HVAC system modeling and optimization: a datamining

Transcription

1 University of Iowa Iowa Researh Online Theses and Dissertations Fall 2010 HVAC system modeling and optimization: a datamining approah Fan Tang University of Iowa Copyright 2010 Fan Tang This thesis is available at Iowa Researh Online: Reommended Citation Tang, Fan. "HVAC system modeling and optimization: a data-mining approah." MS (Master of Siene) thesis, University of Iowa, Follow this and additional works at: Part of the Industrial Engineering Commons

2 HVAC SYSTEM MODELING AND OPTIMIZATION: A DATA-MINING APPROACH by Fan Tang A thesis submitted in partial fulfillment of the requirements for the Master of Siene degree in Industrial Engineering in the Graduate College of The University of Iowa Deember 2010 Thesis Supervisor: Professor Andrew Kusiak

3 Copyright by FAN TANG 2010 All Rights Reserved

4 Graduate College The University of Iowa Iowa City, Iowa CERTIFICATE OF APPROVAL MASTER S THESIS This is to ertify that the Master s thesis of Fan Tang has been approved by the Examining Committee for the thesis requirement for the Master of Siene degree in Industrial Engineering at the Deember 2010 graduation. Thesis Committee: Andrew Kusiak, Thesis Supervisor Yong Chen Gideon Zamba

5 To My Parents and Family ii

6 Strength alone knows onflit, weakness is below even defeat, and is born vanquished. Swethine iii

7 ACKNOWLEDGMENTS I would like to express my sinere gratitude to my advisor Professor Andrew Kusiak, for his devotion to this researh. He has been the most instrumental person for my aademi and researh ahievements. He provided the motivation, enouragement, guidane and advie whih have prepared me for the hallenges of future life. I was fortunately exposed to industrial appliations while working in the Intelligent Systems Laboratory. This invaluable experiene has allowed me to maintain a balane between theory and pratie leading to realisti solutions. I would like to thank Professor Yong Chen and Professor Gedion Zamba for serving on my Thesis Committee and providing valuable suggestions and feedbak on my researh. I am also grateful for the finanial support from Iowa Energy Center. Disussions with energy experts: Curt Klaassen (Iowa Energy Center), Xiaohui Zhou (Iowa Energy Center), William Haman (Iowa Energy Center), Jiong Zhou (Failities Management, The University of Iowa) and George Paterson (Failities Management, The University of Iowa) have provided me invaluable information for this researh. I thank all the members of the Intelligent Systems Laboratory who have worked with me and provided advie, reviews and suggestions. Speial thanks to my olleagues: Mingyang Li, who worked with me to solve hallenging problems in HVAC system; Zijun Zhang, who provided valuable advies for me; Wenyan Li, who shared the researh experiene with me; Evan Roz, who disussed with me about data analysis and system modeling; Anoop Verma, who disussed the problems I enountered; and Guanglin Xu, who ooperated with me to deal with existing problems. And finally, and most importantly, I would like to express my sinere gratitude to my parents and my girlfriend, who solidly supported me in pursuing my areer. iv

8 ABSTRACT Heating, ventilating and air-onditioning (HVAC) system is a omplex non-linear system with multi-variables simultaneously ontributing to the system proess. It poses hallenges for both system modeling and performane optimization. Traditional modeling methods based on statistial or mathematial funtions limit the harateristis of system operation and management. Data-driven models have shown powerful strength in non-linear system modeling and omplex pattern reognition. Suffiient suessful appliations of data mining have proved its apability in extrating models that aurately desribe the relation of inner system. The heuristi tehniques suh as neural networks, support vetor mahine, and boosting tree have largely expanded to the modeling proess of HVAC system. Evolutionary omputation has rapidly merged to the enter stage of solving the multiobjetive optimization problem. Inspired from the biology behavior, it has shown the tremendous power in finding the optimal solution of omplex problem. Different appliations of evolutionary omputation an be found in business, marketing, medial and manufaturing domains. The fous of this thesis is to apply the evolutionary omputation approah in optimizing the performane of HVAC system. Energy saving an be ahieved by implementing the optimal ontrol setpoints with IAQ maintained at an aeptable level. A trade-off between energy saving and indoor air quality maintenane is also investigated by assigning different weights to the orresponding objetive funtion. The major ontribution of this researh is to provide the optimal settings for the existing system to improve its effiieny and different preferene-based operation methods to optimally utilize the resoures. v

9 TABLE OF CONTENTS LIST OF TABLES... viii LIST OF FIGURES... ix CHAPTER 1 INTRODUCTION Review of analytial approahes in modeling and optimization Review of data-driven approahes in modeling Review of evolutionary omputation in system optimization Thesis struture...4 CHAPTER 2 SHORT-TERM PREDICTION OF HVAC ENERGY WITH A CLUSTERING APPROACH Introdution HVAC system struture desription Data desription Modeling of AHU system and AQI sensors Parameter seletion Algorithm seletion Model onstrution and validation Clustering-based model of AHU energy The modeling arhiteture of the AHU energy Clustering algorithm Case study Clustering Modeling based on lustering Clustering-based short-term predition of AHU energy Summary...29 CHAPTER 3 MULTI-OBJECTIVE OPTIMIZATION OF HVAC SYSTEM WITH AN EVOLUTIONARY COMPUTATION ALGORITHM Introdution Data desription and optimization methodology Data desription Optimization approah HVAC system modeling Parameter seletion Constrution and validation of the preditive model Optimization Algorithm Model formulation Optimization Summary...48 CHAPTER 4 MODELING AND OPTIMIZATION OF ENERGY RELATED COMPONENTS IN HVAC SYSTEM Introdution Data desription Parameter and algorithm seletion...50 vi

