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An enhanced PCA method with Savitzky-Golay method for VRF system sensor fault detection and diagnosis
Energy and Buildings 142 (2017) 167–178
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Full Length Article
An enhanced PCA method with Savitzky-Golay method for VRF system sensor fault detection and diagnosis Yabin Guo a , Guannan Li a , Huanxin Chen a,∗ , Yunpeng Hu b , Haorong Li c , Lu Xing a , Wenju Hu d a
Department of Refrigeration & Cryogenics, Huazhong University of Science and Technology, Wuhan, China Department of Building Environment and Energy Application Engineering, Wuhan Business University, 816 Dongfeng Avenue, Wuhan, Hubei 430056, China c Durham School of Architectural Engineering and Construction College of Engineering, University of Nebraska-Lincoln, Omaha, NE, USA d Beijing Key Lab. of Heating, Gas Supply, Ventilating and Air Conditioning Engineering, Beijing University of Civil Engineering and Architecture, Beijing, China b
a r t i c l e
i n f o
Article history: Received 23 April 2016 Received in revised form 23 December 2016 Accepted 9 March 2017 Available online 10 March 2017 Keywords: Principal component analysis Satizky-Golay method Variable refrigerant flow Sensor fault detection and diagnosis Optimal index
a b s t r a c t Sensor faults of air conditioning systems are harmful to optimal control strategies and system performance resulting in poor control of the indoor environment and waste of energy. In order to improve the fault detection and diagnosis (FDD) performance, this paper presents an enhanced sensor fault detection and diagnosis method based on the Satizky-Golay (SG) method and principal component analysis (PCA) method for the VRF system, namely SG-PCA method. Due to the volatility of the original data set of VRF system, the original data are smoothed using SG method at first. Then, the smoothed data are used for PCA model training and fault detection and diagnosis. In order to determine parameters of the SG method, an optimization index is proposed, which is calculated by the signal to noise ratio (SNR), the standard deviation (SD) and the self-detection efficiency. This SG-PCA method for VRF system sensor FDD is validated using field operation data of the VRF system. Various sensor faults at different fault levels are introduced. The results have showed that the SG-PCA method can significantly improve the fault detection and diagnosis performance compared to conventional PCA method. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Heating ventilating and air-conditioning (HVAC) systems accounted for closed to 41 percent of site energy consumption in U.S. building primary energy consumption [1]. Therefore, energy saving of the HVAC system is very important. There are two key issues which are suitable control strategies and reliable measurements to ensure good performance of HVAC system. When the bias of return air flow rate sensor was 20%, the energy consumption of AHU system increased closed to 14% [2]. Consequently, sensor fault detection and diagnosis (FDD) of HVAC system is of great significance for energy saving and the normal operation of system. There are many studies of sensor FDD in HVAC systems. Wang and Cui [3] developed an online strategy to detect, diagnose and validate sensor faults in the water-cooled centrifugal chillers. Du [4] presented the dual neural networks combined strategy to detect the faults
∗ Corresponding author. E-mail address: [email protected] (H. Chen). http://dx.doi.org/10.1016/j.enbuild.2017.03.026 0378-7788/© 2017 Elsevier B.V. All rights reserved.
of sensors of the air handing unit (AHU). Zhu [5] presented a new fault diagnosis method based on neural network pre-processed by wavelet and fractal for sensors fault in an AHU system. Hu [6] presented a statistical training data cleaning strategy for PCA based chiller sensor fault detection, diagnosis and data reconstruction. Li [7] developed a SVDD model in the residual subspace (Rs) using the PCA modeling residual data to improve the fault detection performance. However, there are rather rare studies regarding the sensor FDD for the VRF system in open literatures. The variable refrigerant flow (VRF) system is an air conditioning unit which allows one outdoor unit connected to two or more indoor units by pipes. Heat exchangers of the VRF system are air-cooled at outdoor and direct evaporation at indoor. There are many significant advantages to the VRF system, such as wide range of cooling and heating temperature, design flexibility, convenient installation, reliable operation, advanced control and less space requirement [8,9]. Therefore, VRF systems have been widely used in small and medium-sized buildings [10]. It is because VRF system has some advantages such as above that make VRF system different
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Nomenclature c Cov COP e fcom1 fcom2 FDD h Icom1 Icom2 IDU n Nwin Npoly OI ODU Pcond Pevap Q␣ i Qcon
TSPR,in TSPR,out Tcom1 Tcom2 Tfan1 Tfan2 W Y
The coefficient The covariance matrix Coefficient of performance Residual vector The first compressor operating frequency, Hz The second compressor operating frequency, Hz Fault detection and diagnosis Specific enthalpy of refrigerant The first compressor electric current, A The second compressor electric current, A Indoor unit Compressor speed The moving window size The polynomial order Optimal index Outdoor unit Condensing saturation pressure, MPa Evaporating saturation pressure, MPa Threshold of the Q-statistic Contribution of the ith variable to the total sum of variations Heat exchange amount of evaporator, kW Heat exchange amount of condenser, kW Squared prediction error The cumulative error Savitzky-Golay filter The signal noise ratio Outdoor temperature, ◦ C Refrigerant temperature at the condenser outlet pipe, ◦ C Liquid refrigerant temperature at the subcooler outlet pipe, ◦ C Vapor refrigerant temperature at the subcooler outlet pipe, ◦ C Vapor–liquid separator inlet pipe temperature, ◦ C Vapor–liquid separator outlet pipe temperature, ◦ C The first compressor module temperature, ◦ C The second compressor module temperature, ◦ C The first fan module temperature, ◦ C The second fan module temperature, ◦ C Power input. kW The value after smooth process
Greeks
Mean isentropic coefficient of refrigerant Efficiency
Q0evap Qcond SPE S SG SNR TOD Tcond,out Tsubc,out,L Tsubc,out,V
Subscripts Com1 The first compressor The second compressor Com2 cond Condenser Evaporator evap Fan1 Outdoor fan 1 Fan2 Outdoor fan 2 in Inlet Outlet out subc Subcooler sta Standardization Vapor–liquid separator SPR
from other air conditioning system. Therefore, it is necessary to establish sensor fault detection and diagnosis model of VRF system. In recent years, there have been a few studies related to sensor FDD methods which are based on data driven method. The combined neural networks which include the basic neural network and auxiliary neural network are developed to detect and diagnose sensor fault of the AHU [11,12]. Du presented a data-driven method combined the PCA and Fisher discriminant analysis to detect and diagnose multiple faults including drifting bias, fixed bias, failure of sensor faults of the AHU [13]. The support vector data descript method was used to detect and diagnose sensor faults of chiller system [14], which has advantages of solving problems on describing non-liner and non-Gaussian distributed data. Zhao [15,16] proposed a diagnostic Bayesian networks-based method to diagnose 28 faults, covering senor faults of the AHU. But most of them are developed for the chiller and AHU systems. The PCA method is a kind of multivariate statistical method, which has been applied to the sensor FDD in the field of HVAC. Wang [2,3,17–19] developed an online strategy based on principal component analysis to detect, diagnose and validate sensor faults in centrifugal chillers, AHU systems and VAV air conditioning systems. Xiao [20] presented an isolation enhanced PCA method the expert-based multivariate decoupling for sensor FDD in VAV air conditioning systems. Xu [21] developed an enhanced sensor fault detection, diagnosis and estimation method combined wavelet analysis and PCA method for centrifugal chillers. Du [22] developed three PCA models based on energy balance and air side and water side to detect whether there is any abnormality in the VAV systems. Hu [23] presented a self adaptive FDD strategy based on PCA method for sensor faults of chillers. The PCA method has been applied maturely to chillers, AHU systems and VAV air conditioning systems, etc. But there is no research on sensor fault in the VRF system using PCA method. Therefore, this paper developed an PCA model to detect and diagnose sensor faults in the VRF system and optimized the FDD results. Wavelet transform is a kind of time-scale (time-frequency) analysis method [24], which has been widely researched in signal de-noising due to its good application effect. There are some studies which improve the performance of sensor FDD by wavelet decomposition signal data [5,11,21,25]. The forms of air conditioning in these studies mostly are AHU system and chiller. But the sensor FDD performance of VRF system using the enhanced PCA model by wavelet transform is not good. Because measurement accuracy of sensor in the VRF system is low (accuracy of temperature sensor is 1 ◦ C and accuracy of pressure sensor is ±0.5%) and measurement data shows zigzag fluctuations, which can be seen in Fig. 2. Therefore, the new method need to be used to improve sensor FDD performance of the VRF system. In order to improve the FDD performance of the VRF system using PCA method, this paper proposed a new PCA model which is enhanced by using the Satizky-Golay (SG) algorithm. The SG algorithm is a method of data smoothing based on local least-squares polynomial approximation, which has been applied in the signal denoising [26,27] and data smoothing [28], etc. This paper presented the SG method to smooth VRF system data. Then PCA model was trained and the faults were detected and diagnosed using smoothed data. The enhanced PCA model (SG-PCA) was evaluated using the VRF system data in real situation. In addition, in order to choose the parameters of SG method, this paper has proposed an optimization index (OI) to select the moving window width and polynomial order. The results show that the FDD performance of the SG-PCA model is improved obviously. This paper is organized into five sections. Section 2 outlines the principle of Satizky-Golay (SG) method; Section 3 is dedicated to obtain the SG-PCA based VRF system sensor FDD strategy, whereas
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the performance of the sensor FDD proposed is validated using the VRF system in Section 4. Conclusions are presented in Section 5.
Then, Eq. (5) can be obtained by extracting the coefficients. c0
m
1 + c1
j=−m m
2. Principle of S-G method
c0
Satizky-Golay filter (SG) method whose basic principle was based on the Least Squares Fitting was proposed by Satizky and Golay in 1964. Fig. 1 is the schematic diagram of SG method. Assuming that a list of data needs to smooth. And a random sample point is selected as an example. P order polynomial is fitted using the 2m + 1 points around the selected point (m points at each side). Supposing polynomial as:
Yi = c0 + c1 i + c2 i2 + · · · + cp ip
(1)
169
j + c2
j=−m m
j + c1
j=−m m
c0
m
j=−m
j2 + · · · + cp
j=−m m
j2 + c2
j=−m m
j2 + c1
m
j3 + c2
j=−m
jp =
j=−m m
j3 + · · · + cp
j=−m m
m
m
jp+1 =
j=−m m
j4 + · · · + cp
j=−m
yi
j=−m m
jyi
j=−m m
jp+2 =
j=−m
(5)
j2 yi
j=−m
· · ·· · · c0
m
jp + c1
j=−m
In the
m
jp+1 + c2
j=−m m
m
jp+2 + · · · + cp
j=−m
m
jp+p =
j=−m
m
jp yi
j=−m
jr , when r is an odd number, this item is zero. Thus,
j=−m
After fitted, the cumulative error can be calculated as:
S=
m
Yj − yj
2
(2)
j=−m
In order to obtain a minimum cumulative error, partial differential of the coefficient in Eq. (2) are equal to zero as the following:
∂S =2 (c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0 ∂c0 m
j=−m m
∂S =2 j(c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0 ∂c1 j=−m m
∂S =2 j2 (c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0 ∂c1
Eq. (5) can be further simplified. Coefficient sequence (c0 , c1 , c2 , · · · cp ) can be obtained by solving the simplified system of liner equations. Then, the fitting values can be calculated with (c0 , c1 , c2 , · · · cp ). Smoothed data is obtained by calculating fitting values of each sample point. Because data smoothing result is not very well at both ends, data within the 1/4 window width at both ends are removed. Fig. 2 is the comparison of data processing effects between the wavelet analysis and the SG method. The data are obtained from VRF system and the variable is condenser outlet temperature. Wavelet de-noising uses db3 wavelet function three-layer decomposition to remove the noise in the data. The data are smoothed using SG method when the window width is 577 and the polynomial order is 5. Due to the low sensor measurement accuracy (accuracy of temperature sensor is 1 ◦ C and accuracy of pressure sensor is ±0.5%), the wavelet de-noising result is not very suitable for VRF system data. When SG method is used for data smoothing, the processed data are relatively smoothing compared to the original data and the useful information of data is retained.
