Optimization of an HVAC system with a strength multi-objective ...

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright

Author's personal copy

Energy 36 (2011) 5935e5943

Contents lists available at SciVerse ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Optimization of an HVAC system with a strength multi-objective particle-swarm algorithm Andrew Kusiak*, Guanglin Xu, Fan Tang Department of Mechanical and Industrial Engineering, 3131 Seamans Center, The University of Iowa, Iowa City, IA 52242-1527, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 January 2011 Received in revised form 16 June 2011 Accepted 15 August 2011 Available online 3 September 2011

A data-driven approach for the optimization of a heating, ventilation, and air conditioning (HVAC) system in an office building is presented. A neural network (NN) algorithm is used to build a predictive model since it outperformed five other algorithms investigated in this paper. The NN-derived predictive model is then optimized with a strength multi-objective particle-swarm optimization (S-MOPSO) algorithm. The relationship between energy consumption and thermal comfort measured with temperature and humidity is discussed. The control settings derived from optimization of the model minimize energy consumption while maintaining thermal comfort at an acceptable level. The solutions derived by the S-MOPSO algorithm point to a large number of control alternatives for an HVAC system, representing a range of trade-offs between thermal comfort and energy consumption. 2011 Elsevier Ltd. All rights reserved.

Keywords: HVAC Optimization Neutral network Evolutionary computation Strength multi-objective particle-swarm algorithm

1. Introduction Heating, ventilating, and air conditioning (HVAC) systems, account for over 50% of the energy consumed by buildings [1]. Therefore, balancing energy consumption and thermal comfort is a major concern in the management of HVAC systems. Energy consumption for HVAC systems has been widely discussed in the literature. Many researchers centered on mathematical models and simulation approaches. Nassif et al. [2e4] proposed a supervisory control strategy to optimize the set points of local-loop controllers used in a multi-zone HVAC system. Gebreslassie et al. [5] applied a mathematical programming approach to design environmentally conscious absorption cooling systems. Integrating building energy simulation software EnergyPlus with a generic optimization program GenOpt, Djuric et al. [6] built a model to optimize parameters influencing energy, thermal comfort, and investment cost. Tashtoush et al. [7] discussed deriving a dynamic model of an HVAC system for control analysis. Mossolly et al. [8] examined optimal control strategies of a variable air volume air conditioning system using a genetic algorithm.

* Corresponding author. Tel.: þ1 319 3355934; fax: þ1 319 3355669. E-mail address: [email protected] (A. Kusiak). 0360-5442/$ e see front matter 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2011.08.024

HVAC systems are complex, nonlinear, and large-scale systems involving numerous constraints, and thus many studies focused on using data mining approaches to build predictive models. Ari et al. [9] applied fuzzy logic and a neural network to approximate indoor comfort and energy optimization. Ben-Nakhi et al. [10] used general regression neural networks to optimize air conditioning setback scheduling in public buildings. To decrease the computational cost, Magnier et al. [11] developed a predictive model with TRNSYS simulations integrated by NSGA-II for HVAC systems. The methodology has been implemented successfully. Kusiak et al. [12e14] presented dynamic models to predict energy consumption and thermal comfort at current time and future time periods using neural networks. Chang et al. [15] employed the Hopfield neural network to determine the chilled water supply temperatures in chillers. Kusiak et al. [16] presented a data mining approach for the optimization of an HVAC system. This paper proposes a next-generation dynamic predictive model derived with data mining algorithms. A similar model has been studied in [14]. This model is optimized with a strength multiobjective particle-swarm optimization algorithm shown to be particularly suitable for solving complex, nonlinear, discrete, and large-scale systems. Many applications in the medical, marketing, manufacturing, and industrial sectors can benefit from data mining and PSO [17e21]. In this research data mining algorithms are applied to build a dynamic model based on a data set obtained from an HVAC system. A strength multi-objective particle-swarm


5936

A. Kusiak et al. / Energy 36 (2011) 5935e5943

Nomenclature Etotal EAHU EVAV ECHL EPump EFan y1 y2 y3 td

total energy consumed by HVAC system (kJ) energy consumption of an air handling unit (kJ) reheating energy in the variable air volume box (kJ) energy consumption of chillers (kJ) energy consumption of water pumps (kJ) energy consumption of supply fan and return fan (kJ) function of the AHU energy consumption function of the room temperature function of the room humidity ðd ¼ 1; 2; 3; .Þ d time steps prior to the current time t

optimization algorithm is used to find the optimal strategies for control of the HVAC system. 2. Problem analysis and solution methodology The total energy consumed by the HVAC system installed in a building includes two major components: the energy consumption of an air handling unit (AHU) EAHU and the reheating energy of the variable air volume (VAV) box EVAV expressed in Eq. (1). The energy consumed by the air handling unit EAHU includes the energy of the chillers ECHL, the energy consumption of the supply fan and the return fan EFan, and the energy consumption of the water pumps EPump expressed in Eq. (2).

