A real-time detection method of abnormal building ...

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Procedia Engineering 205 (2017) 1657–1664

10th International Symposium on Heating, Ventilation and Air Conditioning, ISHVAC2017, 1922 October 2017, Jinan, China

A real-time detection method of abnormal building energy consumption data coupled POD-LSE and FCD Zhongjiao Ma, Jialin Song, and Jili Zhang** Faculty Faculty of of Infrastructure Infrastructure Engineering, Engineering, Dalian Dalian University University of of Technology, Technology, Dalian, Dalian, China China 116024 116024 *Corresponding *Corresponding email: email: [email protected] [email protected]

Abstract Abstract To To understand understand the the energy energy consumption consumption characteristics characteristics of of buildings, buildings, numerous numerous building building energy energy consumption consumption monitoring monitoring platforms platforms and internet and internet of of building building energy energy systems systems have have been been established established in in the the large large public public buildings, buildings, government government office office buildings, buildings, as as well well as as colleges colleges and and universities. universities. Although Although the the platforms platforms provide provide us us with with aa large large amount amount of of energy energy consumption consumption in-formation, in-formation, there there are are serious serious problems. problems. However, However, the the validity validity of of the the energy energy consumption consumption data data is is one one of of the the most most common common problems. problems. In In this this paper, paper, aa realrealtime time detection detection method, method, which which coupled coupled fractal fractal correlation correlation dimension dimension and and proper proper orthogonal orthogonal decomposition decomposition linear linear stochastic stochastic estimation, estimation, is is presented presented to to identify identify abnormal abnormal energy energy consumption consumption data. data. The The proper proper threshold threshold is is selected selected with with varying varying operational operational conditions. conditions. The The result result shows shows that that using using this this real-time real-time meth-od meth-od yields yields aa higher higher correctness correctness rate rate than than using using traditional traditional method method in in fault fault detection of data loss and outlier. It's worth pointing out that a hybrid method combining with other intelligent algorithms detection of data loss and outlier. It's worth pointing out that a hybrid method combining with other intelligent algorithms should should be be promising promising to to identify identify and and classify classify small small bias bias abnormal abnormal data data fault fault in in further further investigation. investigation. © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. © © 2017 The Authors. Published by Ltd. committee of the 10th International Symposium on Heating, Ventilation and Air Peer-review under responsibility responsibility of Elsevier the scientific scientific Peer-review committee of of the the 10th International Symposium Ventilation and and Air Peer-review under under responsibility of of the the scientific committee 10th International Symposium on on Heating, Heating, Ventilation Conditioning. Conditioning. Air Conditioning. Keywords: Keywords: Fractal Fractal correlation correlation dimension, dimension, proper proper orthogonal orthogonal decomposition, decomposition, linear linear stochastic stochastic estimation, estimation, energy energy consumption consumption monitoring monitoring platform, platform, internet internet of of building building energy energy system, system, real-time; real-time;

1. INTRODUCTION Building energy consumption takes a great part in total energy consumption in China (about 41%). One of the priorities is the large public building power consumption, which accounts for a quarter of the building total energy consumption [1]. In order to understand the energy consumption characteristics of buildings, numerous building * * Corresponding Corresponding author. author. Tel.: Tel.: +86-138-4207-7986; +86-138-4207-7986; E-mail E-mail address: address: [email protected] [email protected] 1877-7058 1877-7058 © © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. Peer-review Peer-review under under responsibility responsibility of of the the scientific scientific committee committee of of the the 10th 10th International International Symposium Symposium on on Heating, Heating, Ventilation Ventilation and and Air Air Conditioning. Conditioning.

