Balancing indoor thermal comfort and energy consumption of ACMV systems via sparse swarm algorithms in optimizations

Energy and Buildings 149 (2017) 1–15

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Balancing indoor thermal comfort and energy consumption of ACMV systems via sparse swarm algorithms in optimizations Deqing Zhai, Yeng Chai Soh ∗ School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

a r t i c l e

i n f o

Article history: Received 15 January 2017 Received in revised form 21 April 2017 Accepted 9 May 2017 Available online 15 May 2017 Keywords: Energy consumption Thermal comfort Predicted mean vote (PMV) Extreme learning machines (ELM) Neural networks (NN) Firefly algorithm (FA) Augmented firefly algorithm (AFA) Air-conditioning and mechanical ventilation systems (ACMV)

a b s t r a c t This paper proposes a systematic modelling and optimizing of energy consumption and indoor thermal comfort for air-conditioning and mechanical ventilation (ACMV) systems. The models of extreme learning machines (ELM) and neural networks (NN) are established and evaluated. These well-trained models are then integrated with the computational intelligence techniques of sparse firefly algorithm (sFA) and sparse augmented firefly algorithm (sAFA). The sFA and sAFA aim to locate the global optimal operating points of the ACMV systems in real-time and predict energy saving rate (ESR) with a third order polynomial regression based on minimizing the mean squared errors (MSE) of the cost functions. This study also covers different indoor scenarios, such as general offices, lecture theatres and conference rooms. Given the well trained models, the maximum prediction of potential ESR can be −30% via the sparse AFA optimizations while maintaining indoor thermal comfort in the pre-defined comfort zone. © 2017 Elsevier B.V. All rights reserved.

1. Introduction The progresses made in machine learning (ML) have been overwhelming in the fields of computer vision and pattern recognition, classifications, regressions and many other related fields over the past decade. Some related terms on machine learning (ML) are artificial intelligence (AI) or computational intelligence (CI), which are sophisticated algorithms implemented into machines [1,2], especially computers, so as to make machines perform intelligent tasks. The most well-known milestone of machine learning can be traced back to the invention of perceptrons by Frank Rosenblatt in 1957 [3]. A single perceptron can be implemented as different logic gates with binary inputs and outputs. Since then, the notion of artificial intelligence had drawn significant attentions, such as artificial neural networks (ANN), extreme learning machine (ELM) and Deep Learning and many other topologies [4]. Considering the concepts of smart buildings, the machines (i.e. air-conditioning systems in buildings in this case) are expected to be smart to learn how to operate in an economical way by balancing indoor occupants’ thermal comfort and buildings’ energy consumption. To be more specific,

∗ Corresponding author. E-mail address: [email protected] (Y.C. Soh). http://dx.doi.org/10.1016/j.enbuild.2017.05.019 0378-7788/© 2017 Elsevier B.V. All rights reserved.

the objective of this research is to use computational intelligence techniques to minimize the energy consumption of ACMV systems and maintain the occupants’ indoor thermal comfort in the mean while. The fields of researches in energy efficiency have been developing rapidly over the past decades due to limited fossil fuel reserves and concerns over CO2 emissions and air pollution. Therefore, researches on how to increase energy efficiency, conserve energy and develop the next generation of energy resources are becoming important [5–9]. According to US Department of Energy (DOE), the energy consumed by buildings is about 40% of the total energy demands [10]. Moreover, the most energy consuming components of buildings are air-conditioning and mechanical ventilation (ACMV) systems. Furthermore, the ACMV systems have become a necessity in current buildings because people are spending more time indoor for work and leisure. Besides the statistics of the United States, the National Environment Agency (NEA) in Singapore also reported that the energy consumed by ACMV systems is about 36.7% of the total energy consumed in buildings according to the statistics shown in Fig. 1 [11]. The field of researches in indoor thermal comfort can be dated back to 1970s since P.O. Fanger’s work and subsequent developments [12]. Arising from these works, the very subjective term of “Thermal Comfort” of occupants can be modeled through a series of mathematical expressions, called the predicted mean vote (PMV)

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Fig. 1. Energy consumption by appliances in Singapore 2016.