ETotal ¼ EAHU þ EVAV

(1)

EAHU ¼ ECHL þ EFan þ EPump

(2)

The energy consumed by the hot water heaters, appliances, and lighting is not included in the model due to different control lops. The energy consumption of chillers, supply fan, return fan, and water pumps could be calibrated by the meters originally installed in the system. Since the AHU energy accounts for a large part of the total energy consumed by the HVAC system, the EAHU energy is considered in this paper. The functions y1, y2 and y3 representing the energy, the room temperature, and the room humidity are listed in Eq. (3) [14]:

min y1 ðtÞ y1 ðtÞ ¼ f1 ½y1 ðt dÞd˛D1y ; ½xðt dÞd˛Dx ; ½v1 ðt dÞd˛D1v y2 ðtÞ ¼ f2 ½y2 ðt dÞd˛D2y ; ½xðt dÞd˛Dx ; ½v2 ðt dÞd˛D2v y3 ðtÞ ¼ f3 ½y3 ðt dÞd˛D3y ; ½xðt dÞd˛Dx ; ½v3 ðt dÞd˛D3v

Table 2 Parameter selected based on domain knowledge. Parameter type

Parameter name

Description

Unit

Optimized parameters

SAT-SPT

AHU supply air temperature set point Supply air duct static pressure set point Chilled water coil valve position Supply air humidity Mixed air temperature Chilled water coil entering water temperature Supply air fan speed Return air fan speed Room temperature Outside air temperature Outside air humidity Outside air CO2 concentration Infrared radiation Solar normal flux Solar beam Barometric pressure Outside wind velocity Outside wind direction Energy consumption of AHU system Indoor temperature Indoor humidity

SASP-SPT

Uncontrollable parameters

Table 1 Description of data sets. Data set

Data set type

Time period

Number of instances

1

Cooling season

1488

2 3 4 5

Heating season Transient season Three seasons Test data set

08/01/2009e08/16/2009 & 09/22/2009e10/06/2009 02/03/2010e02/15/2010 04/02/2010e04/14/2010 All three above data sets 04/15/2010e04/17/2010

576 624 2688 144

CHWC-VLV SA-HUMD MA-TEMP CHWC-EWT

(3)

where y1 ðt dÞ˛R includes previous states of y1(t), e.g., y1 ðt 1Þ and y1 ðt 2Þ; x˛Rk is a vector of k optimized parameters at time t

(4)

subject to: xi ˛Sxi , where iis the number of solution vectors; yj ˛Syj ; j ¼ 1; 2; 3, where y1 refers to the energy consumption of AHU, y2 is the room humidity function and y3 is the room temperature function; Diy ,Dx , and Div are the sets containing time parameters of the corresponding function yi ¼ fi ð Þ, i ¼ 1; 2; 3; e.g., the parameter D2v2 ¼ f0; 1g implies that in function y2 the parameter v2 has two values, v2 ðtÞ and v2 ðt 1Þ. Note that the vector x˛Rk includes the optimized parameters (set points) appearing in the three functions of Eq. (4).

Controllable parameters

y1 ðtÞ ¼ f1 ½y1 ðt dÞd˛Dy ; ½xðt dÞd˛Dx ; ½vðt dÞd˛Dv y2 ðtÞ ¼ f2 ½y2 ðt dÞd˛Dy ; ½xðt dÞd˛Dx ; ½vðt dÞd˛Dv y3 ðtÞ ¼ f3 ½y3 ðt dÞd˛Dy ; ½xðt dÞd˛Dx ; ½vðt dÞd˛Dv

