Energy and Buildings 82 (2014) 1–12 Contents lists available at ScienceDirect Energy and Buildings j ourna l ho me page: www.elsevier.com/locate/enbuild Building energy consumption on-line forecasting using physics based system identification Xiwang Li ∗ , Jin Wen Department of Civil, Architectural and Environmental Engineering, Drexel University, 3141 Chestnut Street, Curtis 251, Philadelphia, PA 19104, USA a r t i c l e i n f o Article history: Received 14 March 2014 Received in revised form 8 July 2014 Accepted 9 July 2014 Available online 18 July 2014 Keywords: Building energy modeling System identification Building control and operation Building energy efficiency a b s t r a c t Model based control has become a promising solution for building operation optimization and energy saving. Accuracy and computationally efficiency are two of the most important requirements for building energy models. Existing studies in this area have mostly been focusing on reducing computation bur- den using simplified physics based modeling approach. However, creating even the simplified physics based model is often challenging and time consuming. Pure date-driven statistical models have also been adopted in a lot of studies. Such models, unfortunately, often require long training period and are bounded to building operating conditions that they are trained for. Therefore, this study proposes a novel methodology to develop building energy estimation models for on-line building control and optimiza- tion using a system identification approach. Frequency domain spectral density analysis is implemented in this on-line modeling approach to capture the dynamics of building energy system and forecast the energy consumption with more than 90% accuracy and less than 2 min computational speed. A system- atic analysis of system structure, system order and system excitation selection are also demonstrated. The forecasting results from this proposed model are validated against detailed physics based simulation results using a mid-size commercial building EnergyPlus model. © 2014 Elsevier B.V. All rights reserved. 1. Introduction Buildings roughly account for 40% primary energy use in U.S. It costs a total utility bill of more than $400 billion in 2012. Around 30% of the energy used in building is consumed by heating, ven- tilating and air conditioning (HVAC) [1]. Study has shown that non-optimal control of building energy system could cause the malfunction of equipment or performance degradation from 15% to 30% in commercial buildings [2]. Moreover, it is estimated by the National Energy Technology Laboratory that more than one- fourth of the 713 GW of U.S. electricity demand in 2010 could be dispatchable if only buildings could respond to that dispatch through advanced building energy control and operation strate- gies and smart grid infrastructure [3]. Therefore building control and operation is significant economically and environmentally. In strategies used to improve building control and operation, high fidelity building energy model is the most critical compo- nent. Existing building energy models can be categorized into white box (physics-based) models, black box (data-driven) models and grey box (hybrid) models. One of the most comprehensive white ∗ Corresponding author. Tel.: +1 215 895 6941; fax: +1 215 895 1364. E-mail addresses: [email protected], [email protected] (X. Li). box models is EnergyPlus, which is a whole building energy sim- ulation program that engineers, architects, and researchers use to model energy and water use in buildings [4]. A Building Con- trols Virtual Test Bed (BCVTB) was developed by Wetter and Haves to link the building models with control systems [5]. BCVTB is a middleware tool that allows to data sharing among different sim- ulation programs, such as EnergyPlus, Matlab and Modelica, for distributed simulation. Therefore, through this test bed different user defined building control and optimization strategies can be applied into different building simulation models. Ma et al. pro- posed and demonstrated an economic MPC technique to reduce energy and demand cost [6]. Using BCVTB as middleware, real- time data exchange between EnergyPlus and a Matlab controller was realized. An economic objective function to minimize daily electricity costs was then developed in MPC and applied in Ener- gyPlus model through the middleware. About 25.3% energy saving and 28.5% cost saving were achieved by this MPC in a single story commercial building located in Chicago, Illinois. Corbin et al. [7] utilized a Matlab-EnergyPlus MPC environment and incorporated it with a particle swarm optimizer to predict optimal building control strategies. Every time step, the schedules and setpoints will be wrote into EnergyPlus input IDF file and then Energy- Plus output results will be evaluated within the MATLAB optimal control module, based upon the objective cost function, then the http://dx.doi.org/10.1016/j.enbuild.2014.07.021 0378-7788/© 2014 Elsevier B.V. All rights reserved.
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Bs
XD
a
ARRAA
KBSBB
1
c3tnmttfbtga
hnbg
h0
Energy and Buildings 82 (2014) 1–12
Contents lists available at ScienceDirect
Energy and Buildings
j ourna l ho me page: www.elsev ier .com/ locate /enbui ld
uilding energy consumption on-line forecasting using physics basedystem identification
iwang Li ∗, Jin Wenepartment of Civil, Architectural and Environmental Engineering, Drexel University, 3141 Chestnut Street, Curtis 251, Philadelphia, PA 19104, USA
r t i c l e i n f o
rticle history:eceived 14 March 2014eceived in revised form 8 July 2014ccepted 9 July 2014vailable online 18 July 2014
eywords:uilding energy modelingystem identificationuilding control and operation
a b s t r a c t
Model based control has become a promising solution for building operation optimization and energysaving. Accuracy and computationally efficiency are two of the most important requirements for buildingenergy models. Existing studies in this area have mostly been focusing on reducing computation bur-den using simplified physics based modeling approach. However, creating even the simplified physicsbased model is often challenging and time consuming. Pure date-driven statistical models have alsobeen adopted in a lot of studies. Such models, unfortunately, often require long training period and arebounded to building operating conditions that they are trained for. Therefore, this study proposes a novelmethodology to develop building energy estimation models for on-line building control and optimiza-tion using a system identification approach. Frequency domain spectral density analysis is implemented
uilding energy efficiency in this on-line modeling approach to capture the dynamics of building energy system and forecast theenergy consumption with more than 90% accuracy and less than 2 min computational speed. A system-atic analysis of system structure, system order and system excitation selection are also demonstrated.The forecasting results from this proposed model are validated against detailed physics based simulationresults using a mid-size commercial building EnergyPlus model.
© 2014 Elsevier B.V. All rights reserved.
. Introduction
Buildings roughly account for 40% primary energy use in U.S. Itosts a total utility bill of more than $400 billion in 2012. Around0% of the energy used in building is consumed by heating, ven-ilating and air conditioning (HVAC) [1]. Study has shown thaton-optimal control of building energy system could cause thealfunction of equipment or performance degradation from 15%
o 30% in commercial buildings [2]. Moreover, it is estimated byhe National Energy Technology Laboratory that more than one-ourth of the 713 GW of U.S. electricity demand in 2010 coulde dispatchable if only buildings could respond to that dispatchhrough advanced building energy control and operation strate-ies and smart grid infrastructure [3]. Therefore building controlnd operation is significant economically and environmentally.
