- Email: [email protected]
Refrigerant charge fault diagnosis in the VRF system using Bayesian artificial neural network combined with ReliefF filter
Accepted Manuscript Research Paper Refrigerant charge fault diagnosis in the VRF system using Bayesian artificial neural network combined with ReliefF filter Shubiao Shi, Guannan Li, Huanxin Chen, Jiangyan Liu, Yunpeng Hu, Lu Xing, Wenju Hu PII: DOI: Reference:
S1359-4311(16)32271-2 http://dx.doi.org/10.1016/j.applthermaleng.2016.10.043 ATE 9245
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
5 July 2016 5 October 2016 8 October 2016
Please cite this article as: S. Shi, G. Li, H. Chen, J. Liu, Y. Hu, L. Xing, W. Hu, Refrigerant charge fault diagnosis in the VRF system using Bayesian artificial neural network combined with ReliefF filter, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.10.043
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Refrigerant charge fault diagnosis in the VRF system using Bayesian artificial neural network combined with ReliefF filter Shubiao Shi1, Guannan Li1*, Huanxin Chen1*, Jiangyan Liu1, Yunpeng Hu1, Lu Xing1, Wenju Hu2 1
Department of Refrigeration & Cryogenics, Huazhong University of Science and
Technology, Wuhan, China; 2
Beijing Municipality Key Lab of HVAC&R, Beijing University of Civil Engineering
and Architecture, Beijing, China； Abstract A proper refrigerant charge amount (RCA) is critical for a variable refrigerant flow (VRF) system since RCA may affect the operational performance. However, there were few studies of RCA fault for the VRF system in the open literature. Therefore VRF systems are calling for a fault diagnosis strategy. This paper develops a highly efficient fault diagnosis model (FDM), which employs the ReliefF algorithm for feature ranking (FR) and applies the neural network for fault diagnosis. Firstly, the artificial neural network (ANN) model is built on the N-best features data subset and optimized by the Bayesian regularization algorithm. Secondly, the model is verified by testing data subset, the correct diagnosis rates (CDR) using the N-best features data subset can be obtained. The optimal FDM is selected in consideration of CDR and the computational efficiency. Finally, optimal FDM is further optimized by selecting the best hidden neurons. The results show that the CDR of the FDM based on 6-best features is sufficiently high in comparison to the CDR achieved when 22 * Corresponding author. Tel.: +86 27 87558330; Fax: +86 27 87558330. E-mail address: [email protected] (Guannan Li), [email protected] (H. Chen).
features are used, while the training time decreases by 98.8%. Keywords:
Fault
diagnosis;
Variable
refrigerant
flow
system;
ReliefF
algorithm;
Bayesian neural network; Refrigerant charge amount fault 1.
Introduction Reducing the HVAC (Heating, Ventilation, and Air Conditioning) energy
consumption has become one of the prime targets around the world. According to the statistics, energy consumption in commercial and residential buildings accounts for 41.0% of U.S. in 2010, of which 37.0% is used for HVAC systems [1]. As the HVAC energy consumption increased rapidly, it is crucial to develop some powerful policies or techniques for energy efficiency. Developing efficient and reliable HVAC system is one of the major solutions. The VRF system becomes popular in many countries due to various advantages of VRF systems in terms of energy saving potential, better thermal comfort, etc. [2]. And VRF systems equipping with one outdoor unit and multiple indoor units take the refrigerant as the heat transfer fluid. Consequently, the refrigerant flow path is very complex and then leads to a complicated refrigerant pipeline system. In the long-term operation, the VRF system has the potential to leak because the system installs a long pipeline and pressures in the system are usually many times higher than atmospheric ones. On the other hand, the appropriate refrigerant charge amount in the VRF system is determined by the rule-of-thumb. Hence, based on the above analysis, it is a common phenomenon that the VRF system has either undercharge or overcharge fault in the actual system operation. Consequently, the energy efficiency of the VRF system would be reduced due to the inappropriate refrigerant charge [3]. However, there are relatively few researches about the fault diagnosis for VRF system’s RCA in the open literature [4, 5],
especially those from the viewpoint of important features. Therefore, it is very critical to develop a highly efficient RCA fault diagnosis strategy for the VRF system. From the methodology point of view, three diagnosis methods have been proposed [6], namely, model-based, data-driven, and knowledge-based. Model-based method uses the first principle to construct the mathematical model, which does not require a large operation data of the system. Some researchers had conducted some related studies [7-9]. A knowledge-based approach is used to draw conclusions regarding the state of a system through qualitative relationships or knowledge bases. It consists of expert systems [10, 11], pattern recognition [12, 13] and causal analysis. Data-driven methods use the relation between data patterns and fault classes in terms of
modeling
process.
These
methods
differ
from the
model-based
and
knowledge-based methods since they are dimensional reduction techniques based on rigorous multivariate statistics, whereas pattern classifications learn the pattern of fault performance using the training data [14]. To enhance the performance of an individual diagnosis approach, the combination of various techniques has been developed in terms of hybrid FDD approaches [15, 16]. In this paper, we adopt the combination of knowledge-based method and data-driven approaches for RCA fault in the VRF system. The determination of critical input parameters plays an important role for RCA fault diagnosis. Grace and Tassou’s et al. [17] results showed that the superheat and sub-cooling together with discharge temperature are the three most sensitive parameters associated with the RCA. For the VRF system, limited studies on the correlation between feature and RCA were conducted in the past. Thus, the correlation researched through FR algorithm was meaningful. FR was employed to reduce the number of the features so as to improve the efficiency of building the
model. ReliefF, as one of the FR tools, has proven to be effective in removing unimportant features, and increasing computational efficiency [18]. The artificial neural network (ANN) is a kind of data mining technology that has recently been widely used in engineering fields. E.g. Wang and Chen [19] applied the neural network models to diagnose the measurement faults of both the outdoor and supply flow rate sensors. Fan et al. [20] used the neural network combined with wavelet analysis for sensor fault diagnosis, the result showed the model could detect and diagnose fixed biases and the drifting fault of sensors for the local system of AHU. Zhao et al. [21] developed a generalized neural network to predict the mass flow rate in adiabatic capillary tubes and short tube orifices, the result showed that the overall average and standard deviations are 0.75% and 8.27% respectively. As we expected, the ANN presented a good performance in the HAVC application fields. Hence, it was a pretty good tool for fault diagnosis of RCA in the VRF system. Although the ANN has achieved a great success, it still has a risk of over-fitting and poor generalization ability. In this study, the deficiency is addressed by introducing Bayesian regulation. This paper presents a fault diagnosis strategy for VRF system. The strategy has been developed by organically incorporating ReliefF and neural network algorithm. The validation of the strategy using laboratory data has been presented in the paper. 2.
Relief and ReliefF algorithm The Relief algorithm is utilized to discriminate instances that are near to each
other, its simplicity and effectiveness make it possible to become one of the most successful algorithms [22]. However, suggested by Kira [23] et al., it works only for a binary data. The ReliefF (Relief-F) algorithm [24] is introduced to solve the
multi-classification problem. Given a randomly selected instance Ri (1
W [ A] W [ A] diff ( A, Ri , H j ) / ( m k ) j1
C ≠class ( Ri )
[
k
P (C )
diff ( A, R , M (C ))] / (m k) 1 P(class ( R )) i
i
j
j 1
（1） Where function diff(A, Ri , Hj ) calculates the difference between the feature for two instances ( Ri and Hj ), P(class(R1)) is the probability of the label Ri . The numerical feature is expressed as follows: diff（A,R1 ,H1）=
| value （A,R1）- value （A,H 2）| max （A）- min （A）
(2)
Where value(A,R1) means the difference between A and R1，value(A,H2) means the difference between A and H2.
3. 3.1
Machine learning-Bayesian neural network Bayesian neural network ANN is wildly used in engineering applications. Generally, ANN has a
three-layer structure: the input layer, the hidden layer, and the output layer. RCA fault diagnosis is a complex nonlinear issue, which can be approximated by a three-layer ANN based on strong nonlinear mapping capability according to Kolmogorov’s theorem [25]. The neuron numbers in the input layer are equal to the number of input features while such numbers in the output layer are determined by the number of classes. The numbers of neurons in the hidden layer have a substantial impact on the neural model quality, and they are determined according to the Eq. (3). Back propagation structure is illustrated in Fig.1.
N h 2 Ni 1
(3)
Where N h is the number of hidden layer nodes, N i is the number of input layer nodes
[Approximate position of Figure 1]
Two main steps should be carried out to apply a neural network for the fault diagnosis process. Firstly, the data collected from the VRF system is spit into training data and testing data. The neural network is trained using an abundance of training data including both normal and faulty operation conditions. Secondly, the fault diagnosis in the VRF systems is conducted by comparing the objective vectors with the ones derived from the well-trained neural network. And three objective vectors are selected as (1,0,0), (0,1,0) and (0,0,1). When testing data is used to test the FDM, the corresponding output close to (1,0,0), it represents the undercharge operation condition; the output close to (0,1,0) implies the normal condition; and (0, 0, 1)
suggests overcharge operation condition. Despite the fact that the algorithm is very mature in the applications, it can lead to over-fitting and poor generalization capabilities phenomenon. Model optimization is taken by using the proposed Bayesian regularization mainly constraining the size of the network weights. When the weights in a network are kept small, the network response will be smooth. That will improve the generalization ability of the ANN model. Bayesian artificial neural network (BANN) uses the linear combination of the mean square error and the weight for network performance evaluation function, more details can be obtained from the literature [26].
