Shock and Vibration

Volume 2016 (2016), Article ID 9507540, 17 pages

http://dx.doi.org/10.1155/2016/9507540

## Knock Detection in Spark Ignition Engines Base on Complementary Ensemble Empirical Mode Decomposition-Hilbert Transform

State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China

Received 31 October 2015; Revised 28 January 2016; Accepted 2 February 2016

Academic Editor: Mohamed El badaoui

Copyright © 2016 Fengrong Bi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In spark ignition engines, knock onset limits the maximum spark advance. An inaccurate identification of this limit penalises the fuel conversion efficiency. Thus knock feature extraction is the key of closed-loop control of ignition in spark ignition engine. This paper reports an investigation of knock detection in spark ignition (SI) engines using CEEMD-Hilbert transform based on the engine cylinder pressure signals and engine cylinder block vibration signals. Complementary Ensemble Empirical Mode Decomposition (CEEMD) was used to decompose the signal and detect knock characteristic. Hilbert transform was used to analyze the frequency information of knock characteristic. The result shows that, for both of cylinder pressure signals and vibration signals, the CEEMD algorithm could extract the knock characteristic, and the Hilbert transform result shows that the energy of knock impact areas has the phenomenon of frequency concentration in both cylinder pressure signal and cylinder block vibration signal. At last, the knock window is then determined, based on which a new knock intensity evaluation factor is propose, and it can accurately distinguish between heavy knock, light knock, and normal combustion three states.

#### 1. Introduction

In the recent years, the reduction of fuel consumption has become a mandatory goal in the development of internal combustion engines [1]. With the purpose of high torque output and low fuel consumption, compression ratio (CR) has to be increased or turbocharger has to be taken in modern SI engines to improve thermal efficiency [2]. However, as the engine thermal efficiency is improving, the probability of occurrence for knocking in the engine is also increasing; heavy knock leads to reduce engine performance and cause unpleasant noise and structural vibration. Meanwhile light knock can improve the power performance of an engine. Therefore, it has been a main challenge for current SI engines to extract knock characteristic and evaluate knock intensity.

Engine knock is defined as abnormal combustion induced by autoignition in the combustion chamber. Both inhomogeneous mixture composition and temperature distribution in the end gas affect the location of autoignition centers [3]. When the knock occurs, high frequency oscillation pressure waves will be created within the combustion chamber and induce high frequency vibration of cylinder block.

The popular and valid approach is to measure knock impact by using several types of sensors such as pressure sensors and acceleration sensors [4]. Cylinder pressure oscillations clearly indicate what happens during a knock cycle inside the combustion chamber. But the cylinder pressure sensors are very expensive. So the most widely used method of measuring knock is using a simple acceleration senor attached to the cylinder block. This method is an easy and cost-effective task. However, vibrations induced by resonances in the combustion chamber have to be detected against a complex background of heavy noise and other vibrations. Vibration signal need to be reprocessed.

Signal transform techniques are useful tools for knock detection methods, such as fast Fourier transform (FFT [5]), short-time Fourier transform (STFT [6]), Wigner-Ville distribution (WVD [7]), cyclostationary signal analysis [8], continuous wavelet transform (CWT [9, 10]), discrete wavelet transform (DWT [11, 12]), and nonlinear wavelet transform (NWT [13]). These methods have been utilized to analyze engine vibration signals for detect knock. But these methods have their weakness. FFT cannot reflect the time domain information of signal. STFT can reflect signal’s time domain information but the time window is fixed. Actually, in the process of analyzing the knock signal, we want analysis of signal’s high frequency components and low frequency components with different precision. But resolution of STFT is fixed and cannot adapt to the requirement of signal change. Wavelet transform has the features of high resolution and can solve the problems existing in the STFT. But the result of wavelet analysis is restricted by selected wavelet bases, and when the signal frequency is mutation, the result of wavelet is not ideal. Hilbert transform can accurately reflect the distribution of the signal energy in both time domain and frequency domain. But, for a nonstationary signal, if using Hilbert transformed directly, the original physical meaning will be lost. And the signal after the Complementary Ensemble Empirical Mode Decomposition (CEEMD) decomposes gets some intrinsic mode functions (IMFs); each IMF component is stationary. So the CEEMD needs to be done. And, in this paper, on the basis of CEEMD-Hilbert transforms, SI engine knock detection approach using engine cylinder pressure signal and cylinder block vibration signals is proposed.

