1 Introduction

Embodied energy is the energy consumed by all of the processes associated with the production of a building, from the mining and processing of natural resources to manufacturing, transport and product delivery [1,2,3,4,5,6,7,8,9,10,11,12]. Analysis across Australia and elsewhere found that the building’s energy is a large part of the annual intake of working energy [13]. It ranges from 10 average homes to more than 30 offices (CSIROFootnote 1 2000). Increasing the energy efficiency in buildings such as houses typically entails more energy and more ratio. However, experience in the trade sector has shown that the effect of energy on the overall building footprint is increasing as energy efficiency in buildings increases because of the ratios between energy and total energy usage [14,15,16,17]. CSIRO analysis indicates that building requires an average of about 1000 GJ of energy incorporated in building materials, which corresponds to the normal use of operating resources for around 15 years [18]. This is more than 10% of the electricity used in a house that lasts 100 years. The use of energy figures in construction should be careful. It is also possible to recycle certain products and to reduce the effects during their life cycle, e.g. aluminium from a recycled source contains less than 100% of the energy of the aluminium produced from raw materials [18,19,20,21,22,23,24]. In Canada for example, only non-renewables in embodied energy sources were considered. Thus, it can be shown that many considerations must be weighed when evaluating potential areas in which commercial buildings can reduce their energy levels by retrofitting [13]. Researchers were interested in the interactions between building materials, construction practices, also their environmental effects have researched energy in building materials. Figure 1 shows the effective use of cork as a light weight material during a concrete mixed processing.

Fig. 1
figure 1

Using cork in construction materials mixed with concrete to reduce the weight and cost of materials

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For many decades, low-energy materials, such as concrete, bricks or wood are highly used, however, materials with more energy level, such as stainless steel are rarely used [25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]. Around 2003 and 2030, global energy consumption is predicted to increase to 71%. At the moment, great energy use is dependent on fossil fuels and it is unclear if such a demand trend will be followed environmentally sustainable considering significant developments in renewable energy technologies. Therefore, it is recommended that only the order-of-magnitude enhancements to energy quality should be achieved, particularly as the ratio of resources delivered to energy consumed to prevent a dramatic decrease in agreed living standards [40,41,42,43,44,45,46]. Energy is one of the main drivers in all countries for economic growth and social development [47] as the increasing reason of CO2 energy emissions in past 20 years [40, 48, 49]. Construction projects account for 38% of the world’s overall energy usage [50]. More responsibility for the pollution issue needs to be taken by the construction sector. Energy is used at various levels in each phase of the construction life cycle. Because of its environmental positive elements, energy-efficient materials will sustain constructions both economically and ecologically. In comparison, energy-reducing products cause less harmful emissions, also the waste from building materials is being decreased. They also contribute to the development of comfort in indoors due to their different thermal features, such as heat conservation and heat retention [51]. Finally, it is because of these considerations that choosing of the best material at the outset of design process must take account of energy-efficient properties along with several requirements for the environmental features. As the population and urbanization rise, energy demand is growing rapidly.

Depending on the environment, the form and degree of construction energy differ from region to region [52]. Construction consumes 38% of the world's energy annually [50]. The energy usage of buildings and their potential detrimental effects on the atmosphere are becoming extremely severe. Several new studies have sought to classify energy efficiency, environmental impacts of housing and construction materials. The use of overall energy for the given sample room was explored by [40, 53]. The paper focuses on comparing two structures of bricks made from fire clay and structures made from ash blocks. While ash blocks are three times more expensive than flames, their scale, total use of electricity, and their ultimately total construction costs (due to their light weight and isolation) have been considerably reduced [54]. The embodied energy of various construction materials was studied (conventional building materials and alternative building materials). These researches involved the efficiency of few operating energy materials. In comparison to traditional construction materials, it is seen that alternative building materials and systems have minimized and/or equivalent impacts on life cycle costs [55,56,57,58,59,60]. Furthermore, stability and instability analysis of the composite, conceit, and smart material and structures take the attentions of researchers in different filed of engendering [61,62,63,64,65].