[13]. Since the smart building concept is not only about minimizing energy consumption but also maintaining indoor thermal comfort levels of occupants in buildings, the techniques of computational intelligence can be effectively applied for evaluating the trade-offs and balancing of ACMV systems’ energy consumption and occupants’ indoor thermal comfort. This study of the ACMV systems’ energy consumption and occupants’ indoor thermal comfort will be demonstrated through experimental results using the thermal laboratory in the School of Electrical & Electronic Engineering, Nanyang Technological University. The experiments were carried out in the thermal laboratory with an isolated Air-Conditioning and Mechanical Ventilation system. The experimental data were collected and trained into two different types of machine learning topologies, which are extreme learning machines (ELM) and neural networks (NN). The trained models predicted the energy consumption of the ACMV system, the ambient air temperature and ambient air velocity of occupants. The models of ambient air temperature and ambient air velocity were further integrated with the developed thermal comfort model. Therefore, indoor thermal comfort and energy consumption can be optimized via computational intelligence algorithms for different scenarios. The novelty of this study is the proposed systematic approaches of the machine learning techniques to model energy consumption and indoor thermal comfort and following with the proposed computational intelligence techniques (sparse FA and sparse AFA) to optimize formulated problems. The rest of the paper is organized as follows: Section 2 briefly reviews the literature on related works. Section 3 describes the methodologies of the studies. Section 4 presents the experimental results and analysis from the models developed. Section 5 draws conclusions and outlooks for future studies.

2. Literature reviews The recent studies on energy efficiency and indoor thermal comfort are mostly based on the methodologies of modified modelbased predictive control (MPC) [8]. According to the studies by Ruano et al., an intelligent model-based predictive control (MBPC) solution was developed from radial basis function (RBF) neural networks [14]. The MBPC algorithm was additionally designed with Multiple-Objective Genetic Algorithm in optimization techniques [14]. Based on the proposed techniques, the IMBPC could mini-

mize the economic cost needed to maintain the room in a state of thermal comfort for occupants presenting. Based on the studies by A. Acosta et al., a non-linear predictive controller (NLPC) was developed for regressions of thermal loads based on radiant time series (RTS) method [15] in two hotel rooms. However, the study was only for regressions of thermal temperature. If ambient air velocity, humidity and occupants activities (metabolic rates) were taken into considerations, the models would be more thorough and adaptable. Based on the studies of F. Ascione et al., a multiple objectives (energy saving and thermal comfort maintaining) simulation-based MPC was proposed. The target was to optimize hourly operating point temperatures with a day ahead planning, based on weather forecasting and occupants’ conditions [16]. The optimization was implemented by genetic algorithm to find the Pareto front of the multiple objectives problem. The nondominated subset of Pareto front solutions could be a selection pool for users according to their own thermal comfort and economical conditions. The proposed method could reduce about 56% of the operating cost with improvement of thermal comfort considerations at the same time [16]. However, the proposed method had to continuously operate online in order to make sure the optimal updates for the following days’ configuration. If there were interrupts happening between consecutive days, the Pareto front non-dominated solutions would become non-optimal. In addition, the proposed simulation-based MPC is a time-consuming method, and the occupants’ profiles are not widely illustrated for different occupants’ scenarios in the same room [16]. Based on the study of Kim et al., the novelty of this study was to propose a weighted objective function combining both energy consumption matters and indoor thermal comfort matters [17]. The study showed that the green systems could have an effectively potential to reduce energy consumption by 11% and to improve indoor thermal comfort (in terms of PPD) by 2.18% [17]. Based on the work by Yu et al., the problem was similarly formulated from a Pareto front solution pool and it was applied by Non-dominated Sorting Genetic Algorithm 2 (NSGA2) to obtain the optimal solutions from the solution pools satisfying both energy consumption and indoor thermal comfort [18]. Similar studies done by Wang et al. in Germany also focused on thermal comfort and energy consumption [19]. The study showed that the heating and cooling demands are highly depended upon indoor temperature set-points, occupant and heat recovery rate. Based on the study of Wang et al., the building’s energy perfor-

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Fig. 2. Structure of air-conditioning and mechanical ventilation system and thermal laboratory.

mance achieved an expected energy efficiency through optimized control system and sun-shading systems of ACMV. Simulations and predictions were data-driven based on their heating and cooling demands. The novelty of this study was the conduct of experiments regarding load demands, sun-lighting, occupants’ profiles and heat recovery [19]. Based on the study of Lin et al., the novelty was to propose a simple automatic supervisory control system, which was based on an energy saving decoupling indoor comfort control for regulating the indoor comforts of an office building [20]. Moreover, the activities in a building could be considered as a discrete event system. Therefore, the system could be modelled as different topologies, such as Finite State Automata, Petri Net, Markov Chain and Queuing Network [21]. A Petri Net model was selected as states transitions model for simplicities, and the testing results showed that it achieved respectively about 47% and 15% of energy saving while maintaining indoor thermal comfort simultaneously [20]. 3. Methodology This study is to propose an efficient systematic method to track optimal operating points (OOPs) as control feedbacks of our ACMV system for minimizing the energy consumption of ACMV systems and maintaining the occupants’ indoor thermal comfort simul-