10 4.4. Modeling building and validating Optimization model formulation and solving Optimization results and disussion Summary...65 CHAPTER 5 MULTI-OBJECTIVE OPTIMIZATION OF HVAC SYSTEM ENERGY MANAGEMENT Introdution Data desription and parameter seletion Algorithm seletion Modeling building and validation Model formulation and solving Single-objetive optimization model formulation and solving Formulation and solving of the quad-objetive optimization model Weight assignment and solution seletion Optimization results and disussion Summary...85 CHAPTER 6 CONCLUSION...87 REFERENCES...89 vii

11 LIST OF TABLES Table 2.1. Data desription....9 Table 2.2. Parameter desription Table 2.3. Parameter seletion result of the orresponding target value by boosting tree algorithm Table 2.4. Training and testing results for models extrated from different data-mining algorithms Table 2.5. Charaterization of the four MLP Ensemble models Table 2.6. Correlation oeffiients between observed and predited values of the four models Table 2.7. Clusters based on CHWC-VLV Table 2.8. Clusters based on OA-Temp Table 2.9. Predition results for four senarios Table 2.10.Short-term predition results for Senario 1 and Senario Table 3.1. Data desription Table 3.2. Results of different wrapper algorithms Table 3.3. Parameter desription Table 3.4. Predition results of energy onsumption model Table.3.5. Predition results of room humidity model Table.3.6. Predition results of room temperature model Table 3.7. Results of different deisions made by their preferenes Table 4.1. Data desription Table 4.2. Preditor importane produed by the boosting tree algorithm Table 4.3. The results of parameter seletion by the wrapper approah Table 4.4. Parameter desription Table 4.5. Algorithms seletion for building the total energy model Table 4.6. Training and test results of the four models viii

12 Table 4.7. Energy savings with varied adjustment length of setpoints Table 5.1. Data desription...68 Table 5.2. Parameter desription...68 Table 5.3. Training and testing auray results for models extrated with different data-mining algorithms...70 Table 5.4. Correlation oeffiient of the observed and predited values of the four models...73 Table 5.5. Instane used in single-objetive optimization...74 Table 5.6. Desription of the eight weight assignment senarios Table 5.7. Solutions for the eight senarios at some time stamp...82 ix

13 LIST OF FIGURES Figure 1.1 Struture of the thesis....4 Figure 2.1. Shemati of zones in the building served by AHU-A and AHU-B....7 Figure 2.2. Shemati of AHU-B of HVAC system....7 Figure 2.3. Outside air temperature of the data olleted in the whole period....9 Figure 2.4. Test results obtained from the energy onsumption model Figure 2.5. Test results obtained from the indoor temperature model Figure 2.6. Test results obtained from the indoor humidity model Figure 2.7. Test results obtained from the CO2 onentration model Figure 2.8. Cluster-based sheme for model building...20 Figure 2.9. Satter plots showing relationships between energy onsumption and seleted parameters Figure Graphial interpretation of lustering based on CHWC-VLV Figure Graphial interpretation of lustering based on OA-Temp Figure Mean absolute error for four senarios Figure Mean absolute perentage error for four senarios Figure The arhiteture of lustering-based short-term predition of AHU energy. 27 Figure Short-term predition of AHU energy for Senario Figure Short-term predition of AHU energy for Senario Figure 3.1. The daily shedule of supply air stati pressure and internal load Figure 3.2. Optimization framework Figure 3.3. Change of CHWC-VLV position on 04/06/ Figure 3.4. Feasible solutions solved by SPEA at some time stamp Figure 3.5. Test results of optimized energy onsumption Figure 3.6. Test results of thermal onstraints Figure 3.7. Test results of optimized room temperature Figure 3.8. Test results of optimized room humidity ix

14 Figure 3.9. Reommended supply air temperature set point Figure Reommended supply air stati pressure set point Figure 4.1. Test results for the hiller energy model Figure 4.2. Test results for the fan energy model Figure 4.3. Test results for the pump energy model Figure 4.4. Test results for the reheat energy model Figure 4.5. The total energy before and after optimization Figure 4.6. The air temperature setpoint before and after optimization Figure 4.7. The supply air stati pressure setpoint before and after optimization Figure 4.8. The fan energy before and after optimization Figure 4.9. The pump energy before and after optimization Figure The reheat devie energy before and after optimization Figure The hiller energy before and after optimization Figure The ooling output before and after optimization Figure Comparison of the IAQ metris before and after optimization Figure 5.1. Test results from the total energy model...71 Figure 5.2. Test results from the faility temperature model...72 Figure 5.3. Test results from the faility relative humidity model...72 Figure 5.4. Test results from the faility CO 2 onentration model...73 Figure 5.5. Two dimensional solution spaes...78 Figure 5.6. The solution proess...78 Figure 5.7. The original and reommended setpoints of the supply air temperature...82 Figure 5.8. The original and reommended setpoints of the supply air stati pressure...83 Figure 5.9. The original and the optimized total energy...83 Figure The original and the optimized faility temperature...84 Figure The original and the optimized faility relative humidity...84 Figure The original and the optimized faility CO 2 onentration...85 x

