Issue 
Mechanics & Industry
Volume 21, Number 6, 2020



Article Number  612  
Number of page(s)  11  
DOI  https://doi.org/10.1051/meca/2020085  
Published online  20 November 2020 
Regular Article
Detection method of combustion oscillation characteristics under strong noise background
^{1}
School of Power and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, PR China
^{2}
School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, 350116, PR China
^{*} email: thz@nuaa.edu.cn
Received:
26
May
2020
Accepted:
14
October
2020
After the lean fuel premixed combustion technology is applied to aero engines, severe combustion oscillations will be cased and led to hidden safety hazards such as engine vibration, further energy waste and other problems. Therefore, it is increasingly important to actively control combustion oscillations. In this paper, a multispectral radiation thermometry (MRT) is used to analyze the hydroxyl group, which is a measurable research object in the combustion chamber of an aero engine, and to fit the functional relationship between the radiation intensity ratio and the temperature in different bands. The theoretical value of the error is <2%. At the same time, in order to solve the problem of weak detection signal and excessive interference signal, an improved frequency domain filtering method based on fast Fourier transform is designed. Besides, the FPGA platform is used to ensure the realtime performance of the temperature measurement system, and simulations and experiments are performed. An oscillating signal with an oscillation frequency of 315 Hz is obtained on the established test platform, and the error is only 1.42%.
Key words: Signal processing / strong noise / multispectral radiation thermometry (MRT) / characteristics extraction / combustion oscillation
© AFM, EDP Sciences 2020
1 Introduction
As the needs for sustainable development become more and more urgent, the requirements for low pollution emissions of aero engines are becoming higher and higher. Figure 1 shows the relationship between combustion emissions and equivalent ratio [1]. The main countermeasure for major airlines is to adopt lean fuel premixed combustion technology. However, lean fuel combustion is close to the extinction limit, and it is prone to periodic selfexcited oscillations, which is the socalled combustion oscillations [2]. Figure 2 is a partial view of a certain aircraft engine [3] after combustion oscillation. When combustion oscillations occur, they are often accompanied by a series of problems such as the intense pulsation of discharge and pressure, leading to an increase in combustion noise and thermal load. Combustion oscillations will affect the quality of the thermal energy generated, causing more serious resource and energy waste problems. Therefore, it is necessary to control the combustion oscillation.
At present, the major control method of combustion oscillation is active control. Active control forms negative feedback with the oscillation parameters detected by the detector by adjusting the external energy of the system [4], and achieves the suppression of oscillations [1,5]. However, the active control has higher requirements for the performance of the sensor, coupled with the high temperature and pressure conditions of the aero engine combustion chamber, it is imminent to design a reliable combustion oscillation detector in a strong noise environment [6].
According to the Rayleigh criterion [7] for judging the combustion oscillations, this will occur when the heat release rate and sound pressure fluctuations are in phase, and the two phenomena will form a positive feedback to further intensify the oscillations. Therefore, the characteristic parameters of combustion oscillation include pressure and heat release rate. The first solution is to use the pressure sensor in order to measure the pressure signal, but the result is out of phase with the actual pressure [8] and cannot reflect the real oscillation information. The other method at present, the detection of heat release rate, is indirectly measured by spectrometry, which can meet the requirements of nonintrusive, realtime and long service life [9]. For example, Furlong et al. [10] designed an experimental system based on the InGaAsP laser generator for infrared light with a wavelength of 1,343 nm and 1,392 nm that can be absorbed by water molecules using absorption spectroscopy, and successfully measured the flame heat release rate in the combustion chamber. At the same time, a large number of scholars have studied the emission characteristics of −OH, −CH and other free radicals [11,12]. This article focuses on the emission spectroscopy method. This method involves the particles absorbing photons excited to an energetic state with higher energy, releasing energy by radiation or nonradiation methods and returning to the ground state. Emission spectroscopy can ensure that the accuracy of the test and the low cost [13].