taneously. This is an extension of our previous work [22]. The experimental data was stored inside servers through a data acquisition (DAQ) interface script, which was written and run in MATLAB. As the total experimental data was obtained, the data was randomly divided into two groups. One group of data (80%) was used for training the models. Another group of data (20%) was used for testing the trained models. The groups were randomly formed for trainings, therefore the trained models were cross-validated. As a result of that, the models of energy consumption, ambient air temperature and air velocity were well trained and selected under the topologies of extreme learning machines (ELM) and neural networks (NN). What to be noted is the ELM topology was used in this study with no-bias neurons in the hidden layer and output layer due to its simplicity and acceptable error tolerance. While the NN topology was used in this study as classical paradigms as shown in Fig. 4. The first step of this study is to build models (i.e. ELM and NN models) of energy consumption, ambient air temperature and ambient air velocity based on experimental data collected in the thermal laboratory of the School of Electrical and Electronic Engineering. The second step is to realize the developed PMV model of indoor thermal comfort according to ASHRAE Standard 55. According to the developed PMV, there are environmental and occupant

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Legend:

f1

Environmental Parameters

Energy Model

Occupant Parameters

Air Temperature Objecve Funcon

Air Velocity

f2

Relave Humidity Mean Radiant Temperature

Firefly Algorithm

Thermal Comfort Model

Metabolic Rate Clothing Insulaon Factor

f3

External Work Done

Feedback Loop Opmize/Control Fig. 3. Overview of optimization systems.

parameters affecting different thermal comfort sensations of occupants. The environmental parameters are ambient air temperature, ambient air velocity, air relative humidity and mean radiant temperature. Due to the thermal isolations of the experimental room, the outdoor environmental conditions are not influencing the indoor environmental conditions, therefore the indoor environmental conditions can be fully controlled by the ACMV system. The occupant parameters are metabolic rates (human activities), clothing insulation factors and external work done. The metabolic rates of occupants can be measured through peripheral devices (e.g. wristbands) and the clothing insulation factors of occupants can be evaluated through images processing of occupants’ attires by cameras mounted in the hallway of the laboratory and tables of clothing insulation factors corresponding to different attires [23]. The third step is to formulate an objective function jointly between energy consumption and indoor thermal comfort. The objective is to minimize the objective function via computational intelligence approaches of “sparse Firefly Algorithm (sFA)” and “sparse Augmented Firefly Algorithm (sAFA)”. Based on the results of optimizations, the third order polynomial regressions predict energy consumption, thermal comfort PMV index and the Energy Saving Rates (ESR) at different degrees of occupant preferences (i.e. ) values. The benchmark level of energy consumption is selected from the median values of appliances’ frequencies in ACMV systems. In Figs. 2 and 3, the ACMV system covers Air-Handling Unit (AHU), Liquid Dehumidication Unit (LDU), Water Chiller Unit (WCU) and ducts-pipes connections [24], and the main energy consuming units are the AHU and WCU based on the scope of this study. The LDU is out of this study scope because of its independency in function and operation with other units. The AHU has a supply-air fan and cooling-coils. The WCU has a water pump, a compressor, an evaporator and a condenser. The AHU takes high temperature and low velocity air from outdoor environment. The air is moved by the supply-air fan, then it is cooled down through cooling-coils (i.e. heat exchanger between air and water). The chilled water is running inside the cooling-coils and it is circulated by the water pump and chilled by the compressor, evaporator and condenser of the WCU. The energy consuming components under the scope of study are the supply-air fan motor, compressor, water pump and condenser of this ACMV system. The operating points of the supplyair fan motor, compressor and water pump can be varied, while the condenser is designed to operate at its rated constant state once it

+1

+1

Σ A.F. f1

Σ A.F. Σ

f2

Energy/ Air Temperature/ Air Velocity

Σ A.F.

f3

Σ A.F.

Fig. 4. Different topologies of models.

starts. Therefore, the total energy consumed by the ACMV can be formulated as a function of variable operating frequencies of the supply-air fan motor, compressor and water pump. 3.1. Models of energy consumption, ambient air temperature and ambient air velocity The Extreme Learning Machines (ELM) model can be regarded as a special topology of Neural Networks (NN), which the partial parameters of hidden layer neurons are not required to be tuned. In this study, the particular ELM models do not consist of any bias, unlikely from the following NN models as shown in Fig. 4. Therefore, the topologies of ELM and NN are slightly different in this study. The ELM model is constructed as a topology of three-layer network, which are input layer, hidden layer and output layer in this specific study as shown in Fig. 4 without the dashed bias terms. Moreover, the parameters of the output layer neurons can be solved analytically by Least Square Error (LSE) method easily. Therefore the computational complexity of ELM models is far lower as compared to the NN models which are using Back-Propagation (BP) method. Through the experiments, the ELM models of energy are evaluated from different numbers and different activation functions of hidden layer neurons. A reasonably good model could be selected as the final ELM model of energy consumption within acceptable error tol-

