Studies on the online intelligent diagnosis method of undercharging sub-health air source heat pump water heater

Applied Thermal Engineering 169 (2020) 114957

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Studies on the online intelligent diagnosis method of undercharging subhealth air source heat pump water heater

T

Zhe Suna, Huaqiang Jina,c, Jiangping Gua,c, Yuejin Huanga,c, Xinlei Wangb, Hua Yangc,d, ⁎ Xi Shena,c, a

School of Mechanical Engineering, Zhejiang University of Technology, 288 Liuhe Road, Hangzhou 310023, China Department of Agricultural and Biological Engineering, University of Illinois at Urbana-Champaign, 1304 W. Pennsylvania Avenue, Urbana, IL 61801, United States c Joint Laboratory of Refrigeration Compressor Reliability Evaluation, Zhejiang University of Technology, Ltd, 288 Liuhe Road, Hangzhou 310023, China d JiaXiPera Compressor Co., Ltd, 40 Baile Road, Jiaxing 314011, China b

H I GH L IG H T S

the subhealth operation concept of heat pump systems to distinguish the transition state between normal and faulty; • Proposed a diagnosis method for undercharging subhealth using RNN and expert rules; • Proposed • The diagnostic method can be well applied to the unsteady system, which means the method is an online diagnosis method.

A R T I C LE I N FO

A B S T R A C T

Keywords: Sub-health ASHPWH Undercharge Online diagnosis RNN Deep learning

Due to its significant energy savings, the use of air source heat pump water heater (ASHPWH) has increased rapidly in recent years. Pipeline seal issues, improper installation, and other reasons can cause refrigerant leakage. Minimal refrigerant leakage causes slight changes in system characteristics and is difficult to notice, thus people always determine the system to be normal. Refrigerant leakage can cause the system to deviate from the reasonable working conditions for a long time, resulting in the decline of system performance, efficiency drop, and increase in energy consumption. In this paper, the concept of sub-health operation of heat pump systems is proposed to distinguish the transition state between normal and faulty. Based on this concept, the research on the changes of sub-health is proposed with an online intelligent diagnosis method. This diagnosis method utilizes the data of normal system operations to train a diagnostic model, and it does not need fault marking data, which reduces the difficulty of data acquisition. The proposed method can achieve accurate fitting of unsteady systems with resistance to heat transfer environment fluctuations and is better suited for online diagnosis. It has been verified by experiments that this method can achieve online diagnosis of refrigerant leakage of ASHPWH, and it is a feasible and efficient sub-health diagnosis method.

1. Introduction Energy shortages have become a global issue, and building energy consumption contributed more than half to the increased total energy usage [1], half of which includes the energy used for heating, ventilation, and air-conditioning (HVAC) systems [2]. Therefore, energy saving in heating and ventilation equipment has become the focus of research in the field of energy conversion. Regarding another global issue, environmental protection is also receiving widespread attention. China has suffered from severe hazy weather related to PM2.5 (The particulate matter in air with equivalent diameter smaller than 2.5 μm,

⁎

which is very harmful to human health and air quality) since 2012 [3]. It has been found that 22.4% of the PM2.5 concentration in Beijing (capital of China) is caused by coal consumption and space heating claims with 92% the consumption of coal in Beijing rural region [4]. To combat this problem, the Chinese government has promoted ‘coal-toelectricity’ policies [5]. An air source heat pump is usually recommended as an alternative to the original coal-fired heating because of its significant energy savings. Air source heat pump water heaters (ASHPWH), used as heating equipment, can provide domestic hot water supply, and have great energy saving potential. Due to the large amount of use, the efficient

Corresponding author at: School of Mechanical Engineering, Zhejiang University of Technology, 288 Liuhe Road, Hangzhou 310023, China. E-mail address: [email protected] (X. Shen).

https://doi.org/10.1016/j.applthermaleng.2020.114957 Received 2 September 2019; Received in revised form 12 January 2020; Accepted 14 January 2020 Available online 16 January 2020 1359-4311/ © 2020 Elsevier Ltd. All rights reserved.

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Nomenclatures

Tdis Tsuc Tc Te Tin|c Tout c Tin e Tout e pdis psuc Toutdoor TTank Tsc Tsh S υ r ηm ρ V Q̇ h

A ΔT ṁ Cd Ch R n M

discharge temperature suction temperature condensing temperature evaporating temperature temperature of condenser inlet temperature of condenser outlet temperature of evaporator inlet temperature of evaporator outlet discharge pressure suction pressure outdoor temperature temperature of water tank temperature of sub-cooling temperature of superheat speed of compressor opening of expansion valve thermal resistance volumetric efficiency density volume heat transfer rate heat transfer coefficient

heat transfer area temperature difference mass flow rate section coefficient constant coefficient residual number of molecules molar mass

Subscripts ts a r c e in out pre mea sh sc

two-phase region air side refrigerant side condenser evaporator inlet outlet predicted measured superheat subcooling

designed value is called sub-health operating state. The factors that lead to sub-health of the system include: refrigerant leakage, reduced condenser heat transfer, reduced evaporator heat transfer, compressor leakage, compressor performance degradation, liquid line restrictions, and non-condensable gas in the refrigerant, etc. This definition differs from the traditional definition of faults. Traditional definitions are defined by the cause, but the sub-health is defined by the effect on system performance and can be better integrated with work energy savings. The authors found that in parts of China, more than 30% of the actual operation heat pump systems are in sub-health state, which proves that such phenomena are very common. In order to better suppress this phenomenon, it is necessary to conduct theoretical research on this mechanism. Because of the many factors affecting subhealth, there are many dimensions of mechanism research. This paper focuses on the undercharge sub-health.

operation of the technology is very important. When the system is poorly sealed and initial installation is not proper, there will be a slight leakage of refrigerant in the ASHPWH, and the system will be undercharge resulting in increased system energy consumption, reduced efficiency, and reduced performance. Unfortunately, such phenomena are difficult to be observed by users. Related studies have shown that timely detection and diagnosis of refrigerant leakage can not only achieve good performance but also reduce system energy consumption by about 15–30% [6]. Therefore, research on online intelligent diagnostic technology for refrigerant leakage of ASHPWH is very necessary. In order to accurately diagnose the leakage of refrigerant, it is necessary to thoroughly study the variation trends of system characteristics and to find out the mechanism of the influence of refrigerant leakage on the system.