and the past states, e.g., x1 is the supply air temperature set point parameter at time t and x1 ðt 1Þ is the same parameter at time ðt 1Þ; v˛Rm is a vector of m uncontrollable and controllable parameters, e.g., v1 ðt 0Þ is the outside air temperature parameter at time t and v1 ðt 2Þ is at time ðt 2Þ; Dy, Dx, and Dv are sets containing parameter values for the three functions in Eq. (3), e.g., Dx1 ¼ f0; 1g indicates that the three functions contain two values for x1, x1 ðt 0Þ and x1 ðt 1Þ measured at the current time and t 1, respectively. Each functiony1 ¼ f1 ð Þ, y2 ¼ f2 ð Þ and y3 ¼ f3 ð Þdefined in [14] consideres identical controllable and uncontrollable parameters. This impacts accuracy of the predictive model as the parameters depend on the target functions. Therefore, in this paper the parameter selection algorithm selects the most important controllable or uncontrollable parameters for each function. A model minimizing AHU energy consumption is presented in Eq. (4).

Target parameters

SA-CFM RA-CFM RM-TEMP OA-TEMP OA-HUMD OA-CO2 IR-RADIA SOL-HORZ SOL-BEAM BAR-PRES WIND-VEL WIND-DIR AHU-ENERGY INDOOR-TEMP INDOOR-HUMD

F

in. WG %Open %RH F F

CFM CFM F F %RH PPM B/HFt2 B/HFt2 B/HFt2 mBar MPH Deg kJ F %RH


A. Kusiak et al. / Energy 36 (2011) 5935e5943 Table 3 AHU parameters selected for building predictive model at time t þ 1.

5937

Table 4 Room humidity parameters selected for building predictive model at time t þ 1.

Parameter

Point name

Description

Parameter

Point name

Description

y1 ðtÞ x1 ðtÞ

AHU energy SAT-SPT

y2 ðtÞ x1 ðtÞ x2 ðtÞ

RM-HUMD SAT-SPT SASP-SPT

x2 ðtÞ

SASP-SPT

v11 ðtÞ

CHWC-VLV

v12 ðtÞ v13 ðtÞ v12 ðt 1Þ v14 ðtÞ v15 ðtÞ

MA-TEMP RA-CFM MA-TEMP SA-CFM CHWC-EWT

v21 ðtÞ v22 ðtÞ v21 ðt 1Þ v22 ðt 1Þ v23 ðtÞ v23 ðt 1Þ v24 ðtÞ v25 ðtÞ

SA-HUMD OA-TEMP SA-HUMD OA-TEMP IR-RADIA IR-RADIA OA-CO2 CHWC-EWT

Room humidity at time t Supply air temperature set point at time t Supply air duct static pressure set point at time t Supply air humidity at time t Outside air temperature at time t Supply air humidity at time t 1 Outside air temperature at time t 1 Infrared radiation at time t Infrared radiation at time t 1 Outside air CO2 concentration at time t Chilled water coil entering water temperature at time t

v11 ðt 1Þ

CHWC-VLV

v16 ðtÞ

OA-TEMP

AHU energy at time t Supply air temperature set point at time t Supply air duct static pressure set point at time t Chilled water coil valve position at time t Mixed air temperature at time t 1 Return air fan speed at time t Mixed air temperature at time t 1 Supply air fan speed at time t Chilled water coil entering water temperature at time t Chilled water coil valve position at time t 1 Outside air temperature at time t

3. Experiment description and parameter selection The data set used in this research was collected from an experiment conducted at the Energy Resource Station (ERS) of the Iowa Energy Center. ERS is a facility for testing and demonstration of commercial HVAC systems including two independent test areas A and B. Each of the two test areas has four thermal zones and an airhandling unit (AHU) which is used to serve the four thermal zones. For each zone, a variable air volume (VAV) box connects to the corresponding AHU to maintain the thermal comfort of the zone. The data set also includes the outside weather condition records observed by sensors implemented around the building. Since the AHU accounts more than 60% of the total energy consumed by the HVAC system it is the focus of this research. There are two set points, namely the AHU static pressure set point (SA-SPSPT) and the supply air temperature set point (SAT-SPT) adjusted during the experiment in order to reflect

To build a dynamic model, time delay should be considered while performing the parameter selection. The past states of parameters may significantly impact the accuracy of the predictive model. The boosting tree and wrapper algorithms were applied to select the most significant parameters including their current and past states. Tables 3e5 list the parameters selected to model AHU energy consumption, room temperature, and room humidity at time stamp t þ 1. Each of the objective functions includes two parameters, SAT-SPT and SASP-SPT (see Table 2) optimized in Section 5. 4. Model building and validation In this section, a predictive model is built with a multi-layer perception (MLP) ensemble algorithm. According to [25], the MLP ensemble performed better than the chi-squared automatic interaction detector (CHAID), classification and regression tree (C&RT) algorithm, support vector machine (SVM), multi-layer perception (MLP), boosting tree, random forest, and multivariate adaptive regression spline (MARSpline) algorithms. Based on the parameters selected in Section 3, the predictive model is expressed in Eq. (5).

