Artificial neural network (ANN) based prediction and optimization of an organic Rankine cycle (ORC) for diesel engine waste heat recovery

Artificial neural network (ANN) based prediction and optimization of an organic Rankine cycle (ORC) for diesel engine waste heat recovery

Energy Conversion and Management 164 (2018) 15–26 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www.e...

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Energy Conversion and Management 164 (2018) 15–26

Contents lists available at ScienceDirect

Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Artificial neural network (ANN) based prediction and optimization of an organic Rankine cycle (ORC) for diesel engine waste heat recovery ⁎

T



Fubin Yanga,b,c, Heejin Chob, , Hongguang Zhanga,c, , Jian Zhangb, Yuting Wua,d a

College of Environmental and Energy Engineering, Beijing University of Technology, Pingleyuan No. 100, Beijing 100124, China Department of Mechanical Engineering, Mississippi State University, 210 Carpenter Engineering Building, P.O. Box 9552, Mississippi State, MS 39762, USA c Collaborative Innovation Center of Electric Vehicles in Beijing, Pingleyuan No. 100, Beijing 100124, China d Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Ministry of Education, Beijing University of Technology, Pingleyuan No. 100, Beijing 100124, China b

A R T I C L E I N F O

A B S T R A C T

Keywords: Diesel engine Organic Rankine cycle Artificial neural network Waste heat recovery Optimization

This paper presents performance prediction and optimization of an organic Rankine cycle (ORC) for diesel engine waste heat recovery based on artificial neural network (ANN). An ANN based prediction model of the ORC system is established with consideration of mean squared error and correlation coefficient. A test bench of combined diesel engine and ORC waste heat recovery system is developed, and the experimental data used to train and test the proposed ANN model are collected. A genetic algorithm (GA) is also considered in this study to increase prediction accuracy, and the ANN model is evaluated with different learning rates, train functions and parameter settings. A prediction accuracy comparison of the ANN model with and without using GA is presented. The effects of seven key operating parameters on the power output of the ORC system are investigated. Finally, a performance prediction and parametric optimization for the ORC system are conducted based on the proposed ANN model. The results show that prediction error of the ANN model with using the GA is lower than that without using GA. Therefore, it is recommended to optimize the weights of the ANN model with GA for a high prediction accuracy. The proposed ANN model shows a strong learning ability and good generalization performance. Compared to the experimental data, the maximum relative error is less than 5%. The experimental results after optimizing the operating parameters are very close to ANN’s predictions, indicating one or more operating parameters can be adjusted to obtain a higher power output during the experiment process.

1. Introduction With the rapid development of automotive industry, energy saving and emission reduction have become important aspects in recent decades. Generally, a traditional internal combustion (IC) engines can only convert less than 40% of the fuel combustion energy into useful power output. Although many innovative technologies, including gasoline direct injection (GDI), turbo direct injection (TDI), homogeneous charge compression ignition (HCCI), and fuel stratified injection (FSI), have been considered and adopted in recent years, the thermal efficiency of the IC engine has not been improved much. Waste heat recovery is considered to be one of the most promising methods for improving the overall energy conversion efficiency of the IC engine [1,2]. Among various technologies of recovering waste heat from the IC engines, organic Rankine cycle (ORC) has been widely considered because of its outstanding features, such as low initial investment,

configuration simplicity, and high efficiency [3–6]. Most of current investigations are mainly focused on the theoretical or thermodynamic analysis [7–11]. Chen et al. designed a novel cascade ORC system, which can recover waste heat from both engine exhaust gas and coolant [12]. Zhao et al. developed a simulation model of diesel engine and ORC combined system and discussed the steady and transient performances of the combined system [13]. Galindo et al. optimized a bottoming ORC system coupled with a gasoline engine from the view point of thermoeconomic and sizing criteria [14]. Yang et al. investigated the economic performance of a transcritical ORC for recovering waste heat from exhaust gas, coolant, scavenge air cooling water and lubricating oil of a large marine diesel engine [15]. Yue et al. proposed two thermodynamic models of a bottoming ORC and diesel engine combined power system and studied the effect on the power output of the proposed models [16]. While thermodynamic analysis of ORC systems has been widely

⁎ Corresponding authors at: Department of Mechanical Engineering, Mississippi State University (H. Cho); College of Environmental and Energy Engineering, Beijing University of Technology (H. Zhang). E-mail addresses: [email protected] (H. Cho), [email protected] (H. Zhang).

https://doi.org/10.1016/j.enconman.2018.02.062 Received 21 October 2017; Received in revised form 11 February 2018; Accepted 16 February 2018 0196-8904/ © 2018 Elsevier Ltd. All rights reserved.

