Performance evaluation and prediction for electric vehicle heat pump using machine learning method

Performance evaluation and prediction for electric vehicle heat pump using machine learning method

Applied Thermal Engineering 159 (2019) 113901 Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.c...

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Applied Thermal Engineering 159 (2019) 113901

Contents lists available at ScienceDirect

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

Research Paper

Performance evaluation and prediction for electric vehicle heat pump using machine learning method Yufeng Wanga, Wanyong Lia, Ziqi Zhanga, Junye Shia,b, Jiangping Chena,b, a b

T



Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, Shanghai, China Shanghai High Efficient Cooling System Research Center, Shanghai, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Electrical vehicle Heat pump Refrigerant injection Machine learning SVR Adaboost.R2

A method to predict the performance of R134a heat pump with EVI (Economized Vapor Injection), is proposed in the present study. Models using SVR (Support Vector Regression) as the base estimator and Adaboost.R2 as the ensemble method, are established to predict the heating capacity and COP of the heat pump. Different feature sets for the model input are formed, based on the working principle of the heat pump system and correlation analysis. Parameters of the models are optimized to improve prediction performance. The simulation results are compared with the experimental results, and the relative errors for heating capacity and COP prediction are within 8.5%. Moreover, the impacts of injection pressure on the EVI heat pump system are discussed and simulated using the model established. The optimum injection pressure of the heat pump system can be obtained from the model under different working conditions.

1. Introduction

superheated in the economizer. The injected refrigerant will increase the mass flow rate into the condenser, thus improving the heating capacity of the system. Also, the injected refrigerant will cool down the compression process, making compressor discharge temperature lower [10]. Studies have been performed to prove that heat pumps with EVI perform better than heat pumps without EVI under low temperatures [6,11,12]. A numerical model is necessary for predicting the heat pump performance. Generally, there are two kinds of models, namely, the white box model and the black box model. The white box model is based on physical principles. Details of the system should be taken into consideration and appropriate assumptions should be made when modeling. Jung and Kwon [13,14] used such strategy to simulate the heating performance of EVI heat pump systems, and they concluded that a COP improvement is achieved using EVI. However, in such models, numerous attributes and detailed physical processes are required, increasing the complexity of the model. Also, semi-empirical relationships, whose accuracy cannot be guaranteed, are needed to calculate the heat transfer process or refrigerant properties, making the model less accurate. Black box model mainly uses machine learning methods. With the adaption of advanced modeling algorithms, black box model can model nonlinear or complex relationships. Hence, the black box model is of better practical use and is widely used in the refrigeration system.

Electrical vehicles (EV) are becoming increasingly popular recently. Unlike traditional vehicles, waste heat from combustion engines cannot be utilized to warm up the passenger chamber in electric vehicles [1]. Positive Temperature Coefficient heater utilizes materials that exhibit a positive resistance change in response to the increase in temperature. The material allows current to pass when it's cold and restricts current to flow as the threshold temperature increases. It is a simple solution to the heating problems but at the cost of high energy consumption, which can severely damage the driving range, causing a decrease up to 50%. Air Source Heat Pump (ASHP) is a promising way to meet the requirement of climate control and save energy at the same time [2–5]. However, ASHPs using R134a suffer from significant performance decrease under extreme ambient temperatures (lower than −20 ℃) [6]. The low evaporating pressure leads to a low density of compressor suction, and the high-pressure ratio leads to low volumetric efficiency of the compressor [7]. Both of them do harm to the mass flow rate of the heat pump system, which decreases the heating capacity. The introduction of EVI (Economized Vapor Injection) into the heat pump is a promising solution to this problem [8]. As is shown in Fig. 1, EVI means injecting a middle-pressure refrigerant into the compression port of the compressor [9]. Refrigerant at the condenser outlet is separated into two branches, and the injected refrigerant is first throttled and then



Corresponding author at: Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, Shanghai, China. E-mail address: [email protected] (J. Chen).

