A Pressure Fluctuation Prediction Algorithm for High

A Pressure Fluctuation Prediction Algorithm for High Pressure Common Rail System Based on CNN

The 9th International Symposium on Computational Intelligence and Industrial Applications (ISCIIA2020)

CITIC Jingling Hotel Beijing, Beijing, China, Oct.31-Nov.3, 2020

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Abstract. In this paper, aiming at the pressure fluctuation problem of high-pressure common rail system, based on the convolution neural network of WaveNet structure, a pressure fluctuation prediction algorithm is proposed. Compared with other pressure fluctuation algorithms, deep learning is applied in this algorithm. The effectiveness of the proposed algorithm is approved in the experiment in different target rated injection pressure, different injection interval and other working conditions. The results of the experiment show that the average accuracy of the prediction algorithm is about 99.1%, and meets the demand. The accuracy of the prediction the pressure fluctuation from the injection interval to the starting point of the main injection is higher, and the accuracy of the prediction of the pressure fluctuation and its attenuation process slightly decreases after the main injection duration.

Keywords: Prediction Algorithm, High Pressure Common Rail System， Pressure Fluctuation， CNN

1. INTRODUCTION Multiple injections technology in high pressure common

rail system can effectively optimize the combustion process,

reduce pollution emissions and reduce combustion noise [1].

The pressure fluctuation produced in the fuel injection

process of the high pressure common rail system has a

significant impact on the fuel injection quantity of the

system, which will seriously reduce the cycle consistency of

the fuel injection quantity of the system, and then have a

great impact on the power, economy and stability of the

engine [2]. Therefore, accurate prediction of pressure

fluctuation characteristics according to specific conditions

is the premise of accurate control of circulating oil quantity.

At present, most of the studies are based on numerical

model and simulation to predict the pressure fluctuation.

Ubertini et al [3] built a simplified simulation model of

high-pressure common rail system to simulate the real rail

pressure fluctuation. After parameter correction, it can

basically meet the prediction requirements. However, due to

the excessive simplification of the model, the generalization

ability of the simulation model is not enough, the model can

not accurately predict. In order to study the pressure

fluctuation in the high pressure common rail system,

Catalano et al [4] established a numerical model for

simulation. The research results show that the sharp drop of

pressure during fuel injection is caused by the acceleration

of fuel flow caused by the opening of fuel injection clock

valve. The numerical model only predicts the theoretical

fluctuation of fuel pressure, but not the actual situation, so it

has low practicability and generalization ability.

Compared with the traditional numerical model simulation

method, the deep learning method has unique advantages,

such as simple modeling, high precision and low

computational resource consumption [5]. Due to the lack of

research on the prediction of pressure fluctuation by using

deep learning method, this paper explores the prediction

algorithm of pressure fluctuation in high pressure common

rail system by using deep learning method, which is of great

significance for many problems like circulating oil control.

Convolution neural network can realize parallel input by

convolution sliding operation on input features. The

convolution neural network has fast training speed and low

computing resource consumption. In order to make use of

the advantages of convolutional neural network and

enhance its learning ability for time series information, this

paper uses WaveNet network structure to build prediction

model [6]. The prediction model of convolution neural

network is built by the hole causal convolution, residual

module and receptive field design in WaveNet.

In the experiment, the original data required by the

prediction model were collected through multiple injections

bench tests of high pressure common rail system. Based on

the structure of WaveNet, the pressure fluctuation

prediction model of high pressure common rail system is

established and a lot of comparative experiments are carried

out. The results of the experiment show that the average

accuracy of the prediction algorithm is about 99.1%. The

results show that the larger the receptive field is, the higher

the accuracy of the model is. Finally, the receptive field of

200 is used to predict the best effect.

In Section 2: the structure of algorithm is presented. In

Section 3: the experiment is presented and the experimental

results are analyzed.