In recent years, flame temperature detectors based on photodiodes have gradually emerged. Dale [15] designed a flame temperature detector based on photodiodes to achieve noncontact measurement of flame temperature, with an accuracy of 10 K and a frequency response of 1,000 Hz. This sensor can realize the conversion of light and signal, and change the detection band of the ultraviolet spectrum by coating technology [16]. By comparing two sets of silicon carbide photoelectric sensors, flame temperature parameters with good linearity were obtained [17].
This article starts with the detection principle of heat release rate, and establishes the model from spectral radiant intensity to temperature. To solve the problem of weak detection signal and low signaltonoise ratio caused by the extreme environment of the aero engine combustion chamber, a sine signal filter circuit and a signal processing circuit are designed. Finally, a test platform is built to detect the heat release rate of the actual combustion oscillation and verify the reliability of the new detection method.
As shown in Figure 3, the main purpose of the whole system is to detect the vibration characteristics of the flame in the aircraft. Section 2.1 evolves the spectral intensity of the flame into the commonly used temperature parameters. Section 2.2 designs for sine signal, based on fast Fourier transform designed highfrequency sound filter circuit. The optical signal is converted into a stable voltage signal by the photoelectric secondary tube. Finally, the characteristic parameters of combustion oscillation are obtained by measuring the frequency, amplitude and phase of voltage fluctuation in Section 4.
Fig. 1
Pollutant emission and equivalent ratio curve. 
Fig. 2
Damage chart of aeroengine combustion oscillation structure. 
Fig. 3
Choreography of the full text. 
2 Methodology
2.1 Temperature measurement principle and model simulation
In the aero engines, hydrocarbon fuels are mainly used. During the combustion process, nitrogen oxides, hydroxyl groups, and oxycarbons are formed. For the selection of research objects, the combustion products contain a large number of hydroxyl groups and have a high emission power. As shown in Figure 4, the hydroxyl emission band is about 310 nm, and the emission power of products such as −CO (220 nm), −CN (390 nm), −CH (430 nm) are relatively small, and are all far away from 310 nm [14]. The test interference is small. Therefore, a hydroxyl group is selected as an object to detect the heat release rate.
According to the relevant principles of colorimetric method, the color temperature of the material is(1)
where B_{b} is the ratio of spectral radiance. When λ_{1} and λ_{2} are determined, there is a uniquely determined relationship between the ratio and the color temperature. For ordinary gray bodies, the effect of emissivity must also be considered. Equation (1) will be rewritten as follows:(2)
In order to eliminate the influence of emissivity, we use multiwavelength spectrum to solve Equation (2). The data obtained by LIFBASE simulation software is imported to MATLAB, and we select three local extreme value bands of 306.3 nm, 309.0 nm and 311.2 nm for research according to the requirements of multispectral radiation thermometry (MRT). Because the difference between each band is very small, it can be considered that the spectral emissivity changes linearly, so it is approximately as(3)
Therefore, we define the spectral intensity ratio according to Equation (3) and further simplify it as:(4)
It can be seen from Figure 5 that the change trend between 1000 K and 1800 K is monotonically increasing, which satisfies the onetoone correspondence between the temperature and the spectral intensity ratio, and meets the temperature requirements obtained by the inversion of the light intensity ratio. Finally, a secondorder fitting is performed to get the corresponding functional relationship(5)
As shown in Figure 6, the absolute relative error between the fitting results and the actual ones are <2%.
Fig. 4
OH emission spectrum at 2000 K. 
Fig. 5
Relationship between spectral radiant intensity ratio and temperature. 
Fig. 6
Relative error of temperature expression inversion of light intensity ratio at different temperatures. 
2.2 The Principle of improved frequency domain filtering method
The precision of the detection of flames is of great significance in aircraft engines. In order to achieve highfrequency flame combustion status collection, optical sensors are generally used, but the signal strength of optical sensors is extremely low, which is susceptible to interference, resulting in extremely low signaltonoise ratio. Among the optical sensors, the silicon carbide photoelectric sensor is chosen for high precision and quick response. While the signal collected by this sensor is extremely weak, which is close to 100 pA, the signal needs to be amplified. During the amplification process, many interference signals will also be amplified with the effective signal. So the interference signal needs to be filtered.