#### 2. Methods

##### 2.1. CEEMD Algorithm

###### 2.1.1. EMD Algorithm

For a real-valued signal, , standard EMD finds a set of IMFs, and the IMFs are defined so as to have symmetric upper and lower envelopes with the number of zero crossings and the number of extreme differing at most by one. To extract IMFs, an iterative process called sifting algorithm is employed, which is described below [14]:(1)Find the locations of all the extrema of .(2)Interpolate between all the minima to obtain the lower signal envelope on . Interpolate between all the maxima to obtain the upper signal envelope, .(3)Compute the local mean:(4)Subtract the mean from to obtain the “oscillatory mode”, :(5)If meet the required conditions, then define as the first IMF; otherwise, set new and repeat the process from Step (1).

The same procedure is applied iteratively to the residue, , to extract other IMFs.

###### 2.1.2. Mode Mixing

Although EMD process is an ideal approach for decomposing nonstationary and complicated nonlinear signals, it suffers from some deficiencies, one of which is the mode mixing. Mode mixing is a characteristic of a single IMF consisting of either signals of widely disparate scales or signals of similar scales residing in different IMFs. Mode mixing would not only cause frequency aliasing between two IMFs but also damage the physical meaning of a certain IMF [15].

###### 2.1.3. EEMD Algorithm

In order to alleviate the problem of EMD, Ensemble Empirical Mode Decomposition (EEMD) is proposed by Wu and Huang, and this method defines the true IMF components as the mean of an ensemble of trials. Each trial consists of the decomposition results of the signal plus a white noise of finite amplitude [16]. This method can effectively inhibit the modal mixing caused by abnormal disturbance.

The procedure of the EEMD method can be briefly summarized as follows:(1)Add white noise with predefined noise amplitude to the signal for analyzing.(2)Use EMD method to decompose the newly generated signal.(3)Repeat the above signal decomposition with different white noise, when the amplitude of the added white noise is fixed.(4)Calculate the ensemble means of the decomposition results as final results.

###### 2.1.4. The Problem of EEMD

The EEMD algorithm performs the EMD over an ensemble of the signal plus Gaussian white noise. The addition of white Gaussian noise solves the mode mixing problem by populating the whole time-frequency space to take advantage of the dyadic filter bank behavior of the EMD; however it creates some new ones.

The main question of EEMD method is the residue white noise. When we use EEMD method to extract knock characteristics, if the knock intensity are more mild, residual white noise will interfere the effect of knock feature extraction, although increased the average number of collections can reduce white noise residual, it will significantly increase the computation, and it is bad for the realization of knock characteristic real-time detection.

###### 2.1.5. CEEMD Algorithm

Complementary EEMD (CEEMD) approach not only solves the mode mixing and white noise residues, but also improves the calculation efficiency of EEMD. CEEMD includes the following steps.

In the CEEMD method, white noise is added in pairs to the original data (one positive and one negative) to generate two sets of ensemble IMFs. Therefore, two mixtures composed of the original data can be added noise by the following method:

In the above equation, is the original data; is the added white noise; is the sum of the original data with positive noise; and is the sum of the original data with the negative noise.

Then, the ensemble IMFs obtained from those positive mixtures contribute to a set of IMFs with positive residues of added white noises like EEMD method. Similarly, the ensembles IMFs obtained from those negative mixtures and produce the negative residue of added white noises. Thus, the final IMF is the ensemble of both the IMFs with positive and negative noises [17].

To illustrate the advantage of CEEMD, a simulation signal is listed. In this experiment, the simulated signal contains three sinusoid waves having different initial phases, amplitudes, and frequencies and an intermittent signal. The main components of the simulated signal are given as

In addition, the intermittent sections of stochastic signal are appearing in different time points. The sinusoid waves and intermittent turbulence of the simulated signals are shown in Figure 1.