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Nomenclature

V̇ p T Tor Ẇ w b

out h o

volume flow rate (L/min) pressure (bar) temperature (°C) torque (N m) power (kW) weight bias

Acronyms ORC ANN GA GDI TDI HCCI FSI BP MSE R

Subscripts

exp con p in

outlet hidden layer output layer

expander condenser pump inlet

organic Rankine cycle artificial neural network genetic algorithm gasoline direct injection turbo direct injection homogeneous charge compression ignition fuel stratified injection back propagation mean squared error correlation coefficient

that includes five main components (i.e., evaporator, expander, condenser, reservoir, and pump), performance with various component designs and operating conditions may not be accurately predicted because of nonlinear behaviors. Therefore, improving the modeling accuracy of ORC system is a critical path to determine optimal system configurations and control strategies in more precise and reliable manner. To address this challenge, this study proposes an ANN-based model to predict and optimize the transient performance of the ORC system for IC engine exhaust waste recovery. Artificial neural network, as a nonlinear modeling tool, is inspired by the biological neural networks. To the best of our knowledge, there is currently no existing ANN-based ORC models that are established for IC engine waste heat recovery. Furthermore, at the present time there is a lack of valid experimental data for IC engine waste heat recovery based on ORC system. We authors would like to open a broad range of possibilities for system performance prediction and optimization and try different methods of improving as high as possible the prediction accuracy for the transient performance of the ORC system. In this paper, a test bench of combined diesel engine and ORC waste heat recovery system is developed first to generate the experimental data used to train and test the ANN model. A genetic algorithm (GA) is also considered in this study to increase prediction accuracy, and the ANN model is evaluated with different learning rates, train functions and parameter settings. Then an ANN based prediction model of the ORC system incorporated with GA is established and a prediction accuracy comparison of the ANN model with and without using GA is presented. The effects of key operating parameters are further investigated using the proposed ANN model. Finally, a performance prediction and parametric optimization for the ORC system are conducted based on the proposed ANN model.

performed, some researchers have investigated its performance experimentally. It has been realized that although the whole ORC system, mainly including five components, is not complex, achieving an theoretical power output for a small scale ORC system experimentally is difficult and challenging [17,18]. One of the main barriers is due to the technical limitation of kW-scale expanders [19–21] and some research works have been conducted to understand/address such issues through experimentally studies. Zhang et al. developed an ORC-based experimental system to recover exhaust waste heat from a diesel engine with a single screw expander [22]. Their results indicated that the maximum power output of 15 kW using an ORC system can be achieved at a diesel engine rated condition of 250 kW. Shu et al. constructed a thermal oil storage/ORC system for exhaust waste heat recovery from a 240 kW diesel engine [23]. In their study, the expander was replaced by an expansion valve to estimate the potential power output. Galindo et al. evaluated the effect of adding an ORC waste heat recovery system on a turbocharged gasoline engine and showed that the maximum power output of 1.83 kW could be achieved using a swash-plate expander [24]. Gaps between theoretical and experimental studies are not only present in the area of ORC-based heat recovery, but also in many thermal energy engineering fields. Many researchers have tried to fill this gap by adopting new modeling techniques that can predict system performance in more accurate manners. In recent years, the artificial neural network (ANN) method has been widely adopted in the field of thermal energy engineering for design and performance optimization because of the advantages of self-adaption, self-learning, nonlinear mapping and fault tolerance. Li et al. compared three different types of ANN models for wind speed forecast [25]. Zhao et al. designed and trained an ANN model to optimize the geometrical compression ratio and operating parameters of an Atkinson cycle engine [26]. Boukelia et al. presented an optimization of a parabolic trough solar thermal power plant based on a feed-forward back-propagation ANN model [27]. Arslan et al. proposed an ANN model for the evaluation of a supercritical ORC-Binary geothermal power system by considering various learning algorithms [28]. Rashidi et al. investigated the thermodynamic performance of an ejector refrigeration cycle using an ANN method [29]. As briefly discussed above, the current literature shows that the experimental results from many ORC studies are far from theoretical values [23,30]. Most of the thermodynamic models cannot provide accurate transient predictions of the ORC system behavior [18,23]. This is due to the fact that no pressure drops, heat losses and other factors affecting the actual system performance are considered in most of the thermodynamic models. The isentropic efficiencies of the expander and pump are usually kept at a constant value, and the whole system is assumed to be under steady state. Even for a simple ORC configuration

2. Test bench of waste heat recovery system The schematic diagram of the waste heat recovery system is shown in Fig. 1. It can be seen that the whole waste heat recovery system consists of two subsystems including a diesel engine and an ORC system. 2.1. Test bench of diesel engine In this study, exhaust gas discharged from an in-line six cylinder heavy duty diesel engine is the waste heat source for the ORC system. The main technical parameters of the diesel engine are listed in Table 1. An eddy current dynamometer is coupled with the diesel engine to control engine load. Experimental data is collected by the dynamometer control system. The test bench of the diesel engine is shown in Fig. 2. An exhaust port of the diesel engine is connected with an evaporator by bellows. Exhaust gas, after exchanging heat with working fluid in the 16

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Fig. 1. Schematic diagram of the waste heat recovery system.

Table 1 Main technical parameters of the diesel engine. Items

Parameters

Cylinder number Rated power Displacement Maximum torque Cylinder arrangement Ignition type Fuel injection system Air intake type

6 247 9.726 1500 In-line Compression ignition High pressure common rail Turbocharged and Intercooled

Units

kW L Nm

evaporator, is discharged into the environment. Mass flow meter, temperature and pressure sensors are used to measure the exhaust gas parameters of the diesel engine.

Fig. 2. Test bench of the diesel engine.

2.2. Test bench of ORC system

2.2.3. Condenser To reduce the back pressure of the expander, an aluminum parallel flow heat exchanger is considered and adopted as a condenser in this study. High performance louvered fins are used on air side for heat transfer enhancement. A fan is installed inside the heat exchanger to enhance air flow. More detailed parameters of the condenser are listed in Table 4.

