Knock-Prediction System for Kerosene Engines Using In-Cylinder Pressure Signal

Abstract

Piston engines fueled by kerosene have a strong application prospect in special vehicles and small aircrafts, but the low amount of octane in kerosene fuel causes its knock combustion phenomenon to be particularly serious. A knock will deteriorate the power and economy of the engine and will damage the engine in serious cases. Therefore, knocking is the key problem with kerosene engines. We propose a knock-prediction system for kerosene engines based on in-cylinder pressure signals. Firstly, the intrinsic mode function (IMF) caused by knock resonance is extracted from the in-cylinder pressure signal via empirical mode decomposition (EMD) and a time–frequency domain analysis. A time-domain statistical analysis (TDSA) combined with a principal component analysis (PCA) is used to extract features from the IMF. Finally, the data collected from the test bench are trained by a support vector machine to obtain the knock-prediction model. Compared with other technical combinations for training, the proposed scheme achieved more accurate results in knock prediction. Considering the working characteristics of kerosene engines, a slight knock can increase the power of a kerosene engine. Therefore, some incorrectly predicted cycles (slight-knock cycles) do not affect the normal operation of the engine.

1. Introduction

Kerosene has a high flash point, poor evaporation, and high use safety. Transporting and storing kerosene is easier and safer than transporting and storing gasoline, so kerosene is widely used in military products. The two-stroke piston engine using kerosene as fuel has a strong prospect in the field of small aircrafts and special vehicles [1]. However, kerosene has a slow flame propagation speed, rough combustion process, and poor antiknock performance, so kerosene engines are more prone to knocks when running. A knock is an abnormal combustion phenomenon in spark ignition engines. A knock can reduce the power performance of the engine, and a severe knock can damage the engine components, such as the engine block, piston, and piston rings. The occurrence of the knock phenomenon limits the fuel composition of the engine, and the metal-based knock additives used to limit knocks will lead to heavy metal pollution and other problems.

The difficulty of enacting knock control is a key problem with kerosene engines [2]. With the development of sensor technology, scholars have been able to use knock-detection methods to reliably distinguish between knock and non-knock cycles, which makes knock control possible. The traditional knock-control method is based on the detection of knock cycles. The knock controller will control each detected knock cycle through feedback, which results in the ignition advance angle being reduced, the injection pulse width being increased, etc. [3]. However, knocks show considerable randomness during engine operation [4]. Due to combustion instability, the mixture activity at one or more positions in the combustion chamber is high, forming a single or multiple self-ignition points that cause knock, so there are differences between engine cycles even under the same operating conditions. Therefore, traditional control methods may randomly interfere with the electronic control unit (ECU). The random change in the operating conditions of the engine will prevent the engine from maintaining itself under stable operating conditions, and phenomena such as the speed fluctuation phenomenon will occur. The traditional knock-control method cannot be used to solve the knock randomness problem. In recent years, stochastic knock-control methods have been proposed. The main idea of this method is not to pay attention to the occurrence of individual knock cycles, but to generate statistics on the knock characteristics of the engine during operation [5]. A target value is obtained using a statistical method, and the observed value is compared with the target value to adjust the control strategy [6].

Earlier researchers used manual statistics to collect the peak pressure in the cylinder during experiments and to draw a map. The results of studies have shown that the cycles with higher peak pressures are more likely to cause knocks [7]. A threshold value is obtained from the statistical summary of the map, which is recorded as the target peak pressure. The difference between the peak pressure measured in each cycle and the target peak pressure is used as a condition to determine whether a knock occurs. A knock is a random behavior caused by multiple factors, and the accuracy of using a single indicator to judge whether a knock occurred cannot be guaranteed.