In strategies used to improve building control and operation,igh fidelity building energy model is the most critical compo-
ent. Existing building energy models can be categorized into whiteox (physics-based) models, black box (data-driven) models andrey box (hybrid) models. One of the most comprehensive white∗ Corresponding author. Tel.: +1 215 895 6941; fax: +1 215 895 1364.E-mail addresses: [email protected], [email protected] (X. Li).
ttp://dx.doi.org/10.1016/j.enbuild.2014.07.021378-7788/© 2014 Elsevier B.V. All rights reserved.
box models is EnergyPlus, which is a whole building energy sim-ulation program that engineers, architects, and researchers useto model energy and water use in buildings [4]. A Building Con-trols Virtual Test Bed (BCVTB) was developed by Wetter and Havesto link the building models with control systems [5]. BCVTB is amiddleware tool that allows to data sharing among different sim-ulation programs, such as EnergyPlus, Matlab and Modelica, fordistributed simulation. Therefore, through this test bed differentuser defined building control and optimization strategies can beapplied into different building simulation models. Ma et al. pro-posed and demonstrated an economic MPC technique to reduceenergy and demand cost [6]. Using BCVTB as middleware, real-time data exchange between EnergyPlus and a Matlab controllerwas realized. An economic objective function to minimize dailyelectricity costs was then developed in MPC and applied in Ener-gyPlus model through the middleware. About 25.3% energy savingand 28.5% cost saving were achieved by this MPC in a single storycommercial building located in Chicago, Illinois. Corbin et al. [7]utilized a Matlab-EnergyPlus MPC environment and incorporatedit with a particle swarm optimizer to predict optimal building
control strategies. Every time step, the schedules and setpointswill be wrote into EnergyPlus input IDF file and then Energy-Plus output results will be evaluated within the MATLAB optimalcontrol module, based upon the objective cost function, then the
2 nd Bui
uToaribbewpGgtbtmwtlutsOtraEs
SbaacApmt(fimctfwacipdwemicap
cluced
[25]. This reference building EnergyPlus model has been validated
X. Li, J. Wen / Energy a
pdated temperature setpoints will be sent to EnergyPlus again.his procedure will be repeated until some convergence criteri-ns are satisfied. This on-line optimization environment was alsopplied in a DOE benchmark building EnergyPlus models [8]. Theesults showed 5% cost saving just by optimizing the hourly cool-ng setpoint in large office building model, and 54% energy savingy determining hourly supply water temperature in small officeuilding model. Another important control optimization softwarenvironment, Genopt, was also developed by Wetter in 2000 [9],hich can iteratively execute any simulation program based onlain text input/output files until an optimal solution is found.enopt was used by Coffey et al. [10] to incorporate a modifiedenetic algorithm MPC with an EnergyPlus model to study theemperature control optimization in office buildings and its effectuilding energy demand. Even though these elaborate simulationools are very effective and accurate, they require detailed infor-
ation and parameters of buildings, energy system and outsideeather conditions. Identifying these parameters, however, is very
ime consuming and need expert work. What is even more chal-enging, the simulation speed is relative low and not suitable to besed in on-line MPC. Therefore, the two major researching objec-ives of recent studies on building MOC are increasing simulationpeed and maintaining simulation accuracy. Cole et al. [11] usedpenStudio to reduce the EnergyPlus model by perturbing the sys-
em and fitting the results into a reduced-order linear model Theeduced model is able to simulate an one-day simulation within 1 snd the discrepancy between this reduce-order linear model andnergyPlus model is less than 2.3% under an optimal temperatureetpoints setting situation.
Black box model is also known as purely data driven model.tatistical models are simply applied to capture the correlationetween building energy consumption and several building oper-tion variables. This method needs the on-site measurements over
certain period of time to train the statistical models whichan calculate the accurate predictions under different conditions.utoregressive with exogenous (ARX) model was implemented toredict the 1 h ahead building load by Yun et al. [12]. This predictiveodel is applied on several different DOE benchmark buildings [8]
o choose the building control strategies. Artificial neural networkANN) is another popular method in building energy predictionor building operation purpose. Adaptive ANNs for on-line build-ng energy prediction was investigated by Yang et al. [13]. These
odels are capable of adapting themselves to unexpected patternhanges in the incoming data, and therefore can be used for the real-ime on-line building energy prediction, which is the fundamentalor building optimal control. Chen et al. [14] developed a day-basedavelet ANN method for next day load forecasting. They selected
historical day with the same weekday index and similar weatherondition as next day. They similar day load was then decomposednto multiple levels by using wavelet decomposition. These decom-osed components were fed into different ANNs to predict the nextay load at each component. After all, all these prediction resultsill be combined into an overall forecasting result. Black box mod-
ls are easy to build and computationally efficient, however, suchodels often require long training period and are bounded to build-
ng operating conditions that they are trained for which sometimesan cause huge forecasting error when training data does not coverll the forecasting range, and moreover, black box always sacrificehysical insights to obtain high accuracy and calculation speed.
Resistance and Capacitance (RC) network model is the mostommon grey model for building energy estimation, which requiresess training data and has less parameter to determine. RC model
sually uses state space model to estimate the building heating andooling load [15], and control building temperature [16,17]. Differ-nt optimization and searching algorithms have been utilized inetermining the resistances and capacitances [18,19]. Ma et al. [20]ldings 82 (2014) 1–12
reduced the order of RC model to increase the calculation speed,sing balance realization method. It still took 28 min for this reducedmodel to run a one-week simulation using a reduced RC model,which is still not suit for on-line building operation optimization.Different to pervious works using single RC models, an integrated3R2C and EKF (Extended Kalman Filter) model was developed toestimate the building energy consumption in Ref. [21]. In this work,an EKF was used to estimate the state vector X using real sensormeasurement data. The estimated load matched the EnergyPlusresults within 10% at 93% of the time.