In practical applications, after transmission through various channels, the signal waveform will inevitably be distorted. Therefore, filtering is a very important part of the research of signal processing.
There are two kinds of traditional filtering methods: spatial filtering and frequency filtering. The spatial ones include the neighborhood mean filtering method and the median filtering method. The disadvantage of these methods is that while smoothing the noise, a lot of texture details and edge information are lost; while the frequency domain filtering is the Fourier Transform of the Image Transform to the frequency domain, and then selectively suppresses or increases various frequency components. However, since many signals are broadband signals and have strong coupling in the timefrequency domain, it is difficult to effectively implement the traditional timefrequency domain filtering.
The filtering method proposed in this paper is similar to the frequency domain filtering, but the traditional one cannot lock the characteristic signal in real time, and this method can achieve the extraction of a single main frequency. The frequency domain filtering is first Fourier transformed, so it takes longer to run. In addition, compared with timedomain filtering, it can get better filtering effects for irregular noise values, but frequencydomain filtering is not as good as timedomain filtering in edge extraction.
A highprecision frequency estimation method based on the amplitudefrequency response of an adaptive filter proposes an estimation method to obtain an accurate frequency in the case of strong noise interference [18]. However, this method involves a large number of calculations and cannot ensure the realtime calculation of highfrequency signals. It is only suitable for offline identification. The local frequencydomain bandpass filtering method can solve the problem of spectrum leakage caused by asynchronous Fourier transform due to asynchronous sampling. However, its frequencysweep signal curve cannot complete the realtime tracking response, and the realtime problem has not been solved [19].
At the same time, in recent years, the computing capacity of the FPGA has been greatly improved and the cost has been reduced. The realtime performance of the frequencydomain filtering can be realized by using FPGA and highspeed fast Fourier transform operations can be obtained.
The improved frequency domain filtering method we put forward includes 5 procedures. The flowchart of this method is shown in Figure 7.
(1) Fast Fourier transform: preliminary judgment of the sinusoidal dominant frequency in the original signal with the help of the calculation result of the fast Fourier transform of the first period;
The fast Fourier transform (FFT) is used to realize the realtime spectrum analysis of the time domain signal as shown in Equation (6).(6)
(2) Preliminary judgment of the main frequency;
(3) Frequency correction and phase locking method: Perform frequency correction based on the calculation results of the first and second periods of fast Fourier transform and lock its phase offset; calculated two times based on the main frequency phase angles j_{k1} and j_{k} of two fast Fourier transforms The phase difference Δϕ of the main frequency after the second change. Since the filter is based on FPGA operation, the input effective signal can be regarded as a continuous signal. Therefore, if there is no frequency analysis error due to noninteger periodic sampling, the phase difference Δϕ of the direct main frequency of the two fast Fourier transforms should be 0. If a noninteger period is generated, the actual main frequency can be calculated according to Δϕ, and the calculation formula is:(7)
where M is the maximum frequency point, f is the sampling rate, and N is the calculated length of the fast Fourier transform.
The phase locking method is: based on the main frequency phase angles j_{k1} and j_{k} after two consecutive fast Fourier transforms, the frequency main phase angle of the next sampling period is predicted and corrected to the output of the next fast Fourier transform period the initial phase angle at. My calculation formula is:(8)
After the phase angle of the main frequency in the next cycle is locked, a prediction signal with the same phase as the input signal can be output to ensure the accuracy of the signal.
(4) Determine the amplitude of the sinusoidal signal: Adjust the sampling rate according to the predicted frequency, suppress the energy leakage phenomenon, and determine the amplitude of the sinusoidal signal. The reason is that the time domain truncation caused by noninteger periods will cause energy leakage. The larger the Fourier transform main frequency phase difference Δϕ, the more obvious the energy leakage phenomenon. The most effective way to suppress this phenomenon is to perform integer periodic sampling, that is, to adjust the sampling rate in real time according to the estimated main frequency to achieve integer periodic sampling. Here is the sampling rate adjustment formula:(9)