With the development of computer technology, machine learning algorithms such as SVMs and neural networks have been gradually applied to knock problems in recent years [8,9]. The core of knock prediction is an estimation of the state of the engine based on the experimental data obtained from the test, which is essentially a machine learning problem. Thanks to the popularization of these algorithms, research on knock prediction has gradually increased. The authors of the paper [10] proposed a knock-margin estimation model based on a logical regression method, which considered the three characteristics of engine speed, intake air temperature, and cylinder pressure. The results showed that the data model established by the machine learning algorithm was superior to the traditional physical model. The authors of the paper [11] proposed a method to predict knock occurrences based on a 1D convolutional neural network trained on in-cylinder pressure data, and the results showed that when training with a small dataset, the model was able to generalize to different operating points in a highly efficient manner. Zhao proposed a knock-prediction system based on multiple feature learning. Various feature-extraction methods are used to obtain engine vibration signals. The extracted features are combined, and the accuracy is compared to select the most effective feature combination. The results showed that multi-feature learning is better than single-feature learning [12].

In the past, studies on knock prediction were mostly conducted on gasoline engines. The application objects and working scenarios of kerosene engines are quite different from those of gasoline engines. The working environment of the kerosene engine is complex, and the collected signal contains more noise, so processing the in-cylinder pressure signal is necessary. When kerosene engines operate, they should output as much power and torque as possible, which causes them to sometimes sacrifice part of their economy for power. Research has shown that when the engine experiences a slight knock, the power and torque output increase [13]. These factors were not considered in the previous model. Additional work on the knock-prediction system of kerosene engines should be conducted; therefore, the following work will be carried out in this paper: (1) the selection of an effective signal-processing method to process the in-cylinder pressure signal and adoption of a useful feature extraction technique; (2) the use of the prediction model to output the distance between the current cycle and knock, which can provide guidance when adjusting the operating parameters of an engine; and (3) the connection of the knock strength with the knock margin, because a slight knock is acceptable in kerosene engines under some working conditions.

We propose a knock-prediction system for kerosene engines based on in-cylinder pressure signals that fully considers the working characteristics of kerosene engines. The overall structure of the full text is as follows. In the Section 2, we introduce the test conditions and data collection procedure. In the Section 3, we briefly describe the working characteristics of knock and kerosene engines. In the Section 4, we introduce the overall framework and specific implementation methods of the prediction model. In the Section 5, we evaluate and compare the performance of the prediction model according to the results.

2. Experimental System

The laboratory that we used was located in Jiangning District, Nanjing. The knock test was performed on a two-stroke kerosene engine. The main parameters of the engine are provided in

Table 1. Engine specifications.

Item	Parameter
Two-stroke kerosene engine	Port fuel injection
Displacement	275 mL
Compression ratio	7.4
Bore	66 mm
Stroke	40 mm
Max power	16 kw
Cooling method	Air cooling
Exhaust port opening	102 °CA ATDC
Exhaust port closing	246 °CA ATDC
Scavenging port opening	114 °CA ATDC
Scavenging port closing	258 °CA ATDC

. The test bench included the following: a kerosene engine (created by Limbach, Xia’men, China), an electric power dynamometer (created by the Xi’an Shin Well Tokki Company, Xi’an, China), two piezoelectric pressure sensors (Kistler 6113A created by Kistler, Winterthur, Switzerland), a dynamic signal collector device (created by DONGHUA, Tai’zhou, China), two oxygen sensors (Bosch Lsu4.9 created by Bosch, Stuttgart, Germany), an air–fuel ratio analyzer (ALM-II created by Ecoefi company, Shijiazhuang, China), and a computer. The test bench is shown in Figure 1. The fuel used in the test was RP-3.

The in-cylinder pressure signals were detected with a Kistler 6113A piezoelectric pressure sensor and were collected with a DH 8302 dynamic signal collector with a maximum sampling frequency of 1 MHz. During the test, the in-cylinder pressure sampling frequency was set to 200 KHz, which could meet the needs of in-cylinder pressure signal collection under various operating conditions. The engine speed was controlled by a CWAC power dynamometer with a speed range of 0 to 8000 rpm and a power measurement error of ±0.4%.