(3) 3. SG-PCA based VRF system sensor FDD strategy
j=−m
· · ·· · ·
3.1. Outline of PCA method in fault detection and diagnosis applications
∂S =2 jp (c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0 ∂c1 m
j=−m
The coefficients of the fitted polynomial can be obtained by solving Eq. (3). In order to solve such difficult and complicated equations, it will be better to simplify them before solving. After simplification, Eq. (3) can be rewritten as follows:
m
(c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0
j=−m m
j(c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0
j=−m m
j2 (c0
+ c1 j + c2
j2
+ · · · + cp
jp
− yi ) = 0
j=−m
· · ·· · · m
jp (c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0
j=−m
(4)
PCA is one of the basic projection model in the multivariate statistical analysis, which has been widely applied in the data dimensionality reduction and process monitoring, etc. x ∈ Rm represents a measurement sample containing m sensors. Dataset has n sampling points. Measurement data matrix can be constructed asX 0 = [x1 , x2 , · · ·, xn ]T ∈ Rn×m . Each column of X◦ represents a measured variable and each row represents a measured sample point. Because the measuring principle and the order of magnitude of the sample data are various differences, so the data matrixX◦ should be normalized to a matrix X with zero mean and unit variance. X, X ∈ Rn × m is called the standardized matrix. Then, the sample covariance matrix Cov of the data set is calculated as Eq. (6). Cov ≈
XT X (m − 1)
(6)
Using principal component analysis, data space can be decomposed into two orthogonal subspaces: one is principal component (PC) space and the other is residual subspace (RS). Usually, Cov has m eigenvectors. Projection matrix of PC space is matrix P composed of eigenvectors which are associated with the first k largest eigenvalues. The number k is determined by cumulative contribution.
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Fig. 1. Schematic diagram of Savitzky-Golay smoothing method.
Fig. 2. Comparison of data processing effects between the wavelet and the S-G method.
When the cumulative contribution of variance of the former k PCs is higher than 90%, the number of principal components is k. P is a matrix with m row and k columns, p ∈ Rm×k , P = [p1 · · ·pk ]. Principal component vector xˆ is standardized sampling data x in the PCs projection, can be obtained by Eq. (7). xˆ = xPP T
(7)
The squared prediction error (SPE), namely the Q-statistic is used as an index of faulty condition in FDD applications. Q-statistic is the squared sum of the residual, which can be calculated using Eq. (9).
Q − statistic = SPE = e2 ≤ Q˛
(9)
Projection matrix of RS space is matrix P˜ composed of the eigenvectors which are associated with the last (m-k) eigenvalues. P˜ is a matrix with m rows and (m-k) columns, p˜ ∈ Rm×(m−k) , P˜ = [pk+1 · · ·pm ]. Residual vector e is standardized sampling data x in the RS projection, can be obtained by Eq. (8). T
e = x − xˆ = x(P˜ P˜ ) = x(I − PP T )
(8)
Where Q␣ is the statistical threshold for the Q-statistic [23]. When no fault occurs, the Q-statistic or SPE is less than the Q␣ . On the contrary, when a sensor fault occurs, the Q-statistic or SPE is larger than the Q␣ . When a fault is detected using the Q-statistic, the faulty sensor can be diagnosed using Q-contribution plot. The contribution of the individual variables to the Q-statistic can be calculated by Eq.
Y. Guo et al. / Energy and Buildings 142 (2017) 167–178
(10). The variable with the largest contribution to the Q-statistic is most probably faulty. i Qcon =
ei 2 Q − statistic
(10)
The self-detection efficiency in the model training process is defined as the ration of number of the Q-statistic within the threshold to the number of all training samples as following: self −det ection =
N normal N
(11)
Fault detection efficiency is defined as the ration of number of the Q-statistic exceeds the threshold to the number of all test samples as following: det ection =
Nfault N
(12)
Fault diagnosis efficiency is defined as the ration of number of the correct diagnosis samples to the number of all test samples as following: diagnosis =
Ncorrect N
(13)
3.2. PCA model of VRF system With respect to energy balance, sixteen variables selected to describe the operation process of VRF system are used to establish the PCA model for the VRF system. These measurements are outdoor environment temperature (TOD ), condenser outlet temperature (Tcond,out ), liquid refrigerant temperature at the subcooler outlet pipe (Tsubc,out,L ), vapor refrigerant temperature at the subcooler outlet pipe (Tsubc,out,V ), vapor–liquid separator inlet pipe temperature (TSPR,in ), vapor–liquid separator outlet pipe temperature (TSPR,out ), the first compressor module temperature (Tcom1 ), the second compressor module temperature (Tcom2 ),The first fan module temperature (Tfan1 ), The second fan module temperature (Tfan2 ), condensing saturation pressure (Pcond ), evaporating saturation pressure (Pevap ), the first compressor operating frequency (fcom1 ), the second compressor operating frequency (fcom2 ), the first compressor electric current (Icom1 ), the second compressor electric current (Icom2 ). Thus, matrix X represents the original matrix with n samples of these variables as follows:
⎡
171
hevap =hevap,out −hevap,in = f (Pevap , TSPR.in ) − f (Pcond , Tsub,out,l ) = f (Pevap , TSPR.in , Pcond , Tsub,out,l ) √ √ Wcom = Wcom1 + Wcom2 = 3UIcom1 cosϕ1 + 3UIcom2 cosϕ2 Wcom = Wcom1 + Wcom2 =
+
n2 2 Pevap 60 (2 − 1)
n1 1 Pevap 60 (1 −1)
Pcond Pevap
(2 −1)/2
Pcond Pevap
(16) (17)
(1 −1)/1
−1
−1
(18)
Qcond ≈ Q0evap + Wcom = f (Tcom1 , Tcom2 , Tsub,out,l , Tsub,out,v , Pcond )(19) 3.3. Structure of SG-PCA based VRF system sensor FDD strategy Based on SG algorithm enhanced PCA model, sensors FDD of the VRF system mainly includes three main steps: model training, fault detection and fault diagnosis. Fig. 3 is the flowchart of the SGPCA method in sensor fault detection and diagnosis. The first part is training of the SG-PCA model, which mainly involves six steps: data preprocessing, determining Nwin and Npoly , SG smoothing, decomposition of covariance matrix, obtaining principal component and calculating the Q␣ of the Q-statistic. It is rewarding to note that the frequency of two compressors (fcom1 and fcom2 ) is not smooth in the process of data smoothing. Because the compressor frequency is the control signal of VRF system, whose characteristic is changing with load of VRF system. The second part is fault detection, which also involves SG smoothing process for the new sample data. The parameters of SG method for fault detection are the same as that in model training. Then, Q-statistic of the smoothed new sample data are calculated and compared with the threshold. The threshold is determined in the modeling process. When the Q-statistic value is higher than threshold. It means a fault occurs. The last part is about fault diagnosis, which uses Q-contribution plot to diagnose sensor fault. Generally speaking, the sensor with the largest contribution to the Q-statistic is most probably faulty. Finally, the FDD result is reported. Two parameters polynomial order (Npoly ) and width of the moving window (Nwin ), are very important for SG smoothing. They
1 1 1 T1 1 1 1 1 1 1 T1 T1 T1 T1 T1 T1 TOD cond,out sub,out,l sub,out,v SPR,in SPR,out Tcom1 Tcom2 fan1 fan2 Pcond Pevap fcom1 fcom2 Icom1 Icom2
⎤
⎢ T2 T2 ⎥ 2 2 2 2 2 2 2 2 2 2 2 2 T2 T2 Tsub,out, ⎢ OD cond,out Tsub,out,l v TSPR,in TSPR,out Tcom1 Tcom2 fan1 fan2 Pcond Pevap fcom1 fcom2 Icom1 Icom2 ⎥ ⎥ ⎣ ··· ··· ··· ··· ··· ··· ··· ··· ··· ⎦ ··· ··· ··· ··· ··· ··· ···
X=⎢
(14)
n n n Tn n n n n n n Tn Tn Tn Tn Tn Tn TOD cond,out sub,out,l sub,out,v SPR,in SPR,out Tcom1 Tcom2 fan1 fan2 Pcond Pevap fcom1 fcom2 Icom1 Icom2
Eqs. (15) – (19) explain the strong correlations among the variables in matrix X. The COP of the VRF system can be calculated as Eq. (15) under stable condition. According to its definition, the cooling capacity (Q0 ) can be thought of as the cooling load of evaporator (Q0ev ). Power consumption is mainly composed of three parts: the compressor power, the fan power and power of other auxiliary equipment. Compressor power is the most important part of system power, which can be obtained from the compressor current as Eq. (17). In addition, compressor power can be calculated by Eq. (18). Due to energy balance of the VRF system under steady state, the condenser load should be equal to the sum of the evaporator load and compressor power as shown in Eq. (19). As a consequence, all the variables in matrix X are strongly correlated with each other from thermodynamic analysis and using matrix X for PCA model is feasible. COP =
Mref hevap Q0evap Q0 = = W Wcom + Wfan + Wother W
(15)
determine the smoothing degree of data. If the smoothing degree is high, the data will lose a lot of useful information. On the contrary, if the smoothing degree is too low, the smoothing effect of the data is not satisfying. Therefore, how to select these two parameters become very important. There is a close relationship between the smoothing degree and the signal to noise ratio (SNR) and the standard deviation (SD) of smoothed data. In addition, the smoothing degree of training data has a greater impact on the self-detection efficiency (self ) which is important for model training. The SNR, SD and self of the smoothed data are standardized toSNRsta , SDsta and self,sta . An optimal index (OI) of the SG algorithm are established by these three parameters in this study as follow OI = SNRsta − SDsta + self,sta
(20)
When the OI is large, the selected Npoly and Nwin are reasonable. Fig. 4 shows the optimization results of the parameter selection of Npoly and Nwin using the training data. When the OI is large, Npoly
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Fig. 3. Flowchart of the SG-PCA method in sensor fault detection and diagnosis.
and Nwin located in this area are selected for data smoothing operation. Two parameters sets are selected for data smoothing and verifying the reliability of the OI. Npoly and Nwin of two models are listed respectively as follows SG-PCA model A:Polynomial order is 5, moving window width is 577. SG-PCA model B:Polynomial order is 7, moving window width is 677.