where M' is the predicted maximum frequency point and an appropriate value needs to be selected. After the sampling rate is corrected in real time, the energy leakage phenomenon can be greatly suppressed, and the amplitude of the sinusoidal signal can be determined. But changing the sampling rate too frequently is not conducive to the stable operation of the system. Therefore, only when Δϕ is too large and the energy leakage phenomenon cannot be ignored, the dynamic adjustment of the sampling rate is selected.
(5) Signal output: Based on the FPGA module, the above calculation logic is completed and output in real time.
This article provides a sine signal filtering system based on improved frequency domain filtering method, including display interface, RT system, signal processing unit, highspeed digitaltoanalog conversion chip, FPGA module, highspeed analogtodigital conversion chip, and signal output unit, as shown in Figure 8. When the sine signal filtering system based on the fast Fourier transform is running, it relies on a highspeed digitaltoanalog conversion chip with a variable sampling rate to collect the conditioned signals, pass the data to the FPGA module through the SPI bus, and perform core logic operations. After outputting the result, it is output based on the highspeed analogtodigital conversion chip through the SPI bus, and the output signal is amplified by the signal output unit; the sinusoidal signal filtering system realizes the parameter configuration and data display function of the FPGA module through the RT system; similarly, the RT system passes The PXI bus performs data interaction with the FPGA module.
The system implements calculation logic based on FPGA modules. Highspeed Fourier changes require extremely high computing capability. Traditional CPU operations cannot guarantee realtime performance. FPGA platforms are required to enable realtime acquisition and input signal analysis and realtime generation output signals. The FPGA module consists of four modules: acquisition module, fast Fourier transform module, signal analysis module, and. Based on the characteristics of the FPGA, these four modules run synchronously. Due to the mismatch between the acquisition module and the Fourier transform module, a set of 4096depth FIFO blocks is used as the data buffer structure. The remaining modules interact through registers. The acquisition module performs highspeed data acquisition and loads the data into the FIFO.
The fast Fourier transform module implements the original spectrum analysis, initially determines the frequency domain characteristics of the input signal, preliminarily judges the main frequency and analyzes the signal phase. The signal analysis module performs frequency correction, phase lock, adjusts the sampling rate of the acquisition module in real time, and finally confirms the output waveform. The output module generates and outputs the final confirmed output waveform. Based on the FPGA platform, the system realizes the synchronous operation of acquisition, operation and output, which effectively guarantees the system's control over time.
Fig. 7
Filter based on fast Fourier transform. 
Fig. 8
Structure of the filtering system. 
3 Signal processing circuit design and experimental setup
3.1 Signal processing circuit design
Due to the influence of electromagnetic noise and the optical noise interference of other molecules and atoms, the intensity of ultraviolet light in the flame detected by the silicon carbide photodiode is very low, and the output current is very small. Considering that the cost of silicon carbide sensors is large and the detection area cannot be increased, we are required to design a signal amplification and conditioning module. This module needs to sensitively detect the weak current signal of several hundred pA inputs, and at the same time it can process and output the signal. Among them, the signal amplification module must also have the characteristics of selfreturn to zero and low offset. The most important thing is that it can withstand the higher temperature load unique to the aeroengine combustion chamber. Because the effective signal strength is very low, the amplification factor of the signal amplification module is very high. Ordinary operational amplifiers cannot achieve a sufficiently high amplification factor.
Therefore, we chose a transimpedance amplifier with a higher amplification factor. The response speed has a greater impact. In order to meet the requirements of dynamic performance and system bandwidth, we have adopted twostage amplification processing. That is, it is not divided into two parts, the primary amplifier and the postamplifier, in order to reduce the system dynamic response caused by the single amplification resistance being too large. The structure diagram of the signal conditioning circuit is shown in Figure 9.
This signal processing circuit includes 4 parts.