1.1. The definition of sub-health in heat pump system and the necessity of its research

1.2. Related work

Through the study of system variation characteristics, the authors found that the system needs to consume more electric energy to achieve fixed heating capacity after the refrigerant leaks, so the energy efficiency ratio is reduced, which is the key reason for the increase of system energy consumption. Although this operating state can achieve the required heating capacity, the running performance is lower than the ideal value of the design. In the current refrigeration research field, such phenomena and other types of faults, such as compressor stall, control system out of control, fan stall, etc., are collectively referred to as system faults. The authors believe that this classification method is not reasonable. Once the latter occurs, the system cannot work normally and must be repaired in time. However, phenomena such as early stage refrigerant leakage and early stage heat exchanger fouling come only at the expense of some energy consumption and do not affect normal use. There is a clear difference between them. The system appears to be very similar to the terminology of ‘sub-health’ in medical science. Based on the above reasons, the author refers to this type of operating state of the heat pump system as ‘sub-health operation’, and the following definition is given: when the heat pump system achieves fixed heating capacity under specific environmental conditions and specific loads, the operating state with lower energy efficiency than the

1.2.1. The effect of undercharge on system characteristics ASHPWH is essentially a refrigeration system, and the effect of undercharge in these systems has been studied. Kim et al. [7] proposed that the refrigerant charge level is a key factor in the optimization of the heat pump system, and has an important impact on the condensation temperature and the degree of subcooling. This paper also proposed that there is an optimal refrigerant charge level, and the system has the highest COP at this level. Siang et al. [8] performed research on the performance of single-duct portable propane air conditioning system under different refrigerant charge levels. In the variation range of ambient temperature from 20℃ to 30℃, the characteristics of refrigerant temperature, mass flow rate, and maximum flow rate were studied, and the cooling capacity, power consumption, and energy efficiency ratio were analyzed. Mehrabi et al. [9] conducted research on the performance of an air conditioning heat pump with a fixed orifice and thermostatic expansion valves under different refrigerant charge levels, and the changes of parameters, such as undercooling, superheat, discharge temperature, condensation temperature etc., were summarized and analyzed. Li et al.[10] performed research on the influence of different charging levels on the characteristics of electric vehicle air conditioning heat pumps. The pressure-enthalpy diagram was drawn by combining 2

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accuracy. Li et al. [24] proposed a deep neural network based fault diagnosis method for centrifugal chillers and shows good results. But reliance on large amounts of labeled data is also the disadvantage of this paper. The author previously proposed a convolution-sequence model based on deep learning for heat pump gradual fault diagnosis [25]. This method has high diagnostic accuracy for multiple faults, but slow diagnostic speed and heavy calculation limit its application in small, simple and low costs refrigeration systems, such as ASHPWHs. And reliance on large amounts of labeled data is also the disadvantage of this method. By analyzing the above research status, it was determined that there are not many studies on air source heat pump water heaters, and there are some shortcomings in the existing charge fault diagnosis methods. Mainly, these include: 1. Existing diagnostic methods are oriented to stable systems, but the actual operating system is often in an unstable state due to fluctuations in environment and operating conditions, which limits the application of existing methods; 2. Most intelligent diagnostic methods rely on a large amount of labeled data, but labeled data is extremely scarce at the moment, and the acquisition cost is high, which limits the application of intelligent methods; 3. The existing studies mainly focus on the diagnosis effect of different charge levels, respectively. However, in an actual system, refrigerant is continuously leaking, and the online diagnostic studies for continuously leaking systems have not been reported; 4. The existing methods require large number of measurement parameters and sensing devices. This is applicable to large-scale air conditioning systems, but it is not suitable for ASHPWH with limited sensors.

experimental research, and the variation of the parameters was analyzed. Based on the above research status, it was found that the existing research on the influence of refrigerant leakage on system characteristics is limited, and the existing research mainly uses experimental methods to observe the variation of parameters under different charge levels and summarize the conclusions. Few studies analyze the theory of the causes of the variation, and this is not beneficial for the further research of sub-health formation mechanism of heat pumps. 1.2.2. The related diagnosis methods There have been related studies on the diagnosis methods for charge fault. Tassou and Grace [11] used the artificial intelligence method to achieve earlier diagnosis of the refrigerant leakage fault of the vapor compression refrigeration system. The artificial neural network was introduced into the field of refrigerant charge fault diagnosis for the first time, and it achieved good results. Yoo et al. [12] proposed a diagnosis method for refrigerant leakage for domestic air conditioners with limited sensor installations. This method obtains the evaporation temperature and condensation temperature by installing a temperature sensor in the middle portion of the heat exchanger, thereby saving the number of pressure sensors and greatly reducing the cost. Liu et al. [13] proposed a PCA-EWMA-based refrigerant leakage fault diagnosis method. Based on the PCA method diagnosis, the EWMA method was used to enhance the diagnostic accuracy and efficiency, achieving good results. Sun et al. [14] proposed an SVM-based method for the charge level diagnosis in variable refrigerant flow systems. This method extracts features with a correlation analysis method, which greatly improved the immunity. Sun et al. [15] used a hybrid ICA-BPNN-based method to perform the diagnosis of refrigerant charge fault in variable refrigerant flow systems. ICA is used for fault detection, and BPNN is used for fault diagnosis. This method has achieved good results. Hu et al. [16] used a Bayesian neural network merged expert rules to realize the diagnosis of charge fault in variable refrigerant flow systems. Then, verification studies were conducted on systems with different charge levels. Shi et al. [17] proposed a PCA-based method merged dual neural network for charge fault diagnosis. This method used PCA to achieve 97% information extraction, and a performance improvement of 9% was achieved by verification with three data sets. Yu et al. [18] used the expert modification C5.0 decision tree to diagnose the charge fault of variable refrigerant flow systems, and the temperature differential variables were used to improve the diagnosis result. The results of the C5.0 decision tree using temperature differential variables shows fault diagnosis error rates under expert experience guidance are 10% lower than without expert experience. Some studies on the others fault diagnosis and control strategy are also relevant. Zhou et al. [19]earlier applied artificial neural networks to HVAC control to replace PID controller. This study successfully proved that the machine learning method represented by ANN has higher advantages than traditional methods. Zogg et al.[20] proposed a fault diagnosis method using parameter identification and clustering methods. This method earlier realized the intelligent fault diagnosis of the heat pump system, but clustering-based methods is weak in time series data processing, which means this method does not implement online diagnosis well. Eom et al.[21] proposed a refrigerant charge fault detection method using convolutional neural network, which shows good diagnostic results. But reliance on large amounts of labeled data is a disadvantage of this method. Yan et al. [22] proposed a semisupervised learning method for early detection and diagnosis of various air handling unit faults. This study greatly reduces reliance on labeled data, but SVM-based method is weak in time series data processing. Guo et al. [23] proposed a rule-based fault diagnosis strategy for variable refrigerant flow air conditioning systems. This method developed 22 expert rules for fault diagnosis and only use label-free data, which greatly reduces the difficulty of data acquisition. But this paper uses multiple linear regression to build the model, which reduces the model