min y1 ðt þ 1Þ y1 ðt þ 1Þ ¼ f1 ðy1 ðtÞ; x1 ðtÞ; x2 ðtÞ; v11 ðtÞ; v12 ðtÞ; v13 ðtÞ; v12 ðt 1Þ; v14 ðtÞ; v15 ðtÞ; v11 ðt 1Þ; v16 ðtÞÞ

(5)

y2 ðt þ 1Þ ¼ f2 ðy2 ðtÞ; x1 ðtÞ; x2 ðtÞ; v21 ðtÞ; v22 ðtÞ; v21 ðt 1Þ; v22 ðt 1Þ; v23 ðtÞ; v23 ðt 1Þ; v24 ðtÞ; v25 ðtÞÞ y3 ðt þ 1Þ ¼ f3 ðy3 ðtÞ; x1 ðtÞ; x2 ðtÞ; v31 ðtÞ; v32 ðtÞ; v32 ðt 1Þ; v31 ðt 1Þ; v33 ðt 1Þ; v34 ðtÞÞ

a range of the HVAC system states. In this experiment, SP-SPT varied from 1.2 in. WG to 1.8 in. WG at 0.2 increments, while SAT-SPT varied from 50 F to 65 F with a 1 F increment. The data with more than 500 parameters was recorded at one-minute sampling intervals. The experiment period was from August 1, 2009 to April 17, 2010. This data used in this research includes five subsets. Data set 1 was collected in the cooling season, data set 2 represents a heating season, data set 3 was collected in a transient (cooling and heating) season, data set 4 contains the data from all three data sets, while data set 5 is used for testing. These data sets are summarized in Table 1. Note that the data in table is 1 h data derived from the original 1 min data. A small subset of the 300 parameters available in this research impact the AHU energy consumption and therefore relevant parameters need to be selected. The selection of appropriate parameters improves the comprehensibility, scalability, and possibly accuracy of the resulting models [22]. First, 21 parameters were selected based on domain knowledge (see Table 2). The boosting tree algorithm has been shown to perform well in [23,24], and therefore it is used in this paper to perform parameter selection using data set 4 of Table 1.

where y1 ðt þ 1Þ is the output for the energy of AHU to be optimized; x1 ðtÞ and x2 ðtÞ represents the set points that need to be optimized. To evaluate the performance of the MLP ensemble algorithm, the following four metrics are used: the mean absolute error (MAE) (Eq. (7)), the standard deviation of absolute error (Std_AE) (Eq. (10)), the Table 5 Room temperature parameters selected for building predictive model at time t þ 1. Parameter

Point name

Description

y3 ðtÞ x1 ðtÞ

RM-TEMP SAT-SPT

x2 ðtÞ

SASP-SPT

v31 ðtÞ v32 ðtÞ v32 ðt 1Þ v31 ðt 1Þ v33 ðt 1Þ v34 ðtÞ

RA-CFM SA-CFM SA-CFM RA-CFM SOL-HORZ MA-TEMP

Room temperature at time t Supply air temperature set point at time t Supply air duct static pressure set point at time t Return air fan speed at time t Supply air fan speed at time t Supply air fan speed at time t 1 Mixed air temperature at time t 1 Solar normal flux at time t 1 Mixed air temperature at time t


5938


Table 6 Prediction accuracy of the MLP ensemble algorithm for AHU energy, humidity, and temperature. Objective

Data set

MAE

AHU consumed energy Training 430.759 Validation 466.436 Room air humidity Training 0.7850 Validation 0.7855 Room air temperature Training 0.3725 Validation 0.3972

MAPE

Std_AE

Std_MAPE

0.036 373.624 0.039 0.036 411.342 0.036 0.02202 0.716 0.019 0.02196 0.765 0.019 0.0052 0.344 0.005 0.0056 0.439 0.006

Fig. 3. Validation of the room temperature model with 404 test points.

Start

Initialization Fig. 1. Validation of the AHU consumed energy for 404 test points.