2. THE STRUCTURE OF ALGORITHM CNN can implement parallel input by convolution sliding

operation on input. However, according to the basic

principle of CNN, ordinary convolution, pooling and other

Zhe Zuo*, Kuichen Quan, Meng Du

School of Mechanical Engineering, Beijing Institute of Technology,

No. 5 Zhongguancun South Street, Haidian District, Beijing 100081, China E-mail: [email protected]


The 9th International Symposium on Computational Intelligence and Industrial Applications (ISCIIA2020)CITIC Jingling Hotel Beijing, Beijing, China, Oct.31-Nov.3, 2020

The 9th International Symposium on Computational Intelligence and Industrial Applications (ISCIIA2020) Beijing, China, Oct.31-Nov.3, 2020




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operations are for two-dimensional or three-dimensional

input [5]. On the one hand, the injector inlet pressure,

driving current and injection rate obtained by bench test are

all time series information, belonging to one-dimensional

information; on the other hand, the ordinary convolution

operation in CNN is sensitive to the spatial position of

features in the calculation process, so it is unable to

effectively extract the time information of features.

Therefore, this paper refers to WaveNet structure, on the

one hand, the original convolution operation is converted

into one-dimensional convolution for operation on

time-series information; on the other hand, through the

design of the network structure, the ability of CNN to

extract the spatial information of input features is

transformed into the extraction ability of time information.

2.1. Causal Convolution The general convolution operation is calculated for

two-dimensional input. In order to model the sequence data,

a special convolution structure is needed. The causal

convolution is a one-dimensional convolution operation

designed for timing information. The basic principle of

causal convolution is shown in formula (1).

𝑝(𝑥) = ∏ 𝑝(𝑥𝑡|𝑥𝑡−𝑛, … , 𝑥𝑡−1)

𝑇

𝑡=1

（1）

The above formula represents the probability 𝑝(𝑥) of

obtaining the information of time step 𝑡 when the sequence

information (𝑥𝑡−𝑛, … , 𝑥𝑡−1) within 𝑡 − 𝑛 to 𝑡 − 1 is input.

The purpose of model training is to maximize the

probability of the real value 𝑥𝑡 of the model output, that is,

𝑝(𝑥) is as close as possible to 1. The basic principle of

causal revolution is shown in Fig. 1.

Fig. 1 Visualization of a stack of causal convolutional layers. The figure shows the forward process of causal

convolution calculation when the convolution kernel size is

2 and the step size is 1. The pink dot represents the input

timing information, the blue dot represents the output result,

the gray and yellow dots represent the intermediate result,

and the arrow represents the forward process direction of

the model. It can be seen from the figure that the prediction

output of the network for a certain time step is determined

by the connected input information. The size of the mapping

area between the output and input information of a node is

called receptive field. The size of receptive field in the

graph is 5. The size of receptive field is shown in formula

(2).

𝑓𝐿 = 𝑓𝐿−1 + (𝑘𝐿 − 1) ∏ 𝑠𝑙

𝐿

𝑙=1

（2）

where 𝑓𝐿 represents the size of receptive field of layer 𝐿, 𝑘𝐿

represents the size of 𝐿 -layer convolution kernel, 𝑠𝑙 is the

convolution step length of the first layer. Since the input

information is time-series information, in order to make the

prediction of time series more accurate, we need to increase

the receptive field as much as possible. For the prediction of

a certain time step, we hope that it can obtain the time series

information in the range as long as possible before the

current time step. One way to increase receptive field is to

increase the number of network layers, but increasing the

number of network layers will increase the burden of

network training and increase the tendency of over fitting;

on the other hand, the efficiency of increasing the number of

network layers is too low to increase the receptive field, so

dilated causal convolution is introduced.

2.2. Dilated Causal Convolution The design principle of dilated causal convolution is to

skip the input value at a specific position during convolution

operation, which is equivalent to expanding the size of

convolution kernel. The empty part in the middle of

convolution kernel is replaced by zero value. The number of

skipped features is controlled by division. The larger the

division is, the more feature points are skipped. The larger

the equivalent convolution kernel size is, the larger the

receptive field area can be obtained, as shown in Fig. 2.

Fig. 2 Visualization of a stack of dilated causal convolutional

layers. Compared with the method of increasing the number of

network layers, the efficiency of increasing receptive field

is greatly improved. The reduced caudal convolution can

keep the larger receptive field while limiting the number of

layers of the model network. Because the number of layers

of the network is small, the efficiency of the network in

training and prediction can still be maintained. In this paper,

in order to expand the receptive field, in the case of

appropriately increasing the number of network layers, this

paper adopts the diffused causal convolution, and gradually

increases the division in different layers.