To collect the knock signals, the engine knock was generated by varying the spark ignition angle in advance. After the engine began experiencing knocks, we adjusted the ignition advance angle to its normal level, and then we gradually increased the ignition advance angle to obtain the different strengths of the knock event. The dynamometer was in constant speed mode during the experiment. The test speed was changed from 2400 to 6000 rpm in 400 rpm increments, and the test torque of every test speed was changed from 10 to 20 N·m. At each working point, the ignition advance angle was modified via communication between the computer and ECU. To avoid engine damage, the sampling time for each ignition advance angle was 15 s. The excess air ratio is a key parameter in knocks. During the experiment, we measured the excess air ratio with the oxygen sensor and applied an excess air ratio of 0.95. Due to the scavenging loss of the two-stroke engines, the measured excess air ratio was slightly higher than that in the actual combustion process. Regarding the collected data, several laboratory personnel independently marked the knock intensity grade (no, slight, and severe knock) and selected the data with the same marked results as the sample data.

3. Knock-Prediction Model

3.1. Analysis of Knock

A knock is the result of abnormal combustion in the combustion chamber of an engine. Under normal combustion conditions, the combustible mixture in the cylinder is ignited by the spark plug to form a flame; then, the flame front spreads in the cylinder, and the end combustible mixture is finally ignited and consumed. However, when the pressure and temperature in the cylinder are too high, the end mixture will spontaneously ignite before the flame front arrives. The chemical energy of the end mixture is rapidly released, which causes a high local pressure and temperature; additionally, this also causes the pressure waves in the combustion chamber to propagate. At present, the most commonly used knock intensity evaluation index is the maximum amplitude pressure oscillation (MAPO) [14]. The starting time of the knock is characterized by the obvious oscillation of the engine cylinder pressure signal. MAPO can be used to judge the starting time of the knock. The threshold selection should be combined with the engine data analysis. During the experiment, the MAPO threshold of the engine was 0.08 MPa. The high-frequency component of the cylinder pressure signal was extracted using a 4–20 KHz high-frequency filter, and then the knock was determined using the MAPO index:

$$\begin{array}{ll}y(k)=+1\hfill & MAPO(k)\ge \delta \hfill \\ y(k)=-1\hfill & MAPO(k)<\delta \hfill \end{array}$$

(1)

where k represents the k-th cycle and δ is a predetermined threshold. As shown in Figure 2, a distinction can be made between the knock and normal combustion cycle.

The recognition rate of the knock-detection system based on the in-cylinder pressure signal can reach more than 90%, but two problems still exist. One is that only knocks and non-knocks can be identified, and a slight knock cannot be separated from the knock cycle. When a kerosene engine is in a slight-knock cycle, the output power and torque are increased. However, this cycle is judged to be a knock cycle, and the knock controller intervenes to change the engine operating parameters, which thus prevents the engine from reaching its maximum power. The other problem is that under normal combustion conditions, the allowance between the cycle and knock occurrence cannot be quantified. As shown in Figure 3, the total cylinder combustion pressures from different cycles are included. Although no knocks occur in the illustrated cycle, the peak combustion pressure of cycle 5 is considerably higher than that of cycle 1. According to research results, knocking is more likely to occur in cycles with a higher peak pressure. In other words, the conditions of cycle 5 are closer to the conditions under which knock occurs. The quantification of this index that is close to the knock degree can provide a basis to adjust the operating parameters of kerosene engines so that the engine can work as long as possible at the verge of a knock.

To solve these two problems, we marked the light- and severe-knock cycle in the data samples and introduced the knock margin to evaluate the distance between the current cycle and the knock occurrence conditions. In the data sample space, a machine learning algorithm was used to find a suitable hyperplane to divide the knock cycle from the normal combustion cycle. The distance between each sample and the hyperplane is the knock margin of the cycle.