https://doi.org/10.1016/j.applthermaleng.2019.113901 Received 1 January 2019; Received in revised form 7 May 2019; Accepted 1 June 2019 Available online 01 June 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature C Cp E h I k m MFR N P p Q T U w W

cond dis in inj main out ref sat sc sh suc

Penalty parameter specific heat [kJ/kg-K] expectation enthalpy [J/kg] current [A] Kernel function number of samples mass flow rate [kg/s] rotary speed [RPM] pressure [MPa] probability capacity [kW] temperature [K] voltage [V] weight of samples work [W]

Abbreviation AC ASHP BV COND COP EV EVAP EVI EXV FS HVAC HX RBF RMSE SVR T1/T2

Greek letters α β γ ε μ ξ π ρ σ φ

condenser discharge inlet or indoor injection main loop outlet or outdoor refrigerant side saturation subcooling superheat suction

Lagrange multiplier weight of machines RBF kernel coefficient deviation mean value slack variable pressure ratio correlation coefficient standard deviation mass flow rate ratio

air conditioning air source heat pump bypass valve condenser coefficient of performance electrical vehicles evaporator economized vapor injection expansion valve feature set heating, ventilation, and air conditioning heat exchanger radial basis function root mean square error Support Vector Regression outdoor/indoor temperature

Subscripts air

air-side

[20,21]. However, former applications of machine learning method in the refrigeration field mainly focus on domestic or commercial refrigeration and heating systems. When it comes to automotive air conditioning or heat pump, few researches have been found. In this study, models to predict the heating capacity and COP of R134a EVI heat pump for electric vehicles are established. The models use SVR as the base estimator and Adaboost.R2 as the ensemble method. First, different feature sets for the model input are formed based on the working principle of the heat pump system and correlation analysis. Then parameters of the models are optimized to improve prediction performance. The simulation results computed from the optimized model are compared with the experimental result. Finally, the impacts of injection pressure on the EVI heat pump system are discussed and simulated using the model established. Hence optimum injection pressure of the heat pump system can be achieved from the model.

Rasmussen [15] used Linear regression, random forest, and SVR (Support Vector Regression) algorithms to forecast the electrical load of supermarket refrigeration systems. Shi [16] developed a model for detecting refrigerant charge fault using Bayesian neural network. Guo [17] compared the performance of SVR, BPNN (Back Propagation Neural Network), ELM (Extreme Learning Machine) algorithms in forecasting energy demand of building heating system. Apart from predicting system performances, the machine learning method is also capable of investigating the detailed working status of the refrigeration system [18,19] and finding an optimal control strategy for the system

2. Experimental setup 2.1. System structure The structure of the EVI heat pump system is shown in Fig. 2. The system is capable of both air conditioning and heating. When in AC (Air Conditioning) mode, condenser inside the HVAC (Heating, Ventilation, and Air Conditioning) module is blocked on the air side. BV1 is open and the refrigerant flows through it without throttling. The outside HX functions as a condenser. BV3 is closed and the refrigerant has to be throttled by EXV3. The inner evaporator is in charge of cooling the air

Fig. 1. Schematic diagram of EVI heat pump system [2]. 2

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Fig. 2. Experimental setup for EVI heat pump performance test.

Uncertainty analysis is performed in order to verify the measured data of the cooling/heating capacity and COP using Eq. (5) [22]. Propagated uncertainties are estimated while calculating the final results from the experimental measurements. Overall uncertainty is represented as δE, and δXi represents the uncertainty of its affecting factors. After calculation, the relative uncertainties for Q and COP are 5.5% and 6.3% respectively.

entering HVAC. When in heating mode, BV1 is closed and the refrigerant is throttled by EXV1. The outside HX functions as an evaporator this time. The opening of BV3 and EXV3 depend on whether dehumidification is required. When BV2 is closed, there is no vapor injection into the compressor. When BV2 is open, the refrigerant split from the condenser outlet is first throttled by EXV2 and then heated by the economizer. The opening of EXV2 can control the injection pressure and mass flow rate into the compressor. In our case, we investigated the heat pump performance with EVI working.

