1、 Fuxin Niu is a PhD student and Zheng ONeill is an assistant professor in the Department of Mechanical Engineering, The University of Alabama, Tuscaloosa, AL, USA. Bayesian Network Based HVAC Energy Consumption Prediction Using Improved Fourier series Decomposition Fuxin Niu, PhD Zheng ONeill, PhD,
2、PE Student Member ASHRAE Member ASHRAE ABSTRACT An accepted Heating, Ventilation and Air-conditioning (HVAC) energy consumption model is a necessary step for various applications including fault detection and diagnostics, measurement and verification in building retrofit. It is common to use a polyn
3、omial regression to decouple the baseload from total building energy consumption while considering the baseload as a fixed value. To improve the decoupling algorithm, Fourier series is introduced to represent the dynamic baseload. Furthermore, a probabilistic graphical Bayesian network model with di
4、screte and continuous variables is developed to predict the HVAC energy consumption. Sub-metering data from a four-story university dormitory is used to test the proposed Fourier series based decomposition and Bayesian Network based predictions. The results indicate that polynomial regression integr
5、ated Fourier series decomposition method is feasible and has a more accurate performance. Using the decomposed data, the HVAC system electricity energy consumption is predicted using a Bayesian network. The preliminary results suggested that the Bayesian network is a time-saving and accurate predict
6、ion model based on the ASHRAE Guideline 14 recommended metrics. INTRODUCTION Accurate energy performance prediction of Heating, Ventilation and Air-Conditioning (HVAC) system plays a significant role for intelligent building operations to improve energy efficiency and reduce energy consumption in bu
7、ildings. In modern commercial and residential buildings, large amounts of raw data, including electric metering data, are monitored, trended and saved in, for example, Building Automation System (BAS). Due to the complexity of building mechanical and electrical system and the cost, practically speak
8、ing, it is impossible to have sensors/meters to monitor the building at a fine granularity. Building total energy consumption (e.g., total electricity consumption) is one of the most commonly available metering data. How to decompose the total building energy consumption for an accurate estimation o
9、f the HVAC system energy consumption is important to analyze and manage HVAC system performance and operations. There are many approaches for baseline building energy estimation. ASHRAE Guideline 14 (ASHRAE 2002) and Internal Performance Measurement and Verification Protocol (IPMVP) (EVO 2012) provi
10、de rigorous approaches to develop baseline models for estimating energy savings due to retrofits. In practice, linear regression method is a common approach for building energy performance analysis. In a change-point model, the building performance is partitioned into different operating conditions
11、and a linear model is fit to each of the operating modes (Kissock et al. 2002). Both linear regression and Gaussian Process regression were used to develop an inverse model for a commercial building case (Zhang et al. 2013). Multi-variate linear model was developed to estimate a variable air volume
12、(VAV) energy saving potential after the system retrofit (Katipamula et al. 1993). Zhang et al. (2015) reviewed four mainstream baseline data-driven energy models used to characterize building energy performance: change-point regression model, Gaussian process regression (GPR) model, Gaussian mixture
13、 regression (GMR) model, and artificial neural network model. These models were then applied to an office building to predict the HVAC hot water energy consumption. The change-point method is the most appropriate for this case study in terms of accuracy vs. efforts spent for the modeling. This is ac
14、tually well aligned current practice in building measurement and verification industry. The occupant schedules and behavior certainly will have significant impacts on the model prediction accuracy for some cases (Clevenge et al. 2006). These factors could be easily adapted into the current framework
15、. Prediction of building HVAC system energy usage and its associated uncertainty analysis are critical to characterize the building baseline performance for impact assessments of energy saving strategies such as fault detection and diagnosis (FDD), control policies and retrofits. Srivastav et al. (2
16、013) presented a data-driven approach based on GMR for modeling building energy use with locally adaptive uncertainty quantification. GMR approach was found to be comparable to the polynomial model in terms of the accuracy of building energy consumption predictions. The predictive quality of the GPR
17、 model is strongly influenced by the range covered by the training and testing data set. ONeill (2014) presented a data driven probabilistic graphic model to predict building HVAC hot water energy consumption. A directed graphical model namely, a Bayesian Network (BN) model was created for such a pu