3.2. Establishment of the Prediction Model

The engine operated under normal combustion conditions most of the time. Even during the bench tests, staying under knock conditions for a long time to avoid engine damage is impossible, so the data of the knock cycle were quite limited. In addition to the advantages of intuitive interpretation, high adaptability, and generalization, an SVM (support vector machine) is also suitable to train small sample data [15,16]. For a given dataset $\mathrm{D}=\left\{\left({\mathrm{x}}_{\mathrm{i}},{\mathrm{y}}_{\mathrm{i}}\right),\mathrm{i}=1,2,3,\dots ,N,\right\}$, ${\mathrm{x}}_{\mathrm{i}}\in {\mathrm{R}}^{\mathrm{m}},{\mathrm{y}}_{\mathrm{i}}\in \{+1,-1\}$, and N is the number of samples. If the data sample is linearly separable, a hyperplane separates the two sample types. The hyperplane can be written as follows:

$${\omega }^{T}x+b=0$$

(2)

where ω and b are the weight vector and bias terms. The shortest distance from the sample to the hyperplane is called the margin. The goal of support vector machines is to find a hyperplane so that the margin is the maximum value. Then, the optimization problem is formulated as:

$$\begin{array}{l}{\min }_{\omega ,b}\frac{1}{2}\Vert \omega {\Vert }^2\\ \mathrm{s.t.}{y}_i\left({\omega }^T{x}_i+b\right)\ge 1,i=1,\dots \dots ,N\end{array}$$

(3)

The knock problem is a nonlinear separable problem. For linear separable problems, Equation (3) has no solution. ξ is defined to prevent the outcome from being too strict. Then, the optimization problem is as follows:

$$\begin{array}{cc}\hfill & {\min }_{\omega ,b}\frac{1}{2}\Vert \omega {\Vert }^2+C{\displaystyle \sum _{i=1}^N{\xi }_i}\hfill \\ \hfill \mathrm{s.t.}& y_i{\left({\omega }^T{x}_i+b\right)}_i\ge 1-{\xi }_i,{\xi }_i\ge 0,i=1,\dots \dots ,N\hfill \end{array}$$

(4)

For linear inseparable problems in low dimensional spaces, φ(x) is defined to map samples from a low-dimensional to high-dimensional space. Then, the optimization problem is transformed into the one below:

$$\begin{array}{cc}\hfill & \underset{\omega ,b}{\min }\frac{1}{2}{‖\omega ‖}^2-C{\displaystyle \sum _{i=1}^N{\xi }_i}\hfill \\ \hfill \mathrm{s.t.}& 1-{\xi }_i-y_i{\omega }^T\phi (x_i)+y_{i}b\le 0,{\xi }_i\le 0,i=1,\dots \dots ,N\hfill \end{array}$$

(5)

The most impactful SVM feature is the use of a kernel function when mapping samples from a low-dimensional to high-dimensional space [17]. Equation (5) can be solved even without knowing the exact expression of φ(x), which is called the kernel trick. The final hyperplane is shown in Equation (6):

$${\left({\omega }^{*}\right)}^T\phi (x)+b^{*}=0$$

(6)

The distance from any point in the sample to a hyperplane can be expressed as:

$$d=\frac{\left|{({\omega }^{*})}^T\phi (x_i)+b^{*}\right|}{‖{\omega }^{*}‖}$$

(7)

A hyperplane is used to divide the knock sample from the normal sample, and the distance from each sample is understood as the knock margin of the cycle. The specific expression of φ(x) is not solved by an SVM. By using the Karush–Kuhn–Tucker condition [18], the value of ω^Tφ(x) + b can be calculated. ω^Tφ(x) + b is proportional to d, so ω^Tφ(x) + b can be used to indicate the knock margin.