Table 1 Specification and characteristics of the ODU and IDUs in the VRF system. Outdoor unit
Indoor unit
Rated cooling capacity(kW)
45.0
45.7 (12.5;12.5;11.2;5;4.5)
Refrigerant
Type
R410A
Number
Hermetically sealed scroll type 2 Frequency conversion
Compressor
4. Strategy validation using the VRF system 4.1. Description of VRF system The VRF system is an important type of the air-conditioning system in many countries because of its high efficiency, flexible form and small space requirement. A typical VRF system is selected for the study in Wuhan, China. Its schematic diagram is illustrated as Fig. 5. The system consists of two parts which are one outdoor unit (ODU) and five indoor units (IDUs). In ODU, there are two inverter
scroll compressors to drive system operation. In IDUs, there are 5 indoor DX coils. And these are the main differences between the VRF system and the conventional air conditioning system. The specification and characteristics of the ODU and IDUs are summarized in Table 1. In order to guarantee the VRF system work well and control intelligently, VRF system built a series of sensors as shown in Fig. 5. Types of measurement parameters include: temperature, pressure,
Y. Guo et al. / Energy and Buildings 142 (2017) 167–178
173
Fig. 4. Parameter selection of window width and polynomial order.
Fig. 5. Schematic diagram of the VRF system.
current and frequency. Three days normal operating data were collected in real situation. The selected VRF system had been normally running for a long time without sensor faults and other faults. The data of the former 2 days were chosen as the original data set to train the PCA model. Data from the last day were introduced with biases to test the fault detectability and diagnosis ability of the proposed PCA models.
4.2. Training of models Fig. 6 shows the Q-statistic plot of the conventional PCA model and the SG-PCA model using training data. It can be seen that when compared with the traditional PCA model, the threshold of the Qstatistic in the SG-PCA model has decreased. But the number sample points whose Q-statistic exceeds the threshold has reduced. Fig. 6 presents that the aggregation state is improved of the data after
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Fig. 6. Q-statistic plots of the conventional PCA model and the SG-PCA model A using training data.
smooth and the small bias fault of sensor is conductive to recognize when using the SG-PCA model. When using the original data X to train conventional PCA model, the cumulative contribution rate of the former six principal component vectors reaches 92.21%. When the confidence level is 95%, the threshold of the Q-statistic is 2.712. The Q-statistics of 6.45% samples are above the threshold value, in other words, the selfdetection efficiency is 93.55% when the training data are used as a test set. The matrix X can be obtained from the matrix X smoothed by SG method whose polynomial order is 5 and width of moving window is 577. Using the matrixX to train model, the cumulative contribution rate of the former six principal component vectors reaches 93.54%. These six principal component vectors are retained for the SG-PCA model. When the confidence level is 95%, the threshold of the Q-statistic is 2.554, which is lower than that in conventional PCA model. The Q-statistics of 4.11% samples are above the threshold value.
4.3. Validation results and analysis The FDD performance of the traditional PCA model and SGPCA model are evaluated using the practical running data of the VRF system. Therefore, different fault levels are introduced to the outdoor environment temperature (TOD ), condenser outlet temperature (Tcond,out ), liquid refrigerant temperature at the subcooler outlet pipe (Tsubc,out,L ), vapor refrigerant temperature at the subcooler outlet pipe (Tsubc,out,V ), vapor–liquid separator inlet pipe temperature (TSPR,in ), vapor–liquid separator outlet pipe temperature (TSPR,out ), the first compressor module temperature (Tcom1 ), the second compressor module temperature (Tcom2 ),The first fan module temperature (Tfan1 ), The second fan module temperature (Tfan2 ), condensing saturation pressure (Pcond ) and evaporating saturation pressure (Pevap ). Only one bias fault is introduced each time. In this study, fault detection efficiency is used to evaluate the fault detection capability of the PCA model. When the fault efficiency is lower than 20%, it can be considered the fault is not detected successfully.
Fault detection efficiency of VRF system sensor is improved significantly when the data are smoothed using SG algorithm, which can be seen clearly from Fig. 7. Some sample points of the training data exceed threshold value without smoothing process. When the introduced fault level is 8 ◦ C to the condenser outlet temperature, the Q-statistics of some sample points are less than threshold and the detection efficiency is 71.34%. On the other hand, exceeded sample points of training data decrease after smooth process using SG-PCA model A. When introduced the same bias fault level to condenser outlet temperature, almost all the sample points are above the threshold and the detection efficiency is 98.78%. When a sensor fault is detected, it should be diagnosed for further maintenance. The Q-contribution plot usually can be used to isolate the faulty sensor. The sensor with the largest contribution to the Q-statistic is most probably fault. Q-contribution plots of condenser outlet temperature using PCA model and SG-PCA model A are separately illustrated in Figs. 8 and 9. Different colors represent sensors at different locations in the VRF system. When there is normal condition in the former two days, the Q-contribution of different sensors are not obvious different. But when there is faulty condition in the last day, the Q-contribution of condenser outlet temperature sensor is much higher that of other sensors. Therefore, the faulty sensor should be condenser outlet temperature sensor. The diagnosis efficiency of traditional PCA model and SG-PCA model A are 82.89% and 89.73% separately. It is clear that the two models basically can diagnose the fault source. When using the SG-PCA model A, the diagnosis performance improves significantly. Table 2 lists the FDD performances of temperature sensors faults using the conventional PCA model and the two SG-PCA models (SGPCA model A and SG-PCA model B). Temperature sensors include the outdoor environment temperature (TOD ), condenser outlet temperature (Tcond,out ), liquid refrigerant temperature at the subcooler outlet pipe (Tsubc,out,L ), vapor refrigerant temperature at the subcooler outlet pipe (Tsubc,out,V ), vapor–liquid separator inlet pipe temperature (TSPR,in ), vapor–liquid separator outlet pipe temperature (TSPR,out ), the first compressor module temperature (Tcom1 ), the second compressor module temperature (Tcom2 ), the first fan module temperature (Tfan1 ) and the second fan module tempera-
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175
Fig. 7. The condenser outlet temperature sensor Q-statistic plots of the PCA model and the SG-PCA model A at fault level +8 ◦ C.
Fig. 8. The condenser outlet temperature sensor fault diagnosis results using PCA method at fault levels +8 ◦ C.
ture (Tfan2 ). When the 10 ◦ C bias fault level is introduced to Tcom1 , the fault detection efficiency of the conventional PCA model is 69.95%. While, the fault detection efficiency of the SG-PCA model A and SG-PCA model B are 89.31% and 87.75% respectively. The fault diagnosis efficiency of the conventional PCA model is 87.49%. While the fault diagnosis efficiency of the SG-PCA model A and SG-PCA model B are 85.56% and 85.88% respectively. The fault detection efficiency of Tcom1 is improved, whereas the diagnosis efficiency has not been improved. Table 2 shows that fault detection efficiency of each sensor almost has been improved when data are processed by SG method. The fault diagnosis efficiency has been improved except Tcom1 . Table 3 lists FDD performances of pressure sensors faults using the conventional PCA model and the two SG-PCA models (SG-PCA model A and SG-PCA model B). Pressure sensors include condens-
ing saturation pressure (Pcond ) and evaporating saturation pressure (Pevap ). When the 10% bias fault level is introduced toPcond , the fault detection efficiency of the conventional PCA model is 38.43%. While, the fault detection efficiency of the SG-PCA model A and SG-PCA model B are 84.77% and 83.97% respectively. Therefore, detection efficiency increases by 46.34% and 45.54% respectively using SG-PCA model A and SG-PCA model B. In addition, fault diagnosis efficiencies are also increased by 31.62% and 29.93% respectively. As a consequence, the detection efficiency and diagnosis efficiency have been greatly improved. When the sensor faults of the evaporation pressure occur, the detection efficiencies have been improved after SG smoothing process. The fault diagnosis results of evaporator pressure sensor faults are unreasonable using both the PCA and SG-PCA models. Tables 2 and 3 present that the FDD
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Table 2 Comparison of FDD performance on temperature sensor faults between the conventional PCA model and the SG-PCA model. Bias
PCA model
SG-PCA model A
SG-PCA model B
Detection ratio (%)
Diagnosis ration (%)
Detection ratio (%)
Diagnosis ration (%)
Detection ratio (%)
Diagnosis ration (%)
TOD
10 8 6 4 2
99.92 93.17 65.35 39.19 23.49
97.10 92.97 81.91 54.58 19.66
100 100 100 78.19 38.9
100 98.48 96 86.23 41.29
100 100 100 78.74 37.81
100 98.18 95.23 86.03 38.95
Tcond,out
10 8 6 4 2
89.06 71.34 44.64 23.77 15.02
92.80 82.89 66.13 52.17 36.06
100 98.78 82.56 56.54 30.6
94.79 89.73 83.15 62.51 34.4
100 98.70 81.69 57.53 29.56
94.38 89.35 82.21 61.97 33.09
Tsubc,out,L
12 10 8 6 4
48.92 39.19 31.19 25.45 22.14
55.09 46.55 35.16 23.16 14.57
89.81 72.74 58.1 41.44 32.25
77.65 67.40 51.13 32.34 16.16
88.95 72.71 57.09 42.18 30.98
78.39 65.72 51.10 31.82 14.34
Tsubc,out,V
14 12 10 8 6 4
58.18 50.92 42.97 35.08 28.90 24.8
40.62 34.61 28.64 22.08 15.64 9.36
100 97.22 87.75 72.37 55.63 39.75
78.74 72.42 61.69 52.24 39.49 24.11
99.6 95.72 84.94 68.64 50.99 38.84
72.73 67.83 61.31 51.21 39.77 26.48
TSPR,in
10 8 6 4 2
69.28 50.31 39.25 30.31 23
72.18 59.16 41.21 25.12 11.94
100 100 99.67 75.07 40.05
96.66 91.44 79.6 61.12 27.80
100 100 95.15 72.11 37.18
93.79 82.78 69.48 52.72 25.19
TSPR,out
10 8 6 4
42.56 30.91 23.55 19.62
35.14 24.45 16.56 8.61
90.07 73.26 45.79 31.52
60.12 51.37 38.16 16.20
88.95 69.10 42.75 30.17
65.11 55.97 40.84 17.79
Tcom1
12 10 8 6 4
89.62 69.95 51.45 37.33 25.78
93.40 87.49 75.65 53.13 22.42
100 89.31 69.27 45.44 31.99
89.97 85.56 75.78 52.85 25.65
100 87.75 67 45.02 31.09
89.42 85.88 76.09 52.11 25.10
Tfan1
10 8 6 4 2
100 100 99.35 69.64 32.73
100 99.9 98.22 87.76 46.48
100 100 100 86.86 44.01
100 100 100 91.99 50.74
100 100 100 85.73 45.56
100 100 99.58 91.08 49.89
Tcom2
10 8 6 4
81.73 56.15 37.49 26.31
85.67 73.86 57.34 34.51
97.28 76.98 51.91 35.10
93.28 84.58 57.19 29.28
95.5 74.59 49.82 34.76
91.77 83.62 53.56 28.9
Tfan2
10 8 6 4 2
100 99.57 98.49 63.45 30.36
100 99.92 97.18 85.40 38.47
100 100 100 85.12 42.59
100 100 99.85 90.42 48.61
100 100 100 82.78 43.59
100 100 98.75 88.84 48.44
Table 3 Comparison of FDD performance on pressure sensor faults between the conventional PCA model and the SG-PCA model. Bias
PCA model
SG-PCA model A
SG-PCA model B
Detection ratio(%)
Diagnosis ration(%)
Detection ratio(%)
Diagnosis ration(%)
Detection ratio(%)
Diagnosis ration(%)
Pcon
20% 15% 10% 8% 6% 4%
81.75 57.30 38.43 32.03 26.88 23.10
94.66 83.09 63.02 51.04 38.74 24.84
100 97.22 84.77 67.31 50.61 39.47
100 100 94.64 86.21 70.81 42.64
100 96.18 83.97 65.44 49.85 39.17
100 100 92.95 82.94 68.56 41.39
Peva
20% 15% 10%
25.7 23.45 21.87
0 0 0
51.17 44.35 36.36
0 0 0
51.98 44.66 36.28
0 0 0
Y. Guo et al. / Energy and Buildings 142 (2017) 167–178
177
Fig. 9. The condenser outlet temperature sensor fault diagnosis results using SG-PCA model A at fault levels +8 ◦ C.