F = bED aEW
(4)
Where ED is the sum of squared errors, EW is the sum of squares of the network weights, a and b are objective function parameters. 3.2 Evaluation of FDM To evaluate the diagnosis performance of the proposed strategy, this study employs two different standard performance evaluation criteria. The standard criteria includes overall correct diagnosis ratio (HR) and single correctly diagnosis ratio (CR). HR is defined as the percentage of predicted correct samples and all the actual samples. CR represents individual group diagnosis rate defined as the percentage of correctly classified samples and all the samples of each class under investigation. The fault diagnosis of refrigerant charge is mainly discussed in this paper. Table 1 is a confusion matrix (ConfMat) for the three-class case. For CL11 , the first subscript (1) indicates the first actual category and the second subscript (1) represents the first predicted category. Where CL11 (Class1) denotes the number of undercharge samples that are successfully diagnosed. And the ML12 implies the number of samples misdiagnosed as normal charge. And the ML13 reveals the number of the samples
misdiagnosed as the overcharge. HR, CR1 (correctly diagnosis ratio for undercharge fault), CR2 (correctly classification ratio for normal condition) and CR3 (correctly diagnosis ratio for overcharge fault) are expressed as the following equations:
HR CL11 CL22 CL33 / Total
(5)
CR1 undercharge CL11 / CL11 ML12 ML13
(6)
CR2 normalcharge CL22 / CL21 ML22 ML23
(7)
CR3 overcharge CL33 / ML31 ML32 CL33
(8)
[Approximate position of Table 1]
4.
Experimental setup and fault diagnosis framework
4.1 Description of the System The experimental setup is employed to measure VRF performance under different refrigerant charge levels. Fig.2 shows a schematic of the experimental setup, which presents the major sensors [27]. The studied system is an R410A 31.5 kW VRF system with the nominal charge of 9.9 kg. The rated capacity of the outdoor unit and the indoor unit are 28.0 kW and 29.7KW respectively. More details about the system can be found in Li’s and Liu’s researches [27, 28].
[Approximate position of Figure 2]
All the heating condition experiments are accomplished in the standard psychrometric chamber. The psychrometric chamber consists of an indoor room equipped with five indoor units and an outdoor room allocated with one outdoor unit.
In order to develop RCA fault diagnosis model, 9 groups of the experiment are conducted under different refrigerant charge levels ranged from 63.0% to 130.0%, as shown in Table 2. For each group of charge level, three different heating conditions based on different outdoor temperature(– 7℃, 2℃, 7℃respectively) are implemented. Table3 demonstrates the detailed description. Each heating condition includes 3 indoor units operating conditions, i.e. one unit operating, three units operating and five units operating. For each testing condition, the fan speeds (including one outdoor fan and 5 indoor fans) are almost kept constant while the compressor speed is not fixed. The compressor speed and the EEV openings are controlled to adjust the refrigerant flow rate to meet the cooling load (The engineering unit of the compressor speed is the rpm). The compressor operation frequency varies from 0 to 90. The VRF system can still maintain its operation when there is a small amount of undercharge and overcharge fault. Kim and Braun [3] have indicated that the 25% reduction of refrigerant charge leads to energy efficiency decrease and capacity degradation. The refrigerant charge levels are labeled according to the important reference. In this study, 63.0% and 75.4% charge levels are treated as under charge fault, 130.0% charge level is used as overcharge fault.
[Approximate position of Table 2]
[Approximate position of Table 3]
The air temperature and relative humidity of the two rooms are controlled to the test conditions as shown in Table 3, according to adjustment of the proportion integration differentiation (PID) control strategy. To monitor the operation of the VRF
system, a large number of sensors and controllers have been installed. Table 4 lists 22 chosen variables in detail, mainly include temperature variables, frequency variables, current variables, voltage variable and control variables. These features are used for fault diagnosis of VRF refrigerant charge.
[Approximate position of Table 4]
4.2 Data description The VRF system connects an outdoor unit to five indoor units, and it operates under three different heating conditions with 3 indoor units operating conditions. Each heating modes were recorded at 15 seconds intervals in the controller of the VRF system. Each testing lasted for at least 45 minutes. All the experimental data were collected by the data acquisition system. In order to improve the efficiency of simulation and modeling, 3995 data samples was selected from the full data set at the same interval. The experimental data subset with the ratio of 3:1 was randomly split into training data and testing data, respectively. 4.3 Data normalization The observed sample matrix Z ( Z R M N ) consists of N observations and M features. The normalized data matrix Y is obtained by Eq. (9) and (10).
Maxi max( Zi , j ) Mini min( Zi , j ) Y ymax ymin Z ji Mini / Maxi Mini ymin
(9)
(10)
Where Z i , j is an element of matrix Z, Maxi is the maximum of the ith feature.
Mini is the minimum of the ith feature, ymax and ymin are 1,-1 respectively, Y is the normalized matrix.
[Approximate position of Figure 3]
4.4 Diagnosis Scheme of VRF refrigerant charge fault Fig.3 shows the logic diagram of fault diagnosis for VRF refrigerant charge fault. It is composed of three parts: the features ranking, the fault diagnosis, the model selection. The first part is FR composed of the weight calculation and the features ordering. The second part is to build a model for RCA fault diagnosis with BANN algorithm. The third part is model selection and model optimization in consideration of overall CDR and single CDR. 5.
Result and discussion
5.1 Result of FR based on ReliefF The major task of ReliefF algorithm was to iteratively estimate the feature weights according to their ability to discriminate between neighboring patterns. The feature weights were arranged in ascending order as shown in Fig.4. Among them, the higher the weight, the higher correlation between the features and RCA. It was worth pointing out that there were three feature weight (Tdis, Tcom, Ucom) larger than the others. It meant that the features had the higher discriminative ability in comparison to other features. Sun [29] pointed out that the Tdis was obviously the most significant feature for modeling. So the result of the FR can be credible. Meanwhile, from the perspective of the physical principles, it could be further deduced that when RCA fault occurred in the VRF system, the compressor discharge temperature, the compressor module temperature and compressor bus-voltage would undoubtedly deviate from the normal operation conditions obviously. When the VRF system had the undercharge fault, the discharge temperature would have a tendency to rise, while
the discharge temperature would be declined for overcharge fault. The change trend of module temperature was identical with the discharge temperature tendency but was contrary to the bus-voltage of the compressor. It was also reasonable according to our knowledge of VRF system. From the perspective of weights, the three features were better input parameters for FDM than other features.
[Approximate position of Figure 4]
Fig.4 showed that 13 feature weights were closed to zero, which signified that the 13 features did not seriously deviate from the normal condition when the fault occurred. It meant that they were not good indicators to detect the RCA fault. However, the FDM, combined these features, may obtain a comparatively satisfying diagnosis performance. Fig.4 showed the 5 feature weights selected from 22 feature weights were lower than others evidently in the diagram, which indicated these features may be meaningless to establish a model for fault diagnosis. Therefore, they may be removed considering operational efficiency. 5.2 Result of BANN model for fault diagnosis The performance of the classification, in terms of accuracy, for different number of N-best features (N=1, 2, 3..., 22) were presented in Fig. 5-Fig.8. Fig.5 represented the overall CDR curve, and the Fig.6, 7 and Fig.8 represented the CDR curve for undercharge, normal charge and overcharge condition respectively. A random process was normally involved in the training of an ANN model, for example, training and testing sample sets were obtained by random sampling. It led to a result that the CDR of the trained model might not be the same at all times, as it depended on the quality of the training samples. Thus we carried out 10 trials of
model training and testing. Then, the average CDR was seen as the model diagnosis performance. As shown in Fig.5, the column height represented the averaged value of CDR, and the error bars presented the standard errors of 10 trials for CDR. As shown in Fig.5, the BANN fault diagnosis model could achieve a high overall CDR with a small data subset contained a few best features. Specifically, model-6 (model based on the 6-best features as the input parameters) could reach a percentage of 90.3% CDR, which was sufficiently high in comparison to the accuracy achieved when model-22 was used (model based on the all features as the input parameters). And the CDR could reach 94.6% with a subset of 17-best features, the CDR kept unchanged until all features were used.
[Approximate position of Figure5]
[Approximate position of Figure 6]
[Approximate position of Figure 7]
[Approximate position of Figure 8]
It was worth pointing out that a satisfactory model not only had a good diagnosis performance in overall CDR, but possessed a satisfying accuracy for each single class. Diagnosis performances of the single classes were analyzed, the CDR curves for three classes were shown in Fig.6 to Fig.8. Fig.6 plotted the CDR for different number of N-best features, when the VRF system had undercharge fault. Firstly, when the number of the best features was over 8, the CDR curve was not always increasing.