The ORC system constructed in this study is shown in Fig. 3. It mainly consists of an evaporator, an expander, a condenser, a reservoir and a pump, as well as auxiliary pipes, valves, sensors and a set of data acquisition system. To enhance heat dissipation, the condenser is placed outdoor. The main components of the ORC system are introduced in detail below.

2.2.4. Pump A multistage centrifugal pump is selected as a working fluid pump owing to its advantages of stable operation, low vibration, long lifetime and high efficiency [32]. A check valve is placed at the outlet of the pump to regulate the working fluid flow rate. More detailed parameters of the pump are listed in Table 5.

2.2.1. Evaporator The evaporator used in this work is a spiral tube heat exchanger, where exhaust gas is on the shell side and working fluid is on the tube side. In order to achieve weight reduction, heat transfer tube is made of titanium alloy. More detailed parameters of the spiral tube evaporator are listed in Table 2.

2.3. Experimental strategy 2.2.2. Expander The expander is the most important component for heat-to-work conversion in ORC system. As shown in Fig. 4, a single screw expander is used in this work, which is developed by our research group [22]. Main parameters of the expander are listed in Table 3. Single screw expanders are a novel displacement type machine and are more appropriate for small scale ORC applications [31].

Three control methods are used to change the operating conditions. First, when the diesel engine warm-up is completed, the engine load at a certain speed is controlled to vary. Second, surplus working fluid is controlled adding a working fluid return pipe at the outlet of the pump to return it to the reservoir (see Fig. 1). Last, a dynamometer control system is equipped to control expander speed and load. During the 17

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Fuel tank Pump

Diesel engine

Evaporator Expander

Condenser

Reservoir Fig. 3. Test bench of the ORC system.

and presents better thermodynamic performances than other fluids in low temperature waste heat recovery applications [5,22,23,31–33]. The working fluid pump circulates R123 in the ORC system. At this stage, the working fluid does not enter the expander, whereas goes through the by-pass line as shown in Fig. 1. When the diesel engine starts and the load increases to 20%, the fan of the condenser is turned on. To achieve a power output of the ORC system as high as possible, the diesel engine should operate at high speed and high load conditions. In the whole test process, the diesel engine operates at speeds between 1800 and 1900 rpm with the engine load above 70%. During the test period, the engine speed and load remain unchanged. The by-pass line is closed. All testing and recording is conducted under different working fluid flow rates and expander torques, then adjusting the engine load to change the exhaust waste heat characteristics. Until all tests are completed, the ORC system operates for a while at an engine idle condition and the by-pass line is opened again. Finally, the diesel engine, ORC system and water pump are turned off in sequence.

Table 2 Main design parameters of the evaporator. Items

Parameters

Units

Tube inner diameter Tube wall thickness Shell diameter Shell length Shell wall thickness Heat transfer area Weight

16 1.2 500 1500 4 12 142

mm mm mm mm mm m2 kg

2.4. Experimental data According to the aforementioned strategy, the experimental data are obtained. During the test period, the diesel engine operates at a constant condition with the speed of 1900 rpm and torque of 900 N m. After that, two control methods are used to change the operating parameters of the ORC system. The working fluid flow rate, which is the only parameter that can control to change other operating parameters in an actual ORC system, is varied from 14.59 to 25.42 L/min by regulating the valve opening at the outlet of the pump. Considering ORC as an integrated whole, other operating parameters vary with the working fluid flow rate. At the same time, the expander is controlled at the constant torque mode, ranging from 12.7 to 55.4 N m. The whole experiment takes about 40 min and all experimental data are recorded in time sequence by data acquisition system. Some repetitive experimental data are removed and the data sequence is rearranged to improve the prediction accuracy and robustness of the proposed ANN model. Finally, total 2100 typical experimental data are obtained. Part of these experimental data is listed in Table 6, which are used to train and test the ANN model.

Fig. 4. Single screw expander.

experiment process, the expander is controlled at the constant torque mode. At the beginning of the experiment, water pump supplies circulating cooling water to the dynamometers. Lubricant is injected into the expander and mixed with the working fluid. The data acquisition system begins to work and monitor the operating parameters of the ORC system. R123 is selected as the working fluid due to its outstanding performances. R123 has been considered in other experimental studies

3. Artificial neural network Artificial neural network is a computing model, which is composed of a collection of artificial neurons. Each artificial neuron represents a particular output function called activation function, while each 18

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The back propagation refers to that an input vector is propagated forward through the neural network, while the error values are propagated backward. It generally includes an input layer, one or more hidden layers, and an output layer. Gradient descent algorithm is used in a typical BP neural network.

Table 3 Main parameters of the expander. Items

Parameters

Units

Screw diameter Gaterotor diameter Tooth number of Gaterotor Groove number of screw Center distance

155 155 11 6 124

mm mm

3.2. ANN based model of the ORC system mm

This study aims to present a high accuracy prediction on the behavior of an established ORC system. Therefore, the input vector of the ANN model needs to include as much parameter as possible. Seven key operating parameters of the ORC system, including working fluid volume flow rate (V̇ ), expander torque (Torexp ), expander inlet pressure ( pexp,in ), expander outlet pressure ( pexp,out ), expander inlet temperature (Texp,in ), condenser outlet temperature (Tcon,out ) and pump outlet pressure ( pp,out ), are selected as the input vectors. The reasons for selecting the above mentioned seven operating parameters are provided as follows. When operating condition of the diesel engine is determined, volume flow rate and expander torque can be regulated. Working fluid flow rate is the only parameter that we can control to change other operating parameters in an actual ORC system. Expander inlet and outlet pressures determine the expansion ratio affecting the final power output. Superheat degree is also closely related to the expander inlet temperature and pressure. In addition, lowering condenser outlet temperature is beneficial to improve the thermal efficiency of the ORC system. Circulating water flow rate of the cooling tower or operation frequency of the air-cooled heat exchanger need to be regulated based on the condenser outlet temperature. Furthermore, pump outlet pressure affects operation pressure of the whole ORC system. A single hidden layer BP neural network is considered to simplify the computation. The hidden layer neurons number for the BP model is determined by Refs. [25,34]. The output layer is the power output of the single screw expander. The topology of the BP neural network model is illustrated in Fig. 5.