δE = E

2

N

∂E

∑i =1 ( ∂Xi δXi )2

(5)

2.2. Test facility 2.3. Test conditions

The test facility is shown in Fig. 2. The inner condenser and inner evaporator are packaged in an HVAC module, installed in the indoor chamber. Compressor, separator, and outside HX are installed in the outdoor chamber. The location of sensors is shown in Fig. 2. The capacity (Q) of the tested EVI heat pump was determined by the average of air-side and refrigerant side heat transfer rate using Eq. (1). The air side heat transfer was calculated using Eq. (2). The refrigerant side heat transfer rate was obtained by the enthalpy difference calculation, using Eq. (3). The properties of the R134a refrigerant were calculated according to the NIST REFPROP 9.1. The work consumption is the product of compressor voltage and input current, and the overall system COP was determined by Eq. (4). Analysis of the experimental results indicated that the errors between the heat transfer rate for the air side and the refrigerant side were within ± 5%.

Q = (Qair + Qref )/2

(1)

Qair = ṁ air Cp (Tair , out − Tair , in)

(2)

Qref = ṁ ref (href , out − href , in )

(3)

COP = Q/ W

(4)

The test conditions are designed to investigate the EVI heat pump system under different outdoor temperatures, indoor temperatures, and compressor speeds. There are totally 14 test conditions, as is concluded in Table 3. In each condition, the injection pressure is adjusted by EXV2 to 5 levels to investigate the impact of injection pressure on the system heating performance. 3. Methodology 3.1. Feature selection method Choosing appropriate features as the input is vital for the machine Table 1 Sensor type and uncertainty.

The uncertainty of the sensor used in the experiment and the information of the composition applied is presented in Tables 1 and 2. 3

Items

Range

Uncertainty

Temperature sensors Pressure sensors Mass flow rate (Coriolis type) Current sensors Voltage sensors

−50–200 ℃ 0–4 MPa 0–200 kg/h 0–25 A 0–400 V

± 0.05 ℃ ± 10 kPa ± 1.2 kg/h ± 0.05 A ± 0.1

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Table 2 Component information. Components

Information

Compressor Outside HX Inner Condenser Evaporator HVAC Economizer EXV1 EXV2 EXV3

34 cc/r. 1000–8500 rpm. 660 × 500 × 16 (mm) 225 × 125 × 27 (mm) 232 × 239.5 × 38 (mm) Max 400 m3/h @Foot Mode 290 × 73(L × W, mm),12 plate Ф9.2 mm Ф1.65 mm Ф5.5 mm

learning model. When the number of input features is small, it is likely to cause underfitting problems, meaning that the information provided by the data is not enough for the model to make good predictions. Adding additional features to the model or feature engineering are recommended under such circumstances. When too many features are feeding to the model, overfitting occurs due to the increasing model complexity. Choosing appropriate features relies not only on the comprehensive understanding of the system but a good mathematical method to determine whether a feature is important to the prediction outcome or not. In our study, six features will determine the system working status, including three environment features: outdoor temperature, indoor temperature, and indoor air mass flow rate; one feature for the most important device: compressor speed; and two features for the controlling devices: the opening of EXV1 and EXV2. When the six features are fixed, the heat pump heat system will finally converge to a steady state. That means at least six features should be chosen as the input features. In real cases, operating parameters, such as discharge pressure, compressor suction pressure and so on, are often used to investigate the heat pump performance, instead of the opening of the electric expansion valve. Hence, operating parameters which have stronger influences on the system heating capacity and COP, can be used to replace the opening of EXV1 and EXV2 as input features, or be added to the model. Correlation analysis is hence performed. In this paper, the Pearson correlation coefficient method [23] is used to determine which parameter have stronger correlations with the other one. The expression is shown in Eq. (6), where x and y represent two different features, μ represents mean value, and σ represent standard deviation. The value of the Pearson correlation coefficient is between [−1,1]. The larger the absolute value of the Pearson correlation coefficient, the stronger connection between the wo features.