It is common knowledge that determining the parameter ofRC model is computational demanded and the model structuresand parameters are unique from building to building. It is impos-sible to utilize a RC model for one building to another building.System identification is the process of developing or improvinga mathematical representation of a physical system using exper-imental data [22]. System identification techniques have startedbeen applied in building energy model area to obtain better andmore accurate estimation of building performance. Privara et al.[23] proposed an approach combining a EnergyPlus model and asubspace system identification model to forecast the building per-formance. In this study, a six-floor office building was modeled bya Matlab toolbox called N4SID to estimate the building zone tem-perature. However, directly using Matlab toolbox cannot guaranteethe forecasting accuracy every time. The accuracy of Matlab tool-box is depended on the data properties. It is very hard to guaranteethe toolbox suitable to every building under different operationstrategies. On the other hand, there is no systematic discussion ofmodel structure selection and parameter determining presentedin this paper. Agbi et al. [24] studied system structural identifiabil-ity and model parameters identifiability for building energy statespace model. Unfortunately, this paper focuses on the discussionof identifiability of the system upon available data without anyactive building excitation. It did not improve the system identi-fication model developing speed or improve the model forecastingaccuracy. And it still uses the RC network model, so the methoddemonstrated in this paper has the limitation of all the RC modelhas. For example, the parameters identification for those Rs and Csis very difficult and time consuming.
In this study, an EnergyPlus model of a mid-size commercialbuilding was used to provide building operation data in lieu of a realbuilding. Then a systematic discussion system identification modeldevelopment and system excitation base on those operation data ispresented in this paper. The combination of active system excita-tion and a frequency domain spectral density analysis are appliedto develop building energy forecasting models that are genetic(can be easily extended to other building types/operating condi-tions), accurate, and computationally cost-effective. The systemidentification model development will be discussed in Section 2,followed by the development of system identification based build-ing energy on-line forecasting model in Section 3. The forecastingresults will then be analyzed in Section 4. After this system iden-tification approach has been developed and validated in a smallcommercial building, which is then applied in a medium building.
2. Building energy model development
In this study, the on-line building energy forecasting modelis developed based a mid-size reference commercial EnergyPlussimulation model, provided by U.S. Department of Energy (DOE)
and used for optimize designs, operation and advanced controlsin numbers of studies [26–29] The procedure of model structuredetermining, input and output selection, system exciting and modeltraining and validation will be introduced in detail in this section.
X. Li, J. Wen / Energy and Buildings 82 (2014) 1–12 3
2
tbe3tri
zaaac
••••
fsti(cmoTai
2
amfdmsf
TB
Table 2Variables of system identification model.
Parameter zone model
Variable Variable name Type
Qload Zone heating/cooling load (W) OutputEzone Zone heating/cooling energy (J) OutputTout Outdoor air temperature (C) InputTzone Zone temperature (C) InputTadj Adjacent zone temperature (C) InputRin Equipment and occupancy schedule ratio (–) InputTsol-air Solar air temperature (C) InputQvent Ventilation rate (m3/s) InputQdir Direct solar radiation (W/m2) Input
Fig. 1. Small commercial building view.
.1. Building description
This single story office building (Fig. 1) has five zones, andhe total floor area is 510 m2. The window-to-wall ratio of thisuilding’s facades is approximately 21.2%, and the windows arequally distributed. The U-factor of these single pane windows is.4 W/m2 K and the solar heat gain factor is 0.36. The solar absorp-ivity, transmissivity and reflectivity are 0.06, 0.697 and 0.243,espectively. The location of this building selected for this studys Philadelphia, PA, USA.
This building is partitioned into five different air conditioningones, and an unconditioned attic zone. The five conditioned zonere four perimeter zones and one core zone. The roof insulation hasn R-value of 15. The roof is covered in an asphalt membrane, with
solar absorptivity value of 0.9. The exterior wall has the followingonstruction (from outside layer to inside layer):
2.54 cm of stucco.20.32 cm concrete masonry units.R-6 continuous insulation.1.27 cm gypsum wallboard.
Since at the purpose of this study is to develop a building energyorecasting model using system identification approach. For theimplification of the mechanical system, and mainly focusing onhe building thermal response dynamics, the mechanical systemn this building is constant-air-volume (CAV) air handling unitsAHUs). Direct expansion (DX) coil is used in this building, which isonnected to an electrical cooling source with coefficient of perfor-ance (COP) of 3. Heating is provided by gas boiler with efficiency
f 0.95. The baseline model internal load inputs are summarized inable 1. All these assumptions are from Deru et al. [25]. These modelssumptions will be updated in the system identification processn order to enrich the operation data.
.2. System identification model selection
As stated above, the objective of this study is to developn on-line building energy model using system identificationethod. Model structure plays the most important role in model
orecasting accuracy. Privara et al. summarized and compared
ifferent system identification approaches for building energyodeling and control [30]. There are two different categories ofystem identification models, which are time domain models andrequency domain models. There is large number of modeling and
able 1uilding model internal and external gains.
Variable Value
Occupant density 0.1 Person/m2
Ventilation requirement 2.36e−3 m3/(people m2) + 3.05e−4 m3/(s m2)Lighting power density 18 W/m2
Interior small plug loads 10 W/m2
Envelope infiltration rate 9.4e−4 m3/(s m2)
Qdif Diffuse solar radiation (W/m2) InputQfan Supply fan heat gain (J) Input
identification approaches developed over the recent years, butfew of them are suitable for building energy modeling, neithera universal model that can work for different building types andoperation schemes. Building energy systems, especially the HVACsystems, are very complicated nonlinear dynamic systems, whichis hard to model and forecast.
In order to develop a relative simple system model, frequencyresponse function approach is applied in this study due to its excel-lent performance in handling system nonlinearity. Fundamentallya frequency response function is a mathematical representation ofthe relationship between the input and the output of a system infrequency domain, which is a special case of the transfer function,but it can simplify the time domain transfer function and maintainthe useful information (Eq. (1)).
H(jω) = Y(jω)U(jω)
= Syu(jω)Suu(jω)
(1)
where Y(jω) the Fourier is transform of system output y(t), andU(jω) is the Fourier transform of system input U(t). However, bet-ter results can be obtained in practice by computing the frequencyresponse function (Syu) as the ratio of cross-spectrum betweeninput and output to the power spectrum of the input (Suu). Thenby applying the Inverse Fourier Transform, the Impulse ResponseFunctions (IRF) per measurement channel are obtained. In this way,the operational data across the full spectrum of the building oper-ation range will be analyzed accurately. The detailed informationabout the spectral density model implementation in this study willbe presented in Section 3. In this project, two different energy mod-els will be developed for the core zone and perimeter zone of thisbuilding separately, which is because the outside weather condi-tion directly affects the behavior of perimeter zone but not to corezones. Therefore, the perimeter zone model needs to include out-door weather information, such as temperature, solar radiation, etc.in the input.
2.3. Model input and output determining
Besides the model structure, model input and output selectionis also crucial to the accuracy of system identification model. Theinput and output selection should be based on the physical rela-tionship and the data availability. From the objective of this systemidentification model, two different models have been developed.The outputs of the model are relative easy to determine accordingto our modeling objective. They are building cooling and heatingenergy consumption or building heating and cooling load.