There is a slight fluctuation in the local, but the general trend of the fault diagnosis curve was rising with the increase of features. The local fluctuation of fault diagnosis curve could be explained by reason of dual influence of redundancy and weight. As the best features increased, the subset had more noise or redundancy, and the weight behind gradually became smaller. When the test subset was used to test the neural network model, the CDR were 62.40%, 93.04% and 87.12% respectively, using three parameters of the compressor (Tdis, Tcom, Ucom). Compared with the CDR of normal and overcharge fault, the CDR of undercharge was relatively low, attributing to that the three parameters did not have a strong discriminative ability between undercharge condition and normal condition. Therefore, the more features were used, the more information employed for undercharge fault diagnosis would be. Similarly, the more information added to neural network model in the FDD process, the more accurate the results would be. Hence, the CDR curve would rise with the increase of features; it was determined by the richness of information [30]. When 6-best features were used for fault diagnosis, the model only achieved 72 percent of correctly diagnosis rate, the accuracy was still needed to improve. As shown in Fig.7 to Fig.8, the subset redundancy made CDR fluctuate starting from the sixth-best feature for the normal charge, while starting from the seventh-best feature for the overcharge [18]. The CDR curves were fluctuant with the increase of features, which could be explained that the accuracies were determined by the redundancy. That was different from undercharge fault. The CDR of the model based on the 6-best features was 95.5% for the normal charge, while it was 93.3% for the overcharge. In contrast to correctly diagnosis rate of normal and overcharge fault, there was not a very satisfying diagnosis performance for undercharge fault based on model-6.
The main reason was that the discharge temperature had a strong discriminate ability for the overcharge, while it failed in undercharge. And the six best features were Tdis , Tcom , U com , Tcond , Tshell and
T fan respectively.
In order to solve the problem of
the relatively low CDR of undercharge fault compared with normal and overcharge fault, the optimization procedure was taken for the model. The most important model parameters were the weight and the number of the hidden layer nodes respectively. Model weight had been optimized by Bayesian regularization; the hidden layer nodes played a very critical role and determined the network structure. In this study, the number of hidden neurons for the model-6 was investigated ranged from 10 to 16 (i.e. 13 ± 3). The result was shown in Fig.9, and the performances of the models with different numbers of hidden neurons were comparable to each other. It was indicated that the number of hidden neuron within the range was insensitive to the model performance from the viewpoint of overall CDR. Thus the number of hidden neurons determined by the Eq. (3) was justified to be adopted [31].
[Approximate position of Table 5]
The CDRs of the models with 11 and 13 hidden neurons were compared to each other. Result of two models comparison was listed in Table 5. It showed that the overall CDR basically remained unchanged, however the CDR of undercharge fault had a larger increase for 11 hidden neurons, which was greatly improved from 72.0% to 85.0%, while it had not a great impact on the CDR of normal charge and overcharge. Therefore, the overall diagnosis performance of the model with 11 hidden neurons was better in consideration of single CDR and overall CDR.
[Approximate position of Figure 9]
As for the computation time, it could also be noticed that the less features added into the model as the input parameters, the less the time consumed by model training. The model-6 only consumed 133.5s, while the 3874.3s would be consumed for model-22 (All the programs were run on a desktop with a CPU of Intel Core(TM) i5-4590 (3.3 GHz), a memory of 8.00 GB and an operating system of Windows 7). Time-consuming difference was so large, it could be explained as the following: when the 6-best features were used for the input of the model, 13 hidden layer nodes were needed according to the equation (3). At this moment, it would result in 78 weights and 13 thresholds between input layer and hidden layer, and 39 weights between the hidden layer and output layer. Total unknown parameters reached 130. While 22 features were applied for the input of the model, the 45 hidden layer nodes were necessary. And totally unknown parameters were 1170. Therefore, the complexity of the model had increased dramatically. Time consuming for ANN training had also been increased dramatically. The Fig.10 presented the unknown numbers of parameters and operation time under different numbers of features. It was easy to deduce that the model-6 saved 98.8% of time, compared to the model-22.
[Approximate position of Figure 10]
6.
Conclusion This paper presents a highly efficient fault diagnosis model, which employs
ReliefF algorithm for FR and applies the neural network to classify faults. Weight of each feature is calculated based on the ReliefF algorithm, then, we build models based
on different numbers of N-best features, and data subsets redundancy is further study by analyzing the CDR curves. Finally, the model-6 with the optimal hidden nodes is obtained, and the model-6 has a satisfying fault diagnosis performance in the aspects of CDR and computational time. Conclusions are as follows: 1) The CDR of the model-22 can reach more than 90% considering the overall CDR and the single CDR. 2) 6-best features are selected by ReliefF algorithm, and the model-6 can obtain a sufficiently high CDR in comparison to the accuracy achieved when all features are used. However, the training time can be reduced by 98.8%, which greatly improve the operation efficiency. 3) The diagnosis performance for undercharge fault has been improved by optimizing the hidden layer nodes, and the 11 nodes are determined by considering single CDR and overall CDR. The combination of ReliefF algorithm and BANN has been proved to be an efficient strategy for fault diagnosis in the VRF system, meanwhile, it can greatly shorten the operation time and save initial cost on sensors. Acknowledgment The authors gratefully acknowledge the support of National Natural Science Foundation of China (Grant 51576074 and 51328602), Beijing Key Lab of Heating, Gas Supply, Ventilating and Air Conditioning Engineering (Grant NR2016K02).
Nomenclature Aay
Allocation ability [kW]
ANN
Artificial neural network
BANN
Bayesian artificial neural network
Coc
Current operational capability [kW]
C
A class
CDR
Correct diagnosis rate
EXVoutd
Electronic expansion valve opening corresponding to outdoor unit
EXVsubc
Electronic expansion valve opening corresponding to the sub-cooler
F
Error function
FDM
Fault diagnosis model
Fcom
Compressor operating frequency [HZ]
Ffan
Outdoor fan operating frequency [HZ]
FR
Feature ranking
HVAC
Heating, Ventilation and Air Conditioning
I com
Compressor electric current [A]
I fan
Outdoor fan electric current [A]
P(C)
The probability of class C
RCA
Refrigerant charge amount
Taccu ,in
Accumulator inlet pipe temperature [℃]
Taccu ,out
Accumulator outlet pipe temperature [℃]
Tcom
Module temperature of the compressor [℃]
Tcond
Condensing saturation temperature [℃]
Tdis
Compressor discharge temperature [℃]
Tevap
Evaporating saturation temperature [℃]
T ft
Defrost temperature [℃]
T fan
Fan temperature [℃]
TOD
Outdoor temperature [℃]
Tshell
Compressor shell temperature [℃]
Tsubc ,lout
Sub-cooler outlet pipe temperature (liquid)[℃]
Tsubc , gout
Sub-cooler outlet pipe temperature(gas) [℃]
U com,v
Compressor bus-voltage [V]
U fan ,v
Outdoor fan bus-voltage [V]
VRF
Variable refrigerant flow
W
Weight of feature
A
A feature
EW
The sum of squares of the network weights
a ,b
Objective function
ED
The sum of squared errors
Nh
The number of hidden layer nodes
Ni
The number of input layer nodes
ymax , ymin
1 and -1 by default
Z ji
An element of matrix Z
Maxi
The maximum of the sample for the ith feature
Mine
The minimum of the sample for the ith feature
Subscript accu
Accumulator
com
Compressor
cond
Condenser
dis
Compressor discharge
evap
Evaporator
fan
Outdoor fan
outd
Outdoor unit
shell
Compressor shell
in
Inlet
out
Outlet
v
Voltage
subc
Sub-cooler
References: [1] K. J, Buildings energy data book, US Department of Energy, 2011. [2] X. Zhao, M. Yang, H. Li, Field implementation and evaluation of a decoupling-based fault detection and diagnostic method for chillers, Energy and Buildings. 72 (2014) 419-430. [3] W. Kim, J.E. Braun, Evaluation of the impacts of refrigerant charge on air conditioner and heat pump performance, International Journal of Refrigeration. 35 (2012) 1805-1814. [4] X. Lin, H. Lee, Y. Hwang, R. Radermacher, A review of recent development in variable refrigerant flow systems, Science and Technology for the Built Environment. 21 (2015) 917-933. [5] J. Liu, Y. Hu, H. Chen, J. Wang, G. Li, W. Hu, A refrigerant charge fault detection method for variable refrigerant flow (VRF) air-conditioning systems, Applied Thermal Engineering. 107 (2016) 284-293. [6] H. Li, J.E. Braun, A methodology for diagnosing multiple simultaneous faults in vapor-compression air conditioners, HVAC&R Research. 13 (2007) 369-395. [7] T.M. Rossi, J.E. Braun, A Statistical, Rule-Based Fault Detection and Diagnostic Method for Vapor Compression Air Conditioners, HVAC&R Research. 3 (1997) 19-37. [8] H. Yoshida, S. Kumar, Development of ARX model based off-line FDD technique for energy efficient buildings, Renewable energy. 22(2001) 53-59. [9] J. Cui, S. Wang, A model-based online fault detection and diagnosis strategy for centrifugal chiller systems, International Journal of Thermal Sciences. 44 (2005) 986-999. [10] P. Gruber, S. Kaldorf, Practical experiences from developing and implementing
