	Trapezoidal	[-18.12 -5.856 6.111 18.12]
Renewable Energy	Average	Gaussian Combination	[7.2 27.6 8.154 28.2]
Consumption	High	Trapezoidal	[38.4 54.05 62.4 81.6]
Indoor Air Quality	Low	Generalized bell-shaped	[0.2 2.5 0.06614]
Factor	High	Generalized bell-shaped	[0.2 2.5 0.9074]
Water	Low	Trapezoidal	[-36 -4 4 36]
Conservation	Average	Triangular	[20 50 80.03]
	High	Trapezoidal	[64 96 104 136]
Services Accessibility	Low	Trapezoidal	[-0.36 -0.04 0.2 0.4987]
	High	Trapezoidal	[0.5 0.8 1.04 1.36]
	Low	Triangular	[-40 0 40]
Recycled	Average	Trapezoidal	[20 46 54 80.03]
Material	High	Triangular	[60 100 140]
Greenhouse Gas	Low	Gaussian Combination	[1.11e+04 -6117 1.11e+04 1.056e+04]
Emissions	High	Gaussian Combination	[9510 6.442e+04 9510 7.002e+04]
Energy	Low	Trapezoidal	[-36 -4 4 36]
Efficiency	Medium	Gaussian	[13.99 50]
(Output)	High	Trapezoidal	[64 96 104 136]
User	Low	Triangular	[-40 0 40]
Satisfaction	Medium	Trapezoidal	[14 46 54 86]
(Output)	High	Triangular	[60 100 140]
	Low	Generalized bell-shaped	[0.2 2.5 6.939e-18]
Resources	Medium	Gaussian	[0.13 0.5]
Optimization (Output)	High	Generalized bell-shaped	[0.2 2.5 1]
Environment	Low	Triangular	[-0.4 0 0.4]
Quality	Medium	Triangular	[0.1 0.5 0.9]
(Output)	High	Triangular	[0.6 1 1.4]

Table 3. Fuzzy inference rules for the proposed fuzzy based sustainable building model

2.png

Figure 2. Fuzzy input membership functions

3.png

Figure 3. Fuzzy output membership functions