Fitness calculation for evolutionary algorithm

mean absolute percentage error (MAPE) (Eq. (9)) and the standard deviation of absolute percentage error (Std_APE) (Eq. (11)) [26]:

~ AE ¼ y y Pn MAE ¼

i¼1

AEi

N

y ~ y APE ¼ y

Updating elites

(7)

Selection and mutation

(8)

Pn MAPE ¼

Finding non-dominated solutions

(6)

i¼1

APEi

N

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i ¼ 1 ðAEi MAEÞ Std AE ¼ N1

N

(9)

Termination condition

Y Fitness calculation for particle swarm optimization

(10)

Particle swarm optimization update

N

Termination condition Y End

Fig. 2. Validation of the room humidity model with 404 test points.

Fig. 4. The strength of multi-objective particle-swarm optimization algorithm.



5939

Table 7 Four scenarios involving different weight values. Scenario

Weight

Description

1

w1 ¼ 1; w2 ¼ 0; w3 ¼ 0

No AQI constraints

w1 ¼ 2 w2 ¼

8 > < 1; > : 0:5; 8 > < 0; > : 0:5;

if y2 ˛½49; 51 otherwise Preference humidity quality

if y2 ˛½49; 51 otherwise

w3 ¼ 0

w1 ¼ 3

4

8 > < 1; > : 0:5;

if y3 ˛½70:5; 71:5 otherwise

w2 ¼ 0 8 > < 0; if y3 ˛½70:5; 71:5 w3 ¼ > : 0:5; otherwise 8 > > > 1; if y2 ˛½49; 51; y3 ˛½70:5; 71:5 > > > > > < 0:5; if y2 ˛½49; 51; y3 ;½70:5; 71:5 w1 ¼ > > 0:5; if y2 ;½49; 51; y3 ˛½70:5; 71:5 > > > > > > : 0:34; if y2 ;½49; 51; y3 ;½70:5; 71:5

w2 ¼

w3 ¼

8 0; > > > > > > > > < 0;

Preference temperature quality

if y2 ˛½49; 51; y3 ˛½70:5; 71:5 if y2 ˛½49; 51; y3 ;½70:5; 71:5

> > > 0:5; if y2 ;½49; 51; y3 ˛½70:5; 71:5 > > > > > : 0:33; if y2 ;½49; 51; y3 ;½70:5; 71:5 8 > > > 0; if y2 ˛½49; 51; y3 ˛½70:5; 71:5 > > > > > 0:5; if y ˛½49; 51; y ;½70:5; 71:5 < 2

Preferences for humidity and temperature

3

> > 0; if y2 ;½49; 51; y3 ˛½70:5; 71:5 > > > > > > : 0:33; if y2 ;½49; 51; y3 ;½70:5; 71:5

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i ¼ 1 ðAPEi MAPEÞ Std APE ¼ N1

(11)

~ is the predicted value where AE in Eq. (7) is the absolute error, y obtained from the model, y is the actual target value measured, and N is the number of data points used for training or testing. The data in Table 6 shows performance of the MPL ensemble algorithm predicting AHU energy, humidity, and temperature. Fig. 1 illustrates

Fig. 5. AHU consumed energy optimization result for scenario 1.

the predicted and observed values of the AHU consumed energy for 404 1-hour data points drawn from data set 1. The predicted AHU energy function in Fig. 1 follows fairly closely the observed AHU energy curve. Table 6 presents the performance statistics. Figs. 2 and 3 illustrate the observed and predicted values of room humidity and room temperature, respectively. The performance for the three functions is summarized in Table 6.



5940



5. Optimization model A data-driven approach is suitable for modeling dynamic processes and prediction [13,14]. In this research the MLP ensemble algorithm was selected to build predictive models due to its superior performance discussed in [25]. The strength of the multi-objective particleswarm optimization (S-MOPSO) algorithm offers potential solutions. This algorithm is a combination of an evolutionary algorithm (strength pareto evolutionary algorithm (SPEA)) and a multi-objective particleswarm optimization algorithm. Evolutionary algorithms have an advantage in searching for optimal global solutions while particleswarm optimization is applicable in searching for optimal local solutions. Therefore, S-MOPSO is effective in finding optimal solutions of nonlinear multi-objective models. The strength of a multi-objective particle-swarm optimization algorithm is highlighted in Fig. 4. The energy consumption of AHU is minimized by implementing the optimal control settings generated by the S-MOPSO algorithm. The thermal comfort is addressed by including the relevant constraints in the objective function.