15 1 CHAPTER 1 INTRODUCTION HVAC system is designed to provide a omfortable and desired environment for the oupants, in addition to meeting any speial proess requirements, suh as indoor air quality. The maintenane of a healthy indoor ondition of HVAC system is signifiant sine people spend more than half of their time indoors. The issue of growing energy use has merged to the stage whih draws suffiient attentions of not only ommerial managers, but also researhers. Aording to the published statistis, HVAC system frequently onsumes over 60% of the energy use in buildings [1, 2]. Therefore, the operation effetiveness and effiieny of HVAC system has beome a fous. The operation of HVAC system is a multi-angle problem. Simply minimizing the energy onsumption without onsidering the indoor air quality ontrol is not aeptable. The optimal ontrol strategies should redue the system ost and energy use while maintaining the thermal omfort at an allowable level. With both eonomi ost and oupany omfort involved, a omprehensive way of system modeling and performane optimization is addressed in this paper Review of analytial approahes in modeling and optimization The analytial approahes for modeling HVAC system depend on the physis-based models or simulation software. Wang et al [3] presented a simple hybrid model based on the heat transfer mehanism and the energy balane priniple to predit the performane of hilled water ooling oils in a stati state. Yu et al [4] developed and evaluated the simulation model for dynami performane of both dry and wet ooling oils based on energy equations and mass balane equations. Yao et al [5] proposed a dynami model desribing the ooling oils heat and mass exhange using lassial ontrol theory. Suh analytial models are reliable one ertain basi assumptions and simplifiations are ahieved. However, detailed physis-based models are always omputationally expensive due to their omplexity and non-linearity, whih results in the

16 2 troubles in pratial appliation [6]. To overome the barrier, simulation-based models have been widely investigated. Suffiient surveys and summaries have been addressed regarding the different simulation programs [7-10]. Wang [11] developed dynami models inluding multiple omponents to simulate the realisti performanes of the hilling system. The simulation exerises were tested and evaluated by the on-line ontrol of EMCS loal strategy and supervisory strategy in different seasons. Crawley et al [12] broadly introdued twenty simulation programs applied nowadays and a basi omparison was made to show the orresponding features and apabilities. Although the merits in simulation-based modeling exist, one restrition is that many omponents models are steady state whih is not suitable for handling high frequeny disturbanes [13]. To solve optimization problems formulated by analytial models, many nonlinear loal optimization tehniques an be used. Sun et al [14] developed a omprehensive simulation-based sequential quadrati programming (CSB-SQP) algorithm to optimally ontrol the HVAC system. Rink et al [15] applied the state inrement dynami programming to solve the optimization problem of multi-zone HVAC system whih was demonstrated to be effiient in saving energy. Kota et al [16] presented the DDP (differential dynami programming) tehnique of optimal ontrol in HVAC systems and they ompared its performanes with sequential quadrati programming method Review of data-driven approahes in modeling Be different from analytial approahes, a data-driven approah is derived from empirial behavior and heuristi searhing proess of the system. The modeling approah that has drawn the most attention in the last few years seems to be the neural networks [17, 18]. It has a tremendous power in deriving and extrating the aurate patterns from ompliated, noisy, and impreise data. A lot of appliations have been ahieved by using neural networks to onstrut the non-linear energy onsumption model in HVAC system. A typial appliation of data drivenmethods is prediting steam load in buildings [19]. Another example inludes the use of a neural

17 3 network to predit heating energy onsumption [20]. Kalogirou [21-23] applied neural networks to modeling solar water heating systems, and HVAC system. Kreider and Wang [24] used neural networks to predit the rate of energy use in ommerial buildings. One shortoming of datadriven models is that insuffiient data will result in the derease of model auray sine the training data may only over a small range of data patterns Review of evolutionary omputation in system optimization The operation of HVAC system is a ritial ativity in terms of optimizing the ontrol settings to redue the energy onsumption, improving the system effiieny, and preserving the thermal omfort for the oupants. The performane of the existing HVAC system an be largely improved by adjusting the ontrol set points to maximize the overall system apaity and effiieny. Ke and Mumma [25] studied the impat on energy onsumption of tuning the supply air temperature set point in a VAV system and found that an optimal supply air temperature setting existed for minimizing the energy ost. Wang et al. [26] proposed a systemati approah for an on-line ontrol strategy of air-onditioning systems. A ost funtion was formed to weight the energy onsumption of the entire system ontaining fan, pump, and hiller, the indoor thermal omfort, indoor air quality, and the total ventilation rate. The geneti algorithm was applied to searh the optimal ontrol settings resulting in redution of energy based on the inremental dynami models with self-tuning of the VAV system. Nassif et al. [27, 28] applied the multi-objetive evolutionary algorithms to optimize a multi-zone HVAC system, and supervisory ontrol settings were found to redue the energy onsumption as well as maintaining the thermal omfort. Mossolly et al. [29] examined three ontrol strategies on the system omponent models solved by the geneti algorithm, whih is implemented in Matlab. It was proven that huge energy saving ould be ahieved by varying the system parameters. Magnier and Haghighat [30] used a simulation-based artifiial neural network (ANN) to apture the mapping of building behavior, and implemented the ANN model into geneti algorithm for optimization. By doing so, signifiant improvements regarding energy performane and thermal

18 4 omfort were ahieved and a large number of potential designs for operating the HVAC system were revealed Thesis struture Figure 1.1 illustrates the struture of the thesis. Chapter 1 introdues a lustering-based HVAC system modeling and short-term predition. In Chapter 2, an evolutionary omputation algorithm is applied to solve a multi-objetive optimization problem in HVAC system. Energy related omponents suh as heat, fan, pump and reheat are optimized by a single objetive optimization algorithm, respetively in Chapter 3. Finally, Chapter 5 presents an optimal ontrol strategy for HVAC system energy management. Figure 1.1 Struture of the thesis.