Transimpedance amplifier: The core of the conditioning circuit is a signal amplification circuit, that is, a transimpedance amplifier. The ADA4817 transimpedance amplifier was selected as the primary amplification circuit. When the feedback resistance is 500 MΩ, the calculated overall offset voltage is only 20 mV, and the frequency response bandwidth can reach 126 kHz. Fully meet the requirements for signals. To further increase the magnification, you can add a Ttype resistor or a better transimpedance amplifier.

Offset zeroing and notch module: The offset zeroing module is designed to meet the requirements of low zero drift. The adder LM258 is used for zeroing and offset processing. The notch filter circuit selects the F42N50, which is mainly used to isolate and shield 50 Hz power frequency signals. After calculating that the matching resistance of the notch is 80 KΩ, the notch can shield 48.7–51.3Hz interference, and the flame oscillation frequency is about 315 Hz, away from the 50 Hz power frequency band. The influence of the notch on the effective signal can be ignored.

After the primary amplifier, bias conditioner, and notch are conditioned, the signal has been conditioned into a recognizable valid signal. The transimpedance amplifier is simplified to an inertial link. The time constant of the inertial link can be calculated by calculating the relevant parameters. It is 909 Hz, the signal amplitude is 1000 mV, and the driving capacity is 40 mA, which fully meets the detection of combustion oscillation signal at 315 Hz.

In the entire conditioning circuit, the design of the power module is very important. The main requirements include low ripple, high stability, and strong drive capability. The isolation switching power supply has high precision in common power supply, but it will be accompanied by large ripples; while the linear power supply has small ripples, the output accuracy is not high. Therefore, voltage conditioning was selected twice. First use the isolated switching power supply WD324D12 to generate ±12V voltage, and then rely on a pair of linear power supplies 7,905 and 7,805 to generate ±5V voltage. In order to obtain a highquality signal with less ripple, LC filtering is performed at the end to provide a stable and efficient ±5V voltage with very low ripple. The calculated drive capability of this power supply is 1A, which meets the requirements of the conditioning amplifier.
So far, the signal conditioning circuit design is completed, and the input hundred pA level current is amplified to 5V, which basically solves the problem that the signal is weak and should not be collected and transmitted. However, because the noise signal is amplified during the conditioning process, the signaltonoise ratio of the system has not improved. Further filtering is performed to obtain an effective signal with a high signaltonoise ratio.
Fig. 9
Procession circuit structure. 
3.2 Experimental setup
The SiC photodiode was selected (Fig. 10). It mainly measures the ultraviolet spectrum in the 200–380 nm band. The light path emitted from the flame is captured through a window. The lens focuses the light on the SiC chip. The circuit board is used to convert optical and electrical signals. The structure diagram is as follows.
As for the flame, there are two parts, pneumatic and combustion oscillation unit which is shown as Figure 11. We obtain the flame through the combustion of propane and compressed air, and control the oilgas equivalent ratio by adjusting the flow of propane gas. When the fuel is rich, the flame will burn quietly; when the lean fuel is burned, the combustion oscillation phenomenon will occur easily.
Finally, it is processed by the realtime processor and FPGA in cRIO, and uses Ethernet to communicate with the computer, which is shown as Figure 12.
Fig. 10
Structure diagram of SiC sensor. 
Fig. 11
Flame generation process. 
Fig. 12
Overall structure diagram. 
4 Simulation and experimental results
4.1 Simulation results
After the design of the sinusoidal signal filter was completed, we performed a simulation test on it. As shown in Figure 13, when the 1V effective signal is mixed with the amplitude of 1V white noise interference, the system can realize the filtering function and identify the pure effective signal.
Due to the strong noise interference of the combustion oscillation signal, we also performed the test shown in Figure 14. In the signal with a valid signal amplitude of 0.9V and an aliasing amplitude of 9V, the signaltonoise ratio was only 0.1. Therefore, the effective signal has been completely submerged in the noise, and the detector can still obtain a good filtering effect.
The results show that the filter can quickly and accurately track sinusoidal signals at 10–1,000 Hz.
Fig. 13
Filtering effect of a fast Fourier transform sinusoidal signal filtering system on a 20 Hz noise signal. 
Fig. 14
Fast Fourier transform sine signal filtering system for filtering under strong interference. 
4.2 Experimental results
In order to test the effectiveness of the designed heat release rate detector, the following tests were performed to detect and extract the 10 Hz and actual combustion oscillation signals (about 315 Hz).
As for the quiet flame of 10 Hz, the output waveform of the sensor is shown in Figure 15. The flame sensor can capture flame oscillation characteristics. However, due to insufficient effective signal power and excessive highfrequency noise, this signal cannot be used directly. After filtering through a sinusoidal signal filter, a noiseless sinusoidal signal is obtained. The peaktopeak signal is 0.88V and the frequency is 10.24 Hz. Compared with 10 Hz, the error is only 2.4%.
Similarly, the detector can also detect the oscillating flame, which is shown in Figure 16. Under the excitation of the combustion oscillation test system, the flame oscillated at 316.5 Hz. At higher detection frequencies, the highfrequency interference of the sensor is not obvious, but the lowfrequency interference aliasing is strong. After filtering through a sine filter, the filtering system gives a sinusoidal signal without aliasing. After filtering through the sine filter, the signal peaktopeak value is 0.56V, the actual measurement is 312 Hz, and the error is 1.42%.
It can be seen that this test system can realize the extraction of weak and high signaltonoise signals with good results. It can be used to detect the quiet and oscillating flames in the combustion chamber of an aeroengine to obtain its corresponding characteristics.
The innovation points of the final article include the following:

Aiming at the problem of the combustion temperature in aeroengines that needs to detect the flame temperature, the multispectral radiation temperature measurement method is selected to establish the corresponding relationship between the spectral intensity ratio and the temperature. The absolute value of the error obtained by simulation is maintained within 2%.