A knock is a highly random event. When researching knock prediction, not only should the classification judgment be provided, but the prediction of the knock occurrence probability should also be provided. The output value of the SVM to the prediction sample is +1 or −1. The output is converted into probability with the sigmoid function. The probability of a knock occurring in any cycle of the sample is as follows:

$$P(y=1|x_i)=\frac{1}{1+\exp [-{\omega }^T\phi (x_i)-b]}$$

(8)

The following is an example of some data used to establish the knock-prediction model for kerosene engines. At the same speed, the throttle opening and intake air temperature gradually increased the ignition advance angle, which allowed us to obtain the cylinder pressure signal with different knock intensities. As shown in Figure 4a, the engine ignition advance angle gradually increased from 31° to 35°. Figure 4c shows the peak pressure of each cycle of the engine at different ignition advance angles. The normal cycle is marked in green, and the knock cycle is marked in red. We only took the peak pressure of the cylinder as the characteristic, that is, x(k) = P(k). In this case, the feature space is one dimensional, and the hyperplane is a scalar value $\widehat{x}=25.5(bar)$, as shown by the blue dotted line in Figure 4c. The distance from each cycle in the sample to the hyperplane $x(k)-\widehat{x}$ is regarded as the knock margin KM(k). The judgment of each cycle is as follows:

$$\begin{array}{l}y(k)=+1\hspace{1em}KM(k)\ge 0\\ y(k)=-1\hspace{1em}KM(k)<0\end{array}$$

(9)

where y(k) represents the knock judgment results of the kth cycle and KM(k) represents the knock margin of the kth cycle.

As shown in Figure 4b, the red curve is the probability of the knock occurrence output generated by the prediction model. The peak pressure range of the data sample was 15 bar~31 bar. The test data were divided into eight groups according to the peak pressure at an interval of 2 bar. The red triangle represents the proportion of knock events in each data group. Figure 4d shows the proportion of the severe- and slight-knock cycle and normal combustion cycle in each data group. The proportion of slight detonations increased first and then decreased with the increase in the knock margin. With the increase in the ignition advance angle of the engine, the knock intensity gradually increased, and the proportion of severe-knock cycles in the knock events increased.

Considering the working characteristics of kerosene engines, the knock-prediction model of kerosene engines focuses on the knock occurrence probability and the proportion of slight knocks in knock events. A knock is caused by many factors, and a single parameter cannot accurately establish a model. Therefore, an enhanced knock-prediction system is proposed in the next section.

4. Design of the Kerosene Engine Knock-Prediction System

4.1. Outline of the Estimation System

According to the working characteristics of the kerosene engine, the framework and project flow of a kerosene engine knock-prediction system are shown in Figure 5.

The framework includes signal decomposition, feature extraction, and training. The EMD (empirical mode decomposition) method is used to decompose several IMFs (intrinsic mode functions) from the original in-cylinder pressure signal. We compared the center frequency of the IMFs with the in-cylinder oscillation frequency range when the engine was knocking and selected the appropriate IMF as the knock-component signal. A TDSA (time-domain statistical analysis) was used to extract features from the knock signal separated from the original in-cylinder pressure signal, and a PCA (principal component analysis) was used to reduce the dimensions of the data. These features were trained to establish a knock-prediction model. The unknown signal was input into the trained knock-prediction model, and the knock-margin and -occurrence probability were the output variables that were used to provide guidance for the ECU, which not only protected the engine, but also made the engine run at the knock verge as much as possible.

4.2. In-Cylinder Pressure Signal Decomposition

The pressure signal sensor can be used to obtain the combustion pressure in the engine combustion chamber, and the in-cylinder pressure signal has a high signal-to-noise ratio [19]. It can analyze the combustion of the engine and provide the most accurate knock information. The results of studies have shown that scholars can use the in-cylinder pressure signal together with the MAPO index to detect knocks, but the detection effect for weak knocks is not ideal. The in-cylinder pressure signal is a nonstationary signal with varying frequency and contains many components. Therefore, using an effective algorithm to process the in-cylinder pressure signal to obtain the components caused by knocks is necessary [20]. Some studies have shown that a weak knock can be effectively detected by analyzing the signal components extracted from the vibration signal caused by knocks [21]. EMD is an adaptive and efficient algorithm that can decompose complex signals into several IMFs from high to low frequencies [22]. We used EMD to decompose the in-cylinder pressure signal, and the decomposition results are shown in Figure 6.