Table 4 Main design parameters of the condenser. Items

Parameters

Units

Fin spacing Fin height Tube width Tube thickness Windward area Size Weight

1.4 6.85 25.47 2 1.02 980 × 980 × 125 98

mm mm mm mm m2 mm kg

Table 5 Main parameters of the pump. Items

Parameters

Units

Rotational speed Volume flow rate Designed head Stages Weight

2919 2.98 205 32 81.9

rpm m3/h m – kg

connection between two neurons has a weight that represents the memory of an ANN model. ANN method can be used to deal with highly nonlinear, non-limitation and non-convexity systems. The output of an ANN model is dependent on connection modes, weights and activation functions, which can be expressed as:

3.3. Evaluation of the ANN model

where f is the activation function, w is the weight value, x is the input vector, and b is the bias value.

To evaluate the prediction performance of the ANN model, two common metrics are used in this work. The first one is mean squared error (MSE), which is a convenient method to measure the average change in data. Generally, a low MSE value represents a high-accuracy prediction. The MSE can be expressed as:

3.1. BP neural networks

MSE =

y = f ( ∑ wij x j + b) (1)

j

Although various methods have been developed to improve the prediction accuracy of ANN model, back propagation (BP) neural network is still one of the most popular techniques in this field [25,26].

1 Q

Q



[y (k)−t (k)]2 (2)

k= 1

where y (k) and t (k) are the prediction value and experiment data, respectively. The other metric is correlation coefficient between the prediction

Table 6 Part of the experiment data. No.

V̇ (L/min)

pexp,in (bar)

pexp,out (bar)

Texp,in (°C)

Tcon,out (°C)

pp,out (bar)

Torexp (N m)

̇ Wexp (kW)

1 2 3 4 5 6 7 8 9 10 ⋮ 2098 2099 2100

25.42 22.11 21.61 23.22 21.89 18.02 14.84 15.98 19.18 23.78 ⋮ 18.45 21.55 22.93

9.5 10.4 9.8 9.1 8.6 8.4 8.4 8.3 9 11.5 ⋮ 7.9 8.1 8.6

1.7 3.8 1.7 2.1 2.1 2 2 2 1.8 1.6 ⋮ 1.9 1.8 1.6

114.86 120.22 119.81 118.32 118.08 118.37 113.96 110.75 111.45 125.69 ⋮ 107.52 106.91 109.69

37.87 46.04 49.02 46.05 47.07 49.32 48.85 48.16 47.42 41.59 ⋮ 48.15 47.45 45.98

7.8 8.2 8 7.8 7.6 7.4 7.4 7.3 7.5 9 ⋮ 7.2 7.3 7.4

12.9 25.5 23.5 49.8 54.3 51.07 42.7 41.5 44.5 53.3 ⋮ 30.2 33.5 38.2

1.62 2.6 2.2 4.9 5.24 4.74 3.93 3.84 4.22 4.87 ⋮ 3.8 4.21 4.83

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of 0.0049 is achieved. Same with Fig. 6, the ANN model with lowest MSE has the highest R. As shown in Fig. 7(b), R is almost close to 1 for the train function, ‘trainlm’. Also, it can be seen that the ANN model using ‘traingd’ has the lowest R that is 0.973. Genetic algorithm is a global optimization method based on Darwin's theory of evolution, which is used to optimize weights of the ANN model in this study. A flow chart describing the training and prediction process of the ANN model with genetic algorithm is shown in Fig. 8. To achieve the best prediction performance, there are several parameters of the GA need to be determined before the training process. Two of them, including initial population size and mutation functions, are discussed here. Generally, less population size can easily trap in local optimum point, while much population size leads to divergence. Fig. 9 shows the effect of population size of GA on the prediction performances of the ANN model. It can be concluded that the ANN models with less population size result better prediction performances. When population size is 100, the ANN model has the lowest MSE of 0.0012 and the highest R of 0.9959. If population size is above 100, MSE increases linearly while an opposite trend is observed for R. Mutation operator in GA is used to create new individuals and keep diversity of population. Fig. 10 shows the effect of mutation function of GA on the prediction performances of the ANN model. It can be concluded that the mutation function of GA has a little effect on the prediction performances of the ANN model, MSE just varies from 0.0012 to 0.0019 for different mutation functions. The ANN model using mutation function ‘uniform’ has the lowest MSE of 0.0012 and the highest R of 0.9959. Based on the sensitivity analysis described above, the desired parameters of the ANN model are obtained and listed in Table 7.

Fig. 5. Topology of the BP neural network model.

value and experiment data, which can be expressed as [26]:

R=

(y−y )(t −t )T (y−y )(y−y )T (t −t )(t −t )T

(3)

where y and t are the mean values of prediction and experiment data, respectively. A higher R value is expected for an ANN model.