The inputs and outputs of perimeter zone system identifica-
tion model are tableted in Table 2. The inputs and outputs of corezone model are very similar to those of perimeter zone model,but exclude Tsol-air, Qdir and Qdiff in system inputs, because thereis no direct solar radiation or transmission in core zone. Solar air
4 nd Buildings 82 (2014) 1–12
tgbmi
T
wabp
mwiieawvbass
2
tgTnste
••
•
pmtPssllna
T
2
cea
X. Li, J. Wen / Energy a
emperature (Tsol-air) is a variable used to determine the total heatain through opaque exterior surfaces to calculate cooling load of auilding. It is not an output from EnergyPlus model, nor a measure-ent from weather station, and then a specific calculation model
s created, using the following equation:
sol−air = To + ˛I − �Qir
ho(2)
here is absorptivity of each opaque wall; I is global solar irradi-nce (W/m2); and �Qir is extra infrared radiation due to differenceetween the external air temperature and the apparent sky tem-erature (W/m2).
Direct solar radiation and diffuse solar radiation are used to esti-ate the building heat gain due to the solar transmission throughindows. They can be either obtained from weather forecasting
nformation or calculated from global solar irradiance. All thesenput variables are categorized into two groups: unexcited andxcited inputs. The zone temperature, adjacent zone temperaturend equipment and occupancy schedule ratio are excited inputs,hich will be excited during model training period, and the other
ariables are unexcited inputs. The zone temperature is excitedy changing the zone temperature setpoints, and the equipmentnd occupancy schedule ratio is excited by updating their on/offchedule ratio in EnergyPlus model. The details about the excitationignal generation will be introduced in Section 2.4.
.4. System excitation signal generation
In order to develop the spectrum density model and improvehe accuracy of system identification model, exciting signals wereenerated and injected into the system during the training period.hese exciting signals include zone temperature setpoints, inter-al equipment and occupancy schedules. Such signals are needed toatisfy key theoretical assumptions on reliable statistical identifica-ion – persistent exciting signals [31]. Three basic “plant-friendly”xcitation signal constraints were presented by Braun et al. [32]:
Keeping minimum deviations in product quality;Implementing a signal of short duration to minimize the amountof off-spec product;Keeping move sizes small to satisfy actuator constraints and min-imize “wear and tear” on process equipment.
Therefore, certain constraints added into our system excitationrocess, for example, the boundary of temperature setpoints, theinimum temperature setpoint or equipment schedule updating
ime span, and so on. Different system excitation strategies, such asseudo-Random Binary signal, Pseudo-Random Sequences, Multi-ine signal, have been discussed and applied in on-linear processystems in different areas [32–34]. However, there are few pub-ications on building energy system excitation found in existingiterature. Pseudo-random Binary Sequence (PRBS) excitation sig-als (Eq. (3)) for building temperature setpoints was generated andpplied in [6].
sp,i(k)
⎧⎨⎩
21, excited zone, PRBS = 0
25, excited zone, PRBS = 1
25, non-excited zones
(3)
.4.1. Excitation signal generation function
The objective of this on-line model is for building operation andontrol, therefore, the excitation signals do not need to cover thentire frequency domain, but the building operation range. To guar-ntee those signals cover the frequency domain around the building
Fig. 2. Excitation signal generation procedure.
common operation range, sum of sinusoids (SINE) model was usedto generate the exciting signal (Eq. (4)).
U�+1 = U� + A�
√2˛j sin(ω�tT + ϕ�) (4)
where U�+1 is the excitation signal; A is a magnitude scale param-eter from 0 to 1; ω is periodic frequency parameter from 0 to 2�;T is the sampling time, ϕ is the phase lag parameter from 0 to 2�,and ˛j is the Fourier coefficients. These parameters will be updatedevery time step. Another benefit of using sum of sinusoids input sig-nals is that they enable the user to directly specify the shape andcharacter of the power spectrum. The guidelines of excitation sig-nal generation function parameter determining from Rivera et al.[35] is applied to ensure the signals contains necessary frequencyinformation:
1ˇs�H
dom
≤ ω ≤ ˛s
�Ldom
(5)
ϕ� = 2�
i∑j=1
j˛j (6)
where �Hdom
and �Ldom
correspond to the high and low estimates ofthe dominant time constant of the system (denote the slowest andthe fastest systems time constants). ˛s and ˇs are user-decisionson high and low frequency content based on identification require-ment. Typically, ˛s is 2 and ˇs is 3, corresponding to 95% of settlingtime [35]. In additional to function magnitude scale parameter,periodic frequency parameter and phase lag parameter, harmonicsuppression is another important parameter which can decomposethe output signal to obtain a more accurate estimate of the linearand nonlinear components.
2.4.2. Excitation function parameter specification and datageneration
The procedure of excitation signals design is summarized inFig. 2. The response time constant of a dynamic system is a mea-sure of how quickly the system responds. It is usually measuredby experiments. For example, if the impulse response of a dynamicsystem can be expressed as:
x(t) =(
˛
T
)e−t/T (7)
where T is the response time constant, is a state parameter.When x(t) = 0.95, t = T.95. Therefore, with considering the buildingdynamics of the target building in this project, �T
dom= 360 min, and
�Ldom
= 30 min; ˛s and ˇs are 2 and 3, respectively. For the temper-ature setpoint excitation signals in this project, Tmax = 32 ◦C(90 ◦F)and Tmin=10 ◦C (50 ◦F); while for the schedule ratio excitation sig-nals, Rmax = 1 and Rmin = 0.
X. Li, J. Wen / Energy and Buildings 82 (2014) 1–12 5
Table 3Excitation frequency and sampling length testing summary.
R2 Excitation frequency Sampling length Excitation frequency Sampling length Excitation frequency Sampling length15 min 3 h 30 min 4 h 60 min 6 h
ew
2
qlrebetcdTicm
mpa
2
mmbitmDbtsc
Training period 93.65%
Forecasting period 95.30%
Once all the time independent parameters are determined, thexcitation function will generate the signals every time step, whichill then be applied in building model automatically.