19 5 CHAPTER 2 SHORT-TERM PREDICTION OF HVAC ENERGY WITH A CLUSTERING APPROACH 2.1. Introdution The energy used for heating, ventilating, and air-onditioning has beome a onern, as it onstitutes over 50% of the energy onsumed by offie buildings in the US [1, 2]. Suh energy an be optimized if the underlying model is known. In this researh, the energy needed to maintain thermal omfort in an offie-type building is studied. This energy is supplied by a heating, ventilating, and air-onditioning (HVAC) system. For the best optimization results, a short-term predition model is developed. This model is referred to in this setion as the HVAC energy model. The HVAC energy model is omplex, non-linear, and depends on a number of parameters, e.g., weather, fan speed, and hilled water valve position. Consequently, it is not easy to apture the relationship between the input and output parameters. As mentioned in the Chapter 1, neural network has shown tremendous power in HVAC system modeling. In addition to the single neural network model, a different type of model ombining the data partitioning tehniques with neural network algorithm shows a good potential in improving the existing data-driven models. Sfetsos [31] introdued a hybrid lustering model for short-term load foreasting. Sub-models were onstruted based on the lusters using neural network. Predition error was redued by approximately 7.5% ompared with single neural network model. Hiroyuki and Atsushi [32, 33] applied the deterministi annealing lustering model ombined with neural networks to predit short-term load of power system. Kusiak and Li [34] applied the lustering method for short-term predition of wind power. The lustering-based neural network model was developed and it produed aurate predition even using a small number of inputs.

20 6 A four-phase method for the short-term predition of HVAC energy is presented. In Phase 1, the most important parameters are seleted, and a parameter sensitivity analysis is performed. The input data is grouped into lusters in Phase 2. In Phase 3, a multi-layer pereptron (MLP) is onstruted in eah luster. In Phase 4, the effetiveness of the proposed lustering approah is tested. The performane of the luster-based HVAC energy model is disussed and a onlusion is drawn based on the results HVAC system struture desription The investigated HVAC system is installed at Energy Resoure Station (ERS) in Ankeny, Iowa. It onsists of two independent air-handling units (AHU-A and AHU-B) providing the loads for 20 interior zones in the whole building. Eah air-handling unit serves 4 test rooms, whih are used to ollet the original data in this experiment, loated in all the diretions of the building. For eah zone, a variable air volume (VAV) box is onneted to the air-handling unit to meet the load of the room thermal omfort. The outside weather onditions are also reorded by the sensors implemented around the building. The experiment in ERS is designated to investigate the impats of different parameters on the total energy onsumption for ommerial buildings. Figure 2.1 shows the floor plan of the building served by AHU-A and AHU-B. Figure 2.2 shows the shemati of AHU-B of the HVAC system.

21 7 Figure 2.1. Shemati of zones in the building served by AHU-A and AHU-B. Figure 2.2. Shemati of AHU-B of HVAC system.

22 Data desription The data olleted in this researh was obtained from an experiment performed at the ERS of the Iowa Energy Center. Two setpoints, namely the AHU supply air temperature setpoint and stati pressure setpoint were adjusted in both AHU-A and AHU-B systems. The supply air temperature (SAT) setpoint varied from 50 F (10 C) to 65 F (18.33 C) with 1 F (0.55 C) inrements. The supply air stati pressure (SASP) setpoint varied from 1.2 in WG (0.3 kpa) to 1.8 in WG (0.45 kpa) with 0.2 in WG (0.05 kpa) inrements. Data on more than 500 parameters was olleted at 1 min sampling intervals. Sensors measured air temperature, air humidity, and CO 2 onentration in eah thermal zone of HVAC system. Weather patterns suh as outside air temperature, humidity, solar normal flux, were also reorded. The original data was reorded over three different time periods overing summer, winter, and a transient season. In the summer season, data was olleted from two experiments performed from August 1 to August 16, 2009 and from September 22 to Otober 6, For the winter and transient season, the data was olleted from February 3 to February 15, 2010 and from April 1 to April 14, 2010, respetively. A three-day validation experiment was onduted from April 15 to April 17, 2010 with the AHU SAT setpoint set at 55 F and the SASP setpoint set at 1.4 WG. The data olleted from the three seasons was ombined to obtain the joint data set of 2688 instanes from AHU-A and AHU-B. Figure 2.3 illustrates the outside air temperature hange during all three time periods. To redue the error produed by time delay and system error, the original 1 min data was aggregated to 1 h interval data by averaging the values of all of the parameters. After preproessing, The joint data set of 2688 instanes was randomly sampled to produe a training set of 1882 instanes (70% of the data) and a test set of 806 instanes (30% of the data). Table 2.1 summarizes the data olleted in ERS experiment in detail.

23 9 Table 2.1. Data desription. Data set Data Type Time Period No. of Instanes 1 Summer season 08/01/ /16/2009 & 09/22/ /06/ Winter season 02/03/ /15/ Transient season 04/02/ /14/ The whole year umulating the three separate seasons Predition 04/15/ /17/ OA-TEMP Outside air temperature [F] -20 Figure 2.3. Outside air temperature of the data olleted in the whole period Modeling of AHU system and AQI sensors Parameter seletion Parameter seletion is ritial in the onstrution of models. A typial HVAC system may ontain hundreds of parameters. Some of the parameters olleted are relevant to the output, while others ould be irrelevant or redundant. The presene of irrelevant or redundant parameters may mask the primary patterns disovered in data mining. Redundant parameters dupliate the information ontained in other parameters, making the model more omplex than it should be. Eliminating redundant or less important parameters may improve the auray, salability, and omprehensibility of the resulting model [35].