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erances. Similarly, the final ELM models of ambient air temperature and ambient air velocity are also evaluated in the similar ways. Neural networks (NN) can be dated back to 1957, in which Rosenblatt proposed a concept of perceptron [3]. The neural network is constructed as a topology of three-layer network in this study. Differing from the ELM models, the NN models required the whole parameters to be tuned. The evaluations of activation functions from ELM models showed the better results of sigmoid activation function than other activation functions in Figs. 9, 13 and 14. Moreover, the NN models are trained via BackPropagation (BP) algorithm. Due to the simplicity of derivatives of activation function (i.e. sigmoid function) in BP processes, the sigmoid activation function was selected in training NN models thoroughly. Besides the evaluations on the number of hidden neurons like ELM models, there are two more aspects to be evaluated with the NN models, which are learning rates and the number of iterations. Based on the evaluations of the number of hidden neurons, learning rate and number of iterations, the final reasonably good NN models could be selected under acceptable error tolerances. Furthermore, the stopping criteria for training NN models is constrained by the maximum number of iterations. 3.2. Thermal comfort Thermal comfort is a very subjective term to evaluate the thermal sensations of each occupant in a room. Dated back in 1970s, P.O. Fanger proposed a mathematical way to quantify this subjective term, which was called the Predicted Mean Vote (PMV) index [13]. The PMV index was developed and experimentally verified by P.O. Fanger and many successors. There are two categories of parameters, which are environmental parameters and occupant parameters. The environmental parameters are ambient air temperature, ambient air velocity, air humidity and mean radiant temperature. The occupant parameters are occupants’ metabolic rates (human activities), clothing insulation factor and external work done (generally assumed to be zero) [13]. The version of developed PMV model is adopted from ASHRAE 2013 Standard 55 ISO-7730 [23].

Fig. 5. FA optimization pseudo-codes.

The Energy Saving Ratio (ESR) is defined as: ESR(E(f)) =

E(f) − Ebench × 100% Ebench

(4)

Remarks: E(f) is the energy consumption at given vector (f) of operating points of ACMV systems. Ebench is the benchmark energy consumption at median operating points [40, 40, 40]T . The optimization problem is formulated as: Minimize :

min (g(, f))

∀,∀f

Subjectto : 3.3. Problem formulation

0≤≤1

Our balancing problem is formulated as a minimization problem, where the objectives of energy consumption and indoor thermal comfort are weighted in a complementary relation. The objectives of energy consumption and indoor thermal comfort are normalized to be meaningful in the objective function. The occupants’ preference of energy efficiency or indoor thermal comfort can be quantified through an introduced variable  ∈ [0, 1] in the objective function. The objective function is defined as: g(, f) =  · Enorm (f) + (1 − ) · PMV norm (f)

(1)

Remarks: f is the vector of operating points of ACMV components (i.e. frequencies of supply-air fan, compressor and water pump).  is the occupants’ preference between energy efficiency and indoor thermal comfort sensations. The normalized energy consumption is defined as: Enorm (f) =

E(f) − Emin Emax − Emin

(2)

The normalized PMV is defined as: PMV norm (f) =

|PMV (f)| − |PMV |min |PMV |max − |PMV |min

(3)

Remarks: Emin , Emax , |PMV|min , |PMV|max are offline results obtained from experiments in the laboratory.

30 ≤ fi ≤ 50

(5)

∀i

0 ≤ |PMV | ≤ 0.5

Remarks: fi is the ith element in the vector (f) of operating points of ACMV systems.  is the occupants’ preference between energy efficiency and indoor thermal comfort sensations. 3.4. Sparse firefly algorithm and sparse augmented firefly algorithm optimizations With the aforementioned models of energy consumption and indoor thermal comfort, sparse Firefly Algorithm (sFA) [25] and sparse Augmented Firefly Algorithm (sAFA) optimizations are applied to search for optimal OOPs. The pseudo-codes of FA and AFA are shown in Figs. 5 and 6, and the flowcharts of algorithms are shown in Figs. 7 and 8. Due to non-linear property of the solutions and avoidance over-fitting of the regression predictions, the energy-saving rate (ESR) is predicted from a third order polynomial regression with weight coefficient  varying from 0 to 1. The polynomial regression is achieved through minimizing a cost function (i.e. mean squared error) in a batch gradient descent (BGD) approach. The BGD approach is based on the whole training samples dataset. The BGD approach is guaranteed to locate the global optimum after suf-

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Start

Firefly Algorithm

Define Objective Function Necessary Environmental & Occupant Parameters

Generate Firefly Population

Energy Model Evaluation

PMV Model Evaluation

Intensity Evaluations Define light absorption coefficient

IF Intensity(i) < Intensity(j) ?