2.3. Residual Structure In this paper, referring to the structure of activation

function in PixelCNN [7], two kinds of activation function

Sigmoid and Relu with restriction conditions are adopted, as

shown in equation (3) and (4).

𝑠𝑖𝑔𝑚𝑜𝑖𝑑(𝑥) =1

1 + 𝑒−𝑥 （3）

𝑅𝑒𝑙𝑢(𝑥) = {0, 𝑥 ≤ 0

𝑥, 0 < 𝑥 < 11, 𝑥 ≥ 1

（4）

For the pressure fluctuation prediction problem, the

sigmoid function value is between 0 and 1, which can be

used to predict the pressure fluctuation after standardization.

At the same time, due to the influence of circulating pump

oil and control algorithm, the starting point of pressure in

multiple injections is not always the rated injection pressure.

The relu function with constraints can adjust the amplitude

of the predicted current pressure fluctuation, as shown in

Fig. 3.






3

Sigmoid

Dilated Causal

Convolution

Relu function with

constraints

Output

Input

Fig. 3 Visualization of activation layer.

The input in the figure passes through the dilated causal

convolution layer and enters into two activation function

layers respectively for operation. The final output is as

shown in equation (5), where ∗ denotes a convolution

operator and ⨀ denotes an element-wise multiplication

operator.

𝑜𝑢𝑡 = 𝑟𝑒𝑙𝑢(𝑊𝑓 ∗ 𝑥) ⨀𝑠𝑖𝑔𝑚𝑜𝑖𝑑(𝑊𝑔 ∗ 𝑥) （5）

In CNN, if there are too many intermediate layers in the

network, the network performance will be greatly reduced.

This performance decline is not caused by the

disappearance of gradient or the explosion of gradient,

because batch standardization layer has solved these two

problems well. Generally speaking, this kind of complex

network structure reduces the model learning ability, which

is called degradation phenomenon. When the network is

learning, this phenomenon is due to the long feature transfer

path ,so the convolution layer is difficult to learn effective

features. In theory, the deeper network structure should

have better performance than the shallow network. If a part

of the network is transformed into identity mapping, the

network can achieve the same performance as the shallow

network. However, it is difficult to learn identity mapping

by gradient descent method. In order to solve this problem,

residual structure is introduced, as shown in Fig. 4.

Convolution layer

Convolution layer

Relu

Relu

x

F(x)

x

F(x)+x

ResidualShortcut

Fig. 4 Visualization of residual structure.

The basic principle of residual structure is to copy the

calculated output features of a certain layer into two copies,

one of which continues to carry out forward propagation for

subsequent calculation; the other part passes through

several layers of convolution layers and directly adds the

features after several convolution layers. It is difficult to

make the output 𝐹(x)equal to the original output x when

there is no residual error. However, after adding the residual

error, the output 𝐹(x) + x is equal to x, which only needs to

make 𝐹(x) be zero, which is easier for network learning.

2.4. Design of Network Structure In order to smooth the input features, an embedded layer is

used to improve the nonlinearity of the model. In order to

improve the prediction effect of the model, residual

structure and skip connection are adopted. The final

prediction model structure is shown in Fig. 5. In the graph, 1

× 1 is the convolution kernel of size 1, which is mainly used

for dimension transformation. The rectangular box in the

figure is a complete residual module. The activation layer in

the residual module is shown in Fig. 4. Each module

contains its corresponding cavity causal convolution layer.

The original pressure fluctuation data first improves the

nonlinearity through the embedding layer, and then it is

input to the residual module of the first layer. After the

operation of hole convolution and activation layer, one

output is used for skip Connection, the other way is added

together with the residual to input to the next residual

module. Finally, the skip connections of each layer are

added and the final output result is obtained through

sigmoid layer.

Dilated Conv

Activation Layer

1X1

Residual

K Layers

Output

Input

Embedding layer

1X1

1X1 Sigmoid

Predict Outcomes

Skip-connections

Original sample

Fig. 5 The Structure of Algorithm.