Table 4 The parameters of different SG-PCA models. SG-PCA model
Polynomial order
Width of moving window
OI value
Model A Model B Model C Model D Model E Model F
5 7 5 5 8 2
577 677 877 277 577 577
2.43 2.89 2.18 −1.47 −0.24 0.67
Fig. 11. Q-contribution maximum proportion of each variable.
Fig. 10. The FDD performance of the SG-PCA model with different parameters.
performance of SG-PCA model is better than the conventional PCA model. Tables 2 and 3 show the SG-PCA-A model and SG-PCA-B model have good FDD performances. The parameters of the two models are chosen by the optimal index determined by Eq. (20). In order to further verify the reliability of optimization index, another four SG-PCA models with different parameters are established whose parameters can be seen in Table 4 and FDD performances are shown in Fig. 10. Table 4 lists the parameters of different models and the OI values. Fig. 10 is the FDD performance of the SG-PCA model with the different parameters when the bias fault level of Pcond is 10%.
It can be seen from Fig. 10 that the FDD performances are good when the OI value is large. Therefore, The OI value which established by the standard deviation, SNR and self-detection efficiency of the smoothed training data is proved reliable. It can be concluded from Tables 2 and 3 that the fault diagnosis efficiencies of most sensors exceed 50%. The fault can be isolated correctly when the sensor fault diagnosis efficiency is above 50%. But when the diagnosis efficiency is lower than 50%, two kinds of diagnosis results may occur. If the fault diagnosis correct ratio is much higher than misdiagnosis ratio of other variables, the fault is isolated correctly. For example, when the fault level of Tcond,out is 2 ◦ C, the fault diagnosis efficiency of the conventional PCA model is 36.06%. In this case, the fault misdiagnosis ratios of other variables are calculated. Fig. 11 is the diagnosis result of each variable. Although the fault diagnosis efficiency of Tcond,out is no more than 50%, the fault diagnosis efficiency is much higher than misdiagnosis ratio of other variables. On the other hand, it fails to diagnose the
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fault when there is no obvious difference among the fault diagnosis efficiency of each sensor. 5. Conclusion Sensor accuracy and reliability have played important roles for the VRF system efficiency, healthy operation and energy saving. Generally, the PCA method can be used for sensor fault detection and diagnosis. However, due to large fluctuations of operating conditions and sensor measurement accuracy limits, the conventional PCA model for VRF system sensor FDD is not suitable. As a consequence, this paper proposes a new PCA model enhanced by the SG method for VRF system sensor FDD. The FDD performance of the SG-PCA model is evaluated by the VRF system data in real situations. The results have demonstrated that the FDD performance of SG-PCA model is more effective and reliable than the conventional PCA model. Besides, under the same fault level, SG-PCA model can increase the sensor fault detection efficiency and fault diagnosis efficiency of the VRF system. In addition, the OI for selecting the parameters of SG method is proposed, whose reliability is evaluated by six SG-PCA models of the VRF system. The results show that the OI value which is established by the standard deviation, SNR and self-detection efficiency of the smoothed training data is reliable. Moreover, this paper also has discussed the fault identification method when the fault diagnosis efficiency is below 50%. The SG-PCA model is a promising method for fault detection and diagnosis in actual VRF system. In the future works, the SG-PCA model applied to the online sensor fault strategy will be carried out based on the present work. Acknowledgments The authors gratefully acknowledge the support of National Natural Science Foundation of China (Grant 51576074 and 51328602), and Beijing Key Lab. of Heating, Gas Supply, ventilating and Air Conditioning Engineering (Project NR2016K02). References [1] Building energy data book 2011, U.S. Department of Energy, 2011. [2] S. Wang, F. Xiao, AHU sensor fault diagnosis using principal component analysis method, Energy Build. 36 (2004) 147–160. [3] S. Wang, J. Cui, Sensor-fault detection, diagnosis and estimation for centrifugal chiller systems using principal-component analysis method, Appl. Energy 82 (2005) 197–213. [4] Z. Du, B. Fan, J. Chi, X. Jin, Sensor fault detection and its efficiency analysis in air handling unit using the combined neural networks, Energy Build. 72 (2014) 157–166. [5] Y. Zhu, X. Jin, Z. Du, Fault diagnosis for sensors in air handling unit based on neural network pre-processed by wavelet and fractal, Energy Build. 44 (2012) 7–16. [6] Y. Hu, H. Chen, G. Li, H. Li, R. Xu, J. Li, A statistical training data cleaning strategy for the PCA-based chiller sensor fault detection, diagnosis and data reconstruction method, Energy Build. 112 (2016) 270–278.
[7] G. Li, Y. Hu, H. Chen, L. Shen, H. Li, M. Hu, J. Liu, K. Sun, An improved fault detection method for incipient centrifugal chiller faults using the PCA-R-SVDD algorithm, Energy Build. 116 (2016) 104–113. [8] L. Kwon, Y. Hwang, R. Radermacher, B. Kim, Field performance measurements of a VRF system with sub-cooler in educational offices for the cooling season, Energy Build. 49 (2012) 300–305. [9] L. Kwon, H. Lee, Y. Hwang, R. Radermacher, B. Kim, Experimental investigation of multifunctional VRF system in heating and shoulder seasons, Appl. Therm. Eng. 66 (2014) 355–364. [10] Y. Shin, S.W. Karng, S.Y. Kim, Indoor unit fault detector for a multi-split VRF system in heating mode, Int. J. Refrig. 40 (2014) 152–160. [11] B. Fan, Z. Du, X. Jin, X. Yang, Y. Guo, A hybrid FDD strategy for local system of AHU based on artificial neural network and wavelet analysis, Build. Environ. 45 (2010) 2698–2708. [12] Z. Du, B. Fan, X. Jin, J. Chi, Fault detection and diagnosis for buildings and HVAC systems using combined neural networks and subtractive clustering analysis, Build. Environ. 73 (2014) 1–11. [13] Z. Du, X. Jin, Multiple faults diagnosis for sensors in air handling unit using Fisher discriminant analysis, Energy Convers. Manage. 49 (2008) 3654–3665. [14] G. Li, Y. Hu, H. Chen, H. Li, M. Hu, Y. Guo, S. Shi, W. Hu, A sensor fault detection and diagnosis strategy for screw chiller system using support vector data description-based D-statistic and DV-contribution plots, Energy Build. 133 (2016) 230–245. [15] Y. Zhao, J. Wen, S. Wang, Diagnostic Bayesian networks for diagnosing air handling units faults—part II: faults in coils and sensors, Appl. Therm. Eng. 90 (2015) 145–157. [16] Y. Zhao, J. Wen, F. Xiao, X. Yang, S. Wang, Diagnostic Bayesian networks for diagnosing air handling units faults—part I: Faults in dampers, fans, filters and sensors, Applied Thermal Engineering 111 (2017) 1272–1286. [17] S. Wang, F. Xiao, Detection and diagnosis of AHU sensor faults using principal component analysis method, Energy Convers. Manage. 45 (2004) 2667–2686. [18] S. Wang, Y. Chen, Sensor validation and reconstruction for building central chilling systems based on principal component analysis, Energy Convers. Manage. 45 (2004) 673–695. [19] S. Wang, J. Qin, Sensor fault detection and validation of VAV terminals in air conditioning systems, Energy Convers. Manage. 46 (2005) 2482–2500. [20] F. Xiao, S. Wang, X. Xu, G. Ge, An isolation enhanced PCA method with expert-based multivariate decoupling for sensor FDD in air-conditioning systems, Appl. Therm. Eng. 29 (2009) 712–722. [21] X. Xu, F. Xiao, S. Wang, Enhanced chiller sensor fault detection, diagnosis and estimation using wavelet analysis and principal component analysis methods, Appl. Therm. Eng. 28 (2008) 226–237. [22] Z. Du, X. Jin, Detection and diagnosis for sensor fault in HVAC systems, Energy Convers. Manage. 48 (2007) 693–702. [23] Y. Hu, H. Chen, J. Xie, X. Yang, C. Zhou, Chiller sensor fault detection using a self-adaptive principal component analysis method, Energy Build. 54 (2012) 252–258. [24] G. Strang, Wavelet transforms versus Fourier transforms, Bull. Am. Math. Soc. 28 (1993) 288–305. [25] S. Li, J. Wen, A model-based fault detection and diagnostic methodology based on PCA method and wavelet transform, Energy Build. 68 (Part A) (2014) 63–71. [26] O. Abdel-Aziz, M.F. Abdel-Ghany, R. Nagi, L. Abdel-Fattah, Application of Savitzky-Golay differentiation filters and Fourier functions to simultaneous determination of cefepime and the co-administered drug, levofloxacin, in spiked human plasma, Spectrochim. Acta Part A: Mol. Biomol. 139 (2015) 449–455. [27] Y. Zhang, C. Bingham, Z. Yang, B.W. Ling, M. Gallimore, Machine fault detection by signal denoising—with application to industrial gas turbines, Measurement 58 (2014) 230–240. [28] A.A. Candan, H. Inan, A unified framework for derivation and implementation of Savitzky-Golay filters, Signal Process. 104 (2014) 203–211.