an expert system diagnostic tool / Discussion, ASHRAE Transactions. 108 (2002) 826-840. [11] Y. Qian, X. Li, Y. Jiang, Y. Wen, An expert system for real-time fault diagnosis of complex chemical processes, Expert Systems with Applications. 24 (2003) 425-432. [12] H. Han, B. Gu, J. Kang, Z.R. Li, Study on a hybrid SVM model for chiller FDD applications, Applied Thermal Engineering. 31(2011) 582-592. [13] K. Sun, G. Li, H. Chen, J. Liu, J. Li, W. Hu, A novel efficient SVM-based fault diagnosis method for multi-split air conditioning system’s refrigerant charge fault amount, Applied Thermal Engineering. 108(2016) 989-998. [14] Y. Yu, D. Woradechjumroen, D. Yu, A review of fault detection and diagnosis
methodologies on air-handling units, Energy and Buildings. 82(2014) 550-562. [15] S. Wu, J. Sun, Cross-level fault detection and diagnosis of building HVAC systems, Building and Environment. 46 (2011) 1558-1566. [16] 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, Building and environment. 45(2010) 2698-2708. [17] I.N. Grace, D. Datta, S.A. Tassou, Sensitivity of refrigeration system performance to charge levels and parameters for on-line leak detection, Applied Thermal Engineering. 25 (2005) 557–566. [18] H. Han, B. Gu, T. Wang, Z. Li，Important sensors for chiller fault detection and diagnosis (FDD) from the perspective of feature selection and machine learning, International journal of refrigeration, 34 (2011) 586-599. [19] S. Wang, Y. Chen, Fault-tolerant control for outdoor ventilation air flow rate in buildings based on neural network, Building and Environment. 37 (2002)
691-704. [20] 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, Building and Environment. 45 (2010) 2698-2708. [21] L. Zhao, C. Zhang, L. Shao, L. Yang, A generalized neural network model of refrigerant mass flow through adiabatic capillary tubes and short tube orifices, Journal of Fluids Engineering-Transactions of the ASME. 129 (2007) 1559-1564. [22] Y. Sun, D. Wu, A RELIEF Based Feature Extraction Algorithm., SDM, 2008, pp. 188-195. [23] K. Kira, L.A. Rendell, A practical approach to feature selection, Proceedings of the ninth international workshop on Machine learning, 1992, pp. 249-256. [24] F. Bergadano, L. De Raedt, I. Kononenko, Estimating attributes: Analysis and extensions of RELIEF, in: F. Bergadano, L. De Raedt (Eds.), Springer Berlin Heidelberg, 1994, pp. 171-182. [25] F. Wang, The use of artificial neural networks in a geographical information system for agricultural land-suitability assessment, Environment and planning A. 26(1994) 265-284. [26] F.D. Foresee, M.T. Hagan, Gauss-Newton approximation to Bayesian learning, IEEE, 1997, pp. 1930-1935. [27] G. Li, Y. Hu, H. Chen, L. Shen, H. Li, J. Li, W. Hu, Extending the virtual refrigerant charge sensor (VRC) for variable refrigerant flow (VRF) air conditioning system using data-based analysis methods, Applied Thermal Engineering. 93 (2016) 908-919. [28] J. Liu, Y. Hu, H. Chen, J. Wang, G. Li, W. Hu, A refrigerant charge fault
detection method for variable refrigerant flow (VRF) air-conditioning systems, Applied Thermal Engineering. 107 (2016) 284–293. [29] K. Sun, G. Li, H. Chen, J. Li, J. L, W. Hu, A novel efficient SVM-based fault diagnosis method for multi-split air conditioning system’s refrigerant charge fault amount, Applied Thermal Engineering, 108 (2016) 989-998. [30] Y. Zhao, F. Xiao, S. Wang, An intelligent chiller fault detection and diagnosis methodology using Bayesian belief network, Energy and Buildings. 57 (2013) 278-288. [31] P . Leung, E. Lee, Estimation of electrical power consumption in subway station design by intelligent approach, Applied energy. 101 (2013) 634-643.
Figure Captions
Fig.1 Neural network back propagation structure Fig.2 A schematic of the experimental setup Fig.3 Fault diagnosis Scheme of VRF refrigerant charge Fig. 4 Weights by the ReliefF for the features Fig.5 The overall CDR for different number of features Fig.6 CDR for different number of features (under charge condition) Fig.7 CDR for different number of features (normal condition) Fig.8 CDR for different number of features (overcharge condition) Fig.9 Performances of the models under different numbers of hidden neurons Fig.10 Numbers of parameters and operation time under different numbers of features
Fig.1 Neural network back propagation structure
Fig.2 A schematic of the experimental setup
Operation Operation data data under under normal&fault normal&fault conditions conditions
Variables selection
Weight Weight calculation calculation using using ReliefF ReliefF Features Features sort sort according according to to weight weight N=0;N=N+1； N=0;N=N+1； The The N-best N-best features features
Data Data selection selection
Training Training data data
Normalize Normalize
Neural Neural network network model model
Fault diagnosis Testing Testing data data
Normalize Normalize
Fault Fault diagnosis diagnosis
No
Bayesian Regularization Improve Improve the the generalization generalization ability ability of of the the model model
Save Save FDD FDD result result
N>22? N>22?
Yes Selection Selection of of model model Model Model optimization optimization
Total Total fault fault diagnosis diagnosis rate rate curve curve
Select FDD model
Fig.3 Fault diagnosis Scheme of VRF refrigerant charge
Fig. 4 Weights by the ReliefF for the features
Fig.5 The overall CDR for different number of features
Fig.6 CDR for different number of features (under charge condition)
Fig.7 CDR for different number of features (normal condition)
Fig.8 CDR for different number of features (overcharge)
Fig.9 Performances of the models under different numbers of hidden neurons
Fig.10 Numbers of parameters and operation time under different numbers of features
Table Captions
Table 1 ConfMat for the three-class case Table 2 Nine groups of RCLs and corresponding class Table 3 Three different heating conditions: the low, the medium and the nominal temperature heating modes Table 4 Twenty-two features Table 5 Results of two models comparison
Table 1 ConfMat for the three-class case Predicted Class
Actual Class
Undercharge
Normal charge
Overcharge
Undercharge
CL11
ML12
ML13
Normal charge
ML21
CL22
ML23
Over charge
ML31
ML32
CL33
Table 2 Nine groups of RCLs and corresponding class Test index
Refrigerant charge levels (%)
Class
1
63.0
undercharge
2
75.4
undercharge
3
79.8
normal charge
4
84.8
normal charge
5
95.7
normal charge
6
103.7
normal charge
7
111.7
normal charge
8
120
normal charge
9
130
overcharge
Table 3 Three different heating conditions: the low, the medium and the nominal temperature heating modes Indoor room inlet
Outdoor room inlet
air parameters
Group
air parameters
Test mode index
Dry-bulb
Wet-bulb
Dry-bulb
Wet-bulb
Temp(℃)
Temp(℃)
Temp(℃)
Temp(℃)
10
6
-7
-8
15
5
2
1
20
8
7
6
Low temperature 1 heating Medium 2
temperature heating Nominal
3
temperature heating
Table 4 Twenty-two features No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Name of feature Outdoor temperature Allocation ability Current operational capability Compressor operating frequency Outdoor fan operating frequency Condensing saturation temperature Evaporating saturation temperature Compressor discharge temperature Compressor shell temperature Defrost temperature Sub-cooler outlet pipe temperature (liquid) Sub-cooler outlet pipe temperature (gas) Accumulator inlet pipe temperature Accumulator outlet pipe temperature Electronic expansion valve opening corresponding to outdoor unit Electronic expansion valve opening corresponding to the sub-cooler Compressor electric (current) Compressor voltage Compressor module temperature Outdoor fan electric current Outdoor fan voltage Module temperature of the compressor
1
Abbreviation TOD Aay Coc Fcom Ffan Tcond Tevap Tdis Tshell Tft Tsubc,lout Tsubc,gout Taccu,in Taccu,out EXVoutd EXVsubc Icom Ucom,v Tcom Ifan Ufan,v Tcom
Table 5 Results of two models comparison
11hidden neurons 13 hidden neurons
Overall CDR
Undercharge
Normal charge
Overcharge
0.90064
0.85
0.92169
0.93023
0.90372
0.72093
0.95152
0.95122
2
Highlights
(1) Correlation between RCA and features is investigated through ReliefF algorithm (2) Over 90% CDR can be achieved based on 22 features considering two indices (3) The RCA fault can be diagnosed only based on 6-best features (4) Training time of the model-6 is reduced by 98.8%
3
S1359-4311(16)32271-2 http://dx.doi.org/10.1016/j.applthermaleng.2016.10.043 ATE 9245
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
5 July 2016 5 October 2016 8 October 2016
Please cite this article as: S. Shi, G. Li, H. Chen, J. Liu, Y. Hu, L. Xing, W. Hu, Refrigerant charge fault diagnosis in the VRF system using Bayesian artificial neural network combined with ReliefF filter, Applied Thermal Engineering (2016), doi: http://dx.doi.org/10.1016/j.applthermaleng.2016.10.043
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Refrigerant charge fault diagnosis in the VRF system using Bayesian artificial neural network combined with ReliefF filter Shubiao Shi1, Guannan Li1*, Huanxin Chen1*, Jiangyan Liu1, Yunpeng Hu1, Lu Xing1, Wenju Hu2 1
Department of Refrigeration & Cryogenics, Huazhong University of Science and
Technology, Wuhan, China; 2
Beijing Municipality Key Lab of HVAC&R, Beijing University of Civil Engineering
and Architecture, Beijing, China； Abstract A proper refrigerant charge amount (RCA) is critical for a variable refrigerant flow (VRF) system since RCA may affect the operational performance. However, there were few studies of RCA fault for the VRF system in the open literature. Therefore VRF systems are calling for a fault diagnosis strategy. This paper develops a highly efficient fault diagnosis model (FDM), which employs the ReliefF algorithm for feature ranking (FR) and applies the neural network for fault diagnosis. Firstly, the artificial neural network (ANN) model is built on the N-best features data subset and optimized by the Bayesian regularization algorithm. Secondly, the model is verified by testing data subset, the correct diagnosis rates (CDR) using the N-best features data subset can be obtained. The optimal FDM is selected in consideration of CDR and the computational efficiency. Finally, optimal FDM is further optimized by selecting the best hidden neurons. The results show that the CDR of the FDM based on 6-best features is sufficiently high in comparison to the CDR achieved when 22 * Corresponding author. Tel.: +86 27 87558330; Fax: +86 27 87558330. E-mail address: [email protected] (Guannan Li), [email protected] (H. Chen).