In recent years, in addition to the experimental and numerical techniques, artificial intelligence (AI) algorithms have been developed and employed in various fields, especially civil engineering [66,67,68,69,70]. In fact, AI is able to accurately optimize and predict the experimental data. Researchers have developed several sub-sets of AI algorithms such as ANFIS, PSO, machine learning, and hybrid algorithms-like PSO-ELM, ANFIS-PSO [71,72,73,74,75]. The advantages of AI models compared to experimental methods are high accuracy and cost-effectiveness. Also, they require lower time to process the data than other numerical approaches [76,77,78,79,80] (Figs. 2 and 3).

Fig. 2
figure 2

Frame of light-weight construction processing by the integration of cork and wood

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Fig. 3
figure 3

Using cork palates in a building to reduce the energy losing and noise

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2 The related literature

Regarding the energy efficiency of building materials, energy needs to be used less quickly in each step of the life cycle, particularly in the overall energy use of construction process and the proportion of energy utilized for the production and transport of building materials [81,82,83,84]. Therefore, in all phases, the preferential of building materials, by the production, transportation, use and destruction of their raw material offers energy efficiency to construction [36, 40, 51, 85,86,87,88,89]. The selection of a building material can influence the energy usage of that building over the various phases of its life cycle and can have opposite consequences. Given that properties like a high level of insulation can provide relative efficiency savings in operating energy along with greater embodied energy costs. The balance of the exterior building system and envelope (roof, board, walls and windows) seems to represent the highest part of its energy [50]. In the case of building materials, the proportion of energy consumed to its overall energy consumption is calculated at 50 years, but ranges from 6 to 20% according to the method and environment of construction [90, 91]. Energy performance requirements for building materials can be categorized in two categories: directly and indirectly effective criteria [92, 93].

The US building industry uses more than 48% annual electricity in construction and service, which contributes to substantial emissions of carbon dioxide into the air. This electricity is often incorporated and working energy is used over the life span of a structure [94] Building uses operating energy in hot water supply, lighting, space conditioning and powering building appliances. Studies have proposed using a systemically based approach to a life cycle energy assessment in a building to significantly minimize this carbon footprint and extensive energy [95]. A systematic energy evaluation is used for the use of energy, as well as for the use, regeneration, and reuse of energy by means of green energy technologies and recycler efforts. The main focus of research activities has been on operational energy optimization with new innovative building envelope and machinery materials [96,97,98,99,100,101]. Then, the electricity in building is increased because much of this specialized products or machinery are made by energy-intensive manufacturing methods [83, 102,103,104,105,106]. In a building, the energy is used directly through construction by the use of construction materials. The construction, manufacturing, logistics, administration, and related processes include a number of on-site and off-site energy sources. Furthermore, any building material includes energy during its production and distribution. The overall energy of a building during its life cycle consists of initial (IEE), recurrent (REE) and demolition embodied energy (DEE) [107, 108]. IEA involves both resources used directly and indirectly (e.g. during transport and construction) to build a construction. The completeness of an energy measurement is based on the system boundary covered. There are few methods for measuring the embodied energy, such as IO-based, process-based and hybrid methods. Each process uses various data source types and covers differing systems boundary dimensions [109,110,111,112,113]. The findings are not identical because of these variations. In addition, any process has data quality and device integrity limitations. For example, a process-based approach uses real data from manufacturers' sources, which are known to be robust in their reliability and representation [109, 114, 115]. This approach has insufficient findings, because it lacks inputs from which data cannot be available [102, 116,117,118,119] (Figs. 4 and 5).