4.2. Training performance comparison with and without using GA After determining the parameters setting of the ANN model, experimental data listed in Table 6 are selected as the training dataset, and the total 100 experimental data are used to test the ANN model. A prediction performance comparison of the ANN model with and without using GA is presented in this section. Fig. 11 shows the comparison of ANN predictions without using GA and experimental data in time sequence. It can be seen that although overall prediction trend is acceptable, ANN predictions cannot match well with experimental data at inflection points. To further evaluate the ANN model, prediction errors are shown in Fig. 12. It can be concluded that the ANN model has high prediction errors at some inflection points. As can be seen in

4. Results and discussion 4.1. Sensitivity analysis of the ANN model According to the experimental results above, the ANN model is evaluated first under different learning rates, train functions and parameter settings of the GA. Learning rate is used to adjust the weights and biases of an ANN model. A high learning rate can result in oscillation and instability, while a low learning rate leads to a long convergence time. Fig. 6 shows the effect of learning rate on the prediction performances of the ANN model. It can be seen that the learning rate varies from 0.05 to 0.4 with an interval of 0.05. As shown in Fig. 6(a), no matter how the learning rate changes, MSE always has a low value indicating that the ANN model established in this work performs high prediction accuracy. When the learning rate is 0.2, the lowest MSE of 0.0012 is achieved. Generally, a lower MSE corresponds to a higher R. Accordingly, as can be seen in Fig. 6(b), the highest R of 0.9958 is also obtained at the learning rate of 0.2. BP neural network adopts many train functions corresponding to different train algorithms to achieve the best prediction performances. Four different train functions, including ‘traingd’, ‘traingdm’, ‘traingda’ and ‘trainlm’, are tested in this section. ‘Traingd’ is a common gradient descent algorithm. ‘Traingdm’ represents the gradient descent algorithm with momentum, which is a revised method of ‘traingd’. Prediction performance of an ANN model is sensitive to the learning rate. For a common gradient descent algorithm, the learning rate is fixed during the training process. Therefore, a gradient descent algorithm with adaptive learning rate (traingda) is analyzed. Furthermore, as one of the most popular algorithms in BP neural network, LevenbergMarquardt (trainlm) is also investigated. The effect of train function on the prediction performances of the ANN model is shown in Fig. 7. It can be clearly seen from Fig. 7(a) that the ANN model using ‘trainlm’ generates the lowest MSE of 0.0012, while for ‘traingd’, the highest MSE

MSE

0.0025 0.002 0.0015 0.001 0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.3

0.35

0.4

Learning rate (a) 0.998

R

0.996 0.994 0.992 0.99

0.05

0.1

0.15

0.2

0.25

Learning rate Fig. 6. (a). Effect of learning rate on MSE of ANN model. (b). Effect of learning rate on R of ANN model.

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0.006

0.0025

0.005 0.002

MSE

MSE

0.004 0.003

0.0015

0.002 0.001 0

0.001

traingd

traingdm

traingda

150

200

0.998

1.0

0.996

R

0.99

R

100

Population size (a)

Train function (a)

0.98

0.994 0.992

0.97 0.96

50

trainlm

0.99

traingd

traingdm

traingda

50

100

150

200

Population size (b)

trainlm

Train function (b)

Fig. 9. (a). Effect of population size of GA on MSE of ANN model. (b). Effect of population size of GA on R of ANN model.

Fig. 7. (a). Effect of train function on MSE of ANN model. (b). Effect of train function on R of ANN model.

0.002 0.0018

MSE

Start

0.0016 0.0014 0.0012

Input experimental date

0.001

uniform

boundary

multiNonUniform

nonUniform

Mutation function (a) 0.997

Experimental date normalization

0.996

R

0.995 0.994

ANN weights encoding

0.993 0.992

uniform

boundary

multiNonUniform

nonUniform

Mutation function

Weights optimization by genetic algorithm Fig. 10. (a). Effect of mutation function of GA on MSE of ANN model. (b). Effect of mutation function of GA on R of ANN model.

Optimal weights decoding

Table 7 Final parameters setting of the ANN model.

Train of ANN

Prediction of the ORC system by ANN

Parameters

Value

Learning rate Train function Population size Mutation function Training precision Hidden layer function Output layer function

0.2 trainlm 100 uniform 0.001 tansig purelin

observed that the prediction relative errors are in the range of –14.17% to 17.45%. To improve the prediction precision, genetic algorithm is used to optimize the weights of the ANN model. Fig. 13 shows a comparison of ANN predictions with using GA and experimental data in time sequence. Compared with Fig. 11, ANN predictions with using GA can match better with the experimental data, especially at inflection points. Therefore, it can be concluded from Figs. 11 and 13 that the ANN model established in this work shows great robustness no matter whether GA

End Fig. 8. Flow chart of training and prediction process of ANN model with GA.

Fig. 12(a), the maximum prediction absolute error can reach up to 0.94 kW, and most of the prediction absolute errors are between –0.4 and 0.4 kW. Fig. 12(b) shows the prediction relative errors. It can be 21

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8

8

ANN predictions Experimental data

7

ANN predictions Experimental data

7 6

5

5

exp (kW)

6

4 3

4 3

2

2

1

1

0 0

10

20 Time (min)

30

40

0 0

10

20 Time (min)

Fig. 11. Comparison of ANN predictions and experimental data without using GA.