1.3. The contributions of this study Based on the above problems, this paper first proposed the subhealth operation concept of heat pump system and uses the recurrent neural network (RNN) and expert rules to propose an undercharge subhealth online intelligent diagnosis method for ASHPWH. This method has the following novelty: firstly, using the time sequence learning ability of RNN, the hysteresis characteristics of the system are modeled to achieve accurate diagnosis for unsteady systems. Secondly, this method relies solely on normal operational data for model training, which greatly reduces the difficulty of data acquisition. Thirdly, fewer sensors are needed for sub-health diagnosis, which increases the universality of the method. Lastly, the experimental platform was used to conduct online diagnostic research on the continuously leaking system, which is different from other stable undercharge level studies. 1.4. Organization of this paper This paper used RNN and expert rules to conduct online diagnostic research on undercharge sub-health for ASHPWH. The organization of the paper presented as follows: in Section 2, the theoretical analysis of the sub-health mechanism of the vapor compressor refrigeration system under refrigerant leakage condition is carried out. The transfer process of the refrigerant leakage to the system performance is explained from the perspective of a complete refrigeration cycle; Section 3 is dedicated to deriving the proposed diagnosis method, including the theoretical basis of the method; Section 4 outlines the structure of the experimental platform, including system structure description, experimental working condition description, data acquisition method description, etc.; Section 5 presents the performance of the proposed method; and some concluding remarks are given in Section 6. 2. Theoretical analyses on the vapor compressor refrigeration system impacted by undercharge sub-health There have been related studies on the effects of refrigerant leakage on systems characteristics, including heat pump, split air conditioners, variable flow systems, etc. [9,10,26], ranging from system temperature 3

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According to Eq. (4), the decreasing density will cause pressure decrease under the same temperature. Therefore, the pressure of condenser superheating area will decrease, and the pressure on the condensation side is mainly depends on the superheating area, which cause the pressure on the condensation side will be decreased, too.

and pressure parameters to power, cooling capacity, and performance characteristics. However, most of the existing research pertains to experimental research. That is to say, by adding different quality refrigerants to the refrigeration system, the experimental changes of various parameters and performance are observed. Although the experimental research is convenient and intuitive, there are two shortcomings. Firstly, there are errors in the experimental measurement, and different environmental conditions also interfere with the experimental results; thus the experimental results may be inconsistent. For example, reference [8], which describes the inconsistency of many papers. Secondly, experimental research focuses on summarizing conclusions from the results, but it lacks analysis of the causes of the results. Therefore, theoretical analysis helps to more clearly understand the essential causes of changes in characteristics. This section uses a vapor compression refrigeration system as an example to simplify the analysis process. And the results are equally applicable to complex systems, including air source heat pump water heaters. This paper studies the diagnostic method of undercharge sub-health, which belongs to the gray box model and needs to qualitatively analyze the changes of system characteristics. This section uses thermodynamic theory and refrigeration principles to describe the dynamic characteristics of the system in one cycle, and theoretically explains the essential causes of its characteristic changes.

pV = nRT

p=

(4)

(5)

Qts = hts Ats ΔTts

hts =

1 1 hr

+

1 ha

+r

(6)

It can be seen that the heat transfer rate of the two-phase zone is determined by the heat transfer coefficient, the heat transfer area, and the heat transfer temperature difference. The total heat transfer coefficient is determined by the heat transfer coefficient of the refrigerant side, the heat transfer coefficient of the air side, and the thermal resistance of the material. Due to the influence of mass flow variation on the heat transfer coefficient of refrigerant side is negligible, and the air side heat transfer coefficient and the material thermal resistance remain constant. Therefore, the total heat transfer coefficient of the two-phase region is basically constant. Therefore, the reduction of the heat transfer temperature difference will cause an increase in the required heat transfer area. That is to say, a longer heat transfer distance is required for complete condensation. This change will lead to a reduction in the area of the subcooling zone and a decrease in the degree of subcooling, Tsc ↓. Jin et al. [12] described the temperature variation in the condenser under refrigerant leakage conditions, as shown in Fig. 2. It can be seen that after the refrigerant leaks, the condensation temperature is lower, the area of the two-phase heat transfer zone is larger, and the degree of subcooling is reduced. This is consistent with theoretical analysis. As the condensation temperature decreases and the subcooling decreases, the effect of both factors on the condenser outlet temperature, Tc, out , is reversed. Therefore, the final change of Tc, out depends on which factor dominates. Numerous studies have described the trend of this parameter [7,9], and the conclusion is more consistently expressed as

The following assumptions were used in the theoretical analyses: (1) The heat losses in the pipeline are negligible. (2) The fluid expansion in the throttling valve is considered isenthalpic. (3) The clearance volume in the compressor is negligible. 2.2. Theoretical analyses on the changing characteristics of system parameters Fig. 1 shows a schematic diagram of a simple vapor compression refrigeration cycle. This diagram was used to analyze the effect of refrigerant leakage on the system. The meaning of the points represented in the figure is given in Table1. It is known that a simple vapor compression refrigeration system mainly consists of four major components: condenser, expansion valve, evaporator, and compressor. It is assumed that the refrigerant leak point is located on the compressor discharge pipe line, and then, one must analyze the changes in the parameters of the condenser, expansion valve, evaporator, and compressor. It is known from the refrigeration principle that the location of the refrigerant leakage does not affect the final sub-health results. 2.2.1. Condenser Firstly, assuming that the amount of refrigerant leakage on the condensing side is Δm and ignoring the leak time, the system must be described both from the transient steady state before leaking and the unsteady state after leak, as well as in another transient steady state process. From the perspective of a mass micro-unit ∇, one must describe the complete dynamic change characteristics of one refrigeration cycle. The initial position of ∇ is at point 2, which is located at the discharge pipe line, and the mass is equal to the discharge mass of one piston stroke.

Fan 8

Condenser 5

3

4

2

9

Expansion Valve

Compressor

(1)

when the high-pressure side leaks Δm , the mass flow rate into the condenser will decrease. Volume flow remains constant due to inertia, which means the density of flow will decrease according to Eq. (2). Bring Eq. (2) into Eq. (3), we can give Eq. (4).

m nM ρ= = V V

ρRT M

Also, the degree of the decrease is related to some factors, such as the refrigerant mass on the condensing side, the heat transfer rate, the flow rate, and the condenser volume. The pressure on the condensation side decreasing, Pc ↓, will cause the condensation temperature to decrease, Tc ↓. If the heat transfer environment on the condensing side does not change, which means T8 does not change, the heat transfer temperature difference of the twophase heat transfer zone will decrease. The heat transfer rate of the twophase zone can be expressed by Eq. (5).