.4.3. Excitation signal injection frequencyAccording to Braun’s guidelines, the excitation injection fre-
uency cannot be too high. The injection time step should bearger than the system response time. The building response time iselated to building thermal mass, which can only be found throughxperiment test. The building studied in this project is a small lightuilding. It system response time is relatively short. A parametricxperiment test has been conducted to find out the best injec-ion frequency. However, once the system excitation frequencyhanged, the building dynamics would change, and the powerensity model sapling length should also be updated accordingly.able 3 presents the excitation frequency and sampling length test-ng results. Finally, 30 min with 6 h and 30 min with 4 h have beenhosen for excitation frequency and sampling length for core zoneodel and perimeter zone model, respectively.One case temperature setpoints and equipment schedule excite-
ents used in this study are shown in Fig. 3, where all thearameters are updating every time step and the excitation signalsre injected into the building model every 30 min.
.5. Training and validation data generation
The system excitation signals discussed in Section 2.4 wasodeled and generated in Matlab. In order to apply these excite-ents into EnergyPlus model, BCVTB is used to exchange data
etween Matlab and EnergyPlus. Here BCVTB plays a master rolen data exchange between Matlab and EnergyPlus through run-ime coupling, as shown in Fig. 4. During the entire study, typical
eteorological year (TMY) weather data for Philadelphia is used.uring the training and validation period, excited and unexcited
uilding control signals will be sent to EnergyPlus model followinghe procedure in Fig. 2, respectively. Simulation results and controlignals will be sent back and stored in Matlab for system identifi-ation model training and validation, as discussed in Section 2.3.Fig. 3. Temperature setpoint and equipment schedule excitement.
93.70% 92.21%95.30% 91.01%
The connection between Matlab and EnergyPlus through BCVTBis illustrated in Fig. 5, where the Matlab simulator is the excited orunexcited control signal generator, and EnergyPlus simulator is thebuilding model discussed in Section 2. The length of training timeis changeable according to the forecasting accuracy requirement.
3. Building energy on-line estimation model
3.1. Building energy system identification model development
The system identification model structure selection has beendiscussed in Section 2.2. Frequency response function model hasbeen chosen for this project. Fig. 6 shows the system identificationmodel development from building operation data using spectraldensity model for frequency response function. In this figure, U istraining inputs, h is a reference signal to analyze the input data, Yis training outputs data, PSD is power spectral density model forinputs data, CPSD is cross power spectral density model for inputand output, Suu is the result of PSD, Syu is the result of CPSD, G is thetransfer function from input to output, and y is the output estima-tion. Suu and Syu are estimation the correlation between input andoutput. G(z) is the transfer function in frequency domain, which canbe transferred to time domain transfer function G(t) using inverseFourier function transformation.
As discussed before, in order to calculate the frequency responsefunction, power spectral density model is applied. Power spectraldensity describes how the power of a signal or time series is dis-tributed over the frequency spectrum, which is property of thesystem signal and very useful in frequency domain system iden-tification (Eqs. (8) and (9)).
Suu = 1l
l−1∑�=1
Ruu(�)e−j 2�k�l (8)
Syu = 1l
l−1∑�=1
Ryu(�)e−j 2�k�l (9)
where Ruu is the auto-correlation between the inputs and Ryu is thecross-correlation between input and output [22], which are calcu-lated in Eqs. (10) and (11). u is the input vector, y is the output
Fig. 4. Building operation data for on-line model training and validation.
6 X. Li, J. Wen / Energy and Buildings 82 (2014) 1–12
VTB-E
vtbs2
R
R
(Dbaumf
Fig. 5. Matlab-BC
ector, and l is the length of the sampling data. l is a very impor-ant parameter which affect the estimation accuracy and speed,ecause within one data sample, the power density is calculatedimultaneously, which has been introduced and tested in Section.4.3.
uu(�) = 1l
l−1∑i=1
u(i)uT (i − �) (10)
yu(�) = 1l
∞∑�=0
y(k)uT (i − �) (11)
Fig. 7 shows the procedure of using system identification modelSID model hereafter) to develop the on-line building energy model.uring the training process, the excited building control signals wille generated in Matlab according to the exciting scheme discussed
bove and sent to EnergyPlus through BCVTB. The EnergyPlus sim-lation results of the excited system will be used to train the SIDodel, and calculate its Markov parameters for each input in trans-er function. On the other hand, the EnergyPlus simulation results
Fig. 6. System identification mod
nergyPlus model.
of the unexcited control signals will be used to validate the systemidentification model.
3.2. Building energy system identification model performanceindex
Model forecasting accuracy when compared with EnergyPlusresults and speed are two most important indices in this study.Coefficient of determination, R2 (Eq. (12)) is used to measure theforecasting data accuracy [36].
R2 =∑n
i=1(yi − y)(yi − ¯y)∑ni=1(yi − y)2∑n
i=1(yi − ¯y)(12)
where yi is the energy consumption data from EnergyPlus, yi is theenergy consumption forecasting data, y and ¯y are their average.
4. System identification model estimation results
Two different models, core zone model and perimeter zonemodel, have been developed and applied to model and forecast the
el development procedure.
X. Li, J. Wen / Energy and Buildings 82 (2014) 1–12 7
gy mo
hfJfccsri
4
rhmsveTwsttbb
F
Fig. 7. On-line building ener
eating/cooling load and energy, individually. The training periodor building load and heating energy estimation models is fromanuary 1st to January 10th, and the forecasting period for them isrom January 11th to January 13th. While the training period forooling energy estimation models is July 1st to 10th, and the fore-asting period is July 11th to 13th. During training period, all theystem exciting signals are applied into the building model, butegular control signals are used in the building during the forecast-ng/testing period (Fig. 8).
.1. Building heating and cooling load off-line estimation results
In order to test the SID model’s capability in capture the thermalesponse dynamics of building thermal mass, especially the solareat gains, an off-line building heating and cooling load estimationodel is developed. This testing study is based on the EnergyPlus
imulation for from January 1st to January 10th. As discussed in per-ious sections, for both core zone and perimeter zone models thexcitation signals are injected into the building model every 30 min.he time step of training data generation EnergyPlus model is 5 min,hile that of SID model is 15 min. The shorter training model time
tep is to better capture the building dynamics. With consideringhe dynamics difference between core zone and perimeter zone,
he data sampling length are 240 and 180 min, respectively. Sinceuilding heating/cooling load is hard to measure in real field, theuilding load estimation is an off-line process. The load estimationig. 8. Temperature setpoints and equipment schedule during forecasting period.
del development procedure.
building is trained based on the EnergyPlus simulation results forJanuary 1st to January 10th.