ρx , y =

Fig. 3. Schematic diagram of the main loop and second loop.

model. Feature engineering can be performed in this process to build new features that are related to the system performance in physical meaning. The same method applies to the second loop. Fig. 4 shows the correlation coefficients of different features with Q and COP. Different feature sets can be formed using the idea mentioned above, as presented in Table 4. Features in Table 4 such as πmain, πinj and Tsh,inj can be calculated using the present features without being further collected from the experiment test bench. The expressions are presented below: (7)

πinj = Pdis / Pinj

(8)

Tsh, inj = Tinj − Tsat (Pinj )

(9)

3.2. Machine learning method 3.2.1. SVR algorithm SVR (Support Vector Regression) is a powerful machine learning tool which is firmly grounded in the framework of statistical learning theory [24]. In this study, ε -SVR with Gaussian RBF (Radial Basis Function) kernel is proposed to predict the EVI heat pump performance. In ε-SVR, our goal is to find a function f (x) that has at most ε deviation from the actually obtained targets y for all the training data, and at the same time is as flat as possible [25]. The introduction of kernel function into SVR makes the model capable of addressing nonlinear problems. The kernel function can transform data into another (usually larger) dimension to be more separable. The Gaussian RBF kernel used in this study is expressed in Eq. (10).

E ((x − μx ) ∗ (y − μ y )) σx ∗ σy

πmain = Pdis / Pevap, in

(6)

k〈x i , x j 〉 = exp(−γ ||x i − x j ||2 )

As is illustrated in Fig. 3, the EVI heat pump system consists of two loops: the main loop and the second loop. EXV1 is in charge of controlling the operating parameters along the main loop, and EXV2 is in charge of controlling those on the second loop. Using Pearson correlation coefficient method, operating parameters along the main loop, which has larger Pearson correlation coefficient with Q or COP than EXV1, can be used to replace the EXV1 feature, or be added to the

(10)

The SVR algorithms can be expressed in the form of a convex optimization problem shown in Eq. (11). The equation can be considered as a combination of empirical risk and structure risk. m

Min

1 ||ω||2 + C ∑ lε (f (x i ) − yi ) 2 i=1

(11)

Table 3 Test conditions. Index

Outside HX facing velocity (m/s)

Indoor air volume (m3/h)

Tout door (°C)

Tin door (°C)

Compressor speed (RPM)

Injection pressure level

1 2 3 4 5 6

4

300

0 0 −10 −10 −20 −20

0 20 0 20 −7 20

5500 5500 4000/5500/7000 4000/5500/7000 4000/5500/7000 4000/5500/7000

5

4

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R134a Q

MFR_inj T_sc ʌ_ inj T_sh,inj COP T_dis ij_inj T_cond,out EXV1-Opening ʌ_ main P_dis EXV2-Opening T_inj T_sh,dis P_inj T_suc MFR_main P_suc P_evap,in 0.0

0.1

0.2

0.3

0.4

0.5

0.6

R134a COP

P_inj T_inj Q EXV2-Opening T_suc T_sc EXV1-Opening P_suc T_sh,inj P_evap,in ij_inj MFR_main T_sh,dis MFR_inj ʌ_ inj T_dis P_dis T_cond,out ʌ_ main

0.7

0.0

0.1

0.2

Absolute Correlation Coefficient

0.3

0.4

0.5

0.6

0.7

0.8

Absolute Correlation Coefficient

Fig. 4. Absolute correlation coefficient with Q and COP. Table 4 Feature sets for the model input. Name

Including features

FS1 FS2 FS3 FS4 FS5

N, N, N, N, N,

Tout, Tout, Tout, Tout, Tout,

Tin, Tin, Tin, Tin, Tin,

MFRair,in, MFRair,in, MFRair,in, MFRair,in, MFRair,in,

EXV1-Opening, EXV2-Opening Pdis, Pinj, πinj Pdis, Pinj, πinj, Pevap,in, πmain Pdis, Pinj, πinj, Pevap,in, πmain, Tinj, Tsh,inj Pdis, Pinj, πinj, Pevap,in, πmain, Tinj, Tsh,inj, Tdis, Tcond,out

Feature numbers

Collected feature numbers

6 7 9 11 13

6 6 7 8 10

0.25 1.00 0.20

0.15

Score R134a Train Score R134a Test RMSE R134a Train RMSE R134a Test

0.90

RMSE

R2_score

0.95

0.10

0.85

0.05

0.00

0.80 1

2

3

4

5

Feature Sets Fig. 6. Performances of different feature sets for (a) heating capacity prediction and (b) COP prediction (b).