18、rpose. Each node in the BN represents a random variable and the links between the nodes are probabilistic dependencies among these corresponding variables. These dependencies are statistically learnt and/or estimated by using measured data and augmented by domain expert knowledge. The prediction res
19、ult by BN indicated that it was acceptable prediction method while providing more information such as uncertainty associated with predictions for risk management. Niu et al. (2015) analyzed air conditioning unit energy consumption prediction from different algorithms including BN, AutoRegresive with
20、 eXternal inputs, State Space and Subspace state space models. The results indicated that BN method has the most accurate estimation. In buildings, the baseload is the energy consumption irrelative with outdoor conditions such as outdoor air temperature. In general, it includes plug, lighting, refri
21、geration load, etc. (Ge and Tassou 2011). In this paper, in order to enhance the accuracy of building baseload estimation, an improved Fourier series decomposition based on linear regression method is proposed to estimate the total building energy consumption, corresponding baseload energy consumpti
22、on and HVAC system energy consumption. And then discrete and continuous variables BN models are applied to estimate HVAC system energy consumption based on the decoupled results from Fourier series decomposition. Finally, the comparison analysis of two BN models is conducted. TECHNICAL APPROACH In t
23、his case, there are two steps to estimate the HVAC energy consumption using BN method. Firstly, an improved Fourier series decomposition method is proposed to decouple the baseload from measured total building energy consumption. And then, HVAC system energy consumption will be predicted using BN mo
24、dels. Improved Fourier series Decomposition Currently, the polynomial regression method is widely used (Spyrou et al. 2015). It is assumed that total building energy consumption is only dependent on outdoor air temperature as shown in Equation (1). 230 1 2 3y d d T d T d T (1) Where d0 is the baselo
25、ad; T is outdoor air temperature; d1, d2 and d3 are coefficients. It is well known that the occupant schedules and behavior have significant impacts on the building energy consumption. The baseload (e.g., lighting and plug load) is highly correlated with occupant behaviors. Thus, the baseload should
26、 be varied along with the time rather than a constant value of d0 as stated in Equation 1. The proposed baseload decoupling method based on Fourier series makes a full use of its time variation with a strong regression function to reflect the impacts from dynamic occupant schedules and behaviors. Th
27、e Fourier series based decoupling regression model can be written in Equation (2). The sum of the first two terms of Fourier series stands for the baseload and the sum of other terms is HVAC system energy consumption. 230 0 1 2 311 c o s s i n2 nnny a a n t b n t c t T d T d T d T (2) Bayesian Netwo
28、rk Based Prediction method A Bayesian Network (BN) is a probabilistic graphical model that represents a set of random variables and conditional dependence through a direct acyclic graph (DAG). In the graphical model, the node that causes another node is called a parent and the affected node is calle
29、d its child. The child is conditioned by the parent. Given A is a parent and B is a child of A, the probability of B conditioned by A is noted P(B|A). Bayes theorem describes probabilistic dependencies between A and B as follows (Jensen 2001): P(A|B )P(B)P(B|A )= P(A) (3) For continuous variables, t
30、he conditional probability distribution will follow the normal distribution regulation N (, 2). stands for the mean value and is the standard deviation. The probability formula is shown in Equation 4. 2221()2xP X e (4) CASE STUDY Sub-metering data from a four-story university dormitory is used to te
31、st the proposed Fourier series based decomposition and BN based predictions. The total electricity energy consumption, covering lighting, plug load and HVAC load for each floor, is sub-metered. There is an on-site weather station with measurements of outside air temperature, relative humidity, wind
32、speed and direction, and solar radiation. Data from September 15th to October 29th, 2014 are used for Fourier series regression model to separate HVAC system electricity consumption from the baseload. The baseload decomposition equation coefficients from the polynomial and Fourier series regression
33、methods are computed and listed in Tables 1 and 2. The R-square value of the polynomial regression method is 0.732. When Fourier series method was applied in the decomposition regression. The R-square value was improved to 0.772. Table 1: Coefficients of polynomial regression equation d0 d1 d2 d3 Co