In Fig. 9a and b, ten days’ heating and cooling load trainingresults from the system identification model are compared withthose from EnergyPlus model. The results in this figure are theamount of heating load subtracting that of cooling load. Hence thevalue above zero is heating load, while the value below zero is cool-ing load. Since the internal heat gains are very large in the building,the core zone just need some heating in the morning. After all theequipment turning on, core zone requires cooling in the afternoon.Similar phenomenon is identified for the perimeter zones, but inthe morning more heating is requested. From this plot, we can seethe green line (SID) mostly capture dynamics of the blue line (Ener-gyPlus). The seventh day of the training is a holiday, when all theHVAC system is off. For the simplification of the presentation, onlythe results of core zone and west perimeter zone are illustratedhere. Those estimation results of other perimeter zones are verysimilar to that of west perimeter zone. Without considering theoutliers, the R2 value of the training data estimation is summarizedin Table 4. Both of these two are above 0.95.
Once the building load system identification model is trainedto have good estimation accuracy, it is then used to forecast thefuture building load. Fig. 9c plots the building load forecastingresults using the system identification model discussed above. Inthe perimeter zone load estimation result plot of Fig. 9d the Ener-gyPlus simulated load (Qep) is zero at night when system if off.However, forecasted load from SID model (Qes) does not have asystem on/off identifying variable. It has been added into cool-ing energy estimation model. Therefore, SID model load estimationmodel cannot identify the system off period. It will calculate thebuilding load as the system is on, which the energy estimationmodel will read in the system on and off schedule first and thencalculate the energy consumption. In the perimeter zone simula-tion results plots, we can see that our model will overestimate the
cooling load and energy at noon from 11 am to 2 pm and overes-timate the heating load and energy at late afternoon from 4 pm to10 pm. That is because of this on-line model does not consider theTable 4Building load system identification model training estimation accuracy.
R2 Training Forecasting
Core zone 0.937 0.953Perimeter zone 0.961 0.948
8 X. Li, J. Wen / Energy and Buildings 82 (2014) 1–12
Fig. 9. Building heating and cooling load estimation results: (a and b) Building heating/cooling load training results; (c and d) Building heating/cooling load fore castingr
he
tslacettdt
esults; (e and f) Building load forecasting error.
eat storage in the building thermal mass, which will cause the lagffect for building heating and cooling load.
And Fig. 9e and f plot the discrepancy between the results fromhe system identification model (Qes) and those from EnergyPlusimulation model (Qep), all the blue circles are clustered around theine: Qes = Qep. From these two figures, we can see the forecastingccuracy of core zone is better than that of perimeter zone, whichoordinate to the load estimation. And the on-line model will over-stimate the load at 8 am when the system is starting up. Those are
he outliers in Fig. 9e and f, which are acceptable, because the sys-em has a very huge dynamic change at the starting up and shuttingown periods. And this period is very short, which will not affecthe overall results too much.4.2. Building cooling energy on-line estimation results
Different to heating/cooling load, building cooling energy con-sumption is easy to measure in real field. The heating/coolingenergy forecasting model is essential to building model predictivecontrol for energy saving. Heating system coefficient is a constantvalue, so heating energy consumption is very easy to estimate basedon the heating load estimation. It is not necessary to develop a newSID model for heating energy forecasting. Therefore, this study will
only focus on the cooling energy modeling and forecasting.One very important variable was added into energy estimationmodel, which is supply fan heat into the air stream. Fig. 10 showsthe plots of cooling energy forecasting results. Similar to the results
X. Li, J. Wen / Energy and Buildings 82 (2014) 1–12 9
F forecasting; (b) South zone cooling energy forecasting; (c) West zone cooling energyf y forecasting.
ocTthwr
thf
Table 5System identification model forecasting accuracy.
R2 Accuracy (R2) Speed (S)
Training Forecasting Training Forecasting
East zone 0.967 0.957 18.30 0.0041South zone 0.971 0.963 19.54 0.0094West zone 0.969 0.966 19.90 0.0042
ig. 10. Building cooling energy forecasting results: (a) East zone cooling energyorecasting; (d) North zone cooling energy forecasting; (e) Core zone cooling energ
f load estimation, the model would also overestimate the energyonsumption when the system is starting up and shutting down.he accuracy of heating energy forecasting results is better thanhat of cooling energy forecasting (Table 5). That is because theeating energy efficiency coefficient is usually a constant value,hile the cooling energy efficiency is depended on the partial load
atio, and zone temperature setpoint, etc.
The core zone cooling energy forecasting results are betterhan training results, because during training period, the systemas been excited, which has much more dynamics than that at
orecasting period. These five plots show that the on-line model
North zone 0.954 0.943 18.93 0.0043Core zone 0.965 0.955 18.64 0.0035Whole building 0.944 0.956 47.33 0.0089
10 X. Li, J. Wen / Energy and Buildings 82 (2014) 1–12
oling
uzTsbeoitibda
4
cbabtrTim
fieeswau(
urbcefma
provided by a natural gas (NG) boiler, which have a70% annualfuel efficiency utilization (AFUE). Zone reheat is provided electricresistance heating.
Table 6Mechanical systems of the medium building.
Specifications
System 3 VAV, AHUsMain cool coil DX, COP 3
Fig. 11. Whole building co
nderestimates the cooling energy consumption, especially in westone and zone, at afternoon when direct solar radiation is strong.his is because solar radiation at afternoon is very strong and theolar angle is keep changing which brings in huge dynamics of theuilding energy system. However, east perimeter zone model over-stimates the cooling energy because the solar only directly radiaten the east envelop at morning, and direct solar radiation at morn-ng is very small. In additional to the direct solar radiation changing,he building thermal mass heat storage also affects the cool-ng energy consumption. The solar radiation transmitted into theuilding would not become cooling load of the HVAC system imme-iately. It will be first absorbed by the internal walls, floor, furniturend etc., and then released out by convection and radiation.
.3. Whole building energy estimation results
The models discussed above are zone based models, which fore-ast building cooling energy consumption zone by zone. Since theuilding studied in this paper is a one-floor small building, an over-ll model is also developed for the whole building. In this wholeuilding model, the system identification method is the same ashat of zone model, including system excitation signals, frequencyesponse function model, just with model input and output adjust.he output is the cooling energy of the whole building, and thenputs are all the inputs of core zone model and perimeter zone
odels.The whole building energy consumption forecasting results
rom the whole building model are plotted in Fig. 11a and b. Fig. 11bllustrates the comparison of EnergyPlus simulated whole buildingnergy consumption (Qes) and SID model forecasted while buildingnergy consumption (Qep). Due to the underestimation of directolar radiation related cooling energy consumption at afternoonhen cooling load is very high, a large discrepancy between Qes
nd Qep exists, as highlighted in green dashed circles. Even with thisnderestimation, the overall forecasting accuracy is still desirableTable 5).