Introduced with slack variables ξ , Eq. (11) can be rewritten as: Fig. 5. Flow chart of the machine learning procedure.

m

Min Table 5 Optimization range of SVR and Adaboost.R2 parameter. Parameter C ε γ n_round

1 ||ω||2 + C ∑ (ξi + ξi∗) 2 i=1 f (x i ) − yi ≤ ε + ξi ⎫ ⎧ ⎪ ⎪ yi − f (x i ) ≤ ε + ξi∗ ⎨ ⎬ ⎪ ⎪ ξi, ξi∗ ≥ 0 ⎩ ⎭

Range

Constraints:

[0.1, 0.2, 0.5, 0.8, 1, 2, 5, 8, 10, 15, 20] [0.01, 0.02, 0.05, 0.1, 0.2, 0.5] [1/50, 1/40, 1/30, 1/20, 1/15, 1/10, 1/8, 1/7, 1/6, 1/5] [25, 50, 100, 200]

The dual optimization problem is shown below. The kernel function is applied in this process.

The ε -insensitive loss function can be expressed as such:

0, if |x| ≤ ε l∊ (x ) = ⎧ ⎨ ⎩|x| − ε , otherwise

(13)

m

Max αi∗, αi ∑i = 1 yi (αi∗ −αi ) − ε (αi∗ +αi ) − (12) 5

1 2

m

m

∑i = 1 ∑ j = 1 (αi∗ −αi )(α∗j −αj ) k〈x i , x j 〉

(14)

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(a)

3.5

3.5

Simulation Capacity +10% -10%

2.5

2.0

2.5

2.0

1.5

1.5

1.0

1.0 1.0

1.5

Simulation COP +10% -10%

3.0

Simulation COP

Simulation Capacity (kW)

3.0

(b)

2.0

2.5

3.0

1.0

1.5

Experiment Capacity (kW)

2.0

2.5

3.0

Experiment COP

Fig. 7. Comparison between simulation result and experiment result (a) Heating capacity (b) COP.

Q(kW) ij_inj T_cond,in (

50

0.4

45

0.3

40

ij_inj

Q (kW)

2.0

0.5

0.2

35

0.1

30

0.0 0.40

25

They have to be fine-tuned to improve model performance. The C parameter is regarded as the regularization coefficient. The γ parameter defines how far the influence of a single training example reaches, with small values meaning ‘far’ and large values meaning ‘close’. The larger C and larger γ have the same influence on the model: more support vectors, more complexity, and more chances of overfitting. If they are too small, the model is too ‘flat’, and underfitting occurs. The ε parameter defines the maximum deviation that can be tolerated by the SVR. When ε is small, it has the same effect as a large C and large γ .

T_cond,in (°C)

2.4

1.6

1.2 0.20

0.25

0.30

0.35

3.2.2. Adaboost.R2 algorithm Boosting is an ensemble method often used in machine learning to build a committee of regressors that may be superior to a single regressor. Adaboost.R2 [26] is a famous boosting algorithm for regression, and it is applied in this paper for regression tasks. Briefly, the Adaboost.R2 algorithm is intended to adjust the weights for training samples. If the predicted value of a certain sample deviates from its true value, then the weight of it will be increased in the next round, making the sample paid more attention to by the model. The machines are trained sequentially in this algorithm. The calculating procedure can be expressed as followed. In the first round, the weight of each sample in the training set is initialized as 1. And the probability that training sample i is in the training set is regarded as pi.

Injection Pressure (Mpa)

Fig. 8. Effect of injection pressure on the heat pump system (@-10/20 ℃, 4000RPM). m

Constraints:

∗ ⎧ ∑i = 1 (αi −αi ) = 0 ⎫ ⎨ 0 ≤ αi∗,αi ≤ C ⎬ ⎩ ⎭

And the function that we obtain from the optimization problem is: m

f (x ) =

∑ (αi∗ −αi) k〈xi , x〉 + b

pi =

The penalty parameter C, the deviation ε and the kernel coefficient γ are 3 important hyper-parameters during the SVR calculating process.