Fig. 4
figure 4

Using the tree trunk in a processing of concrete mixed materials for energy, lightweight and cost issues

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Fig. 5
figure 5

Construction of building based on the tree trunk and cork

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2.1 Embodied energy calculation: energy and cost relationship

Studies have shown that despite efforts at defining a standard system boundary and deriving an appropriate method of calculating embodied energy, they are reliable, consistent, and consistent. Few materials are used in construction materials to reduce the cost and energy losing, say cork, trunk of tree, coffee husks, newspaper woods, mycelium, recycled diapers, plastic bricks, polyurethane plant based foam fly ash, silica fume and etc. On the other hand, an energy analysis is costly and time-consuming and is dependent on many assumptions [114]. Furthermore, energy research is not well incorporated into the existing design and building practices, so decisions are mostly taken only on the basis of cost. Studies have found a relationship between consumption of embodied energy and cost. Stern and Cleveland [120] agreed that economic growth means a proportional growth in energy usages. Also, at the project stage, Langston et al. [121] found a clear and optimistic connection between the costs and the energy in a house [122] (Fig. 6).

Fig. 6
figure 6

The strength diagram of concrete while adding light-weight aggregates

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Some researchers investigated the connection of energy consumption and cost optimization in a study of three low-rise apartments in Indonesia. Since the buildings consisted of hollow blocks in the interior and outside walls, two other light-weight concrete and brick walls alternatives were also studied (Table 1).

Table 1 Concrete mix proportions of silica fume and fly ash as light aggregates to concrete
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2.2 Problem statement

Due to lack of total, precise, and detailed energy data, the measurement of energy is complicated, then this study employed PSO to accurately calculate the strength, energy and cost optimization of building materials [123,124,125,126,127,128,129,130,131,132]. The aim of this paper is to accurately predict the cost and energy reduction in using alternative wall material for construction, through detailed analysis in a residential building [4, 133,134,135,136,137,138,139,140,141] (Figs.7, 8 and 9).

Fig. 7
figure 7

The installing of wooden construction parts for a building built from cork and wood

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Fig. 8
figure 8

The strength content of concrete while adding light-weight aggregates as cork and wood

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Fig. 9
figure 9

Molding the mixture of fly ash and cement

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3 Methodology

3.1 Statistical data

150 data were originally extracted. The current study has investigated the strength, energy and cost optimization of materials in construction building using PSO. The model was developed and the results were analyzed by regression indicators.

3.2 Particle Swarm Optimization (PSO)

PSO as an optimization algorithm is determined in six phases [142,143,144,145,146,147,148]:

  1. 1.

    A group of random potential resolution is determined as the searching space. It is assumed that \(N\) is the number of particles and \(D\) is the dimensions of searching space. Both are used as the random “position” (\({X}_{i}^{k})\) and “velocity” \((v{i}^{k})\) of \(i\mathrm{th}\) particle at iteration k as Eqs. (1) and (2).

    $$\begin{aligned} v_{i}^{k} \left( {t + 1} \right) & = wv_{i }^{k} \left( t \right) + C_{1} \cdot {\text{rand()}}\left( {p_{i}^{k} \left( t \right) - X_{i}^{k} \left( t \right)} \right) \\ & \quad + C_{2} \cdot {\text{rand()}} \left( {g _{i}^{k} \left( t \right) - x_{i}^{K} \left( t \right)} \right), \\ \end{aligned}$$
    (1)
    $$x_{i}^{K} \left( {t + 1} \right) = x_{i}^{K} \left( t \right) + v_{i}^{k} \left( {t + 1} \right) 1 \le i \le N,\quad 1 \le k \le D,$$
    (2)

    w is the iteration weight; rand ()” is a constant value in 0, 1 interval while set randomly; \({C}_{1}\) and \({C}_{2}\) is the different acceleration coefficients; \(g{ }_{i}^{k}\) is the the global best position found in group; \({p}_{i}^{k}\) is the the best position of ith particle in a search phase.

  2. 2.

    Evaluate the fitness of each particle in the swarm

  3. 3.

    Compare the fitness of each particle to its prior best-obtained fitness \({p}_{i}^{k}\) in each iteration. If the current variable is better than \({p}_{i}^{k}\), then \({p}_{i}^{k}\) is selected as the current variable and the \({p}_{i}^{k}\) positon as the current position in d-dimensional space.

  4. 4.

    Compare the \({p}_{i}^{k}\) of particles with one another and updating the swarm global best position with the most fitness \(g{ }_{i}^{k}\) [149].

  5. 5.