features are used, while the training time decreases by 98.8%. Keywords:
Fault
diagnosis;
Variable
refrigerant
flow
system;
ReliefF
algorithm;
Bayesian neural network; Refrigerant charge amount fault 1.
Introduction Reducing the HVAC (Heating, Ventilation, and Air Conditioning) energy
consumption has become one of the prime targets around the world. According to the statistics, energy consumption in commercial and residential buildings accounts for 41.0% of U.S. in 2010, of which 37.0% is used for HVAC systems [1]. As the HVAC energy consumption increased rapidly, it is crucial to develop some powerful policies or techniques for energy efficiency. Developing efficient and reliable HVAC system is one of the major solutions. The VRF system becomes popular in many countries due to various advantages of VRF systems in terms of energy saving potential, better thermal comfort, etc. [2]. And VRF systems equipping with one outdoor unit and multiple indoor units take the refrigerant as the heat transfer fluid. Consequently, the refrigerant flow path is very complex and then leads to a complicated refrigerant pipeline system. In the long-term operation, the VRF system has the potential to leak because the system installs a long pipeline and pressures in the system are usually many times higher than atmospheric ones. On the other hand, the appropriate refrigerant charge amount in the VRF system is determined by the rule-of-thumb. Hence, based on the above analysis, it is a common phenomenon that the VRF system has either undercharge or overcharge fault in the actual system operation. Consequently, the energy efficiency of the VRF system would be reduced due to the inappropriate refrigerant charge [3]. However, there are relatively few researches about the fault diagnosis for VRF system’s RCA in the open literature [4, 5],
especially those from the viewpoint of important features. Therefore, it is very critical to develop a highly efficient RCA fault diagnosis strategy for the VRF system. From the methodology point of view, three diagnosis methods have been proposed [6], namely, model-based, data-driven, and knowledge-based. Model-based method uses the first principle to construct the mathematical model, which does not require a large operation data of the system. Some researchers had conducted some related studies [7-9]. A knowledge-based approach is used to draw conclusions regarding the state of a system through qualitative relationships or knowledge bases. It consists of expert systems [10, 11], pattern recognition [12, 13] and causal analysis. Data-driven methods use the relation between data patterns and fault classes in terms of
modeling
process.
These
methods
differ
from the
model-based
and
knowledge-based methods since they are dimensional reduction techniques based on rigorous multivariate statistics, whereas pattern classifications learn the pattern of fault performance using the training data [14]. To enhance the performance of an individual diagnosis approach, the combination of various techniques has been developed in terms of hybrid FDD approaches [15, 16]. In this paper, we adopt the combination of knowledge-based method and data-driven approaches for RCA fault in the VRF system. The determination of critical input parameters plays an important role for RCA fault diagnosis. Grace and Tassou’s et al. [17] results showed that the superheat and sub-cooling together with discharge temperature are the three most sensitive parameters associated with the RCA. For the VRF system, limited studies on the correlation between feature and RCA were conducted in the past. Thus, the correlation researched through FR algorithm was meaningful. FR was employed to reduce the number of the features so as to improve the efficiency of building the
model. ReliefF, as one of the FR tools, has proven to be effective in removing unimportant features, and increasing computational efficiency [18]. The artificial neural network (ANN) is a kind of data mining technology that has recently been widely used in engineering fields. E.g. Wang and Chen [19] applied the neural network models to diagnose the measurement faults of both the outdoor and supply flow rate sensors. Fan et al. [20] used the neural network combined with wavelet analysis for sensor fault diagnosis, the result showed the model could detect and diagnose fixed biases and the drifting fault of sensors for the local system of AHU. Zhao et al. [21] developed a generalized neural network to predict the mass flow rate in adiabatic capillary tubes and short tube orifices, the result showed that the overall average and standard deviations are 0.75% and 8.27% respectively. As we expected, the ANN presented a good performance in the HAVC application fields. Hence, it was a pretty good tool for fault diagnosis of RCA in the VRF system. Although the ANN has achieved a great success, it still has a risk of over-fitting and poor generalization ability. In this study, the deficiency is addressed by introducing Bayesian regulation. This paper presents a fault diagnosis strategy for VRF system. The strategy has been developed by organically incorporating ReliefF and neural network algorithm. The validation of the strategy using laboratory data has been presented in the paper. 2.
Relief and ReliefF algorithm The Relief algorithm is utilized to discriminate instances that are near to each
other, its simplicity and effectiveness make it possible to become one of the most successful algorithms [22]. However, suggested by Kira [23] et al., it works only for a binary data. The ReliefF (Relief-F) algorithm [24] is introduced to solve the
multi-classification problem. Given a randomly selected instance Ri (1
W [ A] W [ A] diff ( A, Ri , H j ) / ( m k ) j1
C ≠class ( Ri )
[
k
P (C )
diff ( A, R , M (C ))] / (m k) 1 P(class ( R )) i
i
j
j 1
（1） Where function diff(A, Ri , Hj ) calculates the difference between the feature for two instances ( Ri and Hj ), P(class(R1)) is the probability of the label Ri . The numerical feature is expressed as follows: diff（A,R1 ,H1）=
| value （A,R1）- value （A,H 2）| max （A）- min （A）
(2)
Where value(A,R1) means the difference between A and R1，value(A,H2) means the difference between A and H2.
3. 3.1
Machine learning-Bayesian neural network Bayesian neural network ANN is wildly used in engineering applications. Generally, ANN has a
three-layer structure: the input layer, the hidden layer, and the output layer. RCA fault diagnosis is a complex nonlinear issue, which can be approximated by a three-layer ANN based on strong nonlinear mapping capability according to Kolmogorov’s theorem [25]. The neuron numbers in the input layer are equal to the number of input features while such numbers in the output layer are determined by the number of classes. The numbers of neurons in the hidden layer have a substantial impact on the neural model quality, and they are determined according to the Eq. (3). Back propagation structure is illustrated in Fig.1.
N h 2 Ni 1
(3)
Where N h is the number of hidden layer nodes, N i is the number of input layer nodes
[Approximate position of Figure 1]
Two main steps should be carried out to apply a neural network for the fault diagnosis process. Firstly, the data collected from the VRF system is spit into training data and testing data. The neural network is trained using an abundance of training data including both normal and faulty operation conditions. Secondly, the fault diagnosis in the VRF systems is conducted by comparing the objective vectors with the ones derived from the well-trained neural network. And three objective vectors are selected as (1,0,0), (0,1,0) and (0,0,1). When testing data is used to test the FDM, the corresponding output close to (1,0,0), it represents the undercharge operation condition; the output close to (0,1,0) implies the normal condition; and (0, 0, 1)
suggests overcharge operation condition. Despite the fact that the algorithm is very mature in the applications, it can lead to over-fitting and poor generalization capabilities phenomenon. Model optimization is taken by using the proposed Bayesian regularization mainly constraining the size of the network weights. When the weights in a network are kept small, the network response will be smooth. That will improve the generalization ability of the ANN model. Bayesian artificial neural network (BANN) uses the linear combination of the mean square error and the weight for network performance evaluation function, more details can be obtained from the literature [26].