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Full Length Article
An enhanced PCA method with Savitzky-Golay method for VRF system sensor fault detection and diagnosis Yabin Guo a , Guannan Li a , Huanxin Chen a,∗ , Yunpeng Hu b , Haorong Li c , Lu Xing a , Wenju Hu d a
Department of Refrigeration & Cryogenics, Huazhong University of Science and Technology, Wuhan, China Department of Building Environment and Energy Application Engineering, Wuhan Business University, 816 Dongfeng Avenue, Wuhan, Hubei 430056, China c Durham School of Architectural Engineering and Construction College of Engineering, University of Nebraska-Lincoln, Omaha, NE, USA d Beijing Key Lab. of Heating, Gas Supply, Ventilating and Air Conditioning Engineering, Beijing University of Civil Engineering and Architecture, Beijing, China b
a r t i c l e
i n f o
Article history: Received 23 April 2016 Received in revised form 23 December 2016 Accepted 9 March 2017 Available online 10 March 2017 Keywords: Principal component analysis Satizky-Golay method Variable refrigerant flow Sensor fault detection and diagnosis Optimal index
a b s t r a c t Sensor faults of air conditioning systems are harmful to optimal control strategies and system performance resulting in poor control of the indoor environment and waste of energy. In order to improve the fault detection and diagnosis (FDD) performance, this paper presents an enhanced sensor fault detection and diagnosis method based on the Satizky-Golay (SG) method and principal component analysis (PCA) method for the VRF system, namely SG-PCA method. Due to the volatility of the original data set of VRF system, the original data are smoothed using SG method at first. Then, the smoothed data are used for PCA model training and fault detection and diagnosis. In order to determine parameters of the SG method, an optimization index is proposed, which is calculated by the signal to noise ratio (SNR), the standard deviation (SD) and the self-detection efficiency. This SG-PCA method for VRF system sensor FDD is validated using field operation data of the VRF system. Various sensor faults at different fault levels are introduced. The results have showed that the SG-PCA method can significantly improve the fault detection and diagnosis performance compared to conventional PCA method. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Heating ventilating and air-conditioning (HVAC) systems accounted for closed to 41 percent of site energy consumption in U.S. building primary energy consumption [1]. Therefore, energy saving of the HVAC system is very important. There are two key issues which are suitable control strategies and reliable measurements to ensure good performance of HVAC system. When the bias of return air flow rate sensor was 20%, the energy consumption of AHU system increased closed to 14% [2]. Consequently, sensor fault detection and diagnosis (FDD) of HVAC system is of great significance for energy saving and the normal operation of system. There are many studies of sensor FDD in HVAC systems. Wang and Cui [3] developed an online strategy to detect, diagnose and validate sensor faults in the water-cooled centrifugal chillers. Du [4] presented the dual neural networks combined strategy to detect the faults
∗ Corresponding author. E-mail address: [email protected] (H. Chen). http://dx.doi.org/10.1016/j.enbuild.2017.03.026 0378-7788/© 2017 Elsevier B.V. All rights reserved.
of sensors of the air handing unit (AHU). Zhu [5] presented a new fault diagnosis method based on neural network pre-processed by wavelet and fractal for sensors fault in an AHU system. Hu [6] presented a statistical training data cleaning strategy for PCA based chiller sensor fault detection, diagnosis and data reconstruction. Li [7] developed a SVDD model in the residual subspace (Rs) using the PCA modeling residual data to improve the fault detection performance. However, there are rather rare studies regarding the sensor FDD for the VRF system in open literatures. The variable refrigerant flow (VRF) system is an air conditioning unit which allows one outdoor unit connected to two or more indoor units by pipes. Heat exchangers of the VRF system are air-cooled at outdoor and direct evaporation at indoor. There are many significant advantages to the VRF system, such as wide range of cooling and heating temperature, design flexibility, convenient installation, reliable operation, advanced control and less space requirement [8,9]. Therefore, VRF systems have been widely used in small and medium-sized buildings [10]. It is because VRF system has some advantages such as above that make VRF system different
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Nomenclature c Cov COP e fcom1 fcom2 FDD h Icom1 Icom2 IDU n Nwin Npoly OI ODU Pcond Pevap Q␣ i Qcon
TSPR,in TSPR,out Tcom1 Tcom2 Tfan1 Tfan2 W Y
The coefficient The covariance matrix Coefficient of performance Residual vector The first compressor operating frequency, Hz The second compressor operating frequency, Hz Fault detection and diagnosis Specific enthalpy of refrigerant The first compressor electric current, A The second compressor electric current, A Indoor unit Compressor speed The moving window size The polynomial order Optimal index Outdoor unit Condensing saturation pressure, MPa Evaporating saturation pressure, MPa Threshold of the Q-statistic Contribution of the ith variable to the total sum of variations Heat exchange amount of evaporator, kW Heat exchange amount of condenser, kW Squared prediction error The cumulative error Savitzky-Golay filter The signal noise ratio Outdoor temperature, ◦ C Refrigerant temperature at the condenser outlet pipe, ◦ C Liquid refrigerant temperature at the subcooler outlet pipe, ◦ C Vapor refrigerant temperature at the subcooler outlet pipe, ◦ C Vapor–liquid separator inlet pipe temperature, ◦ C Vapor–liquid separator outlet pipe temperature, ◦ C The first compressor module temperature, ◦ C The second compressor module temperature, ◦ C The first fan module temperature, ◦ C The second fan module temperature, ◦ C Power input. kW The value after smooth process
Greeks
Mean isentropic coefficient of refrigerant Efficiency
Q0evap Qcond SPE S SG SNR TOD Tcond,out Tsubc,out,L Tsubc,out,V
Subscripts Com1 The first compressor The second compressor Com2 cond Condenser Evaporator evap Fan1 Outdoor fan 1 Fan2 Outdoor fan 2 in Inlet Outlet out subc Subcooler sta Standardization Vapor–liquid separator SPR
from other air conditioning system. Therefore, it is necessary to establish sensor fault detection and diagnosis model of VRF system. In recent years, there have been a few studies related to sensor FDD methods which are based on data driven method. The combined neural networks which include the basic neural network and auxiliary neural network are developed to detect and diagnose sensor fault of the AHU [11,12]. Du presented a data-driven method combined the PCA and Fisher discriminant analysis to detect and diagnose multiple faults including drifting bias, fixed bias, failure of sensor faults of the AHU [13]. The support vector data descript method was used to detect and diagnose sensor faults of chiller system [14], which has advantages of solving problems on describing non-liner and non-Gaussian distributed data. Zhao [15,16] proposed a diagnostic Bayesian networks-based method to diagnose 28 faults, covering senor faults of the AHU. But most of them are developed for the chiller and AHU systems. The PCA method is a kind of multivariate statistical method, which has been applied to the sensor FDD in the field of HVAC. Wang [2,3,17–19] developed an online strategy based on principal component analysis to detect, diagnose and validate sensor faults in centrifugal chillers, AHU systems and VAV air conditioning systems. Xiao [20] presented an isolation enhanced PCA method the expert-based multivariate decoupling for sensor FDD in VAV air conditioning systems. Xu [21] developed an enhanced sensor fault detection, diagnosis and estimation method combined wavelet analysis and PCA method for centrifugal chillers. Du [22] developed three PCA models based on energy balance and air side and water side to detect whether there is any abnormality in the VAV systems. Hu [23] presented a self adaptive FDD strategy based on PCA method for sensor faults of chillers. The PCA method has been applied maturely to chillers, AHU systems and VAV air conditioning systems, etc. But there is no research on sensor fault in the VRF system using PCA method. Therefore, this paper developed an PCA model to detect and diagnose sensor faults in the VRF system and optimized the FDD results. Wavelet transform is a kind of time-scale (time-frequency) analysis method [24], which has been widely researched in signal de-noising due to its good application effect. There are some studies which improve the performance of sensor FDD by wavelet decomposition signal data [5,11,21,25]. The forms of air conditioning in these studies mostly are AHU system and chiller. But the sensor FDD performance of VRF system using the enhanced PCA model by wavelet transform is not good. Because measurement accuracy of sensor in the VRF system is low (accuracy of temperature sensor is 1 ◦ C and accuracy of pressure sensor is ±0.5%) and measurement data shows zigzag fluctuations, which can be seen in Fig. 2. Therefore, the new method need to be used to improve sensor FDD performance of the VRF system. In order to improve the FDD performance of the VRF system using PCA method, this paper proposed a new PCA model which is enhanced by using the Satizky-Golay (SG) algorithm. The SG algorithm is a method of data smoothing based on local least-squares polynomial approximation, which has been applied in the signal denoising [26,27] and data smoothing [28], etc. This paper presented the SG method to smooth VRF system data. Then PCA model was trained and the faults were detected and diagnosed using smoothed data. The enhanced PCA model (SG-PCA) was evaluated using the VRF system data in real situation. In addition, in order to choose the parameters of SG method, this paper has proposed an optimization index (OI) to select the moving window width and polynomial order. The results show that the FDD performance of the SG-PCA model is improved obviously. This paper is organized into five sections. Section 2 outlines the principle of Satizky-Golay (SG) method; Section 3 is dedicated to obtain the SG-PCA based VRF system sensor FDD strategy, whereas
Y. Guo et al. / Energy and Buildings 142 (2017) 167–178
the performance of the sensor FDD proposed is validated using the VRF system in Section 4. Conclusions are presented in Section 5.
Then, Eq. (5) can be obtained by extracting the coefficients. c0
m
1 + c1
j=−m m
2. Principle of S-G method
c0
Satizky-Golay filter (SG) method whose basic principle was based on the Least Squares Fitting was proposed by Satizky and Golay in 1964. Fig. 1 is the schematic diagram of SG method. Assuming that a list of data needs to smooth. And a random sample point is selected as an example. P order polynomial is fitted using the 2m + 1 points around the selected point (m points at each side). Supposing polynomial as:
Yi = c0 + c1 i + c2 i2 + · · · + cp ip
(1)
169
j + c2
j=−m m
j + c1
j=−m m
c0
m
j=−m
j2 + · · · + cp
j=−m m
j2 + c2
j=−m m
j2 + c1
m
j3 + c2
j=−m
jp =
j=−m m
j3 + · · · + cp
j=−m m
m
m
jp+1 =
j=−m m
j4 + · · · + cp
j=−m
yi
j=−m m
jyi
j=−m m
jp+2 =
j=−m
(5)
j2 yi
j=−m
· · ·· · · c0
m
jp + c1
j=−m
In the
m
jp+1 + c2
j=−m m
m
jp+2 + · · · + cp
j=−m
m
jp+p =
j=−m
m
jp yi
j=−m
jr , when r is an odd number, this item is zero. Thus,
j=−m
After fitted, the cumulative error can be calculated as:
S=
m
Yj − yj
2
(2)
j=−m
In order to obtain a minimum cumulative error, partial differential of the coefficient in Eq. (2) are equal to zero as the following:
∂S =2 (c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0 ∂c0 m
j=−m m
∂S =2 j(c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0 ∂c1 j=−m m
∂S =2 j2 (c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0 ∂c1
Eq. (5) can be further simplified. Coefficient sequence (c0 , c1 , c2 , · · · cp ) can be obtained by solving the simplified system of liner equations. Then, the fitting values can be calculated with (c0 , c1 , c2 , · · · cp ). Smoothed data is obtained by calculating fitting values of each sample point. Because data smoothing result is not very well at both ends, data within the 1/4 window width at both ends are removed. Fig. 2 is the comparison of data processing effects between the wavelet analysis and the SG method. The data are obtained from VRF system and the variable is condenser outlet temperature. Wavelet de-noising uses db3 wavelet function three-layer decomposition to remove the noise in the data. The data are smoothed using SG method when the window width is 577 and the polynomial order is 5. Due to the low sensor measurement accuracy (accuracy of temperature sensor is 1 ◦ C and accuracy of pressure sensor is ±0.5%), the wavelet de-noising result is not very suitable for VRF system data. When SG method is used for data smoothing, the processed data are relatively smoothing compared to the original data and the useful information of data is retained.