2.1. Basic assumptions

m∇ = ηm ρsuc Vcyl

(3)

11 6

1

7

Evaporator 10 Fan

(2)

Fig. 1. Simple vapor compression refrigeration cycle. 4

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Table 1 Description of the different points shown in Fig. 1. Point

Description

1 2 3 4 5 6 7 8 9 10 11

Evaporator outlet and compressor inlet Compressor outlet and condenser inlet Saturated vapor inside the condenser Saturated liquid inside the condenser Condenser outlet and expansion valve inlet Expansion valve outlet and evaporator inlet Saturated vapor inside the evaporator Air/Water at condenser inlet Air/Water at condenser outlet Air at evaporator inlet Air at evaporator outlet

Fig. 3. Temperature distribution at evaporator.

reduced; secondly, the differential pressure before and after the expansion valve is increased, thereby improving the inflow quality of the evaporator. The two factors are simultaneously performed until the mass flow of the inflow and outflow is equal, and the evaporation pressure will ultimately drop, Pe ↓. 2.2.3. Evaporator According to related research, the refrigerant of evaporator inlet is two-phase [28], therefore, Te, in = Te ↓. If the heat transfer environment of the low-pressure side is constant, which means T10 is constant, the heat transfer temperature difference of the two-phase zone will then increase, and the heat transfer rate will also increase. Combined with the reduction of total heat transfer, the two-phase refrigerant will enter the superheat zone faster, which causes the degree of superheat to increase. According to a study by Jin et al. [12], the variation of the temperature in the evaporator is shown in Fig. 3. From the experimental results, it can be determined that the temperature of evaporator outlet is increased, Tsuc ↑, and the suction enthalpy of compressor is also increased, isuc ↑.

Fig. 2. Temperature distribution at condenser.

Tc, out ↑. Due to Tc, out ↑, the enthalpy of the condenser outlet will increase, ic, out ↑. 2.2.2. Expansion valve As can be seen from the above section, the enthalpy of the condenser outlet is increased due to refrigerant leakage, and the enthalpy of the inlet of the expansion valve is also increased when neglecting the loss of the pipe line between the condenser and the expansion valve. According to Eq. (7), under the premise that the sectional area of the expansion valve is constant, the decline of the pressure before the valve will cause the mass flow rate through the expansion valve to decrease [27].

ṁ = Cd A 2ρin (Pin − Pout )

2.2.4. Compressor Due to the lower evaporation pressure, the refrigerant vapor density at the suction of the compressor is reduced. The mass flow rate of the compressor is calculated as Eq. (8) without considering the clearance volume. Therefore, the decrease of vapor density causes a decrease in mass flow rate.

(7)

Assuming that the compressor speed is constant, the volumetric flow rate through the compressor will then be constant too. The refrigerant flow rate through the compressor at the initial time does not change, and the refrigerant flow rate through the expansion valve decreases, which is discussed in Section 2.2.1. Then, the refrigerant mass in the evaporator will be decreased, and the flow velocity will be decreased. The decreased refrigerant mass will cause the evaporation pressure to decrease. The decreased evaporation pressure will cause the mass flow rate through the compressor to decrease. And the decreased evaporation pressure will also cause the higher pressure difference, further causing the mass flow rate through the expansion valve to increase according to Eq. (7). When the mass flow rate through compressor is equal to mass flow rate through expansion valve, the pressure in the evaporator reaches equilibrium. The evaporation pressure reduction has two effects: firstly, the refrigerant suction density of the compressor is reduced, and the suction quality is reduced, which means the mass flow rate of the evaporator is

ṁ = ρsuc Vcyl S 60

(8)

Compressor piston work is related to suction and discharge pressure. The piston starts to compress from bottom dead center, and the initial pressure is Pe Acyl . As the compression process continues, the cylinder pressure gradually increases linearly until the discharge pressure is reached. Then, this pressure is maintained until reaching top dead center. Therefore, the work of the piston can be expressed by Eq. (9).

Wcyl = Acyl

1− 1 L ∫0 ( λ ) ⎡ ⎛⎝ Pc −L Pe ⎞⎠ x + Pe ⎤ dx

⎣

⎦

(9)

It can be seen from the above analysis that the refrigerant leakage will cause Pc ↓ and Pe ↓, and therefore, the piston work will be reduced. As the suction temperature of the compressor increases but the piston work decreases, the effect of the two on the discharge temperature is reversed. On the other hand, less work will reduce the heat generated 5

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3. The diagnosis methodology

by the motor, which causes the compressor shell to reduce heat dissipation to the environment. Therefore, the trend of the discharge temperature needs to consider a variety of factors. Fortunately, many studies [9,26] describe the variation very consistently, indicating that the discharge temperature is on the rise, Tdis ↑.

In this paper, RNN (Recurrent Neural Network) is used to model the heat pump system, and the theoretical value of the required system parameters is calculated using the model. The theoretical value is subtracted from the measured value to obtain the residual value. The basis for sub-health diagnosis used is the result of whether the residual value exceeds the threshold or not. Since the RNN model has a time memory function, it can fit its hysteresis characteristics according to the dynamic changes of the system, thus achieving high-precision modeling of the unsteady system.

2.3. Theoretical analyses on the changing characteristics of the performance The performance parameters of the heat pump system mainly include three types: power, heating capacity, and coefficient of performance (COP). This section mainly analyzes the variation of three performance parameters under the condition of refrigerant leakage. The power of the compressor can be expressed as equation (10). Under small changes in working conditions, the power factor, ηe , is approximately constant. It can be seen from the previous analysis that refrigerant leakage causes the piston work to decrease, which in turn causes the compressor input power to decrease, Win ↓.

Win = Wcyl ηe

3.1. Theoretical basis of RNN The RNN [29] is one of the deep learning algorithms designed to process sequence data. In the fully connected neural network, the calculation results are independent of each other, and for RNN, each calculation result is related to the current input and the previous hidden layer output result. In this way, the results of the RNN calculations are characterized by the results of the memory. The RNN structure diagram is shown in Fig. 4. The left side is a simple structure diagram, and the right side is an expanded structure diagram. From left to right, the time series data is sequentially input, and the output of the previous time point is also transmitted to the neuron as the next input. The historical data and the current data affect the current output at the same time, which means the effect of memory is achieved. RNN is designed to learn from sequence data, but the structure causes it to have worse memory of previous or older data. One way to solve this challenge is using Long Short-Term Memory (LSTM) model which is a variant on the RNN. LSTM adds three types of gates in normal RNN: the forget gate, the external input gate, and the output gate. The added gates make the system have a good memory of data processed much earlier. LSTM was thus used to replace the normal RNN, and it achieved a good result. Due to the detailed principle of LSTM, it does not fall within the present research contents, so more information on LSTM function will not be shown in this paper. There are many kinds of variants on the RNN, and LSTM belongs to one kind of it. For convenience, this paper uses “RNN” as a general name for all kinds of variants.

(10)

The heating capacity can be expressed as equation (11).

Q̇ = ṁ (ic, in − ic, out )

(11)

The refrigerant flow through the condenser can be divided into three zones: superheat zone, two-phase zone, and subcooling zone. Table 2 shows the enthalpy of R134a from 50 to 60 ℃ under a pressure of 1.47 MPa. From the table, it can be observed that, the enthalpy difference in the superheat zone is about 1.25KJ/(Kg K), the subcooling zone is about 1.58 KJ/(Kg.K), and the enthalpy difference of phase transition is 146.43 KJ/Kg. Therefore, the latent heat released by the phase transition is much greater than the single phase lowering by one K. In the case of slight refrigerant leakage, the change in the discharge temperature and the subcooling is very small, and therefore, the mass flow rate variation plays a decisive role. Based on this conclusion, the enthalpy variation of the condenser inlet and outlet can be neglected, and the Eq. (11) can be simplified to Eq. (11).