30

40

Fig. 13. Comparison of ANN predictions and experimental data with using GA.

is adopted or not. Fig. 14 shows the prediction errors of ANN model with using GA. It can be seen that the prediction errors of ANN model with using GA is lower than that without using GA as shown in Fig. 12. Most of the prediction absolute errors of ANN model with using GA are between –0.2 and 0.2 kW while the prediction relative errors range from –12.37% to 9.35%. The ANN model with using GA performs well and can be used to predict the power output of the ORC waste heat recovery system. The weight and bias values of the ANN model before and after optimization are listed in Tables 8 and 9.

learning ability and well generalization performance and is suitable to predict and optimize ORC systems for diesel engine waste heat recovery. To further show the prediction accuracy of the proposed ANN model, theoretical power outputs at 10 operating points are calculated based on an ORC thermodynamic model and are compared with the experimental data. More details about the thermodynamic model can be found in the previous papers [6,9]. Note that the thermodynamic model do not consider pressure drops, heat losses and other factors affecting the actual system performance and assume constant isentropic efficiencies of the expander and pump under steady state conditions. All operating parameter values for this thermodynamic model are obtained from the experimental results. Fig. 17 shows the validation and comparison among the experimental data and theoretical values from the thermodynamic and ANN based models. It is obviously seen that theoretical values are far higher than both experimental data and ANN predictions, while ANN predictions almost coincide with the experimental data. For given 10 operating points, theoretical values are all above 9.5 kW. However, the highest experimental power output is only 6.49 kW indicating that the ORC thermodynamic model cannot provide accurate prediction of the experimental results in this work. Adding more factors and performing a detailed calibaration can improve the accuary of the theoretical model further, however it is not considered in this study because the purpose of comparison between the experimental

4.3. Testing performance of the ANN model

1

20

0.8

15

Prediction relative errors (%)

Prediction absolute errors (kW)

After the training process is completed, the ANN model is tested with 100 experimental data. Fig. 15 shows the test results of the ANN model comparing with the experimental data. On the whole, the ANN model predictions match well with the experimental data, except at some inflection points. During the experimental test period, all experimental date are recorded in time sequence and present continuous variation. The appearance of these inflection points is attributed to the rearrangement of data sequence and dynamic operating conditions of the IC engine and ORC system. To verify the prediction precision of the ANN model, test errors of the ANN model are shown in Fig. 16. It can be seen that most of the test errors are ketp in the range of –0.2 to 0.2 kW. Compared with the experimental data, the maximum relative error is less than 5%. Therefore, the proposed ANN model shows strong

0.6 0.4 0.2 0 -0.2 -0.4 -0.6

0

10

20

30

10 5 0 -5 -10 -15 -20 0

40

10

Time (min)

20

Time (min)

Fig. 12. Prediction errors of ANN model without using GA.

22

30

40

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1

20

0.8

15

Prediction relative errors (%)

Prediction absolute errors (kW)

F. Yang et al.

0.6 0.4 0.2 0 -0.2 -0.4 -0.6

0

10

20

30

10 5 0 -5 -10 -15 -20 0

40

10

20

Time (min) (a)

30

40

Time (min) (b)

Fig. 14. Prediction errors of ANN model with using GA.

Table 8 Weight and bias values of the ANN model between the input and hidden layers.

wh

bh

Before optimization

0.1552 0.0074 1.0152

0.7831 −0.0979 −3.4522

−0.2194 −0.0076 −1.9040

−0.1585 0.0005 −0.3702

0.0077 0.0094 0.8622

−0.8959 0.1050 3.7288

−0.3288 0.0527 −2.1921

−1.9951 −0.3713 0.0188

After optimization

1.1651 −0.2331 1.6483

−1.2836 0.2503 −2.4877

−1.7086 0.3905 −0.3492

−1.0555 0.2733 3.9197

−0.0810 0.1603 3.6939

1.0664 −0.1572 2.8833

−1.8449 −0.3630 −2.5246

0.3377 −0.1524 −0.2750

1

Table 9 Weight and bias values of the ANN model between the hidden and output layers.

0.8

wo 10.9216 −0.5225

17.1363 −1.4958

−0.2175 0.1842

0.6

16.4321 −0.1045

Test errors (kW)

Before optimization After optimization

bo

ANN predictions Experimental data

7 6

0.4 0.2 0

(kW)

-0.2

5

-0.4

4

-0.6 0

3

20

30

40

50

60

Test samples

70

80

90

100

Fig. 16. Test errors of the ANN model.

2

0

10

4.4. Performance prediction of the ORC system based on ANN model

10

20

30

40

50

60

Test samples

70

80

One of the most meaningful aspects of using the proposed ANN model is to predict the performance of the ORC system. In this section, the effects of key operating parameters used in the proposed ANN model on the power output of the expander are discussed. The key operating parameters used are working fluid volume flow rate (V̇ ), expander torque (Torexp ), expander inlet pressure ( pexp,in ), expander outlet pressure ( pexp,out ), expander inlet temperature (Texp,in ), condenser outlet temperature (Tcon,out ) and pump outlet pressure ( pp,out ). All parameter ranges are determined according to the experimental data as ̇ . It can listed in Table 6. Fig. 18 shows the effects of V̇ and Torexp on Wexp ̇ increases with increasing V̇ and Torexp . Obviously, the be seen that Wexp

90

Fig. 15. Test results of the ANN model.

data and theoretical values is to show how accurately the proposed ANN model predicts the performance of the ORC system compared to a theoretical model.