(3) 3. SG-PCA based VRF system sensor FDD strategy
j=−m
· · ·· · ·
3.1. Outline of PCA method in fault detection and diagnosis applications
∂S =2 jp (c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0 ∂c1 m
j=−m
The coefficients of the fitted polynomial can be obtained by solving Eq. (3). In order to solve such difficult and complicated equations, it will be better to simplify them before solving. After simplification, Eq. (3) can be rewritten as follows:
m
(c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0
j=−m m
j(c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0
j=−m m
j2 (c0
+ c1 j + c2
j2
+ · · · + cp
jp
− yi ) = 0
j=−m
· · ·· · · m
jp (c0 + c1 j + c2 j2 + · · · + cp jp − yi ) = 0
j=−m
(4)
PCA is one of the basic projection model in the multivariate statistical analysis, which has been widely applied in the data dimensionality reduction and process monitoring, etc. x ∈ Rm represents a measurement sample containing m sensors. Dataset has n sampling points. Measurement data matrix can be constructed asX 0 = [x1 , x2 , · · ·, xn ]T ∈ Rn×m . Each column of X◦ represents a measured variable and each row represents a measured sample point. Because the measuring principle and the order of magnitude of the sample data are various differences, so the data matrixX◦ should be normalized to a matrix X with zero mean and unit variance. X, X ∈ Rn × m is called the standardized matrix. Then, the sample covariance matrix Cov of the data set is calculated as Eq. (6). Cov ≈
XT X (m − 1)
(6)
Using principal component analysis, data space can be decomposed into two orthogonal subspaces: one is principal component (PC) space and the other is residual subspace (RS). Usually, Cov has m eigenvectors. Projection matrix of PC space is matrix P composed of eigenvectors which are associated with the first k largest eigenvalues. The number k is determined by cumulative contribution.
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Fig. 1. Schematic diagram of Savitzky-Golay smoothing method.
Fig. 2. Comparison of data processing effects between the wavelet and the S-G method.
When the cumulative contribution of variance of the former k PCs is higher than 90%, the number of principal components is k. P is a matrix with m row and k columns, p ∈ Rm×k , P = [p1 · · ·pk ]. Principal component vector xˆ is standardized sampling data x in the PCs projection, can be obtained by Eq. (7). xˆ = xPP T
(7)
The squared prediction error (SPE), namely the Q-statistic is used as an index of faulty condition in FDD applications. Q-statistic is the squared sum of the residual, which can be calculated using Eq. (9).
Q − statistic = SPE = e2 ≤ Q˛
(9)
Projection matrix of RS space is matrix P˜ composed of the eigenvectors which are associated with the last (m-k) eigenvalues. P˜ is a matrix with m rows and (m-k) columns, p˜ ∈ Rm×(m−k) , P˜ = [pk+1 · · ·pm ]. Residual vector e is standardized sampling data x in the RS projection, can be obtained by Eq. (8). T
e = x − xˆ = x(P˜ P˜ ) = x(I − PP T )
(8)
Where Q␣ is the statistical threshold for the Q-statistic [23]. When no fault occurs, the Q-statistic or SPE is less than the Q␣ . On the contrary, when a sensor fault occurs, the Q-statistic or SPE is larger than the Q␣ . When a fault is detected using the Q-statistic, the faulty sensor can be diagnosed using Q-contribution plot. The contribution of the individual variables to the Q-statistic can be calculated by Eq.
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(10). The variable with the largest contribution to the Q-statistic is most probably faulty. i Qcon =
ei 2 Q − statistic
(10)
The self-detection efficiency in the model training process is defined as the ration of number of the Q-statistic within the threshold to the number of all training samples as following: self −det ection =
N normal N
(11)
Fault detection efficiency is defined as the ration of number of the Q-statistic exceeds the threshold to the number of all test samples as following: det ection =
Nfault N
(12)
Fault diagnosis efficiency is defined as the ration of number of the correct diagnosis samples to the number of all test samples as following: diagnosis =
Ncorrect N
(13)
3.2. PCA model of VRF system With respect to energy balance, sixteen variables selected to describe the operation process of VRF system are used to establish the PCA model for the VRF system. These measurements are outdoor environment temperature (TOD ), condenser outlet temperature (Tcond,out ), liquid refrigerant temperature at the subcooler outlet pipe (Tsubc,out,L ), vapor refrigerant temperature at the subcooler outlet pipe (Tsubc,out,V ), vapor–liquid separator inlet pipe temperature (TSPR,in ), vapor–liquid separator outlet pipe temperature (TSPR,out ), the first compressor module temperature (Tcom1 ), the second compressor module temperature (Tcom2 ),The first fan module temperature (Tfan1 ), The second fan module temperature (Tfan2 ), condensing saturation pressure (Pcond ), evaporating saturation pressure (Pevap ), the first compressor operating frequency (fcom1 ), the second compressor operating frequency (fcom2 ), the first compressor electric current (Icom1 ), the second compressor electric current (Icom2 ). Thus, matrix X represents the original matrix with n samples of these variables as follows:
⎡
171
hevap =hevap,out −hevap,in = f (Pevap , TSPR.in ) − f (Pcond , Tsub,out,l ) = f (Pevap , TSPR.in , Pcond , Tsub,out,l ) √ √ Wcom = Wcom1 + Wcom2 = 3UIcom1 cosϕ1 + 3UIcom2 cosϕ2 Wcom = Wcom1 + Wcom2 =
+
n2 2 Pevap 60 (2 − 1)
n1 1 Pevap 60 (1 −1)
Pcond Pevap
(2 −1)/2
Pcond Pevap
(16) (17)
(1 −1)/1
−1
−1
(18)
Qcond ≈ Q0evap + Wcom = f (Tcom1 , Tcom2 , Tsub,out,l , Tsub,out,v , Pcond )(19) 3.3. Structure of SG-PCA based VRF system sensor FDD strategy Based on SG algorithm enhanced PCA model, sensors FDD of the VRF system mainly includes three main steps: model training, fault detection and fault diagnosis. Fig. 3 is the flowchart of the SGPCA method in sensor fault detection and diagnosis. The first part is training of the SG-PCA model, which mainly involves six steps: data preprocessing, determining Nwin and Npoly , SG smoothing, decomposition of covariance matrix, obtaining principal component and calculating the Q␣ of the Q-statistic. It is rewarding to note that the frequency of two compressors (fcom1 and fcom2 ) is not smooth in the process of data smoothing. Because the compressor frequency is the control signal of VRF system, whose characteristic is changing with load of VRF system. The second part is fault detection, which also involves SG smoothing process for the new sample data. The parameters of SG method for fault detection are the same as that in model training. Then, Q-statistic of the smoothed new sample data are calculated and compared with the threshold. The threshold is determined in the modeling process. When the Q-statistic value is higher than threshold. It means a fault occurs. The last part is about fault diagnosis, which uses Q-contribution plot to diagnose sensor fault. Generally speaking, the sensor with the largest contribution to the Q-statistic is most probably faulty. Finally, the FDD result is reported. Two parameters polynomial order (Npoly ) and width of the moving window (Nwin ), are very important for SG smoothing. They
1 1 1 T1 1 1 1 1 1 1 T1 T1 T1 T1 T1 T1 TOD cond,out sub,out,l sub,out,v SPR,in SPR,out Tcom1 Tcom2 fan1 fan2 Pcond Pevap fcom1 fcom2 Icom1 Icom2
⎤
⎢ T2 T2 ⎥ 2 2 2 2 2 2 2 2 2 2 2 2 T2 T2 Tsub,out, ⎢ OD cond,out Tsub,out,l v TSPR,in TSPR,out Tcom1 Tcom2 fan1 fan2 Pcond Pevap fcom1 fcom2 Icom1 Icom2 ⎥ ⎥ ⎣ ··· ··· ··· ··· ··· ··· ··· ··· ··· ⎦ ··· ··· ··· ··· ··· ··· ···
X=⎢
(14)
n n n Tn n n n n n n Tn Tn Tn Tn Tn Tn TOD cond,out sub,out,l sub,out,v SPR,in SPR,out Tcom1 Tcom2 fan1 fan2 Pcond Pevap fcom1 fcom2 Icom1 Icom2
Eqs. (15) – (19) explain the strong correlations among the variables in matrix X. The COP of the VRF system can be calculated as Eq. (15) under stable condition. According to its definition, the cooling capacity (Q0 ) can be thought of as the cooling load of evaporator (Q0ev ). Power consumption is mainly composed of three parts: the compressor power, the fan power and power of other auxiliary equipment. Compressor power is the most important part of system power, which can be obtained from the compressor current as Eq. (17). In addition, compressor power can be calculated by Eq. (18). Due to energy balance of the VRF system under steady state, the condenser load should be equal to the sum of the evaporator load and compressor power as shown in Eq. (19). As a consequence, all the variables in matrix X are strongly correlated with each other from thermodynamic analysis and using matrix X for PCA model is feasible. COP =
Mref hevap Q0evap Q0 = = W Wcom + Wfan + Wother W
(15)
determine the smoothing degree of data. If the smoothing degree is high, the data will lose a lot of useful information. On the contrary, if the smoothing degree is too low, the smoothing effect of the data is not satisfying. Therefore, how to select these two parameters become very important. There is a close relationship between the smoothing degree and the signal to noise ratio (SNR) and the standard deviation (SD) of smoothed data. In addition, the smoothing degree of training data has a greater impact on the self-detection efficiency (self ) which is important for model training. The SNR, SD and self of the smoothed data are standardized toSNRsta , SDsta and self,sta . An optimal index (OI) of the SG algorithm are established by these three parameters in this study as follow OI = SNRsta − SDsta + self,sta
(20)
When the OI is large, the selected Npoly and Nwin are reasonable. Fig. 4 shows the optimization results of the parameter selection of Npoly and Nwin using the training data. When the OI is large, Npoly
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Fig. 3. Flowchart of the SG-PCA method in sensor fault detection and diagnosis.
and Nwin located in this area are selected for data smoothing operation. Two parameters sets are selected for data smoothing and verifying the reliability of the OI. Npoly and Nwin of two models are listed respectively as follows SG-PCA model A:Polynomial order is 5, moving window width is 577. SG-PCA model B:Polynomial order is 7, moving window width is 677.