A time–frequency analysis is commonly used for signal processing. To further analyze the time–frequency characteristics of the intrinsic mode function and acquire the center frequency, a fast Fourier transform (FFT) was performed on the IMFs. The spectrum of IMF1~IMF3 is shown in Figure 7. In Figure 7, the center frequency and pressure amplitude of each order of the intrinsic mode function are marked with red dots. The specific data of the center frequency and maximum amplitude are shown in

Table 2. Center frequency and pressure amplitude of each IMF component of in-cylinder pressure signal.

Intrinsic Mode Function	Pressure (MPa)	Center Frequency (KHz)
IMF1	3.42 × 10−3	44.98
IMF2	1.84 × 10−3	28.07
IMF3	5.61 × 10−3	8.58

.

When the engine is knocking, the rapid release of energy causes resonance in the cylinder. The authors of most studies have found that the resonance frequency of the combustion chamber is mainly in the range of 5 kHz~20 kHz [23]. The resonance frequency in the combustion chamber is calculated according to the following formula [24]:

$$f=\frac{\rho c}{\pi b}$$

(10)

where c is the sound speed inside the combustion chamber, b represents the cylinder bore, and ρ is the corresponding wave number. Regarding the engine used in the test, the cylinder diameter was 66 mm, c was about 1000 m/s, and the first wave number was ρ = 1.84. The frequency of the first-order knock resonance was 8–10 KHz. As shown in Table 2, the center frequency of IMF3 was 8.851 KHz, which was within the resonant frequency range of the combustion chamber during engine knocking, and the center frequencies of the other IMFs were not within this range. Therefore, the knock characteristics of the pressure signals exhibited by this engine in the experiment were mainly concentrated in IMF3.

4.3. Feature Extraction

Feature engineering is the key part of machine learning and is used to solve practical problems. Therefore, appropriate methods should be selected to extract features from knock signals (IMF3). The sampling frequency of the test equipment was 200 KHz. Under the working condition of 6000 rpm, each cycle contained 2000 sampling points. We set a proper knock window, which could not only retain the relatively complete high-frequency vibration wave, but also reduce the impact of noise. The signal in the knock window contained 500 sampling points. The selection of feature-extraction methods plays a key role in the performance of the system. The simplest method can be used to extract some specific parameters, such as the peak pressure, maximum pressure gradient, and average signal energy. However, this method is too simple, the parameters described are too local and average, and a risk of losing the effective information of the knock signal exists. A knock signal is a mechanical signal in the time domain, which is usually extracted with a time-domain statistical analysis (TDSA), which mainly includes the mean value, standard deviation, root mean square, peak value, skewness, kurtosis, crest factor, shape factor, and pulse factor [25].

The introduction of multiple indicators can effectively and completely represent the knock signal (IMF3), but the presence of too many characteristics will affect the calculation speed. We used a principal component analysis (PCA) to reduce the dimensions of the data features. A PCA uses a linear projection to maximize the amount of data information on the projected dimension. A PCA not only maps the high-dimensional data to the low-dimensional space, but it also preserves as many original data features as possible in smaller data dimensions [26,27]. For the extracted components, the larger the variance is, the greater the amount of information is; additionally, the contribution rate represents the ratio of the variance of the extracted principal components to the total variance of the original variables [28]. The results of the principal component analysis are shown in

Table 3. Pareto analysis of principle components.

Principal Components	1	2	3	4	5
Variance Explained	58%	19%	14%	5%	2%

. The sum of the contributions of the first three principal components exceeded 90%. The first three PCA coefficients were selected as the characteristics.

After the feature extraction, the last step of the framework is training. Based on the pressure signals of the engine-knock test, the kerosene engine knock-prediction model was established by using the SVM classification method. The first three PCA coefficients, engine speed, and engine throttle opening were chosen as the independent variables.