No.

Vary attractiveness New Intensity Evaluations

Yes. Move Firefly(i) toward Firefly (j) Update New Intensity

Shift to Firefly(i+1)

Fig. 6. AFA optimization pseudo-codes.

ficient iterations for convex or smooth error manifolds [26]. This is the reason that we selected BGD approach in this study. The cost function is based on mean squared errors (MSE) between the predictions data points (obtained from the third order polynomial regression) and the discrete optimized data-set points. The evaluations on different orders of polynomial regressions are shown in Fig. 16. The reason to select the third order polynomial regression is due to its reasonable accuracy, computational complexity and without over-fitting issues as shown in Fig. 16 under different number of optimization populations. However, since indoor environments could varied significantly due to different purposes (e.g. general offices, gyms, classrooms, dancing rooms or basketball halls), the occupants’ thermal comfort will be quite different from each other with respect to their human activities (i.e. metabolic rates) and clothing insulation factors. Hence, different OOPs could be located from sFA and sAFA optimizations under different cases. Two case studies are selected from many different cases due to the most likelihoods of occurrences in different cases. The Case Study 1 is about sedentary activities (e.g. general offices) and the Case Study 2 is about light activities (e.g. lecture theatres and conference rooms) [27]. The experimental results are presented in the next section. 4. Experimental results 4.1. Models of energy consumption The models of energy consumption are based on operating points of the ACMV system. The targets of the energy consuming components are narrowed down into the supply-air fan motor, compressor, water pump and condenser as discussed in the previous section. The tunable parameters of ELM-LSE architectures are merely the number of hidden layer neurons and the types of activation functions of hidden layer neurons. From our studies, the ELM-LSE models would be very inaccurate when the number of hidden layer neurons is very low, while NN-BPBGD models outperform at this stage. The ELM-LSE and NN-BPBGD models can be accurate within 0.001 error tolerance when the number of hidden

No.

IF Firefly(i+1) out of population ?

Yes. Shift to Firefly(j+1)

No.

IF Firefly(j+1) out of population ?

Rank Global Best Firefly

Post Process and Visualization

End

Fig. 7. FA optimization flowcharts.

neurons is reaching 500 onward in our studies of the models of energy consumption as shown in Figs. 9 and 10. In Fig. 9, we define 500 hidden neurons and sigmoid activation function as our reasonably well trained ELM-LSE models of energy consumption during trainings. The ELM-LSE models of energy consumption fluctuate significantly with less than 400 hidden neurons in Fig. 9. With increasing number of hidden neurons, we found that the cost function (i.e. Mean Squared Errors) of the ELM Models of Energy drops significantly to almost zero. Similarly, we define 1000 hidden neurons, 500 iterations and 0.1 learning rate as our reasonably well trained NN-BPBGD models of energy consumption during trainings as shown in Figs. 10–12. With increasing number of hidden neurons, we found that the cost function (i.e. Mean Squared Errors) of the NN-BPBGD models of energy consumption reduces significantly from 100 to 500 in Fig. 10. With increasing number of iterations, we found that the cost function of the NN-BPBGD models of energy reduce rapidly from 100 to 200 in Fig. 11. With increasing degrees of learning rates, we found that the cost function of the NN-BPBGD models of energy obtains minimum values when learning rates vary between 0.01 and 0.5 in Fig. 12. 4.2. Models of ambient air temperature and ambient air velocity The ELM-LSE models of ambient air temperature are evaluated in Fig. 13. With increasing number of hidden neurons, we found

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Evaluations of NN Models with Number of Hidden Layer Neurons Number of Iterations=500 Learning Rate=0.1

Start

Augmented Firefly Algorithm

0.08

Define Objective Function

PMV Model Evaluation

Intensity Evaluations

IF Intensity(i) < Max(Intensity) ?

No.

NN Models of Energy NN Models of Air Temperature NN Models of Air Velocity

0.07 Cost Function (Mean Square Error)

Necessary Environmental & Occupant Parameters

Generate Firefly Population

Energy Model Evaluation

7

0.06 0.05 0.04 0.03 0.02

Ignore.

0.01 0 100

Yes.