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Conditioning. 10.1016/j.proeng.2017.10.334

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energy consumption monitoring platforms (BECMP) and internet of building energy systems (iBES) have been established in the large public buildings, government office buildings, as well as colleges and universities. However, due to interference in perception layer channel and the immature technology to supervise the energy consumption by the platform [2], the statistical energy consumption data derived from the platform may not be always correct or continuous, additionally, some unknown error may be generated in long term process. These inevitably bring about an unexpected analysis and evaluation on the energy consumption performance [3]. Therefore, it is absolutely vital to identify the validity of the energy consumption data. The common factors, which cause the abnormal data in the energy consumption monitoring platforms, could mainly be classified as three categories including data loss, instantaneous outliers and the inherent deviation of the platforms. Dozens of different methods have been applied to detect these abnormal data. Recently, Seem [4] proposed an intelligent data analysis system, which can automatically detect abnormal energy consumption. Kantikoon and Kinnares [5] applied multiple linear regressions to estimate electricity consumption in abnormal automatic meter. Besides, there are some intelligent algorithms including RDP neural network [6], statistical process control methodology [7] and cluster analysis [8], which were used to help detecting abnormal data. The difficulties of these methods are to acquire the accurate fault free parameters and models [9]. Great progress has been made in this field, but fewer studies focus on the validity of the statistical energy consumption data derived from BECMP. In order to identify the validity of these data, a feasible method should be proposed to improve the performance and utility value of BECMP. In this paper, a real-time method, which employs fractal correlation dimension (FCD) standard deviation of temporal coefficients between direct proper orthogonal decomposition and proper orthogonal decomposition (POD) coupled with linear stochastic estimation (LSE) in-stead of the traditional direct residual method, is used to detect abnormal energy consumption data. This method is implemented and validated on Energy Saving Monitoring and Manage-ment Platform of a University in Dalian. 2. Methodology 2.1. POD-LSE technique Proper orthogonal decomposition (POD) [10], a powerful and elegant statistical method of data analysis, aimed at obtaining low-dimensional approximate descriptions of high-dimensional processes. When applying the POD technique to energy consumption data, the matrix C(x, t) = {c(xi, tj)} is the approximate expression of the original energy consumption data, which xi(i=1, 2, …, m) denotes a spatial coordinate and tj(j=1, 2, …, n) denotes a temporal coordinate. In theory, an infinite summation provides the exact reconstruction, but in practice a finite number of POD modes capture most of the variance, therefore the original data is reconstructed using the summation provided as below. p

C ( x, t ) =  ϕk ( x ) α k ( t ) = ϕ1 ( x ) , ϕ 2 ( x ) ,  , ϕ p ( x )  α1 ( t ) , α 2 ( t ) ,  , α p ( t )  k =1

T

(1)

The term φk(x) corresponds to the POD basis function for the kth POD mode, and αk(t) is the set of temporal coefficients corresponding to the kth POD mode, which are uncorrelated and are found from Eq. (2). A single temporal coefficient exists for the entire field for each POD mode in each instance in time.

= α k ( t ) ϕkT ( t ) C ( x, t )

(2)

There exist different versions on the description of the POD mode. The direct method requires the solution to the two-point correlation over the entire field for every variable.



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{ ( )}) (C ( x, t ) − E {C ( x, t )})

(

T   

  C ( x , t ) = E  C ( x, t ) − E C x , t 

(3)

The term ∑C(x, t) is the m×m covariance matrix. From the knowledge of linear algebra and the lagrangian function, ∑C(x, t) is a semi-definite matrix. The Eq. (4) can be inferred.

λ ϕ ( x)  ( x, t ) ϕ ( x ) = k

C

k

(4)

k

It can be seen that the solutions are the eigenvalues and the corresponding eigenvector of the covariance matrix, respectively. The eigenvalues λ1≥λ2≥λ3≥…≥λm are arranged in decreasing order. Now, the proper orthogonal decomposition of the original matrix is completed using the POD. The principle orthonormal basis vectors φ1(x), φ2(x), … , φp(x) are found according to the eigenvalues, which are arranged in decreasing order. Simultaneously, the mean-square error of the approximate expression for the original data is given. This technique allows POD temporal coefficients to be estimated from an original energy consumption data. Then the entire field is reconstructed using the original basis functions. p

Cn* ( x, t ) =  ϕ k ( x ) α k* ( t ) = ϕ1 ( x ) , ϕ 2 ( x ) ,  , ϕ p ( x )  α1* ( t ) , α 2* ( t ) ,  , α *p ( t ) 