Q̇ = Ch ṁ

(12)

where, Ch is a constant coefficient, which value is related to the characteristics of the refrigerant. The mass flow decreases cause the heating capacity to be reduced. The effect of refrigerant leakage on the system COP is of greatest concern. COP can be expressed as Eq. (13).

COP =

Q̇ Win

3.2. RNN and expert rules based sub-health diagnosis method Due to the larger fluctuation in evaporative heat transfer environment and the condenser heat transfer environment of the ASHPWH, it is difficult to directly diagnose the biased feature. Fig. 5 shows the flow of the sub-health diagnosis method proposed in this paper. It can be seen from the figure that the diagnostic process can be divided into two

(13)

Since the heating capacity and input power are simultaneously reduced, the trend of performance needs to consider two factors. Kim et al. [7] determined through experiments that there is an optimal value for refrigerant charge level. When it is less than this value, COP increases with the increase of refrigerant mass. And when it is greater than this value, COP decreases with the increase of refrigerant mass. Generally, the refrigerant mass is less than the optimal value after the refrigerant leaks. Therefore, the larger the leakage, the smaller the COP.

Table 2 Enthalpy at varying temperatures.

2.4. Conclusions of the theoretical analyses In the previous section, a refrigeration cycle was completely analyzed, and the trends of various parameters were summarized. The conclusion is shown in Table 3, and this conclusion is consistent with the conclusions of most experimental studies. This section analyzes the reason for variation in various parameters using thermodynamics theories, and it provides support for the sub-health diagnosis gray box model. 6

Temperature/℃

Enthalpy/kJ/kg

50 51 52 53 54 54.405 54.405 55 56 57 58 59 60

271.56 273.12 274.70 276.28 277.88 278.53 424.96 425.73 427.02 428.29 429.55 430.79 432.03

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variables selection are shown in Table 5.

Table 3 Change characteristic of undercharging refrigeration system. Decline parameters

Increased parameters

Pc ; Pe ;Te ;Tc ;Te, in ;Tsc ; ρsuc ;ṁ ;Win ;Q̇ ;COP

Tdis ;Tsuc ;Tc, out ;i c, out ;i e, in ;Tsh

3.2.2. RNN model training In order to achieve accurate modeling of the system, a large number of normal operation data was used to train the RNN model. With the commercialization of ASHPWH, the same type of products is massproduced and equipped with wireless sensing devices. Therefore, a large amount of normal operation data of the same type of ASHPWH can be obtained. The specific training steps are as follows: Step 1: First select the input and output parameters of the model. The output parameters are the target variables of the sub-health condition, and the input parameters are all the system parameters that affect the target parameters. The details are shown in Table 5. Step 2: Process the normal operation data, extract the data of the input parameters as an input data set, and extract the data of the output parameters as an output data set. Step 3: Train the RNN model with input and output data sets to obtain a system model for refrigerant leakage. Since the RNN structure is sufficiently complex, when the amount of data is large enough, a model with enough accuracy can be obtained. This process is called sub-health modeling. As shown in Fig. 6, the trained RNN model can predict the target variables of the cut-off time point by multiple time points, and the predicted value is the theoretical value of the normal system.

Fig. 4. Structure of recurrent neural network.

major parts: model training and real-time diagnosis. The model training part uses the normal operating data of the database to train the RNN model. The input data are system independent variables, and the output data are the system target variables. The real-time diagnosis process uses the trained RNN model for diagnosis, and it obtains the residual data of each target variable, being the offset between the target system and the normal system. The residual variables are analyzed by the expert system, and the diagnosis results are finally obtained.

3.2.3. Real time diagnosis The real-time data acquisition system collects a set of data at regular intervals, including independent variables and target variables. The independent variables of the current time are input into the RNN model, and the model combines the independent variables of multiple time points to predict the theoretical value of the current target variables, which is the theoretical value of a normal system. Next, the residual data is obtained from the predicted value minus the measured value. Then, using combined expert experience to establish the threshold of the residuals and logic to determine whether the residuals exceed the threshold, the objective of real-time diagnosis can be achieved. Using historical operational data combined with expert experience to develop a reasonable threshold is a necessary step for subhealth diagnosis, and different types of system have different thresholds.

3.2.1. Selection of independent variables and target variables The test variables of the system are divided into two categories: independent variables and target variables. The target variables are the parameters used to diagnose whether the refrigerant leaks. When the refrigerant leaks, the target variables need to have a corresponding change trend, and the change trend should be distinguishable from other sub-health conditions. In Section 2.4, the trends in vapor compressor refrigeration system parameters after refrigerant leakage were summarized. It was observed that many parameters can be used as target variables. However, some special features exist in ASHPWH, mainly including: lower system cost and higher condensing heat transfer temperature. Therefore, the cost of data measurement must be as low as possible, which means the number of sensors must be minimized. On the other hand, the higher condensing heat transfer temperature results in less subcooling, so it is not appropriate to diagnose the refrigerant leakage by the subcooling variation. Mehrabi et al. [30] performed a summary study on the characteristics of faulty systems, such as heat exchanger fouling and noncondensable gas in the refrigerant. Based on the comparative analysis, the evaporation superheat and the condensing temperature were chosen as the target variables. The trends of target variables in other sub-health systems are summarized in Table 4. As can be seen from the Table, selecting these two as target variables can be well distinguished from other sub-health conditions. When the target variables are selected, all factors that affect the target variables need to be used as independent variables. This ensures that for a specific heat pump system, a group of independent variables can uniquely correspond to a group of target variables. According to the knowledge of refrigeration principle, it is known that the working conditions of the system and external heat transfer conditions will affect the target variables, so the ambient temperature, tank temperature, compressor rotor speed, and expansion valve opening were selected as independent variables. The specific independent variables and target

4. System overviews 4.1. Experiment platform structure There are many different types of ASHPWH, and the most common are single-stage heat pump water heaters and cascade heat pump water heaters. Although the latter can supply hot water under cool weather conditions, its efficiency is still low, and the operation technology is not mature, so it has not been widely used. However, the single-stage heat pump water heater has increased its usage year by year, due to its high efficiency and energy saving. Especially in the spring and summer supply of domestic hot water, the performance advantage is very remarkable. Therefore, this paper used single-stage heat pump water heater experimental platform to verify the relevant performance of the diagnosis method. The experimental platform can be divided into three sub-systems: heat pump sub-system, data acquisition sub-system, and control subsystem. The structure of the system is shown in Fig. 7. A single speed reciprocating compressor was used in the heat pump sub-system and the refrigerant selection R404A. The evaporator chosen was a tube-fin heat exchanger. Two coils were installed in the tank for water heating. The expansion device used a thermal expansion valve with an external nitrogen gas. The tank used a water pump to supply cold water, and the hot water was discharged through the hand valve. The details of the heat pump sub-system are shown in Table 6. 7

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Fig. 5. The flow chart of proposed method. Table 4 Change characteristic of various sub-health systems. Sub-health category

Tsh

Tc

Refrigerant leakage Condenser heat transfer reduction Evaporator heat transfer reduction Non-condensable gas in the refrigerant

↑ ↑ ↓ ↑

↓ ↑ ↓ ↑

Table 5 Parameter selection of independent variables. Variables category

Symbol

Independent variables (Input variables) Target variables (output variables)

S ; ν ; Toutdoor ;TTank

Fig. 6. Structure of RNN model.