3. EXPERIMENTS 3.1. Dataset Generation

In this paper, the original data required by the prediction

model are collected through multiple injections bench tests

of high pressure common rail system. The fuel injection

quantity and injection rate of the injector are measured by

single injection instrument, and the driving current signal of

the injector is measured by current caliper. Since it is

difficult to measure the injection pressure in the injector

needle valve chamber, a high sensitivity pressure sensor is

installed at the high pressure fuel inlet of the injector to

measure the change of injection pressure. Because the law

of injector inlet pressure and injection pressure are almost

the same, there is only a certain phase difference, so the

injector inlet pressure is used to replace the injection

pressure. A total of 750 working conditions with different

rated injection pressure, different injection duration and

different injection interval were collected. The pre main

injection time interval was 0.1ms to 4.0ms under each






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working condition, and the step size was 0.1ms. The

sampling frequency is 100kHz.

Since the collected signal contains high-frequency

interference signal, in order to facilitate the construction of

subsequent prediction model, the first-order inertial filtering

is adopted for the inlet pressure, driving current and fuel

injection rate signals to filter out most of the high-frequency

interference signals in the collected signals. The filtering

results are shown in Fig. 6.

Fig. 6 Filtered acquisition signal.

The simulated speed of the bench test is 200 rpm and the

injection interval is 300 ms. Due to the small proportion of

driving current signal and inlet pressure signal in the whole

cycle, a large number of meaningless data will be mixed

with the whole sequence for subsequent processing, which

makes the sample sparsity too high. In order to reduce the

sparsity of the original data, the data about 12ms from the

beginning of the pre injection duration to the main injection

duration and the gradual attenuation of the pressure

fluctuation are intercepted. Since the acquisition frequency

of the bench test is 100kHz, there are about 1200 sampling

points in a cycle.

The causes of multiple injections pressure fluctuation in

common rail system are complex. Through the analysis of

formation mechanism and dynamic characteristics of

multiple injections pressure fluctuation in high-pressure

common rail system, it can be seen that rated injection

pressure and pre main injection time interval will have a

greater impact on pressure fluctuation. In addition,

according to the mathematical model and related research of

high pressure common rail system, the structure of each

component in the system will also have different degrees of

influence on the pressure fluctuation characteristics. The

original characteristics which have great influence on

pressure fluctuation collected in this study are shown in

Table 1.

The structural characteristics of each component in the

system are unstructured data. Unstructured data refers to the

data that is not conducive to the model to read and process

directly. Since the structure and environmental pressure of

various components in the system are constant, such

features will not be selected as basic features.

After selecting the basic features, in order to improve the

information contained in the data, it is necessary to

manually construct new features from the basic features.

Using the potential structure and physical meaning of the

features, new features are created by combining and

transforming the basic features. The new features are shown

in Table 2.

The propagation time of pre-injection pressure fluctuation

in the table has a clear physical meaning with the overall

duration of pre-injection. The propagation time of

pre-injection pressure fluctuation represents the

propagation time of pressure fluctuation caused by

pre-injection before the start of main injection process; the

overall duration of pre-injection represents the total time

from the signal generation of driving current to the complete

end of pre-injection. In physical sense, the rated injection

pressure interval ratio and pre main injection time ratio are

not as obvious as the former two, but through the fusion of

2020 2030 2040 2050 2060 2070120

128

136

144

152

160 入口压力电流

时间 (ms)

入口压力

(M

Pa)

-10

0

10

20

30

40

50

60

70

80

电流

(A

)

Table 1 Basic characteristic variables of pressure fluctuation.

Characteristic Variable Variable Type Data Type Unit Driving Current Time Series FLOAT16 𝐴

Injector Inlet Pressure Time Series FLOAT16 𝑀𝑃𝑎

Injection Rate Time Series FLOAT16 𝑚𝑚3𝑚𝑠−1

Rated Injection Pressure Structured Data FLOAT16 𝑀𝑃𝑎

Pre-main injection interval Structured Data FLOAT16 𝑚𝑠

Starting Point of Pre-Injection Driving Current Structured Data FLOAT16 𝜇𝑠

Starting Point of Pre-Injection Rate Structured Data FLOAT16 𝜇𝑠

Finish Point of Pre-Injection Driving Current Structured Data FLOAT16 𝜇𝑠

Finish Point of Pre-Injection Rate Structured Data FLOAT16 𝜇𝑠

Duration of Pre-Injection and Main Injection Structured Data INT 𝑚𝑠

Environmental Pressure Structured Data INT 𝑀𝑃𝑎

Structural Characteristics of Components in the System Unstructured Data NONE NONE

Table 2 Characteristic variables constructed.