24 10 Based on the domain knowledge, the twenty-one originally seleted parameters were divided into four groups: performane parameters, ontrollable parameters, unontrollable parameters, and target parameters. Two setpoints, the AHU supply air temperature and the supply air dut stati pressure, were seleted as the performane parameters to be adjusted for energy optimization. The ontrollable parameters (e.g., fan speed, hilled water oil valve position (CHWC-VLV), and mixed air temperature (MA-Temp)) were highly orrelated to the AHU energy and AQI (air quality index) values, and thus had a large effet on the output results. The weather data represent unontrollable parameters. Four outputs, the AHU energy onsumption, indoor air temperature, indoor air humidity, and indoor CO 2 onentration, were the target parameters to be predited by the model. Table 2.2 lists all of the parameters and their definitions.

25 11 Table 2.2. Parameter desription. Parameter Type Parameter Desription Unit Name Performane Parameter SAT setpoint AHU supply air temperature set point Deg F SASP setpoint Supply air dut stati pressure set point kpa Controllable Parameter CHWC-VLV Chilled water oil valve position %Open Unontrollable Parameter SA-Humd Supply air humidity % RH MA-Temp Mixed air temperature Deg F CHWC-EWT Chilled water oil entering water Deg F temperature SA-CFM Supply air fan speed CFM RA-CFM Return air fan speed CFM OA-Temp Outside air humidity Deg F OA-Humd Outside air temperature % RH OA- CO 2 Outside air CO 2 onentration PPM IR-Radia Infrared Radiation B/HFt2 SOL-Horz Solar normal flux B/HFt2 SOL-Beam Solar beam B/HFt2 BAR-Pres Barometri Pressure (normalized to sea mbar level) WIND-Vel Outside wind veloity MPH WIND-Dir Outside wind diretion Degn=0 Target Parameter AHU-Energy Energy onsumption of AHU system kj Indoor-Temp Indoor temperature Deg F Indoor-Humd Indoor humidity % RH Indoor- CO 2 Indoor CO 2 onentration PPM To analyze the sensitivity of the parameters and selet the most important parameters for the predition of the target values, the seletion of ontrollable and unontrollable parameters was performed using the boosting tree algorithm [36]. Beause of the different harateristis of the outputs, the input parameters used to build preditive models were ranked. The boosting tree algorithm was applied four times with the orresponding output as the target value. The results are shown in Table 2.3.

26 12 Table 2.3. Parameter seletion result of the orresponding target value by boosting tree algorithm. Energy Consumption Indoor Temperature Variable Importane Variable Importane CHWC-VLV 1.00 SA-CFM 1.00 OA-Temp 0.95 RA-CFM 0.98 MA-Temp 0.93 MA-Temp 0.82 CHWC-EWT 0.92 SA-Humd 0.75 RA-CFM 0.78 OA-Temp 0.71 SA-Humd 0.77 IR-Radia 0.68 IR-Radia 0.76 OA- CO OA- CO SOL-Horz 0.60 SA-CFM 0.69 SOL-Beam 0.58 SOL-Beam 0.69 OA-Humd 0.50 SOL-Horz 0.56 CHWC-VLV 0.49 OA-Humd 0.40 CHWC-EWT 0.47 WIND-Dir 0.19 WIND-Dir 0.43 BAR-Pres 0.13 BAR-Pres 0.36 WIND-Vel 0.12 WIND-Vel 0.23 Indoor Humidity Indoor CO 2 Conentration Variable Importane Variable Importane SA-Humd 1.00 BAR-Pres 1.00 OA-Temp 0.88 IR-Radia 0.83 IR-Radia 0.81 SA-CFM 0.83 CHWC-VLV 0.80 CHWC-EWT 0.79 CHWC-EWT 0.78 MA-Temp 0.78 OA- CO WIND-Vel 0.77 MA-Temp 0.71 CHWC-VLV 0.76 SOL-Beam 0.65 RA-CFM 0.72 RA-CFM 0.44 OA-Temp 0.71 WIND-Vel 0.43 OA-Humd 0.69 BAR-Pres 0.43 SA-Humd 0.65 SA-CFM 0.39 WIND-Dir 0.56 SOL-Horz 0.38 SOL-Horz 0.55 WIND-Dir 0.36 SOL-Beam 0.53 OA-Humd 0.26 OA- CO

27 13 Based on the data shown in Table 2.3, the eight parameters with the largest importane metri values were seleted. Therefore, two performane parameters, along with the eight ontrollable and unontrollable parameters, were ultimately used to build the energy onsumption and AQI models Algorithm seletion After parameter seletion, the preditive models of the AHU system and AQI are expressed in equation (2.1) to (2.4). y ( t) = f ( x, x, x, x, x, x, x, x, x, x ) ( 2.1) Energy SAT _ SPT SASP _ SPT CHWC _ VlV OA _ Temp MA _ Temp CHWC _ EWT RA _ CFM SA _ Humd IR _ Radia OA _ CO2 y ( t) = f ( x, x, x, x, x, x, x, x, x, x ) ( 2.2) Humd SAT _ SPT SASP _ SPT SA _ Humd OA _ Temp IR _ Radia CHWC _ VlV CHWC _ EWT OA _ CO2 MA _ Temp SOL _ Beam y ( t) = f ( x, x, x, x, x, x, x, x, x, x ) ( 2.3) Temp SAT _ SPT SASP _ SPT SA _ CFM RA _ CFM MA _ Temp SA _ Humd OA _ Tmep IR _ Radia OA _ CO2 SOL _ Horz y ( t) = f ( x, x, x, x, x, x, x, x, x, x ) ( 2.4) CO2 SAT _ SPT SASP _ SPT BAR _Pr es IR _ Radia SA _ CFM CHWC _ EWT MA _ Temp WIND _ Vel CHWC _ VlV RA _ CFM Where y E t, y H t, y T t, y CO₂ t denote the total energy onsumption of AHU system, average indoor temperature, average indoor humidity, and the average indoor CO 2 onentration during 1 hour time period, respetively. Five data-mining algorithms were used to extrat the mapping between inputs and the orresponding outputs: Boosting Tree [36], Random Forest [37], Support Vetor Mahine (SVM) [38], Multi-layer Pereptron (MLP) [39] and MLP Ensemble [40]. Boosting tree is a mahine learning meta-algorithm for supervised learning. Boosting is an iterative proedure used to adaptively modify the distribution of training examples so that the base preditors fous on learning instanes mislassified by the previous biased examples. Random forest is a lass of ensemble methods onsisting of multiple deision trees, where eah tree is generated based on the values of an independent set of random variables. Unlike the adaptive approah used in the boosting tree algorithm, the random variables are generated from a fixed probability distribution. SVM is a supervised learning algorithm that uses kernel funtions. It is used in binary lassifiation and regression. Using speifi kernel funtions, the original vetor spae is