T

(5)

k =1

The estimated energy consumption data Cn*(x, t) is calculated by Eq. (5) based on the mathematical formulation for stochastic estimation method, which has been applied in a number of fluids applications similarly. Durgesh et al. [11] coupled POD with a multi-time delayed linear stochastic estimation (LSE) technique to better estimate phase differences in temporal coefficients in wake flows. ms

α k* ( t j ) =  Cn ( xi , t j )Ai k  C ( x1 , t )，C ( x1 , t )    C ( x1 , t )，C ( x2 , t )     C ( x , t )，C x , t 1 ms 

(

)

C ( x2 , t )，C ( x1 , t )



C ( x2 , t )，C ( x2 , t )







(

C ( x2 , t )，C xms , t

)



(6)

s

is =1

( (

) )

(

) (

C xms , t ，C ( x1 , t )   α t ，C x , t   A1k   k ( ) ( 1 )   A   α ( t )，C ( x , t ) C xms , t ，C ( x2 , t )   2 k  k 2 =        Ams k   α ( t )，C x , t    ms  k C xms , t ，C xms , t  

)

(

)

      

(7)

The estimated temporal coefficient αk*(t) is a matrix of LSE coefficients calculated by Eq. (6). Aisk is a matrix of LSE coefficients calculated by Eq. (7) for kth the POD mode at the ith measurement point, Cn(xi, tj) is the new measured event at the jth instant in time for the ith position, and C(xi, t) are the old measured event at the ith measurement point used in the original POD decomposition. Here αk(t) is the actual temporal coefficient for the kth POD mode calculated from Eq. (2), and ms is the number of the specified spatial data points used to estimate entire temporal coefficients. 2.2. Fractal correlation dimension The fractal dimension (FD) is a statistical quantity to indicate how completely a fractal appears to fill space in fractal geometry. Grassberger Procaccia (GP) algorithm [12] is the main algorithm to estimate the fractal correlation dimension of some fractal measure from a given set of points randomly distributed. Although the GP algorithm can be used for any measure, it is mostly used to measure the fractal dimensions of a strange attractor [13] from a onedimensional time series. The points can get close enough to the attractor, and an attractor can be a point, a curve, or even a complicated set with a fractal structure. If the system operation deviates from the normal state, the corresponding attractors, as well as the consequent FCD, will change. In other words, the changes of the state will

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induce different FCD, which implies the changing state. When applying the GP method coupled with POD, the temporal coefficients αk(t) should be described as below.

{

}

α k ( t j ) = α k ( t j ) , j = 1, 2,  , n

(8)

where n is the length of time series, which represent a set of the temporal coefficients for the kth POD mode. Simply, the time series denoted as

{x (t )} , j = 1, 2, , n

(9)

j

The time series x(tj) represents a measurement of the quantity x at the time tj=t0+j△t . We assume stationary, the statistics of the set {x(tj)} is invariant under time translation. Unless the measurements are independent identically distributed, there will be correlations between successive measurements. But they will be weak and short-ranged, if the data are produced by a chaotic system that is to say if they are sampled from a trajectory on a strange attractor. Furthermore, using Takens time delay embedding theorem [14], m denotes the embedding dimension, and there are m points of data in each phase space. Then, the phase of spatial data can be represented as a series of points in an mdimensional space and the jth scalar time series can be recorded as

{

}

x ( t j，m, τ ) = x ( t j ) , x ( t j + τ ) ,  , x ( t j + ( m − 1)τ ) , j = 1, 2,  , n − ( m − 1)τ

(10)

where τ is the time delay parameter and τ=△t. According to the method mentioned above, the time series with � points of data is divided into nm groups.

nm = n − ( m − 1)τ

(11)

nm is the number of the points or coordinate vectors in the fractal set. The m-dimensional hypersphere radius is represented by Euclidean distance. m −1

r ( ti , t j , m, τ ) = x ( ti , m, τ ) − x ( ti , m, τ ) =

( x k =0

i + kτ

− x j + kτ )

(12)

The center of a hypersphere can be defined as the radius. For each i with fixed value, a radius can be calculated from the phase space distances by the spherical triangle method [15], and then the radiuses from different i can be obtained. Changing the center of the reproduced hypersphere will get a series of small spheres. If r is defined as a length scale, the radius smaller than the scale will be reserved but others will be discarded. Thus, the ratio between the number of small spheres and the number of total spheres is defined as the correlation integral function C(r).