Simulation speed is another crucial factor for MPC in practicalse. The training and forecasting speed of SID model are summa-ized in Table 5. The training calculation time is relative longerecause the power density is evaluated step by step. The forecastingalculation time is trivial, because the forecasting model is linear
quation calculation of input data and Markov parameters savedrom training period. Fortunately, if this model is applied in a MPCodel, the training process just need to be conducted once andll the Markov parameters and transfer functions would be saved
energy forecasting results.
and stay unchanging. Therefore, the forecasting period model willrun multiple times as needed in MPC model. Therefore, this modelis still suitable for any “searching” based optimization and controlalgorithms.
5. System identification model application in mediumoffice building
In order to test the accuracy of the system identification mod-eling strategy, the approach developed and validated in previoussections has been utilized in another medium size commercialbuilding. The building structure and mechanical system are differ-ent to the small building tested above, which is introduced in detailin following sections.
5.1. Medium office building description
The system identification modeling approach developed in thisstudy has been utilized in another medium office building, inorder to test its accuracy and robustness. This medium buildingis a 4982.2 m2 (53,628 ft2), three-story, 15-zone building [24]. Thewindow-to-wall ratio of this building’s facades is approximately33.0%, and the windows are also equally distributed. The thermalproperties of the windows of this building are the same as those inthe previous small commercial building.
The mechanical configurations of this building are tabulated inTable 6. Different to the small commercial building, this buildingis using variable-air-volume (VAV) AHU. Primary cooling is alsoprovided by electricity through DX coils. The coefficients of per-formance (COP) of these cooling coils are 3. Primary heating is
Main heat coil NG FurnaceZone reheat ElectricHeat plant Gas Central BoilerHeat efficiency 70% AFUE
X. Li, J. Wen / Energy and Buildings 82 (2014) 1–12 11
Fig. 12. Medium building cooling energy estimation: (a) First floor model training results; (b) First floor cooling energy forecasting; (c) Second floor cooling energy forecasting;(
5i
pam1Twp
bTbe
5
ttarm
of this research will focus on updating forecasting results based onreal measurements when it is necessary to improve the accuracy,especially at the high dynamics period.
Table 7System identification model forecasting accuracy and speed for medium building.
Accuracy (R2) Speed (S)
Training Forecasting Training Forecasting
d) Whole building cooling energy forecasting.
.2. Cooling energy on-line forecasting using systemdentification model
The system identification model developed and validated inrevious sections have been applied in this building with inputdjust based on the system configurations. Since there are 15 ther-al zones in this building, it is very time consuming to develop
5 different models to forecast the cooling energy consumption.herefore three different models were developed for each floorhich consists of five zones: core zone, east perimeter zone, southerimeter zone, west perimeter zone and north perimeter zone.
Same system excitation strategy was used in this building foruilding temperature setpoints and indoor equipment schedules.he inputs and outputs of each model are also similar to the smalluilding model. But in each model, temperature of each room andach adjacent room at each floor are included.
.3. Cooling energy forecasting results
As introduced in Section 5.2, building cooling energy consump-ion was forecasted at each floor individually. Fig. 12 shows the
raining and forecasting results. The forecasting accuracy and speedre summarized in Table 7, which illustrates that the forecastingesults capture the trend of real energy consumption measure-ent. The accuracy and speed are still acceptable for MPC, eventhough they are not as good as those for the small building,because medium building has more disturbances and it requireslonger calculation time to include all these disturbances into themodel.
It is illustrated in Fig. 12 that the on-line estimation modelunderestimates the cooling energy consumption during the HVACstarting up and shutting down periods. Comparing to the fore-casting results of the small building, the forecasting results in thismedium building has lagers errors. That is because there are moredisturbances in the medium building than in small buildings. How-ever, the on-line model still capture the overall trend of the realenergy consumption and the accuracy is still above 88%. Next step
First floor 0.931 0.878 42.6 0.011Second floor 0.941 0.871 52.9 0.015Third floor 0.951 0.877 42.9 0.013Whole building 0.949 0.872 97.3 0.026
1 nd Bui
6
lAtmebirmsfsmia
msttftcotos
A
d
R
[
[
[
[
[
[
[
[
[
[
[
[
[[
[
[
[
[
[
[
[
[
[
[
[
[35] D.E. Rivera, X. Chen, D.S. Bayard, Experimental design for robust process control
2 X. Li, J. Wen / Energy a
. Conclusion and future work
This study introduced a novel systematic methodology for on-ine building energy estimation model development and validation.
system excitement scheme and a Matlab-BCVTB-EnergyPlusestbed was developed and validated for system identification
odel development. The excitement scheme is able to guaranteenough data at the high frequency and low frequency around theuilding operation range, which can be applied in any other system
dentification models for building energy simulation. Frequencyesponse function model with realized by power spectral densityodel was implanted to forecasting building load and energy con-
umption. This on-line building energy model can achieve over 95%orecasting accuracy within 1 s in a small building case, which isuitable for any on-line building operation and MPC model. Thisodeling approach has also been applied in a medium office build-
ng. Limited to the calculation speed, the cooling energy forecastingccuracy is still around 88%.
We expect to further improve the accuracy of this on-line esti-ation model by introducing a thermal mass storage variable to
imulate the thermal storage effect and a solar angle parametero estimate effect of direct solar radiation on energy consump-ion. Data fusion techniques, such as Kalman filter, is planned tourther improve the forecasting accuracy, reduce the calculationime and improve the model robustness. In this study, only DXoil with CAV AHUs have been modeled, but we plan to modelther mechanical system such as VAV and gas heating. In addi-ional, this on-line building model is planned to be applied in someptimization models to determine the optimal building operationtrategies.
cknowledgement
Financial support provided by the U.S. National Science Foun-ation Award 1239247 is greatly appreciated.
eferences
[1] U.S. DOE, Buildings Energy Data Book, http://buildingsdatabook.eren.doe.gov/,2011.
[2] S. Katipamula, M.R. Brambley, Review article: methods for fault detection,diagnostics, and prognostics for building systems—a review, Part I, HVAC&RResearch 11 (1) (2005) 3–25.
[3] National Energy Technology Laboratory (NETL), Demand Dispatch–IntelligentDemand for a More Efficient Grid, in: DOE/NETL-DE-FE0004001, Morgantown,West Virginia, August 2011.