28 14 transformed into a higher-dimensional spae where a separated hyperplane is onstruted with the maximum margin. MLP is also a non-parametri algorithm modeled after ognitive learning for the predition of patterns that are not part of the training data set. MLP derives relations from omplex, noisy, and impreise data, whih are often impossible to model with analytial or parametri tehniques. Reognizing that eah single MLP may make different and perhaps omplementary errors, MLP ensembles are used to pool the results from different MLPs to find a omposite system that outperforms any individual lassifier. The five different data-mining algorithms were tested using the joint data set for the onstrution of preditive models. To evaluate the performane of the different algorithms, the following four metris (see equations (2.5)-(2.8)) have been used to measure the predition auray of the model: the mean absolute error (MAE), the standard deviation of absolute error (Std_AE), the mean absolute perentage error (MAPE) and the standard deviation of absolute perentage error (Std_APE) [41]: MAE = N i= 1 yˆ y i N i (2.5) MAPE = N i= 1 yˆ i yi y N i (2.6) Std _ AE = Std _ APE = N i= 1 yˆ ˆ i= 1 ( yi yi ) N N i= 1 N N 1 i y ( APE( i) MAPE) N 1 2 i 2 (2.7) (2.8) where is the predited value obtained from the preditive model, y is the observed target value measured, and N is the number of data points used for training or testing.

29 15 The predition auraies of the preditive models in terms of energy onsumption, indoor temperature, indoor humidity, and indoor CO 2 onentration are presented in Table 2.4. Both the training and test errors are ompared. The MLP ensemble outperformed the other four algorithms. Therefore, it was seleted to onstrut the preditive models. Table 2.4. Training and testing results for models extrated from different data-mining algorithms. Algorithm MLP MLP Ensemble Boosted Tree Random Forest SVM Algorithm MLP MLP Ensemble Boosted Tree Random Forest SVM Energy model Temperature model Data set Std of Std of Std of Std of MAE MAPE MAE MAPE AE APE AE APE Training % 4.29% % 0.43% Testing % 4.29% % 0.56% Training % 4.04% % 0.42% Testing % 4.80% % 0.52% Training % 10.11% % 0.73% Testing % 9.19% % 0.78% Training % 7.67% % 0.72% Testing % 8.06% % 0.78% Training % 6.83% % 0.83% Testing % 7.08% % 0.81% Humidity model CO₂ model Data set Std of Std of Std of Std of MAE MAPE MAE MAPE AE APE AE APE Training % 2.07% % 1.76% Testing % 2.26% % 2.19% Training % 2.03% % 1.54% Testing % 2.19% % 1.84% Training % 7.93% % 2.52% Testing % 8.55% % 2.74% Training % 5.28% % 2.98% Testing % 6.28% % 3.37% Training % 5.51% % 3.25% Testing % 5.28% % 2.96%

30 Model onstrution and validation The onstrution of neural network models is a self-adaptive proess for minimizing the predition errors. The total squared error is onsidered as the ost funtion. During the training proess, the weights of the hidden units are modified to minimize the ost funtion. For eah individual ensemble model, one hundred networks were trained with the number of hidden neurons in the network varying from 10 to 35. The best five networks were then seleted. Detailed haraterizations of the four MLP ensemble models with five MLPs are shown in Table 2.5. Table 2.5. Charaterization of the four MLP Ensemble models. Hidden units Energy Model Hidden ativation funtion Output ativation funtion Hidden units 30 Exponential Identity 27 Hidden units Temperature Model Hidden ativation Output ativation funtion funtion Hyperboli funtion Identity 23 Hyperboli funtion Logisti 28 Exponential Logisti 32 Hyperboli funtion Exponential 30 Exponential Exponential 27 Logisti Exponential 35 Hyperboli funtion Logisti 18 Exponential Logisti 34 Exponential Exponential Humidity Model CO 2 Conentration Model Hidden ativation Output ativation Hidden Hidden ativation Output ativation funtion funtion units funtion funtion 17 Hyperboli Hyperboli Logisti 31 funtion funtion Exponential 27 Exponential Exponential 22 Logisti 21 Exponential Hyperboli funtion Hyperboli funtion Hyperboli funtion Identity 22 Logisti 21 Hyperboli funtion 33 Logisti Logisti Hyperboli funtion Hyperboli funtion Exponential Identity

31 17 The observed and predited values obtained from the four models of Table 2.5 are shown in Figure 2.4 through Figure Energy predition Predited energy onsumption [kj] Observed energy onsumption [kj] Figure 2.4. Test results obtained from the energy onsumption model. 78 Indoor temperature prediiton 76 ure [F] Predited indoor temperat Observed indoor temperature [F] Figure 2.5. Test results obtained from the indoor temperature model.