Characteristic Variable Construction Method Data Type

Propagation Time of Pre-Injection Pressure

Fluctuation

Starting Point of Pre-Injection Driving Current - Pre-main

injection interval INT

Duration of Pre-Injection Finish Point of Pre-Injection Rate - Starting Point of

Pre-Injection Driving Current INT

Rated Injection Pressure Interval Ratio Rated Injection Pressure / Pre-main injection interval FLOAT16

Pre-Main Injection Time Ratio Duration of Pre-Injection / Duration of Main Injection FLOAT16






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different basic characteristics, it is conducive to enhance the

understanding of the model for data, accelerate the

convergence speed of the prediction model and improve the

prediction accuracy of the model.

In order to predict the future development of the

fluctuation through the pressure fluctuation information of

tenure period, it is necessary to construct samples for model

training or learning from the data level. In this paper, the

sliding window method is used to divide the original

learning samples. The schematic diagram of sliding window

is shown in Fig. 7.

Fig. 7 Sliding window sampling.

3.2. Data Standardization In order to prevent the model from producing partial

distribution among different features, it is necessary to

standardize the original data. In this paper, there are two

methods of Standardization: deviation standardization and

Z-Score standardization. Deviation standardization is a method of linear

transformation of the original data, so that the original data

falls into [0,1]. The conversion function is shown in formula

(6)

𝑥′ =𝑥 − min (𝑥)

max(𝑥) − min (𝑥) （6）

where 𝑥 is the original feature, min is the minimum value of

the data, and max is the maximum value of the data. The

deviation standardization depends on the maximum and

minimum value of the data. If the data is increased or

decreased or updated, it needs to be standardized again.

When the data is stable, the deviation standardization is

better.

Z-Score standardization also uses linear transformation to

put the original data in [0,1]. The conversion function is

shown in equation (7)

𝑥′ =𝑥 − μ

σ （7）

where μ is the expectation of the original data, σ is the

standard deviation of the original data. The Z-Score

standardization is applicable to the case that the maximum

and minimum value of the original data is unknown or there

are outliers with extreme values.

The two kinds of standardization will not change the

distribution of the original data, which is conducive to the

data to retain the original information.

3.3. Experimental Result And Analysis According to the pressure fluctuation model to predict the

demand, the model needs to predict the injector inlet

pressure at the remaining sampling points of the cycle

according to the pressure fluctuation information at the

sampling points during the pre-injection duration.

According to the causal convolution principle, the output

result 𝑥𝑡 of the model at a certain position is related to the

sequence information (𝑥𝑡−𝑛 , … , 𝑥𝑡−1) from t-n to t-1. If the

model can predict the subsequent fluctuation according to

the pressure fluctuation information in the pre-injection, it is

necessary to design the receptive field of the model.

According to the receptive field calculation formula (2), the

network layer number is calculated. Considering the

complexity of the model and the ability of computing

platform hormone, the structural parameters of causal

convolution of the prediction model are shown in Table 3.

As shown in the table, the CNN structure constructed in

this paper shared 10 layers of hole causal convolution, and

the convolution void rate of each layer gradually increased

from 1 to 52. The increasing void rate increased the growth

rate of receptive field, and gradually expanded the receptive

field to 200, so as to complete the information capture

during the pre spray duration.

In order to verify the effectiveness of the prediction model,

this paper carries out comparative experiments between

different model structures and different training strategies,

and analyzes the results. The relevant parameters of the

model are shown in Table 4. The experimental results of

each model are shown in Table 5. In order to verify the

influence of different receptive fields on the prediction

accuracy, the residual block of the original model needs to

be deleted. The receptive field of the original model is 200,

corresponding to 10 residual modules and the empty causal

convolution layer in each residual module. In order to

modify the receptive field to 100 and 50, the corresponding

residual block should be deleted according to table 3.