The parameters of the optimization model have been determined by the boosting tree algorithm. Table 2 lists the candidate parameters that could potentially be used to build the optimization model. Tables 3e5 list the parameters used in the AHU energy, room humidity, and room temperature objective functions. As controllable and uncontrollable input parameters are essentially independent of the optimized ones, the values of these parameters, such as supply air humidity, outside air temperature and other outside weather patterns, can be fixed in seeking the optimal control settings at each time stamp. The two optimized parameters, the AHU supply air temperature and the supply air duct static pressure set points, were varied to obtain optimal solutions. The model is designed to minimize AHU energy consumption as well as maintain thermal comfort at an acceptable level. AHU energy consumption, inside room humidity, and inside room temperature can be calibrated by the meters originally installed in the system. The input-output relationships were expressed by the HVAC system model presented in Eq. (5). AHU energy, humidity, and temperature objective functions are to be minimized. The constraints in the model are identified by assigning the lower and upper bounds of control parameters and set up an acceptable range of room humidity and temperature objectives. The value of the supply air temperature set point, the supply air duct static pressure set point, room temperature, and room humidity are restricted within the limits: Supply air temperature set point must vary between 50 F to 65 F. Supply air static pressure set point must vary between 1.2 in. WG and 1.8 in. WG. Room temperature must be maintained between 70.5 F and 71.5 F. Room humidity is controlled between 49% and 51% to meet the comfort requirements. Consequently, the optimization model is expressed in Eq. (12).

min y1 ðt þ 1Þ x1 ðtÞ;x2 ðtÞ

subject to : y1 ðt þ 1Þ ¼ f1 ðy1 ðt 1Þ; x1 ðtÞ; x2 ðtÞ; v11 ðtÞ; v12 ðtÞ; v13 ðtÞ; v12 ðt 1Þ; v14 ðtÞ; v15 ðtÞ; v11 ðt 1Þ; v16 ðtÞÞ y2 ðt þ 1Þ ¼ f2 ðy2 ðt 1Þ; x1 ðtÞ; x2 ðtÞ; v21 ðtÞ; v22 ðtÞ; v21 ðt 1Þ; v22 ðt 1Þ; v23 ðtÞ; v23 ðt 1Þ; v24 ðtÞ; v25 ðtÞÞ y3 ðt þ 1Þ ¼ f3 ðy3 ðt 1Þ; x1 ðtÞ; x2 ðtÞ; v31 ðtÞ; v32 ðtÞ; v32 ðt 1Þ; v31 ðt 1Þ; v33 ðt 1Þ; v34 ðtÞÞ 50 x1 ðtÞ 65 1:2 x2 ðtÞ 1:8 49 y2 ðt þ 1Þ 51 70:5 y3 ðt þ 1Þ 71:5

(12)

Let Obj1 ¼ y1 ðt þ 1Þ, Obj2 ¼ maxf0; 49 y2 ðt þ 1Þg þ max f0; y2 ðt þ 1Þ 51g and Obj3 ¼ maxf0; 70:5 y3 ðt þ 1Þg þ max f0; y3 ðt þ 1Þ 71:5gThen the constrained model (12) is transformed into an unconstrained model (13):

minðObj1; Obj2; Obj3Þ x1 ðtÞ;x2 ðtÞ

where : Obj1 ¼ y1 ðt þ 1Þ Obj2 ¼ max½0; 49 y2 ðt þ 1Þ þ max½0; y2 ðt þ 1Þ 51 Obj3 ¼ max½0; 70:5 y3 ðt þ 1Þ þ max½0; y3 ðt þ 1Þ 71:5 50 x1 ðtÞ 65 1:2 x2 ðtÞ 1:8 Fig. 8. AHU consumed energy optimization result for scenario 4.

(13)



5941

Fig. 11. Optimized room temperature in scenario 1.

Fig. 9. Optimized room humidity in scenario 1.