32 ] Indoor humidity predition 70 Predited indoor humidity [%RH] Observed indoor humidity [%RH] 80 Figure 2.6. Test results obtained from the indoor humidity model. 550 Indoor CO₂ onentration predition 500 Predited indoor CO₂ [ppm Observed indoor CO₂ onentration [ppm] Figure 2.7. Test results obtained from the CO2 onentration model. As shown in Figure 2.4 through Figure 2.7, the predited values of energy onsumption and indoor humidity were highly orrelated to their observed values. The predited values of the indoor air temperature and CO2 onentration were sattered beause their thermal harateristis were easily affeted by events in the room. Table 6 shows the orrelation between

33 19 the observed and predited values for the four predition models. Table 2.6 shows the orrelation between the observed and predited values for the four predition models. Table 2.6. Correlation oeffiients between observed and predited values of the four models. Variable Means Std. Dev. Correlation Coeffiient Observed Total Energy Predited Total Energy % Observed Indoor Temp Predited Indoor Temp % Observed Indoor Humd Predited Indoor Humd % Observed Indoor CO ₂ Predited Indoor CO₂ % 2.5. Clustering-based model of AHU energy The modeling arhiteture of the AHU energy Figure 2.8 illustrates a lustering sheme, where P is a subset of N parameters representing the ontrollable and unontrollable parameters of an AHU. The parameters in set P are denoted as P 1, P 2,, P N and are seleted as potential andidates to build the model using domain knowledge. Mahine learning algorithms (boosting tree, wrapper, and neural network) were applied to selet M out of N parameters. The luster-based sheme for model building involves four phases, as shown in Figure 2.8.

34 20 Figure 2.8. Cluster-based sheme for model building Some mahine learning tehniques suh as boosting tree, wrapper, and neural networks an be onduted for parameter seletion. All the parameters will be ranked by a value of importane to the orresponding target. Not all the parameters have signifiant impat on the target value. Some may be little relevant or even not related. Considering the exhausted omputation time of building separate lusters for eah parameter, the top parameters with the highest importane are seleted to be lustered. For eah parameter seleted for lustering, several lusters were onstruted. The lusters resulting for the most important parameters are as follows: C 1 = {C 1 1, C 1 2,, C 1 a} C 2 = { C 2 1, C 2 2,, C 2 b }... (2.9) C M = { C M 1, C M 2,, C M } where 1, 2,, M are the most signifiant parameters in the input spae and a, b,, denote the numbers of lusters produed for eah parameter. Building a model for eah luster is omputationally less expensive than onstruting a model from the original data.

35 Clustering algorithm Clustering the data set results in the lusters C 1, C 2,, C M with the orresponding entroids y 1, y 2,, y M. The lusters are reated by grouping data points so that the distane between a entroid and the data in the luster is minimized. The distane funtion is expressed as a squared error funtion (2.10): j= 1 i= 1 2 k n ( j) D = xi y j (2.10) where x ( j) i 2 y is the distane between a data point, ( j) j x i, and the luster entre, y. The K-means algorithm is widely used in data mining. A version of the K-means algorithm with a bounded number of lusters (see Step 1) is presented next: Step 1: Set the range of the initial lusters as [a,b]. Step 2: Classify data into lusters with the losest distane between the enter (entroid) and the data for eah speified number of lusters. Step 3: When all objets have been assigned, realulate the positions of the K entroids. Step 4: Stop if the onvergene riterion is satisfied. Otherwise, return to Step 2. Step 5: Calulate the ost funtion of lusters with different initial lusters. Step 6: Choose the optimal lusters when the differene of ost funtions between the urrent and the following lusters reah the threshold. j 2.6. Case study Clustering To validate the lustering algorithm of Setion 2.5.1, the energy onsumption model from Setion 2.3 was used. As shown in Table 2.3, two parameters, CHWC-VLV and OA-Temp, were ranked as the most important by the boosting tree algorithm. Figure 2.9 (a) and (b) map the relationships between the AHU energy onsumption and the two parameters.

36 Energy onsumption [kj] CHWC-VLV [open%] 70 (a) CHWC-VLV and energy onsumption n [kj] Energy onsumptio OA-Temp [F] (b) OA-Temp and energy onsumption Figure 2.9. Satter plots showing relationships between energy onsumption and seleted parameters. The initial range of lusters was varied from 2 to 25, and the maximum iteration number was 100. Applying the method presented in Setion 4.2, the optimal lusters for CHWC-VLV

37 23 and OA-Temp were 8 and 6, respetively. The lusters orresponding to the two inputs are shown in in Figure 2.10 and Figure Energy onsumption [kj] CHWC-VLV [open%] Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 Cluster 6 Cluster 7 Cluster 8 Figure Graphial interpretation of lustering based on CHWC-VLV ption [kj] Energy onsum OA-Temp [F] Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 Cluster 6 Figure Graphial interpretation of lustering based on OA-Temp. The harateristis of all of the lusters are provided in Table 2.7 and Table 2.8.