C (r) =

1 ( nm − 1) nm

nm

nm

i

j

 H r − r ( t , t , m, τ ), i ≠ j i

j

(13)

H(x) is the Heaviside step function:

1 r − r ( ti , t j , m, τ ) ≥ 0 H  r − r ( ti , t j , m, τ )  =  0 r − r ( ti , t j , m, τ ) < 0

(14)



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r = rmax ( ti , t j , m, τ ) − rmin ( ti , t j , m, τ )

i +1 , i = 1, 2,  , p ( p ≥ log 2 n ) p +1

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(15)

To avoid a twofold calculation of distances and to implement Theiler’s method of enlarging the range of proper scaling [16], the Eq. (13) can be transformed into Eq. (16) with avoiding the same calculation and saving a half of computation.

C (r) =

2 ( nm − 1) nm

nm

nm

i

j= i +1

  sgn r − r ( t , t , m, τ ) i

j

(16)

Because r is sufficiently small and the number of observed values nm is large enough, the reconstructed phase space attractor of FCD can be derived as DC = lim

log 2 C ( r )

(17) log 2 r Therefore, C(r) is proportional to the number of pairs of points of the fractal set separated by a distance less than‫ݎ‬. If the system of points examined is a fractal set, the graph log2C(r)-log2r must be a linear function with slope DC, which equals to the fractal dimension of the system. r →0

2.3. The real-time detection method Statistically, the direct residual-based method always uses considerable residuals between measured and esti-mated real-time data to determine whether abnormity generates or not. As a result of nonlinear characters of the energy consumption, a real-time method employs FCD deviation of temporal coefficients between direct POD and POD-LSE instead of direct residual. The logic diagram of this real-time detection method coupled POD-LSE and POD is shown in Fig. 1.

Fig. 1 The logic diagram of the real-time detection method

The results from the present investigation suggest that the LSE temporal coefficient could accurately reflect right performance character of the energy consumption monitoring platform. If there is a big difference between LSE and direct calculated temporal coefficients, it indicates that the directly calculated temporal coefficient with entire field data may be not the right coefficient. Therefore, the abnormal energy consumption data could be detected according to the principle of the above.

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3. Results

The experimental data from the innovation park building derived from Campus Energy Saving Monitoring and Management Platform of an University in Dalian is used to validate abnormal energy consumption detection method. The lighting energy consumption, which contributes to about 83% of the building total energy consumption, is collected from March 2013 to March 2014. The building includes two blocks and each block has five measured points distributed. Therefore, the 10×365 matrix expresses lighting energy consumption of this building, that is to say, the ith row indicates the ith measured point energy consumption changed over time and the jth column indicates the jth time energy consumption of the entire measured points. One year data were chosen in this study to ensure that multiple operating conditions occurred within the data set. The real-time detection method is evaluated by compared FCDs using POD-LSE technique. With consideration of the time span to be 28, only one parameter, which is known as the step, needs to be decided. If the step is considerate to be 7, it means 7 new data and 21 historical data are used to calculate FCD every time. At the same time, the length of the reference temporal coefficient, which is selected in the normal condition, is the same as the step length. The abnormal energy consumption data will be detected by this progressive algorithm. The FCD standard deviation (SD) between LSE and directly calculated from POD is described as Eq. (19). Table 1, Table 2 and Table 3 describe the result of the real-time detection results. SD =

FCDLSE − FCDPOD FCDPOD

(19)