    The velocity of each particle is changed (accelerated) towards its \({p}_{i}^{k}\) and \(g{ }_{i}^{k}\). This acceleration is weighted by a random term. A new location in the solution space is computed for each particle by adding a new velocity variable to each component of the particle’s position vector.

  6. 6.

    Repeat steps (2)–(5) until convergence is gained on the basis of proper criteria [150] (Figs. 10, 11, 12 and 13).

Fig. 10
figure 10

PSO architecture

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Fig. 11
figure 11

Density plot of aggregate wile added to building material (brick) a lateral load test phase, b lateral load train phase, c compressive strength test phase, d compressive strength train phase

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Fig. 12
figure 12

Molding the mixture of fly ash and cement to produce light-weight bricks

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Fig. 13
figure 13

The molding process of production of fly ash bricks

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3.3 Equations of heat transferring

In this study, for analyzing the energy of composite, two equations are used. Considering the local equations, the two equations could show the transient heat exchange between the PCM and metal foam as follows:

Energy equation for metal foam:

$$\left( {1 - \varepsilon } \right)\rho_{s} C_{s} \frac{{\partial T_{s} }}{\partial t} = \lambda_{{{\text{se}}}} \nabla^{2} T_{s} + hA\left( {T_{p} - T_{s} } \right),$$
(3)

Energy equation for phase change material:

$$\varepsilon \rho_{p} C_{p} \frac{{\partial T_{s} }}{\partial t} + \varepsilon \rho_{p} C_{p} \left( {U \cdot \nabla } \right)T_{p} = \lambda_{{{\text{pe}}}} \nabla^{2} T_{p} + hA\left( {T_{s} - T_{p} } \right) - \varepsilon \rho_{p} L\frac{\partial \beta }{{\partial t}},$$
(4)
$$h = \frac{{\lambda_{p} }}{{d_{f} }}\left[ {1 + \frac{{4\left( {1 - \varepsilon } \right)}}{\varepsilon } + 0.5\left( {1 - \varepsilon } \right)^{0.5} {\text{Re}}^{0.6} \Pr^{1/3} } \right],$$
(5)
$$A = \left\{ {\begin{array}{*{20}c} {694.57\ln \left( {1 - \varepsilon } \right) + 3579.99\quad {\text{PPI}} = 10} \\ {442.2\ln \left( {1 - \varepsilon } \right) + 2378.62\quad {\text{PPI}} = 20} \\ {694.57\ln \left( {1 - \varepsilon } \right) + 3579.99\quad {\text{PPI}} = 40} \\ \end{array} } \right.,$$
(6)
$${\text{Initial condition}}:0 \le X \le 100, \quad 0 \le y \le 300,\quad T_{s} = T_{p} = T_{{{\text{fin}}}} = 323\;{\text{K}},$$
$${\text{Boundary conditions}}:X = 0,\quad 0 \le y \le 300,\quad T_{p} = T_{s} = T_{{{\text{fin}}}} = 351\;{\text{K}},$$
$$0 \le X \le 100,\quad y = 0,\quad \frac{\partial T}{{\partial y}} = 0;$$
$$0 \le X \le 100,\quad y = 300,\quad \frac{\partial T}{{\partial y}} = 0;$$
$$E\left( t \right) = E_{{{\text{PCM}}}} \left( t \right) + E_{{{\text{foam}}}} \left( t \right) + E_{{{\text{fin}}}} \left( t \right),$$
(7)
$$E_{{{\text{PCM}}}} \left( t \right) = \left\{ {\begin{array}{lll} {m_{{{\text{PCM}}}} C_{{\text{s,PCM}}} \left( {T_{{{\text{PCM}}}} \left( t \right) - T_{0} } \right) T \le T_{m } } \\ {m_{{{\text{PCM}}}} C_{{\text{l,PCM}}} \left( {T_{{{\text{PCM}}}} \left( t \right) - T_{m} } \right) } \\ { + m_{{{\text{PCM}}}} C_{{\text{s,PCM}}} \left( {T_{m} - T_{0} } \right) + m_{{{\text{MPC}}}} L T > T_{m} } \\ \end{array} , } \right.$$
(8)
$$E_{{{\text{foam}}}} = m_{{{\text{foam}}}} C_{{{\text{al}}}} \left( {T_{{{\text{foam}}}} - T_{0} } \right),$$
$$E_{{{\text{fin}}}} = m_{{{\text{fin}}}} C_{{{\text{al}}}} \left( {T_{{{\text{fin}}}} - T_{0} } \right),$$
$$P = \frac{{E\left( {t_{{{\text{total}}}} } \right)}}{{t_{{{\text{total}}}} }},$$
$${\text{Continuity equation}}:\nabla \cdot U = 0,$$
$${\text{Momentum equation}}:\frac{\partial U}{{\partial t}} + \frac{1}{\varepsilon }\left( {U \cdot \nabla } \right)U = \frac{\mu }{\rho }\nabla^{2} U - \frac{\varepsilon }{\rho }\nabla P + F + S,$$
(9)