[4] U.S.D.o.E. Office of Energy Efficiency and Renewable Energy, EnergyPlus EnergySimulation Software: About EnergyPlus.
[5] M. Wetter, P. Haves, A Modular building controls virtual test Bed for the Inte-gration of heterogeneous systems, in: Proceedings of 3rd Nation Conference ofIBPSA-USA SimBuild, Berkeley, California, 2008.
[6] J. Ma, J. Qin, T. Salsbury, P. Xu, Demand reduction in building energy systemsbased on economic model predictive control, Chemical Engineering Science 67(1) (2012) 92–100.
[7] C.D. Corbin, G.P. Henze, P. May-Ostendorp, A model predictive control opti-mization environment for real-time commercial building application, Journalof Building Performance Simulation 6 (3) (2013).
[8] E.E.a.R.E.O., U.S. Department of Energy, Building Technology Program,
Net-Zero Energy Commercial Building Initiative, Commercial Building Bench-mark Models, 2009, Available from: http://www1.eere.energy.gov/buildings/commercial initiative/benchmark models.html[9] M. Wetter, Design optimization with GenOptR, in: Building Energy Simulation,Lawrence Berkeley National Laboratory, 2000, September/October.
[
ldings 82 (2014) 1–12
10] B. Coffey, F. Haghighat, E. Morofsky, E. Kutrowski, A software framework formodel predictive control with GenOpt, Energy and Buildings 42 (7) (2010)1084–1092.
11] W.J. Cole, E.T. Hale, T.F. Edgar, Building energy model reduction for modelpredictive control using OpenStudio, in: 2013 American Control Conference,Washington, DC, 2013.
12] K. Yun, R. Luck, P.J. Mago, H. Cho, Building hourly thermal load prediction usingan indexed ARX model, Energy and Buildings 54 (2012) 225–233.
13] J. Yang, H. Rivard, R. Zmeureanu, On-line building energy prediction using adap-tive artificial neural networks, Energy and Buildings 37 (12) (2005) 1250–1259.
14] Y. Chen, P.B. Luh, C. Guan, Y. Zhao, L.D. Michel, M.A. Coolbeth, P.B. Fried-land, S.J. Rourke, Short-term load forecasting: similar day-based wavelet neuralnetworks, IEEE Transactions on Power Systems 25 (1) (2010) 322–330.
15] J.E. Braun, N. Chaturvedi, An inverse gray-box model for transient building loadprediction, HVAC&R Research 8 (1) (2002) 73–99.
16] F. Oldewurtel, A. Parisio, C.N. Jones, D. Gyalistras, M. Gwerder, V. Stauch, B.Lehmann, M. Morari, Use of model predictive control and weather forecastsfor energy efficient building climate control, Energy and Buildings 45 (2012)15–27.
17] K.-H. Lee, J.E. Braun, Development of methods for determining demand-limiting setpoint trajectories in buildings using short-term measurements,Building and Environment 43 (10) (2008) 1755–1768.
18] S. Wang, X. Xu, Simplified building model for transient thermal performanceestimation using GA-based parameter identification, International Journal ofThermal Sciences 45 (4) (2006) 419–432.
19] D. Kim, J.E. Braun, Model-based predictive control for buildings with decouplingand reduced-order modeling, in: 2nd International High Performance BuildingsConference, Purdue University, 2012.
20] J. Ma, S.J. Qin, T. Salsbury, Model predictive control of building energy systemswith balanced model reduction, American Control Conference (ACC), 2012, IEEE(2012) 3681–3686.
21] Z. O’Neill, S. Narayanan, R. Brahme, Model-based thermal load estimation inbuildings, in: Proceedings of SimBuild, 2010.
22] L. Ljung, System Identification, Wiley Online Library, 1999.23] S. Privara, Z. Vána, D. Gyalistras, J. Cigler, C. Sagerschnig, M. Morari, L. Ferkl,
Modeling and identification of a large multi-zone office building, IEEE Interna-tional Conference on Control Applications (CCA), IEEE (2011) 55–60.
24] C. Agbi, Z. Song, B. Krogh, Parameter identifiability for multi-zone building mod-els, IEEE 51st Annual Conference on Decision and Control (CDC), IEEE (2012)6951–6956.
25] M. Deru, K. Field, D. Studer, K. Benne, B. Griffith, P. Torcellini, B. Liu, M.Halverson, D. Winiarski, M. Rosenberg, US Department of Energy CommercialReference Building Models of the National Building Stock, 2011.
26] S.P. Corgnati, E. Fabrizio, M. Filippi, V. Monetti, Reference buildings for costoptimal analysis: method of definition and application, Applied Energy 102(2013) 983–993.
27] L. Hendricken, K. Otto, J. Wen, P. Gurian, W. Sisson, Capital costs and energysavings achieved by energy conservation measures for office buildings in thegreater Philadephia Region, in: SimBuild Madison, WI, 2012.
28] L.C. Ng, A. Musser, A.K. Persily, S.J. Emmerich, Indoor air quality analyses ofcommercial reference buildings, Building and Environment 58 (2012) 179–187.
29] F. Zhao, I.J. Martinez-Moyano, G. Augenbroe, Agent-based modeling of com-mercial building stocks for policy support, in: The 12th International BuildingPerformance Simulation Association Conference, Sydney, Australia, 2011.
30] S. Prívara, Z. Vána, E. Záceková, J. Cigler, Building modeling: selection of themost appropriate model for predictive control, Energy and Buildings 55 (2012)341–350.
31] J.N. Juang, Applied System Identification, Prentice Hall, Englewood Cliffs, NewJersey, 1994.
32] M. Braun, R. Ortiz-Mojica, D. Rivera, Application of minimum crest factormultisinusoidal signals for “plant-friendly” identification of nonlinear processsystems, Control Engineering Practice 10 (3) (2002) 301–313.
33] M. Braun, D. Rivera, A. Stenman, W. Foslien, C. Hrenya, Multi-level pseudo-random signal design and “model-on-demand” estimation applied to nonlinearidentification of a RTP wafer reactor, in: Proceedings of the American ControlConference 1999, IEEE, 1999, pp. 1573–1577.
34] D.E. Rivera, H. Lee, H.D. Mittelmann, M.W. Braun, Constrained multisine inputsignals for plant-friendly identification of chemical process systems, Journal ofProcess Control 19 (4) (2009) 623–635.
using schroeder-phased input signals, American Control Conference, 1993, IEEE(1993) 895–899.
36] J.L. Devore, Probability and Statistics for Engineering and the Sciences,Brooks/Cole Publishing Co., 2004.
Related Documents