Table 1 Real-time detection result when step=14. Step No. Direct POD FCD POD-LSE FCD 1 1.3661 1.3571 2 1.2298 1.2355 3 1.4317 1.3670 4 1.2392 1.2158 5 1.0832 1.1249 6 1.4106 1.3686 7 1.3728 1.3526 8 1.3114 1.2273 9 1.1429 1.0894 10 1.2811 1.2810 11 1.1788 1.2122 12 1.1223 1.2204

DE -0.67% 0.46% -4.73% -1.93% 3.71% -3.07% -1.50% -6.85% -4.91% -0.01% 2.76% 8.04%

Table 2 Real-time detection result when step=7. Step No. Direct POD FCD POD-LSE FCD 1 1.3747 1.3728 2 1.3616 1.3534 3 1.1202 1.1104 … … … 9 1.3115 1.3249 10 1.0992 1.1249 11 1.3594 1.2093 12 1.4106 1.3686 13 1.2439 1.2022 … … … 22 1.1788 1.2122 23 1.2572 1.1821 24 1.1223 1.3322

DE -0.14% -0.61% -0.88% … 1.01% 2.29% -12.41% -3.07% -3.47% … 2.76% -6.36% 15.76%

Start time 8 15 22 … 64 71 78 85 92 … 155 162 169

End time 35 42 49 … 91 98 105 112 119 … 182 189 196

Table 3 Real-time detection result when step=4. Step No. Direct POD FCD POD-LSE FCD 1 1.2650 1.2542 2 1.2318 1.2212 3 1.3522 1.3614

DE -0.86% -0.87% 0.68%

Start time 5 9 13

End time 32 36 40

Start time 17 31 45 59 73 87 101 115 129 143 157 171

End time 44 58 72 86 100 114 128 142 156 170 184 198



Zhongjiao Ma et al. / Procedia Engineering 205 (2017) 1657–1664 Zhongjiao Ma et al. / Procedia Engineering 00 (2017) 000–000 … 17 18 19 20 21 40 41 42 43

… 1.0755 1.1044 1.2179 1.2339 1.4106 … 1.2460 1.2320 1.1223 1.1694

… 1.0960 1.0910 1.0723 1.1701 1.3686 … 1.2022 1.1925 1.2704 1.1388

… 1.87% -1.23% -13.58% -5.45% -3.07% … -3.64% -3.31% 11.66% -2.69%

… 69 73 77 81 85 … 161 165 169 173

1663 7 … 96 100 104 108 112 … 188 192 196 200

Table 1 describes the detection result with the step value set as 14, and the outlier show 8% deviation in No.12 step. Table 2 describes the detection result with the step value set as 7, and the data loss fault show -12% deviation in No.11 step and the outlier value data show 15% in No.24 step. Accordingly, the same results are shown in Table 3 with the different step set as 4. 4. Discussion Either data loss or outlier show higher FCD deviations than normal condition in the same time span with the step value set as 14, 7 or 4. But the data loss fault needs not to be detected with the step value set as 14. As summarized above, the FCD can characterize the abnormal curve variations and distinguish their symptoms. If the threshold is set at ±1.0, the FCD standard deviation of abnormal condition is far beyond the threshold, when the step value equals to 7 or 4, except for that of 14. Therefore, it is very important to select a proper threshold under different condition. Further, due to the complexity of dynamic nonlinear system, the varying operational conditions will lead to distinct changes when the same abnormal data generates. The resulting FCD standard deviation calculations are also dissimilar, so it is very important to find only one threshold to suit all the step values. In the traditional method, the abnormal energy consumption data could be detected with the deviation between the real-time data and the data estimated from the auto regressive (AR) model. The results of the traditional method and POD temporal coefficient are shown in Fig. 2. According to the analysis result, the data loss fault could be detected, but the delay phenomenon exists. Obviously, it is difficult to select a proper threshold to improve the correct rate of the abnormal data detection of the energy consumption. The comparing result implicates that correct rate in Fig. 2 is much lower than the real-time detection method presented in this paper.