200

300

Move Firefly(i) toward Firefly with Max Intensity

400 500 600 700 Number of Hidden Layer Neurons

800

900

1000

Fig. 10. Evaluations of NN-BPBGD models with number of hidden layer neurons. Update New Intensity

Evaluations of NN Models with Iterations Number of Hidden Layer Neurons=1000 Learning Rate=0.1

Shift to Firefly(i+1)

Cost Function (Mean Squared Error)

0.045 IF Firefly(i+1) out of population ?

No.

Yes. Rank Global Best Firefly

Post Process and Visualization

End

Fig. 8. AFA optimization flowcharts.

NN Models of Energy NN Models of Air Temperature NN Models of Air Velocity

0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 100

200

300

400

500

600

700

800

900

1000

Number of Iterations Fig. 11. Evaluations of NN-BPBGD models with number of iterations.

Evaluations of ELM Models of Energy

Evaluations of NN Models with Learning Rates Number of Hidden Layer Neurons=1000 Number of Iterations=500

0.45 Activation Function: Sigmoid Activation Function: Tansig

0.35

0.18

Cost Function (Mean Squared Error)

Cost Function (Mean Squared Error)

0.4

0.3 0.25 0.2 0.15 0.1 0.05

NN Models of Energy NN Models of Air Temperature NN Models of Air Velocity

0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02

0

0

100

200

300 400 500 600 700 Number of Hidden Layer Neurons

800

900

Fig. 9. Evaluations of ELM-LSE models of energy consumption.

1000

0 -5 10

-4

10

-3

10

-2

10

-1

10

Learning Rates (Horizontal Axis in Log Scale) Fig. 12. Evaluations of NN-BPBGD models with learning rates.

0

10

8

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80

Evaluations of ELM Models of Air Temperature 0.18 Activation Function: Sigmoid Activation Function: Tansig

← ACMV System starts at 7:30am.

75

0.14

Relative Humidity (%)

Cost Function (Mean Squared Error)

0.16

0.12 0.1 0.08 0.06

ACMV System ends at 8:00pm. →

70

65

60

0.04

55 0.02 0

0

100

200

300 400 500 600 700 Number of Hidden Layer Neurons

800

900

50

1000

Fig. 13. Evaluations of ELM-LSE models of ambient air temperature.

2

3

4 5 Time (Seconds)

6

7

8 4

x 10

Fig. 15. Relative humidity in one typical experimental day (from 0 to 24 h).

Evaluations of ELM Models of Air Velocity

x 10

ELM Models @ Pop=100 ELM Models @ Pop=50 ELM Models @ Pop=25 NN Models @ Pop=100 NN Models @ Pop=50 NN Models @ Pop=25

0.24

Activation Function: Sigmoid Activation Function: Tansig

7

0.22 0.2

6

Mean Squared Errors

Cost Function (Mean Squared Error)

1

0.26

-4

8

0

5 4

0.18 0.16 0.14 0.12

3

0.1

2 0.08

1 0 0

0.06

100

200

300 400 500 600 700 Number of Hidden Layer Neurons

800

900

1

2

3

4 5 6 7 Orders of Polynomial Regressions

8

9

10

1000 Fig. 16. Evaluations of different orders of polynomial regressions.

Fig. 14. Evaluations of ELM-LSE models of ambient air velocity.

4.3. Sparse firefly algorithm and sparse augmented firefly algorithm optimizations

that the fluctuations (the ambient air temperature cost functions (i.e. Mean Squared Errors) of the ELM models) are diminishing fast from 0 to 150 hidden layer neurons Fig. 13. Therefore, we define 500 hidden layer neurons and sigmoid activation function as our final reasonably best trained ELM-LSE models of ambient air temperature during trainings. Similarly, we will define 500 hidden layer neurons, 500 iterations and 0.1 learning rate as our reasonably well trained NN-BPBGD models of ambient air temperature during trainings in Figs. 10–12. Moreover, the ELM-LSE models of ambient air velocity are evaluated in Fig. 14. We define 500 hidden layer neurons and sigmoid activation function as our final reasonably well trained ELM-LSE models of ambient air velocity during trainings. Similarly, we define 500 hidden layer neurons, 500 iterations and 0.01 learning rate as our reasonably well trained NN-BPBGD models of ambient air velocity during trainings in Figs. 10–12.