Table 1 Specification and characteristics of the ODU and IDUs in the VRF system. Outdoor unit
Indoor unit
Rated cooling capacity(kW)
45.0
45.7 (12.5;12.5;11.2;5;4.5)
Refrigerant
Type
R410A
Number
Hermetically sealed scroll type 2 Frequency conversion
Compressor
4. Strategy validation using the VRF system 4.1. Description of VRF system The VRF system is an important type of the air-conditioning system in many countries because of its high efficiency, flexible form and small space requirement. A typical VRF system is selected for the study in Wuhan, China. Its schematic diagram is illustrated as Fig. 5. The system consists of two parts which are one outdoor unit (ODU) and five indoor units (IDUs). In ODU, there are two inverter
scroll compressors to drive system operation. In IDUs, there are 5 indoor DX coils. And these are the main differences between the VRF system and the conventional air conditioning system. The specification and characteristics of the ODU and IDUs are summarized in Table 1. In order to guarantee the VRF system work well and control intelligently, VRF system built a series of sensors as shown in Fig. 5. Types of measurement parameters include: temperature, pressure,
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Fig. 4. Parameter selection of window width and polynomial order.
Fig. 5. Schematic diagram of the VRF system.
current and frequency. Three days normal operating data were collected in real situation. The selected VRF system had been normally running for a long time without sensor faults and other faults. The data of the former 2 days were chosen as the original data set to train the PCA model. Data from the last day were introduced with biases to test the fault detectability and diagnosis ability of the proposed PCA models.
4.2. Training of models Fig. 6 shows the Q-statistic plot of the conventional PCA model and the SG-PCA model using training data. It can be seen that when compared with the traditional PCA model, the threshold of the Qstatistic in the SG-PCA model has decreased. But the number sample points whose Q-statistic exceeds the threshold has reduced. Fig. 6 presents that the aggregation state is improved of the data after
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Fig. 6. Q-statistic plots of the conventional PCA model and the SG-PCA model A using training data.
smooth and the small bias fault of sensor is conductive to recognize when using the SG-PCA model. When using the original data X to train conventional PCA model, the cumulative contribution rate of the former six principal component vectors reaches 92.21%. When the confidence level is 95%, the threshold of the Q-statistic is 2.712. The Q-statistics of 6.45% samples are above the threshold value, in other words, the selfdetection efficiency is 93.55% when the training data are used as a test set. The matrix X can be obtained from the matrix X smoothed by SG method whose polynomial order is 5 and width of moving window is 577. Using the matrixX to train model, the cumulative contribution rate of the former six principal component vectors reaches 93.54%. These six principal component vectors are retained for the SG-PCA model. When the confidence level is 95%, the threshold of the Q-statistic is 2.554, which is lower than that in conventional PCA model. The Q-statistics of 4.11% samples are above the threshold value.
4.3. Validation results and analysis The FDD performance of the traditional PCA model and SGPCA model are evaluated using the practical running data of the VRF system. Therefore, different fault levels are introduced to the outdoor environment temperature (TOD ), condenser outlet temperature (Tcond,out ), liquid refrigerant temperature at the subcooler outlet pipe (Tsubc,out,L ), vapor refrigerant temperature at the subcooler outlet pipe (Tsubc,out,V ), vapor–liquid separator inlet pipe temperature (TSPR,in ), vapor–liquid separator outlet pipe temperature (TSPR,out ), the first compressor module temperature (Tcom1 ), the second compressor module temperature (Tcom2 ),The first fan module temperature (Tfan1 ), The second fan module temperature (Tfan2 ), condensing saturation pressure (Pcond ) and evaporating saturation pressure (Pevap ). Only one bias fault is introduced each time. In this study, fault detection efficiency is used to evaluate the fault detection capability of the PCA model. When the fault efficiency is lower than 20%, it can be considered the fault is not detected successfully.
Fault detection efficiency of VRF system sensor is improved significantly when the data are smoothed using SG algorithm, which can be seen clearly from Fig. 7. Some sample points of the training data exceed threshold value without smoothing process. When the introduced fault level is 8 ◦ C to the condenser outlet temperature, the Q-statistics of some sample points are less than threshold and the detection efficiency is 71.34%. On the other hand, exceeded sample points of training data decrease after smooth process using SG-PCA model A. When introduced the same bias fault level to condenser outlet temperature, almost all the sample points are above the threshold and the detection efficiency is 98.78%. When a sensor fault is detected, it should be diagnosed for further maintenance. The Q-contribution plot usually can be used to isolate the faulty sensor. The sensor with the largest contribution to the Q-statistic is most probably fault. Q-contribution plots of condenser outlet temperature using PCA model and SG-PCA model A are separately illustrated in Figs. 8 and 9. Different colors represent sensors at different locations in the VRF system. When there is normal condition in the former two days, the Q-contribution of different sensors are not obvious different. But when there is faulty condition in the last day, the Q-contribution of condenser outlet temperature sensor is much higher that of other sensors. Therefore, the faulty sensor should be condenser outlet temperature sensor. The diagnosis efficiency of traditional PCA model and SG-PCA model A are 82.89% and 89.73% separately. It is clear that the two models basically can diagnose the fault source. When using the SG-PCA model A, the diagnosis performance improves significantly. Table 2 lists the FDD performances of temperature sensors faults using the conventional PCA model and the two SG-PCA models (SGPCA model A and SG-PCA model B). Temperature sensors include the outdoor environment temperature (TOD ), condenser outlet temperature (Tcond,out ), liquid refrigerant temperature at the subcooler outlet pipe (Tsubc,out,L ), vapor refrigerant temperature at the subcooler outlet pipe (Tsubc,out,V ), vapor–liquid separator inlet pipe temperature (TSPR,in ), vapor–liquid separator outlet pipe temperature (TSPR,out ), the first compressor module temperature (Tcom1 ), the second compressor module temperature (Tcom2 ), the first fan module temperature (Tfan1 ) and the second fan module tempera-
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Fig. 7. The condenser outlet temperature sensor Q-statistic plots of the PCA model and the SG-PCA model A at fault level +8 ◦ C.
Fig. 8. The condenser outlet temperature sensor fault diagnosis results using PCA method at fault levels +8 ◦ C.
ture (Tfan2 ). When the 10 ◦ C bias fault level is introduced to Tcom1 , the fault detection efficiency of the conventional PCA model is 69.95%. While, the fault detection efficiency of the SG-PCA model A and SG-PCA model B are 89.31% and 87.75% respectively. The fault diagnosis efficiency of the conventional PCA model is 87.49%. While the fault diagnosis efficiency of the SG-PCA model A and SG-PCA model B are 85.56% and 85.88% respectively. The fault detection efficiency of Tcom1 is improved, whereas the diagnosis efficiency has not been improved. Table 2 shows that fault detection efficiency of each sensor almost has been improved when data are processed by SG method. The fault diagnosis efficiency has been improved except Tcom1 . Table 3 lists FDD performances of pressure sensors faults using the conventional PCA model and the two SG-PCA models (SG-PCA model A and SG-PCA model B). Pressure sensors include condens-
ing saturation pressure (Pcond ) and evaporating saturation pressure (Pevap ). When the 10% bias fault level is introduced toPcond , the fault detection efficiency of the conventional PCA model is 38.43%. While, the fault detection efficiency of the SG-PCA model A and SG-PCA model B are 84.77% and 83.97% respectively. Therefore, detection efficiency increases by 46.34% and 45.54% respectively using SG-PCA model A and SG-PCA model B. In addition, fault diagnosis efficiencies are also increased by 31.62% and 29.93% respectively. As a consequence, the detection efficiency and diagnosis efficiency have been greatly improved. When the sensor faults of the evaporation pressure occur, the detection efficiencies have been improved after SG smoothing process. The fault diagnosis results of evaporator pressure sensor faults are unreasonable using both the PCA and SG-PCA models. Tables 2 and 3 present that the FDD
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Table 2 Comparison of FDD performance on temperature sensor faults between the conventional PCA model and the SG-PCA model. Bias
PCA model
SG-PCA model A
SG-PCA model B
Detection ratio (%)
Diagnosis ration (%)
Detection ratio (%)
Diagnosis ration (%)
Detection ratio (%)
Diagnosis ration (%)
TOD
10 8 6 4 2
99.92 93.17 65.35 39.19 23.49
97.10 92.97 81.91 54.58 19.66
100 100 100 78.19 38.9
100 98.48 96 86.23 41.29
100 100 100 78.74 37.81
100 98.18 95.23 86.03 38.95
Tcond,out
10 8 6 4 2
89.06 71.34 44.64 23.77 15.02
92.80 82.89 66.13 52.17 36.06
100 98.78 82.56 56.54 30.6
94.79 89.73 83.15 62.51 34.4
100 98.70 81.69 57.53 29.56
94.38 89.35 82.21 61.97 33.09
Tsubc,out,L
12 10 8 6 4
48.92 39.19 31.19 25.45 22.14
55.09 46.55 35.16 23.16 14.57
89.81 72.74 58.1 41.44 32.25
77.65 67.40 51.13 32.34 16.16
88.95 72.71 57.09 42.18 30.98
78.39 65.72 51.10 31.82 14.34
Tsubc,out,V
14 12 10 8 6 4
58.18 50.92 42.97 35.08 28.90 24.8
40.62 34.61 28.64 22.08 15.64 9.36
100 97.22 87.75 72.37 55.63 39.75
78.74 72.42 61.69 52.24 39.49 24.11
99.6 95.72 84.94 68.64 50.99 38.84
72.73 67.83 61.31 51.21 39.77 26.48
TSPR,in
10 8 6 4 2
69.28 50.31 39.25 30.31 23
72.18 59.16 41.21 25.12 11.94
100 100 99.67 75.07 40.05
96.66 91.44 79.6 61.12 27.80
100 100 95.15 72.11 37.18
93.79 82.78 69.48 52.72 25.19
TSPR,out
10 8 6 4
42.56 30.91 23.55 19.62
35.14 24.45 16.56 8.61
90.07 73.26 45.79 31.52
60.12 51.37 38.16 16.20
88.95 69.10 42.75 30.17
65.11 55.97 40.84 17.79
Tcom1
12 10 8 6 4
89.62 69.95 51.45 37.33 25.78
93.40 87.49 75.65 53.13 22.42
100 89.31 69.27 45.44 31.99
89.97 85.56 75.78 52.85 25.65
100 87.75 67 45.02 31.09
89.42 85.88 76.09 52.11 25.10
Tfan1
10 8 6 4 2
100 100 99.35 69.64 32.73
100 99.9 98.22 87.76 46.48
100 100 100 86.86 44.01
100 100 100 91.99 50.74
100 100 100 85.73 45.56
100 100 99.58 91.08 49.89
Tcom2
10 8 6 4
81.73 56.15 37.49 26.31
85.67 73.86 57.34 34.51
97.28 76.98 51.91 35.10
93.28 84.58 57.19 29.28
95.5 74.59 49.82 34.76
91.77 83.62 53.56 28.9
Tfan2
10 8 6 4 2
100 99.57 98.49 63.45 30.36
100 99.92 97.18 85.40 38.47
100 100 100 85.12 42.59
100 100 99.85 90.42 48.61
100 100 100 82.78 43.59
100 100 98.75 88.84 48.44
Table 3 Comparison of FDD performance on pressure sensor faults between the conventional PCA model and the SG-PCA model. Bias
PCA model
SG-PCA model A
SG-PCA model B
Detection ratio(%)
Diagnosis ration(%)
Detection ratio(%)
Diagnosis ration(%)
Detection ratio(%)
Diagnosis ration(%)
Pcon
20% 15% 10% 8% 6% 4%
81.75 57.30 38.43 32.03 26.88 23.10
94.66 83.09 63.02 51.04 38.74 24.84
100 97.22 84.77 67.31 50.61 39.47
100 100 94.64 86.21 70.81 42.64
100 96.18 83.97 65.44 49.85 39.17
100 100 92.95 82.94 68.56 41.39
Peva
20% 15% 10%
25.7 23.45 21.87
0 0 0
51.17 44.35 36.36
0 0 0
51.98 44.66 36.28
0 0 0
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Fig. 9. The condenser outlet temperature sensor fault diagnosis results using SG-PCA model A at fault levels +8 ◦ C.