Table 3 The structure of causal convolution.

Layers of Dilated Causal

Convolution The Size of

Convolution Kernel Division The size of Equivalent Convolution Kernel Receptive Field

1 layer 2 1 2 2

2 layer 2 2 3 4

3 layer 2 4 5 8

4 layer 2 8 9 16

5 layer 2 9 10 25

6 layer 2 25 26 50

7 layer 2 25 26 75

8 layer 2 25 26 100

9 layer 2 50 51 150

10 layer 2 51 52 200






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It can be seen from the results in the table that with the

increase of receptive field, the accuracy of the model

gradually increases. Because the receptive field is increased

by adding convolution layer, the training time is also

gradually increased. Due to the increase of receptive field,

the network can obtain more time series information and

higher prediction accuracy in pressure fluctuation

prediction, which conforms to the principle of network

design. The prediction effect of different receptive fields is

shown in Fig. 8. Fig. 8(a) shows the comparison of model effect between

receptive field 50 and receptive field 200. The model with

receptive field 50 in the figure has better effect in the

injection interval and main injection duration, but the

prediction of pressure fluctuation in the later stage is

inaccurate. Fig. 8(b) shows the effect comparison between

receptive field 100 model and receptive field 200 model. As

shown in the figure, the model of receptive field 100 can

basically predict the pressure fluctuation, and the effect is

good, but there are some jitters in some parts.

In order to further verify the effectiveness of the prediction

model designed in this chapter, the results of various

working conditions such as different target rated injection

pressure and different injection interval were visualized.

For the same rated injection pressure and different pre main

injection time interval, the experimental results are shown

in Fig. 9. The red solid line is the predicted value of

pressure fluctuation, and the black solid line is the real value

of pressure fluctuation. The injection time interval in the

figure changes from 0.5ms to 4.0ms. From the prediction

effect, it can be seen that the predicted pressure fluctuation

is in good agreement with the real fluctuation curve in the

injection time interval and the main injection duration, and

the prediction curve is relatively smooth, and the prediction

accuracy for the serrated pressure fluctuation in the main

injection duration is slightly lower. In order to further verify

the generalization ability of the model, this experiment also

visualized the prediction effect of the model under the same

injection time interval and different rated injection pressure,

as shown in Fig. 10. The injection time interval in each

diagram is 4ms, and the rated injection pressure is 80MPa,

100MPa and 140MPa respectively. It can be seen from the

prediction results that the prediction results of the model

under different rated injection pressures meet the

2 4 6 8 10 1285

90

95

100

预测值

/MP

a

时间/ms

目标值感受野（50）感受野（200）

2 4 6 8 10 1285

90

95

100

预测值

/MP

a

时间/ms

目标值感受野（100）感受野（200）

(a)Receptive field = 50 and 200 (b)Receptive field = 100 and 200

Fig. 8 Prediction effect of different receptive field models.


Parameter Name Parameter Value

The Number of Training Set Samples 48000

The Number of Test Set Samples 12000

The Length of The Input Sequence 200

The Length of Prediction Sequence 1000

Learning Rate 0.0001

Batch Size 16

The Number of Characteristic Variables 6

Optimizer Adam

Loss Function Mean Square Error (MSE)

Evaluating Indicator MSE、Mean Absolute Percentage Error (MAPE)


Model Step Training Time (s)

Overall Training Time (min)

The Number of Iterations

MSE of Training Set

MSE of Test Set

MAPE of Test Set

WaveNet (Receptive

field =50) 0.032 80.12 150000 4.5e-4 6.5e-4 1.365

WaveNet (Receptive

field =100) 0.051 127.5 150000 1.2e-4 2.7e-4 0.964

WaveNet (Receptive

field =200) 0.087 217.5 150000 6.7e-5 9.7e-5 0.822






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requirements of prediction, and the accuracy is high, which

proves that the model has strong generalization ability.

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预测值真实值喷油速率

时间/ms

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s-1

(g)injection interval is 3.5ms

2 4 6 8 10 1270

75

80

85

90

95

100

喷油间隔


时间/ms

预测值

/MP

a

0

10

20

30

40

50

60

70

80

90

喷油速率

/mm

3m

s-1

(h)injection interval is 4.0ms

Fig. 9 The prediction results of different injection intervals while

the target injection pressure is 100MPa,.