F = bED aEW
(4)
Where ED is the sum of squared errors, EW is the sum of squares of the network weights, a and b are objective function parameters. 3.2 Evaluation of FDM To evaluate the diagnosis performance of the proposed strategy, this study employs two different standard performance evaluation criteria. The standard criteria includes overall correct diagnosis ratio (HR) and single correctly diagnosis ratio (CR). HR is defined as the percentage of predicted correct samples and all the actual samples. CR represents individual group diagnosis rate defined as the percentage of correctly classified samples and all the samples of each class under investigation. The fault diagnosis of refrigerant charge is mainly discussed in this paper. Table 1 is a confusion matrix (ConfMat) for the three-class case. For CL11 , the first subscript (1) indicates the first actual category and the second subscript (1) represents the first predicted category. Where CL11 (Class1) denotes the number of undercharge samples that are successfully diagnosed. And the ML12 implies the number of samples misdiagnosed as normal charge. And the ML13 reveals the number of the samples
misdiagnosed as the overcharge. HR, CR1 (correctly diagnosis ratio for undercharge fault), CR2 (correctly classification ratio for normal condition) and CR3 (correctly diagnosis ratio for overcharge fault) are expressed as the following equations:
HR CL11 CL22 CL33 / Total
(5)
CR1 undercharge CL11 / CL11 ML12 ML13
(6)
CR2 normalcharge CL22 / CL21 ML22 ML23
(7)
CR3 overcharge CL33 / ML31 ML32 CL33
(8)
[Approximate position of Table 1]
4.
Experimental setup and fault diagnosis framework
4.1 Description of the System The experimental setup is employed to measure VRF performance under different refrigerant charge levels. Fig.2 shows a schematic of the experimental setup, which presents the major sensors [27]. The studied system is an R410A 31.5 kW VRF system with the nominal charge of 9.9 kg. The rated capacity of the outdoor unit and the indoor unit are 28.0 kW and 29.7KW respectively. More details about the system can be found in Li’s and Liu’s researches [27, 28].
[Approximate position of Figure 2]
All the heating condition experiments are accomplished in the standard psychrometric chamber. The psychrometric chamber consists of an indoor room equipped with five indoor units and an outdoor room allocated with one outdoor unit.
In order to develop RCA fault diagnosis model, 9 groups of the experiment are conducted under different refrigerant charge levels ranged from 63.0% to 130.0%, as shown in Table 2. For each group of charge level, three different heating conditions based on different outdoor temperature(– 7℃, 2℃, 7℃respectively) are implemented. Table3 demonstrates the detailed description. Each heating condition includes 3 indoor units operating conditions, i.e. one unit operating, three units operating and five units operating. For each testing condition, the fan speeds (including one outdoor fan and 5 indoor fans) are almost kept constant while the compressor speed is not fixed. The compressor speed and the EEV openings are controlled to adjust the refrigerant flow rate to meet the cooling load (The engineering unit of the compressor speed is the rpm). The compressor operation frequency varies from 0 to 90. The VRF system can still maintain its operation when there is a small amount of undercharge and overcharge fault. Kim and Braun [3] have indicated that the 25% reduction of refrigerant charge leads to energy efficiency decrease and capacity degradation. The refrigerant charge levels are labeled according to the important reference. In this study, 63.0% and 75.4% charge levels are treated as under charge fault, 130.0% charge level is used as overcharge fault.
[Approximate position of Table 2]
[Approximate position of Table 3]
The air temperature and relative humidity of the two rooms are controlled to the test conditions as shown in Table 3, according to adjustment of the proportion integration differentiation (PID) control strategy. To monitor the operation of the VRF
system, a large number of sensors and controllers have been installed. Table 4 lists 22 chosen variables in detail, mainly include temperature variables, frequency variables, current variables, voltage variable and control variables. These features are used for fault diagnosis of VRF refrigerant charge.
[Approximate position of Table 4]
4.2 Data description The VRF system connects an outdoor unit to five indoor units, and it operates under three different heating conditions with 3 indoor units operating conditions. Each heating modes were recorded at 15 seconds intervals in the controller of the VRF system. Each testing lasted for at least 45 minutes. All the experimental data were collected by the data acquisition system. In order to improve the efficiency of simulation and modeling, 3995 data samples was selected from the full data set at the same interval. The experimental data subset with the ratio of 3:1 was randomly split into training data and testing data, respectively. 4.3 Data normalization The observed sample matrix Z ( Z R M N ) consists of N observations and M features. The normalized data matrix Y is obtained by Eq. (9) and (10).
Maxi max( Zi , j ) Mini min( Zi , j ) Y ymax ymin Z ji Mini / Maxi Mini ymin
(9)
(10)
Where Z i , j is an element of matrix Z, Maxi is the maximum of the ith feature.
Mini is the minimum of the ith feature, ymax and ymin are 1,-1 respectively, Y is the normalized matrix.
[Approximate position of Figure 3]
4.4 Diagnosis Scheme of VRF refrigerant charge fault Fig.3 shows the logic diagram of fault diagnosis for VRF refrigerant charge fault. It is composed of three parts: the features ranking, the fault diagnosis, the model selection. The first part is FR composed of the weight calculation and the features ordering. The second part is to build a model for RCA fault diagnosis with BANN algorithm. The third part is model selection and model optimization in consideration of overall CDR and single CDR. 5.
Result and discussion
5.1 Result of FR based on ReliefF The major task of ReliefF algorithm was to iteratively estimate the feature weights according to their ability to discriminate between neighboring patterns. The feature weights were arranged in ascending order as shown in Fig.4. Among them, the higher the weight, the higher correlation between the features and RCA. It was worth pointing out that there were three feature weight (Tdis, Tcom, Ucom) larger than the others. It meant that the features had the higher discriminative ability in comparison to other features. Sun [29] pointed out that the Tdis was obviously the most significant feature for modeling. So the result of the FR can be credible. Meanwhile, from the perspective of the physical principles, it could be further deduced that when RCA fault occurred in the VRF system, the compressor discharge temperature, the compressor module temperature and compressor bus-voltage would undoubtedly deviate from the normal operation conditions obviously. When the VRF system had the undercharge fault, the discharge temperature would have a tendency to rise, while
the discharge temperature would be declined for overcharge fault. The change trend of module temperature was identical with the discharge temperature tendency but was contrary to the bus-voltage of the compressor. It was also reasonable according to our knowledge of VRF system. From the perspective of weights, the three features were better input parameters for FDM than other features.
[Approximate position of Figure 4]
Fig.4 showed that 13 feature weights were closed to zero, which signified that the 13 features did not seriously deviate from the normal condition when the fault occurred. It meant that they were not good indicators to detect the RCA fault. However, the FDM, combined these features, may obtain a comparatively satisfying diagnosis performance. Fig.4 showed the 5 feature weights selected from 22 feature weights were lower than others evidently in the diagram, which indicated these features may be meaningless to establish a model for fault diagnosis. Therefore, they may be removed considering operational efficiency. 5.2 Result of BANN model for fault diagnosis The performance of the classification, in terms of accuracy, for different number of N-best features (N=1, 2, 3..., 22) were presented in Fig. 5-Fig.8. Fig.5 represented the overall CDR curve, and the Fig.6, 7 and Fig.8 represented the CDR curve for undercharge, normal charge and overcharge condition respectively. A random process was normally involved in the training of an ANN model, for example, training and testing sample sets were obtained by random sampling. It led to a result that the CDR of the trained model might not be the same at all times, as it depended on the quality of the training samples. Thus we carried out 10 trials of
model training and testing. Then, the average CDR was seen as the model diagnosis performance. As shown in Fig.5, the column height represented the averaged value of CDR, and the error bars presented the standard errors of 10 trials for CDR. As shown in Fig.5, the BANN fault diagnosis model could achieve a high overall CDR with a small data subset contained a few best features. Specifically, model-6 (model based on the 6-best features as the input parameters) could reach a percentage of 90.3% CDR, which was sufficiently high in comparison to the accuracy achieved when model-22 was used (model based on the all features as the input parameters). And the CDR could reach 94.6% with a subset of 17-best features, the CDR kept unchanged until all features were used.
[Approximate position of Figure5]
[Approximate position of Figure 6]
[Approximate position of Figure 7]
[Approximate position of Figure 8]
It was worth pointing out that a satisfactory model not only had a good diagnosis performance in overall CDR, but possessed a satisfying accuracy for each single class. Diagnosis performances of the single classes were analyzed, the CDR curves for three classes were shown in Fig.6 to Fig.8. Fig.6 plotted the CDR for different number of N-best features, when the VRF system had undercharge fault. Firstly, when the number of the best features was over 8, the CDR curve was not always increasing.