Tc ; Tsh

The data acquisition sub-system used ADVANTECH acquisition equipment, the sampling card was PCI1715U, and the temperature and pressure parameters were collected through AD conversion. The software was programmed with LabVIEW 2018, and the data was collected 8

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software was also programmed by LabVIEW, and the control logic is shown in Fig. 8. The evaporator heat transfer environment was controlled by a heating tube using the PID algorithm. The opening degree of the expansion valve was controlled under sinusoidal fluctuation with time, the opening adjustment range from 40% to 90%, which causes the evaporation temperature to fluctuate between about −10 ℃ to 10 ℃, and the condensing temperature to fluctuate between about 55℃ to 63℃ under health state. The control strategy was used to test the effect of the sub-health diagnosis method under different working conditions, and has practical application significance. 4.2. Experimental conditions and simulation methods The experiment used a capillary tube to simulate the refrigerant leakage, and it conducted the online diagnosis method of the continuous leakage system. The capillary tube was placed in a bucket, and the refrigerant leakage rate was calculated by the number and size of leaking bubbles per minute. The leak experiment lasted approximately 11 h. The evaporator heat transfer environment in the experimental process was controlled within the range of 20℃to 25℃ sinusoidal fluctuation, which can be used to test the effect of diagnosis method under fluctuating outdoor temperatures. This temperature is the typical outdoor temperature in the spring of Hangzhou, China. It is of great significance to study the relevant characteristics of the heat pump water heater at this temperature.

Fig. 7. Schematics of the experimental setup. Table 6 Specifications of heat pump sub-system. Part

Specifications

Compressor

Model: embraco NEK6213GK Single speed reciprocating compressor Displacement (cm3): 12 Tube-fin heat exchanger Number of tubes: (Rows/Columns) 12/2 Width/length/height(mm): 370/130/350 Heat transfer area(m2): 5.2 Volume: 60L Coil number/step: 2/13 Thermostatic expansion valve (Adjusted by external nitrogen source) 2000 W 1750 W Evaporation temperature: 7.2℃ Condensing temperature: 54.4℃

Evaporator

Tank Condenser Expansion device Heater Cooling capacity

4.3. Algorithm operating environment The deep learning algorithm was coded in Python 3.6 in the Pycharm 2017 edition development environment. Keras is a wellknown deep learning framework, and the 2.2.4 edition was chosen for this study. The backend of Keras uses Tensorflow, which is a common deep learning development environment. The deep learning algorithm was performed in Intel(R) Xeon(R) E51650 v3, which is a CPU made by Intel. The computer memory was 16 GB, and the operating system was Windows 7 X64. 5. Results and discussion 5.1. The parameter variation characteristics of refrigerant leakage system In Section 2, the theoretical analysis method was used to determine the variation characteristics of the system parameters of refrigerant leakage, and it was concluded that the two variables, condensing temperature and superheat, can be used as target variables for subhealth diagnosis. Fig. 9 shows the trend of the two parameters of the continuous leak system collected by the experimental method and linear fitting. It can be seen from the figure that the condensing temperature has a continuous downward trend, and the superheat continued to rise, which is consistent with the theoretical analysis. However, it was also found that due to the periodic adjustment of the expansion valve opening degree, the condensing temperature and the superheat degree also changed periodically. Also, the variation range is larger than the temperature change caused by the refrigerant leakage. Therefore, the sub-health diagnosis cannot be achieved simply by using the threshold method. When using the target parameters variation to diagnose whether the system is sub-health, the key issue is to accurately

every minute and stored with the MySQL database. Since the initial operating state of the system had not been stabilized, the data for this time period was not used for model training. Therefore, the data acquisition started from the second and following hours. The sensing device included four temperature sensors, one pressure sensor, and one current sensor. The details of acquisition parameters are shown in Table 7. Although the single speed compressor was used in the system, the compressor rotor speed will still change with the load variation. Experimental verification has found that the rotor speed of the compressor can vary by more than 100 rpm. Therefore, the speed measurement is essential to meet high-precision diagnosis requirements. This paper used previous research to measure the compressor rotor speed in real time [31], achieving good results. The control sub-system used the DA output of ADVANTECH and controls the pressure of the external nitrogen gas through the pressure control device to adjust the opening degree of the expansion valve. When the external pressure was 0.5 MPa, the opening degree reaches the maximum, which was recorded as 100% opening degree. And when pressure was 0 mPa, it was recorded as 0% opening. The water pump and hot water valve switches also utilized the DA output. The control

Table 7 Measuring parameters.

9

Part

Parameter

Temperature parameter Pressure parameter Work condition parameter

Tout e , Tin e , Toutdoor , TTank pdis S, υ

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Fig. 10. Accuracy of RNN model with difference activation function and optimizer.

predict the theoretical value of the normal system and, then, diagnose the health status of the target system through its residual.

5.2. RNN model parameter selection In the training process of the RNN model, many hyperparameters needed to be selected. It was important to optimize the value of hyperparameters to improve the accuracy of the model. In this section, the performance of the corresponding model was compared by adjusting the selection scheme of hyperparameters, and finally, the optimal hyperparameter combination was obtained. Each RNN model was trained on a training set containing 5000 sets of data and tested on a test set containing 2500 sets of data. Firstly, the effects of different activation functions and optimizers on model accuracy should be discussed. The basic theory of activation functions and optimizers can be referred to as ‘deep learning’ [29], which are not described here. The mse algorithm was used to calculate the model accuracy, and the other hyperparameters were set to empirical values: batch size = 100, epochs = 50, RNN layer nodes = 100, and RNN steps = 5. Under the above conditions, the accuracy of the model corresponding to the different activation functions and optimizers is shown in Fig. 10. From the test results, Adagrad and Adam performed best under various activation functions, and Adam was slightly better than the Adagrad optimizer. Therefore, the Adam optimizer we selected as the final choice. In activation function selection, the relu has been a more commonly used activation function in recent years, but the original relu has a poor training effect on negative numbers and often fails. Therefore, its variant functions selu and elu are more optimized. From the test results, it was found that the accuracy of several activation functions was relatively close, and the relu and its variant had a slight advantage. Considering stability comprehensively, selu was chosen as the final activation function. Batch size is the amount of data that is trained at one time. In general, a larger batch size results in faster training, but it also lowers the accuracy. However, the actual situation may not be completely consistent with the above rules. Fig. 11a shows the accuracy and training time cost of the model under different batch sizes. Because the optimization function has stochastic optimization characteristics, even if the accuracy of the model obtained by the same training conditions is different, all the models in this section were subjected to repeated training 5 times and took the averaged accuracy. It was found that as the batch size increased, the training time dropped steadily, but the accuracy did not change much. When batch size = 80, the precision shows a peak, and the multiple training results all show a high accuracy, so the batch size of this paper was chosen to be 80. Fig. 11b shows the model performance for different RNN nodes size. RNN nodes size refer to the number of neurons in an RNN unit. The nodes size affects the fitting ability of the model, but it is limited by the

Fig. 8. Control flow chart.