U is the velocity field of liquid paraffin; ρ is the density; ε is the porosity of foam; μ is the viscosity of the paraffin; F is the source term of resistance and driving force of flow expressed as

$$F = - \frac{\varepsilon }{\rho }\frac{\mu }{K}U + \varepsilon g\gamma \left( {T - T_{0} } \right),$$
(10)

K is the permeability; γ is the thermal expansion factor.

The value of K is gained through the following equations [24]:

$$K = 0.00073\left( {1 - \varepsilon } \right)^{ - 0.224} \left( {\frac{{d_{{\text{f}}} }}{{d_{{\text{p}}} }}} \right)^{ - 1.11} d_{{\text{p}}}^{2} ,$$
(11)
$$\frac{{d_{{\text{f}}} }}{{d_{{\text{p}}} }} = 1.18\sqrt {\frac{1 - \varepsilon }{{3\pi }},}$$
$$S_{x} = {\text{Au}}_{x} ,$$
$$S_{y} = {\text{Au}}_{y} ,$$
$$A = - C\frac{{\left( {1 - \gamma } \right)^{2} }}{{\gamma^{3} + \varepsilon }},$$

\({d}_{\mathrm{p}}\) is the diameter of pore; \({d}_{\mathrm{f}}\) is the diameter of the ligament.

The addition of the source term \(S\) in Eq. (9) is to compute the flow velocity in the mushy zone as

$$s = \frac{{C\left( {1 - \beta^{2} } \right)}}{{\alpha + \beta^{3} }},$$
(12)
$$\frac{\partial \rho }{{\partial t}} + \frac{{\partial \left( {\rho u_{x} } \right)}}{\partial x} + \frac{{\partial \left( {\rho u_{y} } \right)}}{\partial y} = 0,$$
$$\frac{{\partial \left( {\rho u_{x} } \right)}}{\partial t} + \nabla \left( {\rho u_{x} \vec{u}} \right) = - \frac{\partial \rho }{{\partial x}} + \nabla \left( {\mu \nabla u_{x} } \right) + S_{x} ,$$
$$\frac{{\partial \left( {\rho u_{y} } \right)}}{\partial t} + \nabla \left( {\rho u_{y} \vec{u}} \right) = - \frac{\partial \rho }{{\partial x}} + \nabla \left( {\mu \nabla u_{y} } \right) + S_{x} + S_{b} ,$$

\(\alpha\) is a constant; \(C\) is the consecutive number for the mushy zone; the value is fixed at 106; \(\beta\) is the liquid fraction.

It could be determined by Eq. (11):