In this research, a strength multi-objective PSO (S-MOPSO) was used to solve the model (14). Considering AHU energy consumption and thermal constraints are two objectives aimed to be both minimized, non-dominated results were found at each time stamp. The algorithm steps are listed next. Step 1 Step 2 Step 3 Step 4 Step 5 Step 6

Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13

Initialize a population P and create an empty external population P* to store elite solutions. Find non-dominated solutions in P and copy them into P*. Find non-dominated solutions in P and update the elite population P*. Assign fitness values to each individual in P and P*. Select a set of Pparent of size Nparent from P þ P* using the binary tournament selection scheme with replacement. Randomly select two individuals and add a better one to Poffspring. Apply recombination and mutation operators to Poffspring. Stopping criterion: the maximum number of generations. If not exceeded, return to Step 2. Using the final external population P* as the particles for PSO. Calculate each particle’s fitness. Update best local solutions from each particle. Update best global solutions from previous global best solutions and current best local solutions. Update the velocity for each particle. Stopping criterion: the maximum number of generations. If not exceeded, return to Step 9.

Fig. 12. Optimized room temperature in scenario 3.

is 0.95, 2, and 2 respectively while the maximum number of iterations is also set at 50. Note that the observed values of the data set 4 are used, rather than the predicted ones, in the optimization. The optimal solution is selected from the final elite set by the weighted normalized objective function (14).

Obj ¼ w1

Obj1 Obj1min Obj2 Obj2min þ w2 Obj1max Obj1min Obj2max Obj2min

þ w3

Obj3 Obj3min Obj3max Obj3min

(14)

The S-MOPSO algorithm is applied to solve model (13). The initial population size is 100 and the maximum number of iterations for SPEA part is set at 50. The weights, c1, and c2 for PSO part

where w1, w2, w3 are the user-defined weights indicating their preferences of the corresponding objective, and Obj1max and Obj1min are the maximum and the minimum values of Obj1 in the final elite set. Similar notation is used for Obj2max, Obj2min, Obj3max

Fig. 10. Optimized room humidity in scenario 2.

Fig. 13. Supply air static pressure set point before and after optimization for scenario 1.


5942

A. Kusiak et al. / Energy 36 (2011) 5935e5943 Table 8 The results from S-MOPSO and traditional MOPSO. Scenario

1

2

3

4

S-MOPSO energy savings of AHU (%) MOPSO energy savings of AHU (%)

21.6 18.8

18.6 11.2

17.9 9.5

13.4 3.32

Fig. 14. Supply air static pressure set point before and after optimization for scenario 4.

Percentage of Energy Saving (%)

25 20 15 10 5 0 1

2

Energy savings by S-MOPSO (%)

3

4

Energy savings by MOPSO (%)

Fig. 17. Comparison of energy savings of AHU by the S-MOPSO and MOPSO algorithms.

Fig. 15. Supply air temperature set point before and after optimization for scenario 1.

P and Obj3min. Note that 3m ¼ 1 wm ¼ 1, with w1 ; w2 ; w3 being either constants or functions of other objectives. Table 7 presents four scenarios representing different preferences to the objectives. Figs. 5e8 show the optimized AHU energy in the four scenarios shown in Table 7. The optimal solutions for AHU energy consumption are just below the observed counterparts indicated from these four figures. Additionally, the percentage of AHU energy saving declines downward with more constraints. Figs. 9 and 10 show optimized room humidity in scenario 1 and scenario 2, which only considers room humidity as a constraint. Figs. 11 and 12 illustrate optimized room temperature in scenarios 1 and 3 with room temperature as a constraint. Figs. 13e16 show the optimized two set points in scenario 1 and scenario 4. Comparing scenario 1 and scenario 4, the supply air

static pressure set point fluctuates more largely in scenario 4. This is because scenario 4 considers inside room humidity and temperature as constraints while scenario 1 only considers AHU energy output. This situation is more obvious for the supply air temperature set point shown in Figs. 15 and 16. Table 8 and Fig. 17 compare the results produced by the strength multi-objective particle-swarm optimization algorithm S-MOPSO and the multi-objective particle-swarm optimization MOPSO algorithm. 6. Conclusion A data-driven approach for optimization of AHU energy consumed by an HVAC system was presented. A multiple-layer perception ensemble (MLP ensemble) algorithm was selected to build a predictive model. Then a strength multi-objective particleswarm optimization algorithm was applied to optimize the predictive model. The dynamic predictive model built by the MLP ensemble algorithm was highly accurate when tested on data set 4. Optimal control settings of the supply air temperature and static pressure were generated at hourly time intervals to minimize AHU energy consumption while maintaining air quality at an acceptable level. The optimization approach provides satisfactory solutions for users with different preferences. An analysis and discussion on indoor air quality (IAQ) metrics were included in this research. Acknowledgement This research has been supported by the Iowa Energy Center, Grant No. 08-01. References

Fig. 16. Supply air temperature set point before and after optimization for scenario 4.