23

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16 Theoretical values ANN predictions Experimental data

14

7

12 (kW)

6 5

exp

(kW)

10 8

4

6

3 150 140

4

Texp,in (

2

55 )

130

50 120

45 110 40

0

1

2

3

4

5 6 7 Test samples

8

9

Tcon,out (

)

̇ . Fig. 20. Effects of Texp,in and Tcon,out on Wexp

10

Fig. 17. Validation and comparison between the experimental data and theoretical values.

6

(kW)

5

exp

4 3 2 1 30 50

25 V (L/min)

40

20

30

Torexp

15 20

̇ . Fig. 18. Effects of V̇ and Torexp on Wexp

exp

(kW)

5 4.5 4 3.5 12

1 11 pexp,in (bar)

10

3

Fig. 21. Flow chart of the optimization process.

2 pexp,out (bar)

̇ varies from 1.88 to process. Under the given parameter ranges, Wexp 5.12 kW with the variation of V̇ and Torexp . ̇ . It can be seen Fig. 19 shows the effects of pexp,in and pexp,out on Wexp ̇ , which may be different from a that pexp,in almost has no effect on Wexp common theoretical analysis. The reason for this is that pexp,in and pexp,out vary while other parameters are set as constant values in this parametric study. During the experiment process, the variation of pexp,in always accompanies with variations of other parameters (i.e., V̇ , Texp,in

9 4 ̇ . Fig. 19. Effects of pexp,in and pexp,out on Wexp

effect of Torexp is larger than that of V̇ . When Torexp is controlled below ̇ is always unsatisfactory no matter how V̇ changes. 30 N m, Wexp Therefore, a higher V̇ and Torexp are expected during the experiment 24

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Table 10 Optimization results of the ORC system using GA based on ANN model. No.

V̇ (L/min)

pexp,in (bar)

pexp,out (bar)

Texp,in (°C)

Tcon,out (°C)

pp,out (bar)

Torexp (N m)

̇ Wexp (kW)

1 2 3 4 5 6 7 8 9 10

24.98 25 25 25 24.99 25 25 25 25 25

8 8 8 8 8.03 8 8 8.01 8 8

1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4

139.94 139.99 139.99 139.96 139.96 139.99 139.99 139.99 140 139.99

40.02 40.04 40.01 40.03 40.02 40.01 40.01 40 40.02 40.01

8.97 8.99 9 8.99 8.98 8.99 9 8.99 9 9

54.98 54.99 54.99 54.98 54.99 54.98 55 54.99 54.99 55

7.12 7.13 7.13 7.12 7.12 7.13 7.13 7.13 7.13 7.13

Table 11 Experimental results of the ORC system at near optimal operating parameters obtained from ANN model. No.

V̇ (L/min)

pexp,in (bar)

pexp,out (bar)

Texp,in (°C)

Tcon,out (°C)

pp,out (bar)

Torexp (N m)

̇ Wexp (kW)

1 2 3 4 5 6 7 8 9 10

24.2 24.55 24.16 24.52 25.09 25.35 24.97 24.84 24.89 25.84

8.2 8 8.1 8.1 8.2 8.2 8.2 8.1 8.2 8.1

1.5 1.6 1.5 1.5 1.7 1.6 1.6 1.6 1.6 1.6

138.19 136.89 136.68 137.91 138.22 136.48 138.58 138.24 138.31 138.45

41.13 40.99 40.78 41.84 40.04 41.52 41.38 40.95 40.17 41.51

8.9 9 9.2 9.2 9 9.1 9 9.2 9.1 9

53.8 54.4 54.2 54 53 54.2 55 53.9 53.5 54.3

6.99 7.03 7.1 7.09 7.04 7.13 7.11 7.06 7.03 7.09

and pexp,out ). As shown in Fig. 19, pexp,in varies from 9 to 11.5 bar with changing Texp,in . This means that only a little change in superheat degree is achieved by varing pexp,in . Fig. 19 also shows that when pexp,out dė increases significantly. However, when creases from 2 to 1.5 bar, Wexp ̇ almost has no change with the variations of pexp,out is above 2.5 bar, Wexp ̇ pexp,in and pexp,out . Although pexp,in is not very high, the maximum Wexp can reach up to 4.82 kW at the low pexp,out of 1.5 bar. So, lowering pexp,out can be more effective compared to varying pexp,in in an ORC system to ̇ . Fig. 20 shows the effects of Texp,in and Tcon,out on achieve a higher Wexp ̇ . It is seen that Wexp ̇ increases with increasing Texp,in and decreasing Wexp Tcon,out . As expected, both increasing superheat degree and decreasing Tcon,out lead to an increase in thermal efficiency of ORC systems, which can be also viewed from the theoretical analysis. In general, it is not ̇ is more easy to decrease Tcon,out during the experiment process and Wexp sensitive to Texp,in than Tcon,out . As shown in Fig. 20, when Texp,in increases ̇ varies from 4.18 to 6.28 kW. from 110 to 150 °C at Tcon,out = 40 °C, Wexp ̇ increases If Tcon,out decreases from 52 to 40 °C at Texp,in = 110 °C, Wexp ̇ from 3.59 to 4.18 kW. Therefore, one realistic method of increasing Wexp

4.5. Parametric optimization of the ORC system based on ANN model 4.5.1. Parametric optimization based on ANN model As expected, the operating parameters jointly affect the performance of an ORC system. A parameter analysis is not comprehensive enough to determine an optimal operating condition to achieve a maximum power output. In such case, the proposed ANN model can be effectively utilized to optimize the operating parameters for the waste heat recovery system. The optimization process using the proposed ANN model is illustrated in Fig. 21. The aim of the parametric opti̇ , which can be expressed as: mization is to maximize Wexp

1.4 < pexp,out < 4 bar

(7)

105 < Texp,in < 140°C

(8)

40 < Tcon,out < 50°C

(9)

7 < pp,out < 9 bar

(10)

20 < Torexp < 55 N.m

(11)

(4) 5. Conclusions

The logical bounds of the operating parameters are determined by the experimental data as listed in Table 6.