(a condensing temperature)

(b degree of superheat) Fig. 9. Target variable trend.

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Table 8 The running performance of RNN model. Training data

5000

Test data Training accuracy Training loss Test accuracy Test loss Training time cost (s) Training memory cost (MB)

2500 0.9915 1.25 × 10−4 0.9918 1.26 × 10−4 32.01 45.7

which are also called time steps. More steps result in longer processing time sequence because the system hysteresis characteristics can be better fitted. However, with the increase of RNN steps, the training difficulty increases, and the training time increases. Fig. 11c shows the model accuracy and training time cost of RNN steps from 3 to 30. It was found that as the steps increases, the training time cost increases gradually, but the accuracy remains basically unchanged. Therefore, considering the training time cost and hysteresis characteristics fitting ability, the steps from 4 to 8 are all suitable ranges. Here, 5 was chosen as the RNN steps value. Finally, the effect of training epochs on the performance of the model should be discussed. As the number of training epochs increases, the accuracy of the model increases gradually, but too many epochs will increase the training time cost and may cause over-fitting. Fig. 11d shows the variation of model accuracy during 200 epochs training. It was found that the convergence process of the model was basically completed in the first 30 epochs, but in order to ensure reliability, the number of epochs was chosen to be 50. Through experimental research on the training parameters of the model, the optimal group of parameters was obtained. The training accuracy, training time cost, and memory cost of the final version of the RNN model are satisfactory, and the details can be seen in Table 8.

(a: activation=selu optimizer=Adam epochs=50 rnn_nodes=100 rnn_steps=5)

(b: activation=selu optimizer=Adam epochs=50 batch_size=80 rnn_steps=5)

5.3. The effect of unsteady system modeling The RNN training process can directly learn from timing sequence data, and the characteristics of the previous step are preserved while learning the characteristics of the next data samples. Therefore, the RNN can better fit the time-varying characteristics of the system, which makes the RNN-based model capable of accurately modeling the unstable system. In this section, the trained RNN model was used to predict the target parameters of the normal system, and the predicted values were compared with the measured values. Higher model accuracy corresponded

(c: activation=selu optimizer=Adam epochs=50 batch_size=80 rnn_nodes=30)

Table 9 Comparison of predicted and measured values.

(d: activation=selu optimizer=Adam batch_size=80 rnn_nodes=30 rnn_steps=5) Fig. 11. The performance of RNN model with varying hyperparameters.

data set size. It can be observed from the figure that the accuracy has a valley, so when considering the training time cost, RNN nodes size was finally chosen as 30. RNN steps refer to the number of RNN units in the model chain, 11

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6. Cost benefit analysis

to a smaller difference between the two value types. The results are shown in Table 9. Since the operating conditions of the experimental system are constantly adjusted with the opening of the expansion valve, the system is always in an unstable state. The fitting effect of the method on the unsteady system can be explained through two examples. The first example shows when the expansion valve opening is gradually increased, and it can be seen the system hysteretic characteristics are different when gradually decreased. It can be seen from Table 9 that there are two states of 84% expansion valve opening, which are covered by green shadows, however, the measured condensing temperature and measured superheat are different. The reason for the difference is that the hysteresis of the system in the two time-points was not same. From the prediction results, it can also be seen that the model could accurately predict the difference. For the second example, the condensing temperature should be largest when the expansion valve is at maximum opening, which is 90% degree. But, due to the instability of system, when the opening is adjusted from the peak value to the minimum, the condensing temperature continues to rise for a while. As can be seen from Table 9 with yellow shadows, the peak value of the measured condensing temperature was not 90% opening, but rather, 86%. The model accurately predicts this hysteresis characteristic, and the peak value of the predicted value is also 86%. The abovementioned two examples prove that the proposed method can not only fit the steady system, but it also had a high fitting accuracy for unsteady system.

This section analyzes the application prospects of the proposed method from the economic applicability. Kim’s [32] research shows the frequency of 32 typical faults in heat pump systems. The results show that the frequency of nonstandard refrigerant charging ranks 7th among 32 typical faults, and the frequency is 42%. And the abstract clearly points out that nonstandard refrigerant charging is the one of three most important faults in heat pump. To further illustrate the impact of nonstandard refrigerant charging on the cost of system use, we perform a specific quantitative analysis. According to Kim’s [32] research, the total energy consumption for heat pump systems in the United States is 396 trillion Btn/yr, and the additional energy consumption due to nonstandard refrigerant charging is 21.7 trillion Brn/yr. This increase in energy consumption is based on the frequency of faults and is a statistical quantity applied to all heat pump systems. Therefore, nonstandard refrigerant charging caused a 5.48% increase in energy consumption. We assume that the increase in energy consumption of ASHPWHs due to undercharging sub-health also conforms to this law. Next, we use a specific ASHPWH for analysis. Xiao et al. [33] from GREE electric appliances had study for an annual performance analysis of an ASHPWH with a rated heating capacity of 18 kW. Considering the control strategy and the stop-open ratio, the total energy consumption of this ASHPWH is 47000–49000 kWh. Considering the statistics of 5.48% increase in energy consumption, undercharging sub-health will cause annual energy consumption to increase by 2630 kWh. In Hangzhou, China, the average annual electricity is $0.087/kWh, which means that undercharging sub-health will cause an additional usage fee of $228. This ASHPWH is a type of large water heaters, and the price is about $4338 to $11568. Next, we analyze a small ASHPWH. We choose an ASHPWH with a rated heating capacity of 5kWh and a water tank of 300L. The price of it is $1300.