$$\beta = \left\{ {\begin{array}{lll} 0 & {T_{p} < T_{m1} } \\ {{{\left( {T_{p} - T_{m1} } \right)} \mathord{\left/ {\vphantom {{\left( {T_{p} - T_{m1} } \right)} {\left( {T_{m2} - T_{m1} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {T_{m2} - T_{m1} } \right)}}} & {T_{m1} \le T_{p} < T_{m2} } \\ 1 & {T_{p} \ge T_{m2} } \\ \end{array} } \right.$$
(13)
$$0 \le X \le 300,\quad y = 100,\quad \frac{\partial T}{{\partial x}} = 0;$$
$$\gamma = \left\{ {\begin{array}{lll} 0 & {T < T_{{{\text{solidus}}}} } \\ {\frac{{T - T_{{{\text{solidus}}}} }}{{T_{{{\text{liquidus}}}} - T_{{{\text{solidus}}}} }}} & { T_{{{\text{solidus}}}} < T < T_{{{\text{liquidus}}}} } \\ 1 & {T > T_{{{\text{liquidus}}}} } \\ \end{array} } \right.$$
(14)
$${\text{At outlet}},\frac{{\partial T_{f} }}{\partial y} = 0,\quad \frac{{\partial u_{y} }}{\partial y} = 0,\quad t > 0.$$
(15)

The wall of the heat storage tank is adiabatic, and the boundary condition is presented below

$$\frac{{\partial T_{f} }}{\partial x} = 0, \frac{{\partial T_{y} }}{\partial y} = 0, u_{x} = u_{y} = 0, \quad t > 0.$$

4 Result and discussion

4.1 Model performance indicators

According to the data derived from the literature, 30% of data is used in testing phase, while 70% is randomly assigned for training part. For comparing the results of PSO, statistical model performance indicators of determination coefficient (R2) and root mean square (RMSE) were used.

$$R^{2} = \frac{{\left[ {\mathop \sum \nolimits_{i = 1}^{N} \left( {O_{i} - \overline{O}} \right) \cdot \left( {P_{i} - \overline{P}} \right)} \right]^{2} }}{{\mathop \sum \nolimits_{i = 1}^{N} \left( {O_{i} - \overline{O}} \right) \cdot \mathop \sum \nolimits_{i = 1}^{N} \left( {P_{i} - \overline{P}} \right)}},$$
(16)
$${\text{RMSE}} = \sqrt {\mathop \sum \limits_{i = 1}^{N} \frac{1}{N}\left( {O_{i} - P_{i} } \right)^{2} ,}$$
(17)

\(P\mathrm{ is the predicted values}\); \(\overline{P }\) is the predicted values; \(O\) is the observed values; \({O}_{i}\) is the observed values in sample \(i\); \(\overline{O }\) is the mean of observed variables; N is the number of training or testing samples; \({P}_{i}\) is the predicted values in sample \(i\).

Note: R2 of 1, and RMSE of 0 are the ideal form in a predictive model (Tables 2 and 3) (Fig. 14).

Table 2 Assembly embodied energy, reduced embodied energy, and renewable energy of concrete slab, concrete tile and timber frame and steel sheets
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Table 3 Assembly embodied energy, reduced embodied energy, and renewable energy of AAC block wall, steel frame and clay
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Fig. 14
figure 14

Light weight fly ash bricks to save energy and cost reduction

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4.2 Data preparation

4.2.1 Data distribution pattern

In this study, PSO was used to accurately measure the embodied strength, energy and cost optimization of materials in construction building. Figures 15, 16, 17, and 18 showed the developing of the model and its diagrams. Figure 15 shows the results of PSO for the observed date (horizental axix) and predicted data (vertical) in determining the energy and cost optimization of materials in test phase. Accordingly, in Fig. 15, the observed data distribution is between − 1 to 1, also the distribution of predicted values is from − 1 to 1. The blue dots are almost over the black bold line, meaning that there is a good correlation between the predicted and obsrved values, showing the accuracy of PSO model in determimng the strength, energy and cost optimization of materials.

Fig. 15
figure 15

AI results for energy and cost optimization values in PSO (test data). H axis = observed energy and cost optimization values. V axis = predicted energy and cost optimization values

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Fig. 16
figure 16

Error distribution for PSO in test phase

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Fig. 17
figure 17

Observed error values for PSO (test phase)

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Fig. 18
figure 18

The strength, energy and cost optimization of materials in construction management in PSO (test data)

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Figure 16 shows the error distribution in PSO model in test phase. In Fig. 16, the horizontal axis is the error distance from − 2 to 1 and the vertical axis is the number of data distance. Also, the variance of value (σ) is 0.328 while the mean of value (μ) is − 0.113 in test phase. According to this diagram, the highest error was seen in 0.01 with 3 data and the lowest error was occurred in − 1 and 1 with roughly 1 data.