8

2 4 6 8 10 1255

60

65

70

75

80

85

主喷射始点


时间/ms

预测值

/MP

a

0

10

20

30

40

50

60

70

喷油速率

/mm

3m

s-1

(a) Target injection pressure is 80MPa

2 4 6 8 10 12

85

90

95

100

105

110

主喷射始点


时间/ms

预测值

/MP

a

0

10

20

30

40

50

60

70

喷油速率

/mm

3m

s-1

(b) Target injection pressure is 100MPa

2 4 6 8 10 12

130

135

140

主喷射始点


时间/ms

预测值

/MP

a

0

10

20

30

40

50

60

70

80

90

喷油速率

/mm

3m

s-1

(c) Target injection pressure is 140MPa

Fig. 10 The prediction results of the model under different target

injection pressures while the injection interval is 0.4ms.

The average prediction accuracy of the model is about

99.1%. The prediction accuracy of the pressure fluctuation

from the injection interval to the starting point of the main

injection is higher, and the prediction accuracy of the

pressure fluctuation and its attenuation process after the

main injection duration decreases. On the one hand, the

decline of accuracy is caused by the accumulation of errors

in the process of increasing the prediction length of the

model; on the other hand, the pressure fluctuation after the

main injection is greatly affected by random factors which

is random and unpredictable.

CONCLUSION In order to meet the emission requirements, the

high-pressure common rail system of diesel engine has

become more and more strict for the precise control of the

circulating oil quantity. Because the pressure fluctuation

caused by the pre-injection of high pressure common rail

system will affect the pressure of main injection, which will

affect the injection fuel quantity, reduce the consistency of

circulating oil quantity, and then affect the fuel injection

quantity. Therefore, accurate prediction of pressure

fluctuation is the premise of controlling the circulating oil

quantity. In this paper, the multiple injections’ pressure

fluctuation of high pressure common rail system is

predicted by deep learning method.

Based on the structure of WaveNet, the pressure

fluctuation prediction algorithm of high pressure common

rail system is proposed and a lot of comparative

experiments are carried out. The results of the experiment

show that the average accuracy of the prediction algorithm

is about 99.1%, and meets the demand. The accuracy of the

prediction the pressure fluctuation from the injection

interval to the starting point of the main injection is higher,

and the accuracy of the prediction of the pressure

fluctuation and its attenuation process slightly decreases

after the main injection duration. The size of the sequence

length has little effect on the accuracy of prediction. The

results show that the larger the receptive field is, the higher

the accuracy of the model is. However, since the duration of

pre-injection in this rail pressure experiment is about 200,

the prediction effect is the best when the receptive field is

200.

REFERENCES: [1] Liyun F, Yun B, Si J, Yang L, Xiuzhen M. Fuel Injection Quantity

Fluctuation in Multiple Injections of High-Pressure Common-Rail Fuel Injection System. Journal of Harbin Engineering University, 2016, 37(08): 1063-9.

[2] Mohebbi M, Aziz A A, Hamidi A, et al. Modeling of Pressure Line Behavior of A Common Rail Diesel Engine Due to Injection and Fuel Variation. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017, 39(3): 661-9.

[3] Ubertini S. Injection Pressure Fluctuations Model Applied to A Multidimensional Code for Diesel Engines Simulation. Journal of Engineering for Gas Turbines and Power, 2006, 128(694-701).

[4] Catalano L, Tondolo V, Dadone A. Dynamic Rise of Pressure in the Common-Rail Fuel Injection System. 2002.

[5] Goodfellow I, Bengio Y, Courville A. Deep Learning. MIT Press, 2016.

[6] Oord A V D , Dieleman S , Zen H , et al. WaveNet: A Generative Model for Raw Audio. 2016, arXiv:1609.03499.

[7] Van Den, Oord A, Kalchbrenner N, Vinyals O, Espeholt L, Graves A, Kavukcuoglu K. Conditional Image Generation with PixelCNN Decoders. 2016, arXiv:1606.05328.



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A Pressure Fluctuation Prediction Algorithm for High