5.4. Verification of fault diagnosis performance A capillary tube was used to slowly discharge the system refrigerant, which was used to simulate the leakage of the system. The whole simulation process was about 11 h and provided favorable test conditions for sub-health online diagnosis. The trained RNN model was used to predict the target parameters of the system, and the predicted value is equal to the theoretical value of the normal system. The measured value can be subtracted from the predicted value to obtain the residual of the target parameters. The residual data and fitted value are shown in Fig. 12, and the thresholds set according to expert experience are also marked in the figure. It can be seen from Fig. 12 that both the residual of condensing temperature and the residual of superheat have an increasing state with the refrigerant leakage, which proves that the RNN model can appropriately diagnose the deviation characteristics of the system, which is also called sub-health characteristics. From Fig. 12, it can be found that the target parameters fluctuate periodically with time, which were caused by the periodic adjustment of the expansion valve. When the expansion valve opening was increased, the system operating load was increased, and the residual was also increased. Therefore, the degree of load (DoL) must be considered in the sub-health diagnosis. Usually, part-load is the most common state of the system. As in the fitted line in Fig. 12, the intersection point with the residual curve is near the 50% load, which means that the residual value of 50% part-load system increases linearly with the degree of leakage. Therefore, the 50% part-load can be used as a criterion to establish a threshold based on expert knowledge. When both residuals exceed the thresholds, it is determined that the system is under subhealth operation, and the decision logic is shown in Fig. 13. According to the characteristics of the experimental system and combined with expert experience, the threshold values of residual condensing temperature and residual superheat are set to −3.5 and 3.5, respectively, and the leakage approximately 8%. As can be seen from the figure, under 50% part-load conditions, the threshold intersects the residual for approximately 150 min. It indicates that the system entered subhealth state after 150 min of operation.

(a residual of condensing temperature)

(b residual of superheat) Fig. 12. Residual of target parameters and fitted lines. 12

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by which refrigerant leakage causes performance degradation. (2) The proposed online undercharge sub-health diagnosis method can accurately diagnostic the offset characteristics of systems under large fluctuations heat transfer environment between 20 ℃ to 25 ℃, and realized the accurate fitting of the hysteresis characteristics of the unsteady systems with 2 min delay. The training loss of the model is lower than 1.25 × 10−4. (3) Big data as labelled data is identified as a limitation of deep learning methods. Fault-labeled operation data of ASHPWH has a very high acquisition cost. The proposed method only usage labelfree health data, which reduced the difficulty of data acquisition. And the additional cost of one device is about $72.3–130, which was suitable for ASHPWHs. (4) The experimental results show that the proposed method can accurately fit the real-time deviation of the system without being affected by the fluctuation of heat transfer conditions and hysteresis characteristics, as well as combine the expert knowledge for achieving online diagnosis of sub-health systems with 8% leakages. The diagnostic delay is less than one period of operating conditions fluctuations, which is 30 min in this experiment.

Fig. 13. Diagnosis logic based on expert knowledge.

According to the conversion of the data in Xiao’s [33] research, the annual energy consumption of this ASHPWH should be 13,333 kWh, which means that the annual usage fee is$1157. Undercharging subhealth will cause additional energy consumption of 731 kWh, or $63. Therefore, the undercharging sub-health will cause a significant increase in the cost of use. In this part, we analyze the cost of the proposed method in this paper. The proposed method is greatly optimized in the usage cost. This method required four temperature sensors, one pressure sensor and 1 current sensor. All the ASHPWH are equipped with two temperature sensors, including water tank temperature sensor and ambient temperature sensor. Therefore, only two temperature sensors need to be added. The temperature sensor price is about$7.2–22, the pressure sensor price is about $29–43, and the current sensor price is about $14.5–29. Hence, the added cost is about $58–116. The proposed method is one kind of deep learning method, which is suitable for cloud computing. Therefore, the local device only needs to implement data collection, adjust the opening of expansion valve and wireless transmission. The cost of local device is about $14.5. In order to implement IoT expansion equipment, electronic expansion valves must be used instead of thermal expansion valves, and which causes in an additional cost of $7.2. Expansion valve opening decision is executed by cloud algorithm, which have no additional hardware costs. The cloud server can be rented. Take Alibaba Cloud as an example, the rent of an ordinary server is 500 per month. And considering the calculation of the proposed method, one cloud server can monitor $144.6 ASHPWH at the same time. Cloud server maintenance costs are another cost. The salary of web engineer who can maintain four cloud servers at the same time is about $1446 per month. Therefore, if the number of ASHPWH devices is enough, the additional cost of one device is about $72.3–130. According to the extra cost of sub-health, the initial investment of the proposed method can pay back in two years. It is necessary to know that the average service life of ASHPWHs is more than 10 years. Traditional low-tech methods also require additional sensors, but the calculations are relatively simple. Due to the introduction of cloud computing, computing costs have been greatly reduced, which makes the proposed method has a broad application prospect. In summary, the additional cost of the proposed method is acceptable, and the advantage becomes more apparent with the number of ASHPWHs increases.

In summary, the proposed method compared to other intelligent diagnostic methods has two advantages: 1. It does not require faultlabeled data, which greatly reduces the difficulty of data acquisition; 2. It can diagnose unsteady systems, which is more suitable for online systems diagnosis. Therefore, the proposed method has wide applicability, low diagnostic cost, and high diagnostic accuracy, which indicates that the proposed method has broad application prospects. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors gratefully acknowledge the support of Primary Research and Development Plan of Zhejiang Province (Grant No. 2020C04010) and Zhejiang Province Public Welfare Technology Application Research Project (Grant No. LGG18E050024, LGG19E050020). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2020.114957. References [1] Y. Wei, X. Zhang, Y. Shi, L. Xia, S. Pan, J. Wu, M. Han, X. Zhao, A review of datadriven approaches for prediction and classification of building energy consumption, Renew. Sustain. Energy Rev. 82 (2018) 1027–1047. [2] S.A. Rashid, Z. Haider, S.M. Chapal Hossain, K. Memon, F. Panhwar, M.K. Mbogba, P. Hu, G. Zhao, Retrofitting low-cost heating ventilation and air-conditioning systems for energy management in buildings, Appl. Energy 236 (2019) 648–661. [3] L. Li, D.-J. Liu, Study on an air quality evaluation model for beijing city under hazefog pollution based on new ambient air quality standards, Int. J. Environ. Res. Public Health 11 (2014). [4] Y. Xu, Y. Huang, N. Jiang, M. Song, X. Xie, X. Xu, Experimental and theoretical study on an air-source heat pump water heater for northern China in cold winter: effects of environment temperature and switch of operating modes, Energy Build. 191 (2019) 164–173. [5] C. Zhang, J. Yang, Economic benefits assessments of “coal-to-electricity” project in rural residents heating based on life cycle cost, J. Cleaner Prod. 213 (2019) 217–224. [6] S. Lazarova-Molnar, H.R. Shaker, N. Mohamed, B.N. Jrgensen, Fault detection and diagnosis for smart buildings: state of the art, trends and challenges, 2016 3rd MEC International Conference on Big Data and Smart City (ICBDSC), 2016, pp. 1–7. [7] D.H. Kim, H.S. Park, M.S. Kim, The effect of the refrigerant charge amount on single

7. Conclusions This paper proposed the sub-health operation concept of heat pump systems, which is used to define the intermediate state of the normal systems and the fault systems. And then, an online undercharge subhealth diagnosis method was proposed, which had a high diagnostic accuracy on unsteady systems. The main conclusions were as follows: (1) The system variation trends were analyzed under undercharge subhealth conditions. And theoretical analysis revealed the mechanism 13

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