[1] Pérez-Lombard L, Ortiz J, Pout C. A review on building energy consumption information. Energy and Buildings 2008;40(3):394e8. [2] Nassif N, Moujaes S. A cost-effective operating strategy to reduce energy consumption in a HVAC system. International Journal of Energy Research 2008;32:543e58. [3] Nassif N, Kajl S, Sabourin R. Evolutionary algorithms for multi-objective optimization in HVAC system control strategy. Fuzzy Information 2004;1:51e6. [4] Nassif N, Kajl S, Sabourin R. Optimization of HVAC control system strategy using two objective genetic algorithm. HVAC & Research 2005;11(3):459e86.


A. Kusiak et al. / Energy 36 (2011) 5935e5943 [5] Gebreslassie BH, Guillen-Gosalbez G, Jimenez L, Boer D. Design of environmentally conscious absorption cooling systems via multi-objective optimization and life cycle assessment. Applied Energy 2009;86(9): 1712e22. [6] Djuric N, Novakovic V, Holst J, Mitrovic Z. Optimization of energy consumption in buildings with hydronic heating systems considering thermal comfort by use of computer-based tools. Energy and Buildings 2007; 39(4):471e7. [7] Tashtoush B, Molhim M, Al-Rousan M. Dynamic model of an HVAC system for control analysis. Energy 2005;30(10):1729e45. [8] Mossolly M, Ghali K, Ghaddar N. Optimal control strategy for a multi-zone air conditioning system using a genetic algorithm. Energy 2009;34(1): 58e66. [9] Ari S, Khalifa HE, Dannenhoffer JF, Wilcoxen P, Isik C. Fuzzy logic and neural network approximation to indoor comfort and energy optimization. Fuzzy Information Processing Society; 2006. p. 692e5. [10] Ben-Nakhi AE, Mahmoud MA. Energy conservation in buildings through efficient A/C control using neural networks. Applied Energy 2002;73(1): 5e23. [11] Magnier L, Haghighat F. Multiobjective optimization of building design using TRNSYS simulations, genetic algorithm, and artificial neural network. Building and Environment 2010;45(3):739e46. [12] Kusiak A, Li M, Tang F. Modeling and optimization of HVAC energy consumption. Applied Energy 2010;87(10):3092e102. [13] Kusiak A, Li M. Reheat optimization of the variable-air-volume box. Energy 2010;35(5):1997e2005. [14] Kusiak A, Li M. Cooling output optimization of an air handling unit. Applied Energy 2010;87(3):901e9.

5943

[15] Chang Y-C, Chen W-H. Optimal chilled water temperature calculation of multiple chiller system using Hopfield neural network for saving energy. Energy 2009;34(4):448e56. [16] Kusiak A, Tang F, Xu G. Multi-objective optimization of HVAC system with an evolutionary computation algorithm. Energy 2011;36(5):2440e9. [17] Zhang C, Shao H, Li Y. Particle swarm optimization for evolving artificial neural network. System, Man, and Cybernetics 2000;4:2487e90. [18] Chau KW. Application of a PSO-based neural network in analysis of outcomes of construction claims. Automation in Construction 2007;16(5):642e6. [19] Lu WZ, Fan HY, Lo SM. Application of evolutionary neural network method in predicting pollutant levels in downtown area of Hong Kong. Neurocomputing 2003;51:387e400. [20] Chatterjee A, Pulasinghe K, Watanabe K, Izumi K. A particle-swarm-optimized fuzzy-neural network for voice-controlled robot. Industrial Electronics 2005; 52(6):1478e89. [21] Cai X, Zhang N, Venayagamoorthy GK, Wunsch DC. Time series prediction with recurrent neural networks using a hybrid PSO-EA algorithm. Neural Networks 2004;2:1647e52. [22] Wang J. Data mining: opportunities and challenges. Hershey, PA: Idea Group Inc; 2003. [23] Friedman J. Stochastic gradient boosting. Stanford, CA: Statistics Department, Stanford University; 1999. [24] Hastie T, Tibshirani R, Friedman J. The elements of statistical learning. New York: Springer; 2001. [25] Kusiak A, Li M, Zhang Z. A data-driven approach for steam load prediction in buildings. Applied Energy 2010;87(3):925e33. [26] Casella G, Berger R, editors. Statistical inference. Pacific Grove, CA: Duxbury Press; 1990.