The experimental results from sparse FA and sparse AFA optimizations are presented in the following figures from Fig. 17–22 , and the experimental results are based on the well-trained ELMLSE and NN-BPBGD models defined from the previous section. According to the experimental results, the ELM-LSE models generally present better results than the NN-BPBGD models do, through the optimizations results in energy consumption and indoor thermal comfort. In addition, the sparse AFA optimizations generally present better results than sparse FA optimizations do for both Case 1 and Case 2 when the weight coefficient () increases from 0 to 1. The trend of energy consumption has been shown to decrease when weight coefficient () increases from 0 to 1. To be noted is that the discrete actual optimized results are plotted and based on the experimental data-driven models (i.e. ELM-LSE and NN-BPBGD models), however, the continuing regression results are interpolated and based on the discrete actual optimized results shown from Fig. 17–22 in details.

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Fig. 17. Sparse FA and AFA optimizations on ELM-LSE and NN-BPBGD models of energy consumption of ACMV systems (Case 1: Sedentary activities, e.g. general offices).

Table 1 Associations of mean radiant temperature and ambient air temperature. Surfaces

Left wall

Angle factors (Case 1) Angle factors (Case 2) Surface temperature (◦ C) Mean radiant temperature (◦ C) Ambient air temperature (◦ C)

0.049945 0.049945 0.176549 0.058998 0.058998 0.208884 22.4 22.4 22.4 22.623 (Case 1) 22.5 (measured via EE21 humidity/temperature transmitter)

Right wall

Front wall

Back wall

Ceiling

Floor

0.176549 0.208884 22.6 22.264 (Case 2)

0.178534 0.217935 22.8

0.37201 0.233431 22.5

Notes: The person is at a sitting position centred at 0.6 m above the centre of floor for Case 1. The person is at a standing position centred at 1.2 m above the centre of floor for Case 2. The dimension of the thermal laboratory is 7.28 m × 3.52 m × 2.50 m.

Some parameters of the experiments are described as follows. There are two focused case studies based on the most likelihood of scenarios. Case 1 is based on occupants with sedentary activities in general offices. Case 2 is based on the occupants with light

activities in lecture theatres and conference rooms. For occupants with sedentary activities (Case 1), the average metabolic rate is 60 W/m2 and the average clothing insulation factor is 0.07 m2 K/W (i.e. normal short T-shirts and light long pants) [28]. For occupants

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Fig. 18. Sparse FA and AFA optimizations on ELM-LSE and NN-BPBGD models of energy consumption of ACMV systems (Case 2: Light activities, e.g. lecture theatres and conference rooms).

with light activities (Case 2), the average metabolic rate is 93 W/m2 and the average clothing insulation factor is 0.1 m2 K/W (i.e. normal long shirts and normal long pants) [28]. The experimental equipment started to operate at 7:30 in the morning, and shut down at 20:00 in the evening. Furthermore, there are time-delays for the thermal laboratory performing stably under the desired conditions as Fig. 15 shows. Therefore, the relative humidity is generally considered as a constant at 58% as shown in Fig. 15 throughout the whole experimental periods. What is to be noted is that the mean radiant temperature is closely associated to the ambient air temperature as shown in Table 1, due to the small dimensions and the thermal-isolating materials applied for the walls, ceiling and floor structures of the thermal laboratory.

Similarly, the indoor thermal comfort is also optimized via sparse FA and sparse AFA optimization algorithms for Case 1 and Case 2. The experimental results are presented in Figs. 19 and 20. Since the indoor thermal comfort would be better if it is closer to the neutral standard (i.e. PMV = 0), the results of ELM-LSE models are slightly worse than those of the NN-BPBGD models. The trend of indoor thermal comfort has been shown to approach the neutral standard when the weight coefficient () decreases from 1 to 0. On the energy saving rate (ESR) evaluations, the benchmarks of the energy consumption of the ACMV is followed at a median operating points. The ESR experimental results are presented in Fig. 21, Fig. 22 and the summary of the two cases optimization results are presented in Table 2. According to the experimental results of the sparse FA and sparse AFA optimizations, the ESR

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Fig. 19. Sparse FA and AFA optimizations on ELM-LSE and NN-BPBGD models of indoor thermal comfort (Case 1: Sedentary activities, e.g. general offices).

results of the ELM-LSE models are generally better than those of the NN-BPBGD models in both Case Study 1 and Case Study 2. In addition, the results of sparse AFA optimization are better than those of sparse FA optimization in both Case 1 and Case 2. In Case 1, the ESRs of sFA and sAFA optimizations are within intervals [−25%,−16%]

and [−24%,−17%] respectively ( = 1) among all different generations at the maximum level of capability as shown in Fig. 21. In Case 2, the ESRs of sFA and sAFA optimizations are within intervals [−30%,−18%] and [−31%,−18%] respectively ( = 1) among all different generations at the maximum level of capability as shown in