3.2

wi m ∑i = 1 wi

(17)

[email protected] [email protected] [email protected] [email protected] [email protected] [email protected]

(a) 2.4

(b)

2.0

2.4

Q (kW)

Q (kW)

2.8

[email protected] [email protected] [email protected] [email protected] [email protected] [email protected]

(16)

wi = 1i = 1, 2, ⋯, m

(15)

i=1

2.0

1.6

1.6 1.2 1.2 0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.10

P_inj (Mpa)

0.15

0.20

0.25

P_inj (Mpa)

Fig. 9. Effect of injection pressure on the heating performance (a) @-10/20 ℃ (b) @-20/20 ℃. 6

0.30

0.35

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prevent one feature from far outweighing another one. In regression tasks, standardization can help reduce multicollinearity issues for models containing interaction terms.

A machine is trained using the weights. And a mapping from input features xi to outcome f(xi) is established using the machine in each round. The loss of each training sample is Li, and the maximum deviation of all the training data is D. And linear loss function is used in this study.

D = sup |yi − f (x i )|

i = 1, 2, ⋯, m

|y − f (x i )| Li = i D

4.2. Feature selection & model optimization

(18) The method for feature selection can be referred to in Section 3.1. Five feature sets as described in Table 4 are selected as the model input to test their performances. The model used for each feature set is optimized, and the optimization target is maximum r2score of the test set. The optimized parameters are C, ε, γ and n_round respectively, and the optimization range of them are presented in Table 5. Fig. 6 shows the performances of different feature sets for heating capacity and COP prediction. A higher r2score and a lower RMSE suggest better prediction performance. As indicated in Fig. 6, with growing numbers of feature input from FS1 to FS5, the r2score of the train set tend to increase, which states that more feature input is likely to increase the ability of the model to fit the train set. In heating capacity prediction, the r2score of FS2 is the highest. In COP prediction, the r2score of FS3 is the highest, but the r2score of FS2 is only a bit lower. This suggests that FS2 is an appropriate feature set for both heating capacity and COP prediction. Also, FS2 requires the least features that have to be collected from the system (same as FS1) among these feature sets, which makes it more applicable when it comes to practical use. A larger number of features seems disadvantageous to the model performance for the test set. This may be attributed to the fact that more features increase the model complexity, and overfitting may occur. The optimized parameters (C, ε, γ and n_round) for the heating capacity prediction model (FS2 as the input) are 20, 0.01, 0.02 and 25. For the COP prediction model, parameters are 5, 0.01, 0.05 and 25.

(19)

The average loss L¯ and the weight for each machine β can be determined. m

L¯ =

β=

∑ Li pi i=1

(20)

L¯ 1 − L¯

(21)

In the next round, the weight for each sample can be updated, and the new weights are used to train a new machine.

wi = wi β1 − Li

(22)

The Adaboost.R2 algorithm will not stop until the maximum training rounds n_round (exactly the number of trained machines) that we set is reached or L¯ exceeds 0.5. The final prediction of the model is the weighed median of all the values predicted by machines, instead of the weighted mean. The reason why we choose Adaboost.R2 as the ensemble method in performance prediction of refrigeration or heat pump system is that the system operates under very different conditions. Data obtained under regular conditions (regular compressor speed, regular ambient temperature, etc.) are much more than those obtained under irregular ones. The Adaboost.R2 algorithm can cope with data nonuniformity and sparsity issues. With the application of Adaboost.R2, data obtained under irregular conditions can be more attended to, and the overall prediction errors can be decreased.

5. Result and discussion 5.1. Comparison with the experiment results A comparison between the simulation results and experiment results (including both train set and test set) is carried out. As illustrated in Fig. 7, the simulation results are in good agreement with the experiment results. The maximum errors for capacity and COP prediction are 8.25% and 8.33% respectively. This indicates that the models established are applicable under almost all the experiment conditions, which are quite complex.