In Fig. 17 (observed error values), the horizontal axis is the number of data from 0 to 15 for PSO. The vertical axis is the errors value for this model.

In Fig. 18, the horizontal axis indicates the observed values of testing samples and the vertical line shows the predicted values. In this diagram, the blue line shows 100% alignment between the predicted and observed values (Ideal form), while in this study, the radial lines have 15% differential from the black line (Fig. 18). Any overlap between these two lines means that our model reaches its ideal form with the least error percentages and high accuracy, however, it is not the case in our research (very less discrepancy). Then, PSO could show better performance in the analysis of the objective of this study. Comparing the R2 of PSO as 0.9867, the results have shown that the R2 value in PSO is nearer to 1 than, showing the best performance of PSO (Table 4) in this study. On the whole, because of the less difference between the predicted values and observed values, PSO has shown its best performance in predicting the strength, energy and cost optimization ofmaterials (Fig. 19).

Table 4 The training and testing phase results PSO
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Fig. 19
figure 19

The diagram of best cost

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Going through Table 4, the corresponding values of RMSE and R2 could define the properness of the model. Obviously, the best RMSE value is the lowest one near to 0. In this study, the RMSE of PSO is 0.9606, also, the R2 value in PSO is 0.9867. Comparing the R2 values, the nearest value to 1 is considered as the best performance. Therefore, PSO could show better performance in terms of the objective of this study and proved itself as a satisfactory method to determine the energy and cost optimization of materials in construction management.

Figure 20 shows the best cost diagram. Regarding PSO, the weight of each neuron is changed to develop the model. In diagram 19, the vertical axis is cost and the horizontal axis is the number or iterations that were ordered to develop itself (90 times) to find its better performance. So, when the decreasing of cost reached to a stable case, it was stopped. It means that in our diagram, the cost was decreased at 10 iterations and was continued up to 90 iterations to find its stability. After 90 iterations, the running is stopped due to adequate stability of cost line. This diagram showed the drastically decline of cost while using non-conventional construction materials (Fig. 21).

Fig. 20
figure 20

Stiffness reduction in concrete due to crack opening using conventional materials

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Fig. 21
figure 21

The energy plot of aggregate added to building material (brick)

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5 Conclusion

Construction materials make up about 60–70% of the overall construction costs. It would not be necessary to minimize the use of traditional materials; thus the net construction expense of a house will be cut off by the new approach of low cost materials. When recycled and reused as construction materials, industrial waste not only tends to solve recycling challenges, but also conserves renewable resources, decreases energy consumption and reduces greenhouse gas emissions. When used as sand and coarse aggregate complements in the manufacturing of wall materials, materials such as copper slag, phospogypsum and fly ash greatly decrease building costs. Moreover, buildings with these materials contribute to more energy-efficient buildings that can be weighted additionally in the Green building approval process. The aim of this paper is to highlight the cost and energy reduction in using alternative construction material. When used as a wall material in buildings, it was obvious that industrial waste brick could greatly reduce the total building cost. Also, using industrial waste materials like copper slag, fly ash and gypsum acts as a supplement to sand and aggregate, thereby highly conserving natural resource. In addition, the size variations of the planned industrial bricks minimize cement mortar quantity, labor costs, construction time and ease of plastering due to its smooth surface. Building development, construction processes and maintenance is one of the main concerns in reducing this energy consumption and reducing greenhouse gas emissions. While the energy used in operational construction could be significant, the growing trend to reduced or zero emissions indicates that reducing energy in construction and pre-construction phases of a building life cycle is significance. The embodied energy from building materials and related energies, such as transport, re-usage, recycling and renewables replacement, which should be used with caution, is a key element in energy use during this process. In this case, for measuring the energy and cost optimization, PSO was used. Comparing the RMSE and r-square results have proved PSO as the best model in predicting the strength, energy and cost optimization of construction materials.