Table 2 Summary of sFA and sAFA optimizations results on energy saving rates (ESRs). Lambda

sFA

sAFA

Case 1

0 0.1 0.2

Case 2

Case 1

Case 2

ELM

NN

ELM

NN

ELM

NN

ELM

NN

−0.03264 −0.07735 −0.1121

−0.1173 −0.1236 −0.1313

0.09403 0.03872 −0.02447

0.1486 0.07043 −0.0024

−0.08441 −0.09375 −0.127

−0.121 −0.1336 −0.1478

0.1014 0.03366 −0.03428

0.1532 0.07489 0.003292

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Table 2 (Continued) Lambda

sFA

sAFA

Case 1

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Case 2

Case 1

Case 2

ELM

NN

ELM

NN

ELM

NN

ELM

NN

−0.1472 −0.1776 −0.2022 −0.2188 −0.2324 −0.2316 −0.2319 −0.2289

−0.1404 −0.1731 −0.1971 −0.2152 −0.2249 −0.2291 −0.2244 −0.2477

−0.08371 −0.1388 −0.1922 −0.2272 −0.2573 −0.279 −0.2922 −0.2967

−0.06829 −0.1256 −0.1683 −0.2062 −0.2284 −0.2325 −0.2255 −0.1966

−0.1627 −0.1947 −0.2174 −0.2355 −0.2434 −0.2388 −0.239 −0.246

−0.1627 −0.1775 −0.1911 −0.2028 −0.2116 −0.2165 −0.2168 −0.2246

−0.107 −0.1579 −0.2072 −0.2438 −0.2645 −0.2963 −0.3101 −0.3102

−0.06383 −0.1237 −0.1736 −0.2108 −0.2324 −0.2358 −0.2223 −0.2091

Notes: The bold values are the more energy efficient ESRs via comparisons between ELM and NN models.

Fig. 20. Sparse FA and AFA optimizations on ELM-LSE and NN-BPBGD models of indoor thermal comfort (Case 2: Light activities, e.g. lecture theatres and conference rooms).

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Fig. 21. Sparse FA and AFA optimizations on ELM-LSE and NN-BPBGD models of energy saving rate (ESR) (Case 1: Sedentary activities, e.g. general offices).

Fig. 22. The negative values of intervals mean that the ACMV system operates at a condition of energy efficiency with respect to median operating conditions. 5. Conclusion Based on the experimental evaluations on the models of ELMLSE and NN-BPBGD, the ELM-LSE models generally outperform NN-BPBGD models in terms of energy consumption, ambient air temperature and ambient air velocity. In terms of training complexity, the ELM-LSE models have less computational complexity than the NN-BPBGD models, since the parameters of the ELM-LSE models can be analytically obtained instead of the need for many iterations in the NN-BPBGD models.

Based on the experimental evaluations on the optimization algorithms of sparse FA and sparse AFA, the sparse AFA is more efficient for both well trained ELM-LSE models and NN-BPBGD models. Since the complexity of sFA is O(n2 ) as shown in FA pseudo-code (Fig. 5) and the complexity of sAFA is O(n) as shown in AFA pseudocode (Fig. 6), the accuracy of sAFA is not only better than that of sFA, but also the computational complexity of sAFA is far less than that of sFA especially for large population cases. Based on the results in Figs. 21 and 22, the maximum prediction of potential ESR can be −30% and −31% via the AFA optimizations for Case 1 and Case 2 while maintaining indoor thermal comfort in the pre-defined comfort zone. In this study, there are some limitations to be noted. First, there are limitations in the experimental results carried on in the labo-

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Fig. 22. Sparse FA and AFA optimizations on ELM-LSE and NN-BPBGD models of energy saving rate (ESR) (Case 2: Light activities, e.g. lecture theatres and conference rooms).

ratory. Since the ACMV system was uniquely designed and isolated from the school ACMV systems, the experimental results are limited for the laboratory so far, but the concept can be generally applied. Second, the experimental results are limited for equator climate regions, since the experiments were carried out in Singapore, a tropical season country. Third, the conceptual aim of this study is to optimize the whole buildings’ air and ventilation controlled by ACMV systems. However, there is a presumption that every single room is identical for simplicity purpose. Therefore, there are zones-dividing techniques required for more comprehensively optimizing buildings’ efficiency, which could also be future study areas as well.

Acknowledgements The authors would like to express their thanks to the Center of EXQUISITUS of Nanyang Technological University for providing the experiment air-conditioning mechanical ventilation systems in the thermal laboratory of Nanyang Technological University, Singapore. This research was partially funded by NTU’s Research Scholarship and the National Research Foundation of Singapore under Grant NRF2011 NRF-CRP001-090, Award Number NRFCRP8-2011-03.

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