3.3. Model performance evaluation Two performance indexes are used to evaluate model performance in this study, namely r2score and RMSE (Root Mean Square Error). m

r 2score = 1 −

RMSE =

∑i = 1 (f (x i ) − yi )2 m

∑i = 1 (y¯ − yi )2

m ∑i = 1

(23) 5.2. Effect of the injection pressure

(f (x i ) − yi )2 m

(24)

The major difference between a conventional heat pump and an EVI heat pump lies in the second loop described in Fig. 3. Hence, the injection parameters along the second loop should be studied to understand their influence on the system performance. Among them, the most critical one is the injection pressure Pinj [27]. The injection pressure has an impact on the condenser inlet temperature, as well as the injection mass flow rate. The experiment shows the effect of the injection pressure, as described in Fig. 8. φinj indicates the injection ratio, and the expression of it is shown in Eq. (25).

The r2score is less than 1. The closer value of r2score to 1, the better model regression performance is achieved. Meanwhile, the smaller the value of RMSE also indicates better model prediction performance. 4. Machine learning modeling The machine learning procedure can be summarized as the flow chart shown in Fig. 5.

φinj = MFRinj/MFRmain

4.1. Data preprocessing

(25)

The expansion valve on the second loop (EXV2 in Fig. 2) controls the injection pressure. When the opening of the valve is larger, the injection pressure grows, and as a result the injection mass flow rate increases, which is beneficial to the heating capacity. A larger injection ratio is also observed due to this effect. However, as the injection ratio grows to some point, the compressor may be further cooled down and the discharge temperature decreases. This is disadvantageous to the heating capacity because the temperature difference between the refrigerant side and air side in the condenser is hence decreased.

As is described in Section 2.3, there are totally 14 test conditions. Under each test conditions, the injection pressure is adjusted to 5 levels. Therefore, 70 samples are available. 80% of the samples are randomly separated into the train set, and the remaining 20% are separated into the test set. Data standardization is needed before we can proceed with machine learning modeling. Standardization means to rescale your data to have a mean of zero and a standard deviation of one. Standardization can 7

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Therefore, there exists an optimum injection pressure, where the system heating capacity reaches its maximum. However, it’s difficult to find the optimum injection pressure because it varies greatly under different working conditions. Also, the working conditions of EVI are quite complex, and the operating parameters of the system are heavily coupled, making us hard to find which parameters we should count on to find the optimum injection pressure. The model established in this study may find a solution to this problem. As illustrated in Fig. 9, the simulated results of injection pressure’s effect share a similar trend with the experiment results: initially, increasing injection pressure leads to a larger heating capacity; when the injection pressure is beyond the optimum one, the heating capacity starts to decrease. Also, there is not much difference between the optimum injection pressure simulated by the model and found in the experiment. Hence the optimum injection pressure can be roughly estimated using the machine learning model.

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6. Conclusion A method to predict the performance of an EVI heat pump is proposed in the present study. The procedure of this method is as the following: data standardization, train/test split, feature selection, model optimization, and performance prediction. SVR and Adaboost.R2 are applied in the modeling process. The conclusions are summarized below: (1) FS2 (including N, Tout, Tin, MFRair,in, Pdis, Pinj, πinj) is the best feature set for model input. (2) The models established can predict the heating capacity and COP within an error margin of 8.25% and 8.33% respectively. (3) The effects of injection pressure on the heat pump system can be simulated and optimum injection pressure for the system can be estimated using the model established. In conclusion, the machine learning model is a powerful tool to predict the performance of EVI heat pump system. Meanwhile, it poses some potential in finding the optimum operating parameters of the system. References [1] H. Khayyam, A.Z. Kouzani, E.J. Hu, S. Nahavandi, Coordinated energy management of vehicle air conditioning system, Appl. Therm. Eng. 31 (5) (2011) 750–764. [2] Z. Zhang, W. Li, C. Zhang, J. Chen, Climate control loads prediction of electric vehicles, Appl. Therm. Eng. 110 (2016) 1183–1188. [3] L. Cichong, Z. Yun, G. Tianyuan, S. Junye, C. Jiangping, W. Tianying, et al., Performance evaluation of propane heat pump system for electric vehicle in cold climate, Int. J. Refrig. (2018) S0140700718303165-. [4] W. Dandong, Y. Binbin, L. Wanyong, S. Junye, C. Jiangping, Heating performance evaluation of a co 2, heat pump system for an electrical vehicle at cold ambient

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