There is a slight fluctuation in the local, but the general trend of the fault diagnosis curve was rising with the increase of features. The local fluctuation of fault diagnosis curve could be explained by reason of dual influence of redundancy and weight. As the best features increased, the subset had more noise or redundancy, and the weight behind gradually became smaller. When the test subset was used to test the neural network model, the CDR were 62.40%, 93.04% and 87.12% respectively, using three parameters of the compressor (Tdis, Tcom, Ucom). Compared with the CDR of normal and overcharge fault, the CDR of undercharge was relatively low, attributing to that the three parameters did not have a strong discriminative ability between undercharge condition and normal condition. Therefore, the more features were used, the more information employed for undercharge fault diagnosis would be. Similarly, the more information added to neural network model in the FDD process, the more accurate the results would be. Hence, the CDR curve would rise with the increase of features; it was determined by the richness of information [30]. When 6-best features were used for fault diagnosis, the model only achieved 72 percent of correctly diagnosis rate, the accuracy was still needed to improve. As shown in Fig.7 to Fig.8, the subset redundancy made CDR fluctuate starting from the sixth-best feature for the normal charge, while starting from the seventh-best feature for the overcharge [18]. The CDR curves were fluctuant with the increase of features, which could be explained that the accuracies were determined by the redundancy. That was different from undercharge fault. The CDR of the model based on the 6-best features was 95.5% for the normal charge, while it was 93.3% for the overcharge. In contrast to correctly diagnosis rate of normal and overcharge fault, there was not a very satisfying diagnosis performance for undercharge fault based on model-6.
The main reason was that the discharge temperature had a strong discriminate ability for the overcharge, while it failed in undercharge. And the six best features were Tdis , Tcom , U com , Tcond , Tshell and
T fan respectively.
In order to solve the problem of
the relatively low CDR of undercharge fault compared with normal and overcharge fault, the optimization procedure was taken for the model. The most important model parameters were the weight and the number of the hidden layer nodes respectively. Model weight had been optimized by Bayesian regularization; the hidden layer nodes played a very critical role and determined the network structure. In this study, the number of hidden neurons for the model-6 was investigated ranged from 10 to 16 (i.e. 13 ± 3). The result was shown in Fig.9, and the performances of the models with different numbers of hidden neurons were comparable to each other. It was indicated that the number of hidden neuron within the range was insensitive to the model performance from the viewpoint of overall CDR. Thus the number of hidden neurons determined by the Eq. (3) was justified to be adopted [31].
[Approximate position of Table 5]
The CDRs of the models with 11 and 13 hidden neurons were compared to each other. Result of two models comparison was listed in Table 5. It showed that the overall CDR basically remained unchanged, however the CDR of undercharge fault had a larger increase for 11 hidden neurons, which was greatly improved from 72.0% to 85.0%, while it had not a great impact on the CDR of normal charge and overcharge. Therefore, the overall diagnosis performance of the model with 11 hidden neurons was better in consideration of single CDR and overall CDR.
[Approximate position of Figure 9]
As for the computation time, it could also be noticed that the less features added into the model as the input parameters, the less the time consumed by model training. The model-6 only consumed 133.5s, while the 3874.3s would be consumed for model-22 (All the programs were run on a desktop with a CPU of Intel Core(TM) i5-4590 (3.3 GHz), a memory of 8.00 GB and an operating system of Windows 7). Time-consuming difference was so large, it could be explained as the following: when the 6-best features were used for the input of the model, 13 hidden layer nodes were needed according to the equation (3). At this moment, it would result in 78 weights and 13 thresholds between input layer and hidden layer, and 39 weights between the hidden layer and output layer. Total unknown parameters reached 130. While 22 features were applied for the input of the model, the 45 hidden layer nodes were necessary. And totally unknown parameters were 1170. Therefore, the complexity of the model had increased dramatically. Time consuming for ANN training had also been increased dramatically. The Fig.10 presented the unknown numbers of parameters and operation time under different numbers of features. It was easy to deduce that the model-6 saved 98.8% of time, compared to the model-22.
[Approximate position of Figure 10]
6.
Conclusion This paper presents a highly efficient fault diagnosis model, which employs
ReliefF algorithm for FR and applies the neural network to classify faults. Weight of each feature is calculated based on the ReliefF algorithm, then, we build models based
on different numbers of N-best features, and data subsets redundancy is further study by analyzing the CDR curves. Finally, the model-6 with the optimal hidden nodes is obtained, and the model-6 has a satisfying fault diagnosis performance in the aspects of CDR and computational time. Conclusions are as follows: 1) The CDR of the model-22 can reach more than 90% considering the overall CDR and the single CDR. 2) 6-best features are selected by ReliefF algorithm, and the model-6 can obtain a sufficiently high CDR in comparison to the accuracy achieved when all features are used. However, the training time can be reduced by 98.8%, which greatly improve the operation efficiency. 3) The diagnosis performance for undercharge fault has been improved by optimizing the hidden layer nodes, and the 11 nodes are determined by considering single CDR and overall CDR. The combination of ReliefF algorithm and BANN has been proved to be an efficient strategy for fault diagnosis in the VRF system, meanwhile, it can greatly shorten the operation time and save initial cost on sensors. Acknowledgment The authors gratefully acknowledge the support of National Natural Science Foundation of China (Grant 51576074 and 51328602), Beijing Key Lab of Heating, Gas Supply, Ventilating and Air Conditioning Engineering (Grant NR2016K02).
Nomenclature Aay
Allocation ability [kW]
ANN
Artificial neural network
BANN
Bayesian artificial neural network
Coc
Current operational capability [kW]
C
A class
CDR
Correct diagnosis rate
EXVoutd
Electronic expansion valve opening corresponding to outdoor unit
EXVsubc
Electronic expansion valve opening corresponding to the sub-cooler
F
Error function
FDM
Fault diagnosis model
Fcom
Compressor operating frequency [HZ]
Ffan
Outdoor fan operating frequency [HZ]
FR
Feature ranking
HVAC
Heating, Ventilation and Air Conditioning
I com
Compressor electric current [A]
I fan
Outdoor fan electric current [A]
P(C)
The probability of class C
RCA
Refrigerant charge amount
Taccu ,in
Accumulator inlet pipe temperature [℃]
Taccu ,out
Accumulator outlet pipe temperature [℃]
Tcom
Module temperature of the compressor [℃]
Tcond
Condensing saturation temperature [℃]
Tdis
Compressor discharge temperature [℃]
Tevap
Evaporating saturation temperature [℃]
T ft
Defrost temperature [℃]
T fan
Fan temperature [℃]
TOD
Outdoor temperature [℃]
Tshell
Compressor shell temperature [℃]
Tsubc ,lout
Sub-cooler outlet pipe temperature (liquid)[℃]
Tsubc , gout
Sub-cooler outlet pipe temperature(gas) [℃]
U com,v
Compressor bus-voltage [V]
U fan ,v
Outdoor fan bus-voltage [V]
VRF
Variable refrigerant flow
W
Weight of feature
A
A feature
EW
The sum of squares of the network weights
a ,b
Objective function
ED
The sum of squared errors
Nh
The number of hidden layer nodes
Ni
The number of input layer nodes
ymax , ymin
1 and -1 by default
Z ji
An element of matrix Z
Maxi
The maximum of the sample for the ith feature
Mine
The minimum of the sample for the ith feature
Subscript accu
Accumulator
com
Compressor
cond
Condenser
dis
Compressor discharge
evap
Evaporator
fan
Outdoor fan
outd
Outdoor unit
shell
Compressor shell
in
Inlet
out
Outlet
v
Voltage
subc
Sub-cooler