15 < V̇ < 25 L/min

(6)

4.5.2. Validation of the ANN model To verify the consistency of the optimization results, the optimization process is repeated 10 times. Table 10 lists the parametric optimization results of the ORC system based on the proposed ANN model. ̇ The optimization results shows a good consistency, and the optimal Wexp can reach up to 7.13 kW. Higher V̇ , pp,out and Texp,in are preferred while ̇ . The results lower pexp,out and Tcon,out are desired to achieve a higher Wexp listed in Table 10 show that the optimal expander inlet pressure is close to its lower bound (8 bar) rather than upper bound (11.5 bar). This indicates that it is not easy to obtain all optimal operating parameters of the ORC system at the same time. Coordinated variation of all operating parameters should be considered for the actual operation process of the ORC system. The ANN based method can provide a useful guidance for the coordinated optimization of the ORC system under various operating conditions. According to the parametric optimization results, the operating parameters of the ORC system are adjusted during the experiment process. Table 11 shows several experimental data when the ORC system is operated at near optimal operating parameters obtained from the ANN model. The comparison between Table 10 and Table 11 shows that the experimental results after optimizing the operating parameters are very close to the ANN’s predictions.

is to superheat the working fluid to a higher temperature.

̇ ) = f (V̇ ,pexp,in ,pexp,out ,Texp,in,Tcon,out,pp,out ,Torexp) max(Wexp

8 < pexp,in < 11.5 bar

In this paper, a test bench of combined diesel engine and ORC waste heat recovery system is developed first, and the experimental data used

(5) 25

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to train and test the ANN model are collected. After evaluating different learning rates, train functions and parameter settings of the genetic algorithm, an ANN based prediction model of the ORC system is established. Furthermore, a prediction accuracy comparison of the ANN model with and without using GA is presented. Subsequently, the effects of seven key operating parameters on the power output of the ORC system are investigated. Finally, a performance prediction and parametric optimization for the ORC system are conducted based on the proposed ANN model. The main originality of this paper lies in the establishment of the ANN-based model to predict and optimize the performance of the ORC system for IC engine waste heat recovery, rather than improving the ANN model itself. This research is helpful in increasing the prediction accuracy and optimizing the operation performance for the IC engine-ORC combined system. More detailed improvement of the proposed ANN model will be part of authors’ future work. The main conclusions can be summarized as follows:

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(1) Different learning rates, train functions and parameter settings of the GA directly affect the prediction accuracy of the ANN model. (2) Prediction errors of the ANN model with using GA are between –0.2 and 0.2 kW. Genetic algorithm is recommended to optimize the weights of ANN model for a high prediction accuracy. (3) The ANN model proposed in this work shows a strong learning ability and good generalization performance. Compared with the experimental data, the maximum relative error is less than 5%. (4) Based on the optimization results, higher V̇ , pp,out and Texp,in are preferred while lower pexp,out and Tcon,out are more expected to ̇ . achieve a higher Wexp (5) The experimental results after optimizing the operating parameters are very close to ANN’s predictions. One or more operating parȧ during the exmeters need to be adjusted to obtain a higher Wexp periment process. (6) Finally it can be concluded that the parametric optimization results of the proposed ANN model can provide a useful guidance for the coordinated control of the ORC waste heat recovery system. The ANN model proposed in this study is used to predict and optimize the transient behavior of the ORC system under the steady condition of the diesel engine. The final goal of our research is to investigate the transient performance of the ORC system under various operating conditions of the IC engine. However, it is not realistic to achieve this goal at this stage. That will be part of authors' future work. Acknowledgments This work was sponsored by the National Natural Science Foundation of China (Grant Nos. 51776005 and 51376011), the Beijing Natural Science Foundation Program (Grant No. 3152005), the Projects of International Cooperation and Exchanges NSFC (Grant No. 51611130193), and the China Scholarship Council (CSC). The authors would like to thank the reviewers for their valuable comments on this research. References [1] Srinivasan KK, Mago PJ, Krishnan SR. Analysis of exhaust waste heat recovery from a dual fuel low temperature combustion engine using an Organic Rankine Cycle. Energy 2010;35:2387–99. [2] He MG, Zhang XX, Zeng K, Gao K. A combined thermodynamic cycle used for waste heat recovery of internal combustion engine. Energy 2011;36:6821–9. [3] Quoilin S, Broek MVD, Declaye S, Dewallef P, Lemort V. Techno-economic survey of Organic Rankine Cycle (ORC) systems. Renew Sustain Energy Rev 2013;22:168–86. [4] Usman M, Imran M, Yang YM, Park BS. Impact of organic Rankine cycle system installation on light duty vehicle considering both positive and negative aspects.

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