Fig. 2 The results of the traditional AR method and POD temporal coefficient

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There are two weaknesses in the traditional method. Firstly, only one spatial point real-time data could be considered to analysis the abnormal data, so the entire field dynamic character could not be utilized to detect the abnormal data. Secondly, there are not accurate threshold and model to distinguish the abnormal data. 5. Conclusions

In this paper, a real-time detection method of abnormal building energy consumption data has been presented with POD-LSE and FCD instead of the traditional way. A practice with this method is performed in energy consumption monitoring platform, as a result, the data loss and the outlier are detected. And the correct rate of the real-time method is much higher than the traditional detection method according to the comparing result. The typical weakness of real-time detection method is that the validity decision is greatly dependent on a proper threshold of the FCD deviation. Different threshold settings will result in various correct detection rates; however, a proper threshold could be obtained under different condition and the different step value will not reflect the correct detection rate. Another relative weakness is that the validity of reference normal data and specified location, but it is easy to obtain the correct data with a preparation of less investment investigation. Further investigation should be carried out to classify the abnormal fault on the real-time detection method combining FCD and POD-LSE. The further approach can be used to classify the other small bias fault, but it requires a period of time to observe the abnormal variations to improve correct detection rate in relatively small bias fault. The hybrid method will be promising to identify other small bias fault. Acknowledgements

We are grateful for the financial support of National Natural Science Foundation of China (Grant No. 51578102， 51378005) and Dalian Municipal Science and Technology Plan Project (Grant No. 2015E11SF052). We are also grateful for the survey team members of Institute of Building Energy, Dalian Uni-versity of Technology. References [1] L. Pérez-Lombard, J. Ortiz, C. Pout. A review on buildings energy consumption information, Energy and Build-ings 40 (3) (2008) 394-398. [2] Y. Chen, X. Mu, J. Zhang, Z. Lu. Development of Monitoring System of Building Energy Consumption, IEEE 2 (2009) 363-366. [3] W.S. Lee, K.P. Lee. Benchmarking the performance of building energy management using data envelopment analysis, Applied Thermal Engineering 29 (16) (2009) 3269-3273. [4] J.E. Seem. Using intelligent data analysis to detect abnormal energy consumption in buildings, Energy and Buildings 39 (1) (2007) 52-58. [5] V. Kantikoon, V. Kinnares. The estimation of electrical energy consumption in abnormal automatic meter read-ing system using multiple linear regression, ICEMS (2013) 826-830. [6] F. Magoulès, H. Zhao, D. Elizondo. Development of an RDP neural network for building energy consumption fault detection and diagnosis, Energy and Buildings 62 (2013) 133-138. [7] L.C. Braga, A.R. Braga, C.M.P. Braga. On the characterization and monitoring of building energy demand using statistical process control methodologies, Energy and Buildings 65 (2013) 205. [8] Q.X. Xia, D. Xiao, B. Wang. A real-time monitoring method of energy consumption based on data mining, Journal of Chongqing University (Natural Science Edition) 35 (7) (2012) 133-137. [9] S. Li, W. Jin. A model-based fault detection and diagnostic methodology based on PCA method and wavelet transform, Energy and Buildings 68 (2014) 63-71. [10] Y. Tamura. An introduction of applying proper orthogonal decomposition to random fields, Transactions of the Japan Association for Wind Engineering 65 (1995) 33-41. [11] V. Durgesh, J.W. Naughton. Multi-time-delay LSE-POD complementary approach applied to unsteady high-Reynolds-number near wake flow, Experiments In Fluids 49 (3) (2010) 571-583. [12] P. Grassberger. Grassberger-Procaccia algorithm. Scholarpedia 2 (5) (2007) 3043. [13] F.M.D. Aguiar, A. Azevedo, S.M. Rezende. Characterization of strange attractors in spin-wave chaos, Phys Rev B Condens Matter 39 (13) (1989) 9448-9452. [14] J.W. Milnor. Attractor, Scholarpedia 1 (2006) 1815. [15] P. N. S. Roy, A. Ram. A correlation integral approach to the study of 26 January 2001 Bhuj earthquake, Guja-rat, India, Journal Of Geodynamics 41 (4) (2006) 385-399. [16] J. Theiler. Phys. Rev. A 34 (1986) 2427.