Aiming at the thermal sound and electromagnetic interference in the combustion chamber of the aero engine, an improved version of the frequency domain filter circuit is designed, which can filter the characteristic signals at 10 Hz and 315 Hz, ensuring the reliability of the detection results;

Using the FPGA platform and appropriate sensors to obtain highprecision data.
Fig. 15
Fast Fourier transform sinusoidal signal filtering system for filtering under strong interference. 
Fig. 16
Detection effect of combustion oscillation phenomenon. 
5 Conclusion
This paper proposes a multispectral temperature measurement theory to obtain the threephase light intensity ratio and temperature inversion relationship. In order to solve the problem of temperature measurement in aero engine, a new multispectral radiation temperature measurement method is designed, and the relative error of the model is controlled within 2%.
This paper also designs a new type of flame detection sensor based on silicon carbide photodiode, and designs a quick, reliable and accurate conditioning unit with ADA4817 crossresistance amplifier as the core. The conditioning unit uses a very large gain resistance, magnifies the low current signal and ensures a certain dynamic response with a theoretical bandwidth of up to 1,000 Hz. To reduce sensor interference.
At the same time, in order to solve the problem of weak detection signal and excessive interference signal, an improved frequency domain filtering method based on fast Fourier transform is designed. Besides, the FPGA platform was used to ensure the realtime performance of the temperature measurement system, and simulations and experiments were performed.
At last, the active combustion control test was carried out, and the main oscillation frequency of 312 Hz and the secondary oscillation frequency of 525 Hz were detected. An oscillating signal with an oscillation frequency of 315 Hz was obtained on the established test platform, and the error was only 1.42%.
Nomenclature
B_{b}: Ratio of spectral radiance
M ^{′} : Predicted maximum frequency
N: Calculated length of fast FFT
: Emissivity of specific wavelength specificwavelength
λ_{1}, λ_{2}: Specific wavelength
Funding
This research received no external funding.
Conflicts of Interest
The authors declare no conflict of interest.
Authors contributions statement
Conceptualization, Qi Xie; methodology, Yunkun Wei; writing—original draft preparation, Yunkun Wei and Yan Zhang; writing—review and editing, Zhonglin Lin; supervision, Tianhong Zhang.
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Cite this article as: Y. Wei, T. Zhang, Z. Lin, Q. Xie, Y. Zhang, Detection method of combustion oscillation characteristics under strong noise background, Mechanics & Industry 21, 612 (2020)
All Figures
Fig. 1
Pollutant emission and equivalent ratio curve. 

In the text 
Fig. 2
Damage chart of aeroengine combustion oscillation structure. 

In the text 
Fig. 3
Choreography of the full text. 

In the text 
Fig. 4
OH emission spectrum at 2000 K. 

In the text 
Fig. 5
Relationship between spectral radiant intensity ratio and temperature. 

In the text 
Fig. 6
Relative error of temperature expression inversion of light intensity ratio at different temperatures. 

In the text 
Fig. 7
Filter based on fast Fourier transform. 

In the text 
Fig. 8
Structure of the filtering system. 

In the text 
Fig. 9
Procession circuit structure. 

In the text 
Fig. 10
Structure diagram of SiC sensor. 

In the text 
Fig. 11
Flame generation process. 

In the text 
Fig. 12
Overall structure diagram. 

In the text 
Fig. 13
Filtering effect of a fast Fourier transform sinusoidal signal filtering system on a 20 Hz noise signal. 

In the text 
Fig. 14
Fast Fourier transform sine signal filtering system for filtering under strong interference. 

In the text 
Fig. 15
Fast Fourier transform sinusoidal signal filtering system for filtering under strong interference. 

In the text 
Fig. 16
Detection effect of combustion oscillation phenomenon. 

In the text 
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