References: [1] K. J, Buildings energy data book, US Department of Energy, 2011. [2] X. Zhao, M. Yang, H. Li, Field implementation and evaluation of a decoupling-based fault detection and diagnostic method for chillers, Energy and Buildings. 72 (2014) 419-430. [3] W. Kim, J.E. Braun, Evaluation of the impacts of refrigerant charge on air conditioner and heat pump performance, International Journal of Refrigeration. 35 (2012) 1805-1814. [4] X. Lin, H. Lee, Y. Hwang, R. Radermacher, A review of recent development in variable refrigerant flow systems, Science and Technology for the Built Environment. 21 (2015) 917-933. [5] J. Liu, Y. Hu, H. Chen, J. Wang, G. Li, W. Hu, A refrigerant charge fault detection method for variable refrigerant flow (VRF) air-conditioning systems, Applied Thermal Engineering. 107 (2016) 284-293. [6] H. Li, J.E. Braun, A methodology for diagnosing multiple simultaneous faults in vapor-compression air conditioners, HVAC&R Research. 13 (2007) 369-395. [7] T.M. Rossi, J.E. Braun, A Statistical, Rule-Based Fault Detection and Diagnostic Method for Vapor Compression Air Conditioners, HVAC&R Research. 3 (1997) 19-37. [8] H. Yoshida, S. Kumar, Development of ARX model based off-line FDD technique for energy efficient buildings, Renewable energy. 22(2001) 53-59. [9] J. Cui, S. Wang, A model-based online fault detection and diagnosis strategy for centrifugal chiller systems, International Journal of Thermal Sciences. 44 (2005) 986-999. [10] P. Gruber, S. Kaldorf, Practical experiences from developing and implementing
an expert system diagnostic tool / Discussion, ASHRAE Transactions. 108 (2002) 826-840. [11] Y. Qian, X. Li, Y. Jiang, Y. Wen, An expert system for real-time fault diagnosis of complex chemical processes, Expert Systems with Applications. 24 (2003) 425-432. [12] H. Han, B. Gu, J. Kang, Z.R. Li, Study on a hybrid SVM model for chiller FDD applications, Applied Thermal Engineering. 31(2011) 582-592. [13] K. Sun, G. Li, H. Chen, J. Liu, J. Li, W. Hu, A novel efficient SVM-based fault diagnosis method for multi-split air conditioning system’s refrigerant charge fault amount, Applied Thermal Engineering. 108(2016) 989-998. [14] Y. Yu, D. Woradechjumroen, D. Yu, A review of fault detection and diagnosis
methodologies on air-handling units, Energy and Buildings. 82(2014) 550-562. [15] S. Wu, J. Sun, Cross-level fault detection and diagnosis of building HVAC systems, Building and Environment. 46 (2011) 1558-1566. [16] 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, Building and environment. 45(2010) 2698-2708. [17] I.N. Grace, D. Datta, S.A. Tassou, Sensitivity of refrigeration system performance to charge levels and parameters for on-line leak detection, Applied Thermal Engineering. 25 (2005) 557–566. [18] H. Han, B. Gu, T. Wang, Z. Li，Important sensors for chiller fault detection and diagnosis (FDD) from the perspective of feature selection and machine learning, International journal of refrigeration, 34 (2011) 586-599. [19] S. Wang, Y. Chen, Fault-tolerant control for outdoor ventilation air flow rate in buildings based on neural network, Building and Environment. 37 (2002)
691-704. [20] 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, Building and Environment. 45 (2010) 2698-2708. [21] L. Zhao, C. Zhang, L. Shao, L. Yang, A generalized neural network model of refrigerant mass flow through adiabatic capillary tubes and short tube orifices, Journal of Fluids Engineering-Transactions of the ASME. 129 (2007) 1559-1564. [22] Y. Sun, D. Wu, A RELIEF Based Feature Extraction Algorithm., SDM, 2008, pp. 188-195. [23] K. Kira, L.A. Rendell, A practical approach to feature selection, Proceedings of the ninth international workshop on Machine learning, 1992, pp. 249-256. [24] F. Bergadano, L. De Raedt, I. Kononenko, Estimating attributes: Analysis and extensions of RELIEF, in: F. Bergadano, L. De Raedt (Eds.), Springer Berlin Heidelberg, 1994, pp. 171-182. [25] F. Wang, The use of artificial neural networks in a geographical information system for agricultural land-suitability assessment, Environment and planning A. 26(1994) 265-284. [26] F.D. Foresee, M.T. Hagan, Gauss-Newton approximation to Bayesian learning, IEEE, 1997, pp. 1930-1935. [27] G. Li, Y. Hu, H. Chen, L. Shen, H. Li, J. Li, W. Hu, Extending the virtual refrigerant charge sensor (VRC) for variable refrigerant flow (VRF) air conditioning system using data-based analysis methods, Applied Thermal Engineering. 93 (2016) 908-919. [28] J. Liu, Y. Hu, H. Chen, J. Wang, G. Li, W. Hu, A refrigerant charge fault
detection method for variable refrigerant flow (VRF) air-conditioning systems, Applied Thermal Engineering. 107 (2016) 284–293. [29] K. Sun, G. Li, H. Chen, J. Li, J. L, W. Hu, A novel efficient SVM-based fault diagnosis method for multi-split air conditioning system’s refrigerant charge fault amount, Applied Thermal Engineering, 108 (2016) 989-998. [30] Y. Zhao, F. Xiao, S. Wang, An intelligent chiller fault detection and diagnosis methodology using Bayesian belief network, Energy and Buildings. 57 (2013) 278-288. [31] P . Leung, E. Lee, Estimation of electrical power consumption in subway station design by intelligent approach, Applied energy. 101 (2013) 634-643.
Figure Captions
Fig.1 Neural network back propagation structure Fig.2 A schematic of the experimental setup Fig.3 Fault diagnosis Scheme of VRF refrigerant charge Fig. 4 Weights by the ReliefF for the features Fig.5 The overall CDR for different number of features Fig.6 CDR for different number of features (under charge condition) Fig.7 CDR for different number of features (normal condition) Fig.8 CDR for different number of features (overcharge condition) Fig.9 Performances of the models under different numbers of hidden neurons Fig.10 Numbers of parameters and operation time under different numbers of features
Fig.1 Neural network back propagation structure
Fig.2 A schematic of the experimental setup
Operation Operation data data under under normal&fault normal&fault conditions conditions
Variables selection
Weight Weight calculation calculation using using ReliefF ReliefF Features Features sort sort according according to to weight weight N=0;N=N+1； N=0;N=N+1； The The N-best N-best features features
Data Data selection selection
Training Training data data
Normalize Normalize
Neural Neural network network model model
Fault diagnosis Testing Testing data data
Normalize Normalize
Fault Fault diagnosis diagnosis
No
Bayesian Regularization Improve Improve the the generalization generalization ability ability of of the the model model
Save Save FDD FDD result result
N>22? N>22?
Yes Selection Selection of of model model Model Model optimization optimization
Total Total fault fault diagnosis diagnosis rate rate curve curve
Select FDD model
Fig.3 Fault diagnosis Scheme of VRF refrigerant charge
Fig. 4 Weights by the ReliefF for the features
Fig.5 The overall CDR for different number of features
Fig.6 CDR for different number of features (under charge condition)
Fig.7 CDR for different number of features (normal condition)
Fig.8 CDR for different number of features (overcharge)
Fig.9 Performances of the models under different numbers of hidden neurons
Fig.10 Numbers of parameters and operation time under different numbers of features
Table Captions
Table 1 ConfMat for the three-class case Table 2 Nine groups of RCLs and corresponding class Table 3 Three different heating conditions: the low, the medium and the nominal temperature heating modes Table 4 Twenty-two features Table 5 Results of two models comparison
Table 1 ConfMat for the three-class case Predicted Class
Actual Class
Undercharge
Normal charge
Overcharge
Undercharge
CL11
ML12
ML13
Normal charge
ML21
CL22
ML23
Over charge
ML31
ML32
CL33
Table 2 Nine groups of RCLs and corresponding class Test index
Refrigerant charge levels (%)
Class
1
63.0
undercharge
2
75.4
undercharge
3
79.8
normal charge
4
84.8
normal charge
5
95.7
normal charge
6
103.7
normal charge
7
111.7
normal charge
8
120
normal charge
9
130
overcharge
Table 3 Three different heating conditions: the low, the medium and the nominal temperature heating modes Indoor room inlet
Outdoor room inlet
air parameters
Group
air parameters
Test mode index
Dry-bulb
Wet-bulb
Dry-bulb
Wet-bulb
Temp(℃)
Temp(℃)
Temp(℃)
Temp(℃)
10
6
-7
-8
15
5
2
1
20
8
7
6
Low temperature 1 heating Medium 2
temperature heating Nominal
3
temperature heating
Table 4 Twenty-two features No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Name of feature Outdoor temperature Allocation ability Current operational capability Compressor operating frequency Outdoor fan operating frequency Condensing saturation temperature Evaporating saturation temperature Compressor discharge temperature Compressor shell temperature Defrost temperature Sub-cooler outlet pipe temperature (liquid) Sub-cooler outlet pipe temperature (gas) Accumulator inlet pipe temperature Accumulator outlet pipe temperature Electronic expansion valve opening corresponding to outdoor unit Electronic expansion valve opening corresponding to the sub-cooler Compressor electric (current) Compressor voltage Compressor module temperature Outdoor fan electric current Outdoor fan voltage Module temperature of the compressor
1
Abbreviation TOD Aay Coc Fcom Ffan Tcond Tevap Tdis Tshell Tft Tsubc,lout Tsubc,gout Taccu,in Taccu,out EXVoutd EXVsubc Icom Ucom,v Tcom Ifan Ufan,v Tcom
Table 5 Results of two models comparison
11hidden neurons 13 hidden neurons
Overall CDR
Undercharge
Normal charge
Overcharge
0.90064
0.85
0.92169
0.93023
0.90372
0.72093
0.95152
0.95122
2
Highlights
(1) Correlation between RCA and features is investigated through ReliefF algorithm (2) Over 90% CDR can be achieved based on 22 features considering two indices (3) The RCA fault can be diagnosed only based on 6-best features (4) Training time of the model-6 is reduced by 98.8%
3