38 24 Table 2.7. Clusters based on CHWC-VLV. Clusters CHWC-VLV (mean) AHU-Energy (mean) Number of ases Perentage (%) Table 2.8. Clusters based on OA-Temp. Clusters OA-Temp (mean) AHU-Energy (mean) Number of ases Perentage(%) Modeling based on lusters To evaluate the effetiveness of using lusters, four senarios were defined. The MLP ensemble was used to build the models. These four senarios are as follows: Senario 1: Model based diretly on the joint data set. Senario 2: Model based on the three season data sets. Senario 3: Model based on lustering CHWC-VLV. Senario 4: Model based on lustering OA-Temp. Senario 1 involved the use of only one model based on a training data set (70%) and a test data set (30%). In Senario 2, three models were built based on the three seasons. Senario 3

39 25 and Senario 4 involved lustering, with eight and six models derived for the two senarios, respetively. Figure 2.12 and Figure 2.13 illustrate the mean absolute error and mean absolute perentage error of the training and test results for eah model. It an be seen that the models based on lustering outperformed the single model of Senario 1 and the season-based model of Senario 2. This onfirmed that lustering improves predition auray. Senario 4, with the input spae lustered on the OA-Temp, offered better predition results than Senario 3, where CHWC-VLV was lustered. The outside air temperature impated the energy demand of the AHU system. Compared with Senario 1, in Senario 4, the mean absolute perentage error was redued by 20.35% for training and 11.05% for testing MAE [kj] Senario 1 Senario 2 Senario 3 Senario 4 Training result Test result Figure Mean absolute error for four senarios.

40 % 3.50% 3.00% 3.44% 3.62% 3.64% 2.99% 2.90% 3.33% 2.74% 3.22% 2.50% MAPE 2.00% 1.50% 1.00% 0.50% 0.00% Senario 1 Senario 2 Senario 3 Senario 4 Training result Test result Figure Mean absolute perentage error for four senarios. Table 2.9 summaries the predition results for Senario 1 through Senario 4. Table 2.9. Predition results for four senarios. Model set Data set MAE Std of AE MAPE Std of APE Senario 1 Training % 4.04% Testing % 4.80% Senario 2 Training % 2.96% Testing % 4.19% Senario 3 Training % 2.78% Testing % 3.21% Senario 4 Training % 2.80% Testing % 3.05% 2.7. Clustering-based short-term predition of AHU energy The predition data set in Table 2.1 is used for the short term predition of the AHU energy. Beause Senario 4 performed the best, it was seleted to onstrut a predition model. Figure 2.14 shows the arhiteture of lustering-based short-term predition. The raw data set was first lustered using the lustering algorithm onstruted in Senario 4. Eah point was

41 27 assigned to the orresponding luster by minimizing the distane to the nearest luster enter. A model representing eah luster was used to validate the predition results. Table 2.10 shows the predition results for Senario 1 and Senario 4. Table 2.10 shows the predition results of the two models. Figure The arhiteture of lustering-based short-term predition of AHU energy. Table Short-term predition results for Senario 1 and Senario 4. Model set MAE Std of AE MAPE Std of APE Senario % 8.97% Senario % 8.34% The results in Table 2.10 show that the lustering-based model outperformed the single model (original data) in the predition of the AHU energy. Compared to Senario 1, Senario 4

42 28 redued the mean absolute perentage error by 12.21%. Figure 2.15 and Figure 2.16 show the predition results for Senario 1 and Senario Energy onsumption [kj] Time [h] Observed energy onsumption Predited energy onsumption Figure Short-term predition of AHU energy for Senario n [kj] Energy onsumptio Time [h] Observed energy onsumption Predited energy onsumption Figure Short-term predition of AHU energy for Senario 4.

43 Summary Data-mining algorithms were used to model the energy onsumption of an AHU, as well as the indoor temperature, indoor humidity, and indoor CO 2 onentration. Of the many parameters available in this researh, the most relevant parameters with respet to the target output were seleted. The AHU energy model and the AQI models derived with the MLP Ensemble method outperformed the models derived using the other data mining algorithms onsidered in this researh. To redue the predition errors and omputation ost, a lustering sheme was applied. The MLP Ensemble algorithm applied to the lustered data provided the most aurate results. Data lustering redued the mean absolute perentage error by 11.05% ompared with the single model derived from the original data. The short-term predition model derived from the lustered data offered improved predition auray and redued omputation time.

44 30 CHAPTER 3 MULTI-OBJECTIVE OPTIMIZATION OF HVAC SYSTEM WITH AN EVOLUTIONARY COMPUTATION ALGORITHM 3.1. Introdution With regard to the strategi management of HVAC system, one of the major fouses is on effetive and effiient energy management. The operation of HVAC system is a ritial ativity in terms of optimizing the ontrol settings to redue the energy onsumption, improving the system effiieny, and preserving the thermal omfort for the oupants. The performane of the existing HVAC system an be largely improved by adjusting the ontrol set points to maximize the overall system apaity and effiieny. Zheng et al. [42] formulated the thermal proess in a variable air volume (VAV) box with onstraints on zone humidity. This provided daily operating strategies ahieving optimal outdoor air-flow rates and energy savings. Fong et al. [43] disussed energy redution by using an evolutionary programming approah to suggest optimal settings in response to the dynami ooling loads and hanging weather onditions. Nassif et al. [27, 28] applied evolutionary algorithms to one-objetive and two-objetive optimization of an HVAC system, and the supervisory ontrol strategies resulted in energy savings. Kusiak and Li [44] applied an evolutionary strategy algorithm to solve a bi-objetive optimization model to minimize the ooling output while maintaining the orresponding thermal properties. The objetive of this work is to investigate the effets of different ontrol settings on energy onsumption in an existing multi-zone offie building while thermal omfort is sustained. The models built with data-mining algorithms were implemented inside an optimization model. Considering the speifi requirements and effets of the thermal omfort, a weight-based onstraints funtion was formed to satisfy the preferenes. A strength Pareto evolutionary algorithm (SPEA) was employed to searh for the optimal ontrol settings of the HVAC system.