34、efficient 36920 196.5 37.17 0.58 Table 2: Coefficients of improved Fourier series regression equation a0 a1 b1 a2 b2 a3 b3 c0 d1 d2 d3 Coefficient 36710 207.1 1799 -64.9 815.8 96.1 576.3 34 -152.8 38.4 0.4 Figure 1 shows total building electricity consumption predictions by Fourier series regression
35、 method. The measured data sampling frequency is two-minute in this case study. The regression can accurately predict the total building electricity consumption compared with actual measurements. Figure 2 presents the baseload decomposed by improved Fourier series regression method, which illustrate
36、s a dynamic performance related with occupant behaviors. This result is more realistic compared with the previous polynomial regression method assuming a constant value of the baseload. Based on the estimated total building energy consumption and the baseload, HVAC electricity consumption can be dec
37、oupled as represented in Figure 3. This data set of HVAC system electricity consumption will be used to the BN model study. 0 9 / 1 8 / 1 4 0 9 / 2 8 / 1 4 1 0 / 0 8 / 1 4 1 0 / 1 8 / 1 402468101214x 1 04D a t eBuildingelectricity consumption(W)00 . 511 . 522 . 533 . 544 . 5x 1 05Buildingelectricity
38、 consumption(BTU/hr)M e a su re me n tEst i ma t i o n b a se d o n F o u ri e s Se ri e s me t h o dFigure 1 Total building electricity consumption predictions by improved Fourier series regression method 0 9 / 1 8 / 1 4 0 9 / 2 8 / 1 4 1 0 / 0 8 / 1 4 1 0 / 1 8 / 1 43 . 43 . 4 53 . 53 . 5 53 . 63
39、. 6 53 . 73 . 7 53 . 83 . 8 53 . 9x 1 04D a t eBaseload(W)1 . 1 61 . 1 81 . 21 . 2 21 . 2 41 . 2 61 . 2 81 . 31 . 3 2x 1 05Baseload(BTU/hr)Figure 2 The baseload decoupled by Improved Fourier series regression method 0 9 / 1 8 / 1 4 0 9 / 2 8 / 1 4 1 0 / 0 8 / 1 4 1 0 / 1 8 / 1 40123456789x 1 04D a t
40、 eHVACsystem electricity consumption(W)00 . 511 . 522 . 53x 1 05HVACsystem electricity consumption(BTU/hr)Figure 3 Decoupled HVAC system electricity consumption by Improved Fourier Series regression method A BN model was created to predict the hourly HVAC system electricity consumption using the dec
41、oupled data for the training and testing. Figure 4 shows the BN structure with three nodes (GeNie 2013). For this case study, discrete and continuous variable BN predictions are conducted. For the discrete BN, based on the domain knowledge and trial-and-error, outdoor air temperatures were discretiz
42、ed into 28 bins with a uniform distribution. Hours of day were discretized into 24 bins, while 50 bins were assigned to HVAC system electricity consumption. Figure 4 The BN structure for the case study RESULTS After the BN structure and probability are trained using the decoupled HVAC data (as shown
43、 in Figure 3) from the September 15th to October 19th, 2014, the discrete and continuous variable BN models are tested to use the data from October 20th to October 29th, 2014. The BN models used the hour of day and outdoor air temperature as input to calculate the HVAC system electricity consumption
44、. For a given hour of day and outdoor air temperature in the discrete variable BN model, the predicted HVAC system electricity consumption falls into the energy consumption bins with the highest probability. For continuous variable BN model, the predicted HVAC system energy consumption will pick up
45、the mean value from the model computation. Figure 5 PDF plot of HVAC system electricity consumption 28 bins of outdoor air temperature (OAT) between the hours of 15:0016:00 Figure 5 shows all the Probability Density Function (PDF) plots of HVAC system electricity consumption for 28 bins of outdoor a
46、ir temperature between the hours of 15:0016:00. These PDFs are learnt from the training data. For example, when outdoor air temperature is below 64.4F (18 oC) for the time of 15:0016:00, the probabilities for all electricity consumption bin are zero. This is because there is not sufficient data for
47、learning for these temperature bins. In order to predict the electricity consumption for the OAT bins with the probabilities of zero for a given hour, a linearly interpolation method is applied using the data with the probabilities of nonzero before and after this hour. Figure 6 and Figure 7 show co
48、mparisons between measurements and predictions for the testing data from October 20th to October 29th, 2014 using discrete variable BN model, which demonstrates that this BN model can accurately predict the time varied HVAC system electricity consumption. Figure 7 shows comparisons of measurements a
49、nd predicted HVAC system electricity consumption with uncertainty. The dark solid lines are 15% error lines. The color of circles indicates the probability of the occurrence of the predicted electricity consumption given an outdoor air temperature and an hour of day. Most of estimations are within 15% error. Figure 8 shows the HVAC system electricity consumption predictions through the continuous variable BN model. Although the predictions can relatively follow