The dataset included 2800 groups of knock and non-knock cycles, and 1400 groups were randomly selected to be used as the training data. The remaining 1400 groups were used as the test data. We normalized the sample data to avoid the impact of the difference in the numerical value of the data on the accuracy of the prediction model.

In Section 3.2, we mentioned that knock prediction is a nonlinear regression problem, so the radial basis function was selected as the kernel function. The expression of the kernel function is as follows:

$$K(x_i,x)=\exp (-\frac{{\left|x-x_i\right|}^2}{{\sigma }^2})$$

(11)

In the SVM classification model, parameters needed to be set, including the penalty factor C, which balances the model’s empirical risk with the confidence range, and gamma, which characterizes the kernel width of the radial basis function of the kernel function of the model and mainly affects the complexity of the model. Hyperparameters have a key impact on the capability of the model. Genetic algorithms were used to optimize the parameters. After the above steps were completed, the knock-prediction model training was completed.

5. Results and Discussion

To verify the performance of the proposed prediction system, the accuracies of different combinations of technologies tested on the same sample were compared. The test accuracies are shown in

Table 4. Accuracies of various combinations of technologies.

Signal-Processing Method	Feature Extraction	SVM	Logistic Regression
Raw data	TDSA	91.29%	88.93%
Wavelet decomposition	TDSA	95.43%	92.21%
EMD	TDSA	97.29%	95.07%
	TDSA + PCA	96.71%	93.64%

.

Table 4 shows that the combination of EMD, TDSA, and SVM had the highest accuracy, reaching 97.29%. By using the same feature-extraction method and machine learning algorithm for the original signal, we found that the final accuracy rate was 91.29%. Compared with the original signal, the recognition rate was greatly increased after signal processing by EMD.

Other signal-processing methods were selected to process the original signal for comparison purposes. The accuracy rate of the in-cylinder pressure signal processing using wavelet decomposition increased, reaching 95.43%. The results showed that the effect of the wavelet decomposition was not as strong as EMD.

As shown in the third and fourth columns of Table 4, when using the same signal-processing and feature-extraction methods, the accuracy rate of the SVM model was higher than that of the logistic regression. A TDSA and PCA were used to extract the features in the proposed system. The TDSA and PCA combination accuracy rate was 96.71%, and the TDSA accuracy rate was 97.29%. After the PCA algorithm was added, the accuracy of the model was only reduced by 0.58%, which is an acceptable loss range, and the calculation time was reduced.

The knock margin estimation performance of the knock-prediction system is shown in Figure 8. The green curve in Figure 8a shows the knock-probability prediction results of the model. The data were divided into 24 groups according to the knock margin and counted the proportion of knock and non-knock events in each group. The proportion of knock cycles in each data group was recorded as the observed value of the knock probability. The observed value of the proportion of knock events is shown by the star in Figure 8a. When the knock margin was less than 2, the knock probability predicted by the model was close to the actual observation value of the sample. However, when the knock margin exceeded two, the proportion of knock cycles in the sample increased rapidly, and the predicted knock probability of the model was far lower than the actual observation value. This indicates that the prediction ability of the knock-prediction model is insufficient when the knock margin is large. When the knock margin of a cycle is less than 2, the probability output by the prediction model can be considered as the possibility of a knock occurring in that cycle. This can be used to adjust the engine control parameters. A one-dimensional engine model was established in GT-POWER for joint simulation with Simulink, and the knock margin and probability of the model output were used to adjust the control parameters of the engine. When the hardware calculation speed is fast enough, the bench test can be conducted.

Working at the knock edge is the ideal working state for kerosene engines, so the proportion of slight and severe knocks in each knock-event group was calculated. The proportion of slight knocks in each knock-event group is shown in Figure 8b.