Table 4 The parameters of different SG-PCA models. SG-PCA model
Polynomial order
Width of moving window
OI value
Model A Model B Model C Model D Model E Model F
5 7 5 5 8 2
577 677 877 277 577 577
2.43 2.89 2.18 −1.47 −0.24 0.67
Fig. 11. Q-contribution maximum proportion of each variable.
Fig. 10. The FDD performance of the SG-PCA model with different parameters.
performance of SG-PCA model is better than the conventional PCA model. Tables 2 and 3 show the SG-PCA-A model and SG-PCA-B model have good FDD performances. The parameters of the two models are chosen by the optimal index determined by Eq. (20). In order to further verify the reliability of optimization index, another four SG-PCA models with different parameters are established whose parameters can be seen in Table 4 and FDD performances are shown in Fig. 10. Table 4 lists the parameters of different models and the OI values. Fig. 10 is the FDD performance of the SG-PCA model with the different parameters when the bias fault level of Pcond is 10%.
It can be seen from Fig. 10 that the FDD performances are good when the OI value is large. Therefore, The OI value which established by the standard deviation, SNR and self-detection efficiency of the smoothed training data is proved reliable. It can be concluded from Tables 2 and 3 that the fault diagnosis efficiencies of most sensors exceed 50%. The fault can be isolated correctly when the sensor fault diagnosis efficiency is above 50%. But when the diagnosis efficiency is lower than 50%, two kinds of diagnosis results may occur. If the fault diagnosis correct ratio is much higher than misdiagnosis ratio of other variables, the fault is isolated correctly. For example, when the fault level of Tcond,out is 2 ◦ C, the fault diagnosis efficiency of the conventional PCA model is 36.06%. In this case, the fault misdiagnosis ratios of other variables are calculated. Fig. 11 is the diagnosis result of each variable. Although the fault diagnosis efficiency of Tcond,out is no more than 50%, the fault diagnosis efficiency is much higher than misdiagnosis ratio of other variables. On the other hand, it fails to diagnose the
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fault when there is no obvious difference among the fault diagnosis efficiency of each sensor. 5. Conclusion Sensor accuracy and reliability have played important roles for the VRF system efficiency, healthy operation and energy saving. Generally, the PCA method can be used for sensor fault detection and diagnosis. However, due to large fluctuations of operating conditions and sensor measurement accuracy limits, the conventional PCA model for VRF system sensor FDD is not suitable. As a consequence, this paper proposes a new PCA model enhanced by the SG method for VRF system sensor FDD. The FDD performance of the SG-PCA model is evaluated by the VRF system data in real situations. The results have demonstrated that the FDD performance of SG-PCA model is more effective and reliable than the conventional PCA model. Besides, under the same fault level, SG-PCA model can increase the sensor fault detection efficiency and fault diagnosis efficiency of the VRF system. In addition, the OI for selecting the parameters of SG method is proposed, whose reliability is evaluated by six SG-PCA models of the VRF system. The results show that the OI value which is established by the standard deviation, SNR and self-detection efficiency of the smoothed training data is reliable. Moreover, this paper also has discussed the fault identification method when the fault diagnosis efficiency is below 50%. The SG-PCA model is a promising method for fault detection and diagnosis in actual VRF system. In the future works, the SG-PCA model applied to the online sensor fault strategy will be carried out based on the present work. Acknowledgments The authors gratefully acknowledge the support of National Natural Science Foundation of China (Grant 51576074 and 51328602), and Beijing Key Lab. of Heating, Gas Supply, ventilating and Air Conditioning Engineering (Project NR2016K02). References [1] Building energy data book 2011, U.S. Department of Energy, 2011. [2] S. Wang, F. Xiao, AHU sensor fault diagnosis using principal component analysis method, Energy Build. 36 (2004) 147–160. [3] S. Wang, J. Cui, Sensor-fault detection, diagnosis and estimation for centrifugal chiller systems using principal-component analysis method, Appl. Energy 82 (2005) 197–213. [4] Z. Du, B. Fan, J. Chi, X. Jin, Sensor fault detection and its efficiency analysis in air handling unit using the combined neural networks, Energy Build. 72 (2014) 157–166. [5] Y. Zhu, X. Jin, Z. Du, Fault diagnosis for sensors in air handling unit based on neural network pre-processed by wavelet and fractal, Energy Build. 44 (2012) 7–16. [6] Y. Hu, H. Chen, G. Li, H. Li, R. Xu, J. Li, A statistical training data cleaning strategy for the PCA-based chiller sensor fault detection, diagnosis and data reconstruction method, Energy Build. 112 (2016) 270–278.
[7] G. Li, Y. Hu, H. Chen, L. Shen, H. Li, M. Hu, J. Liu, K. Sun, An improved fault detection method for incipient centrifugal chiller faults using the PCA-R-SVDD algorithm, Energy Build. 116 (2016) 104–113. [8] L. Kwon, Y. Hwang, R. Radermacher, B. Kim, Field performance measurements of a VRF system with sub-cooler in educational offices for the cooling season, Energy Build. 49 (2012) 300–305. [9] L. Kwon, H. Lee, Y. Hwang, R. Radermacher, B. Kim, Experimental investigation of multifunctional VRF system in heating and shoulder seasons, Appl. Therm. Eng. 66 (2014) 355–364. [10] Y. Shin, S.W. Karng, S.Y. Kim, Indoor unit fault detector for a multi-split VRF system in heating mode, Int. J. Refrig. 40 (2014) 152–160. [11] B. Fan, Z. Du, X. Jin, X. Yang, Y. Guo, A hybrid FDD strategy for local system of AHU based on artificial neural network and wavelet analysis, Build. Environ. 45 (2010) 2698–2708. [12] Z. Du, B. Fan, X. Jin, J. Chi, Fault detection and diagnosis for buildings and HVAC systems using combined neural networks and subtractive clustering analysis, Build. Environ. 73 (2014) 1–11. [13] Z. Du, X. Jin, Multiple faults diagnosis for sensors in air handling unit using Fisher discriminant analysis, Energy Convers. Manage. 49 (2008) 3654–3665. [14] G. Li, Y. Hu, H. Chen, H. Li, M. Hu, Y. Guo, S. Shi, W. Hu, A sensor fault detection and diagnosis strategy for screw chiller system using support vector data description-based D-statistic and DV-contribution plots, Energy Build. 133 (2016) 230–245. [15] Y. Zhao, J. Wen, S. Wang, Diagnostic Bayesian networks for diagnosing air handling units faults—part II: faults in coils and sensors, Appl. Therm. Eng. 90 (2015) 145–157. [16] Y. Zhao, J. Wen, F. Xiao, X. Yang, S. Wang, Diagnostic Bayesian networks for diagnosing air handling units faults—part I: Faults in dampers, fans, filters and sensors, Applied Thermal Engineering 111 (2017) 1272–1286. [17] S. Wang, F. Xiao, Detection and diagnosis of AHU sensor faults using principal component analysis method, Energy Convers. Manage. 45 (2004) 2667–2686. [18] S. Wang, Y. Chen, Sensor validation and reconstruction for building central chilling systems based on principal component analysis, Energy Convers. Manage. 45 (2004) 673–695. [19] S. Wang, J. Qin, Sensor fault detection and validation of VAV terminals in air conditioning systems, Energy Convers. Manage. 46 (2005) 2482–2500. [20] F. Xiao, S. Wang, X. Xu, G. Ge, An isolation enhanced PCA method with expert-based multivariate decoupling for sensor FDD in air-conditioning systems, Appl. Therm. Eng. 29 (2009) 712–722. [21] X. Xu, F. Xiao, S. Wang, Enhanced chiller sensor fault detection, diagnosis and estimation using wavelet analysis and principal component analysis methods, Appl. Therm. Eng. 28 (2008) 226–237. [22] Z. Du, X. Jin, Detection and diagnosis for sensor fault in HVAC systems, Energy Convers. Manage. 48 (2007) 693–702. [23] Y. Hu, H. Chen, J. Xie, X. Yang, C. Zhou, Chiller sensor fault detection using a self-adaptive principal component analysis method, Energy Build. 54 (2012) 252–258. [24] G. Strang, Wavelet transforms versus Fourier transforms, Bull. Am. Math. Soc. 28 (1993) 288–305. [25] S. Li, J. Wen, A model-based fault detection and diagnostic methodology based on PCA method and wavelet transform, Energy Build. 68 (Part A) (2014) 63–71. [26] O. Abdel-Aziz, M.F. Abdel-Ghany, R. Nagi, L. Abdel-Fattah, Application of Savitzky-Golay differentiation filters and Fourier functions to simultaneous determination of cefepime and the co-administered drug, levofloxacin, in spiked human plasma, Spectrochim. Acta Part A: Mol. Biomol. 139 (2015) 449–455. [27] Y. Zhang, C. Bingham, Z. Yang, B.W. Ling, M. Gallimore, Machine fault detection by signal denoising—with application to industrial gas turbines, Measurement 58 (2014) 230–240. [28] A.A. Candan, H. Inan, A unified framework for derivation and implementation of Savitzky-Golay filters, Signal Process. 104 (2014) 203–211.