The proportion of slight knocks decreased with the increase in the knock margin, but the proportion of slight knocks was always greater than 70% when the knock margin was less than zero. In Section 3, we mentioned that when the knock margin of a cycle is less than zero, the cycle is judged as having no knocks, so when the knock margin of knock cycles is less than zero, the cycles are misjudged as no-knock cycles. This incorrect judgment will prevent the knock controller from responding when a knock occurs. However, as shown in Figure 8b, most of the misjudged cycles included slight knocks. For kerosene engines, the power output of the engine increases when a slight knock occurs, so a slight-knock cycle is acceptable. Therefore, when the knock margin is less than zero, the misjudgment of most of the cycles will not affect the accuracy rate of the model. If the misjudgment of slight knock (slight knock is judged as no-knock) is not regarded as a misjudgment, the accuracy of the model will reach over 98%.

We took an operating point as an example. Under the working conditions of 5000 rpm and 50% throttle opening, the ignition advance angle increased from 30 to 35° (before top dead center). With the increase in the ignition advance angle, the severe knock cycles increased. We tested the accuracy of the prediction model under different ignition angles. The ideal accuracy is that misjudgments (a slight knock is judged as no-knock) are true. The result is shown in Figure 9. When the ignition advance angle was 32° and 33°, the ideal accuracy was significantly higher than the actual accuracy. At these ignition angles, the output power of engine was at its maximum, and a slight-knock cycle occurred. In this case, the slight knock had no negative effect and the controller did not need interference, so the misjudgments of slight knock were unaffected. In practical work, the control strategy will make the kerosene engine work near the slight knock, so the accuracy of the prediction model is higher than the actual value.

When the knock margin is positive, the proportion of severe knocks in the total number of knock events increases rapidly, but at this time, the knock cycle will not be misjudged as a no-knock cycle. We mentioned above that the engine model was established in GT-POWER for joint simulation with Simulink to search for a suitable knock margin. The combination of the knock-prediction probability and the proportion of slight knocks can provide guidance when searching for the knock margin.

6. Conclusions

In this paper, we proposed a system to predict knocks in kerosene engines based on in-cylinder pressure signals. EMD was used to extract the intrinsic mode function caused by knock resonance from an in-cylinder signal. The center frequency of each order of the intrinsic mode function was obtained with a time–frequency analysis, and when compared with the knock-resonance frequency, we concluded that IMF3 was caused by knock. We used a TDSA and PCA technology combination to extract the features from IMF3. The first three PCA coefficients, engine speed, and engine throttle opening were chosen as the independent variables that were then trained by the SVM.

Different technology combinations were trained by the same sample, and we found that the knock accuracy of the system proposed in this paper was the highest. The results showed that after processing the cylinder pressure signal, the accuracy of the model was significantly improved and the accuracy of the model using EMD was higher than that using wavelet decomposition. When using the same signal-processing method, the accuracy of the knock prediction model built using SVM was superior to the accuracies of those built using logistic regression. The TDSA and PCA combination was used for feature extraction in the system. Compared with using a TDSA alone, after the PCA algorithm was added, the accuracy of the model was only reduced by 0.58%. The PCA algorithm reduced the calculation time, and the accuracy was almost the same as before.

Considering the working characteristics of kerosene engines, the concept of a knock margin was introduced; the model determined whether knock occurs and predicted the knock possibility with respect to the knock margin. From the test data, when the knock margin was less than 2, the knock probability predicted by the model was close to the actual observed value of the sample. This showed that the prediction model can be used for the closed-loop control of the engine. Through simulation and testing, the appropriate value of the knock margin was determined as the target to adjust the engine control parameters. For example, the ignition advanced angle and injection pulse width were adjusted with the PID algorithm to maintain the knock margin at a certain value (engine working at the knock edge).

Engine knock can be caused by many factors. The characteristics in the proposed system can be extended to more parameters, including the fuel quality, start of injection, and air excess ratios. This is the direction of model optimization. Based on the abovementioned research results, when conducting future work, scholars should consider the fact that the closed-loop control of kerosene engine knocks needs to be realized. Additionally, more effective learning algorithms should be used to increase the accuracy of the prediction system.