=Paper=
{{Paper
|id=Vol-3611/paper9
|storemode=property
|title=Time-frequency analysis of automotive engine performance via short-time Fourier transform
|pdfUrl=https://ceur-ws.org/Vol-3611/paper9.pdf
|volume=Vol-3611
|authors=Zhengmao Ye,Radian Belu,Hang Yin,Habib Mohamadian
|dblpUrl=https://dblp.org/rec/conf/ivus/YeBYM22
}}
==Time-frequency analysis of automotive engine performance via short-time Fourier transform==
https://ceur-ws.org/Vol-3611/paper9.pdf
Time–frequency analysis of automotive engine performance via
short-time Fourier transform
Zhengmao Ye1, Radian Belu1, Hang Yin1 and Habib Mohamadian1
1
College of Engineering, Southern University, Baton Rouge, LA 70813, USA
Abstract
Electronic control of automotive engines for passenger vehicles has been broadly implemented in
order to enhance the overall engine performance. Typical engine control systems include the air/fuel
ratio control system, fuel injection control system, ignition control system, idle speed control system,
emission aftertreatment system, exhaust gas recirculation control system, and so on. Time domain
analysis of engine performances has been well conducted in terms of fuel economy, idle speed
stability, and exhaust emissions. However, frequency domain analysis of various engine
performances is still in infancy. In this preliminary study, time–frequency analysis of automotive
engine performances has been proposed. The time-varying short-time Fourier transform (STFT)
can perform fundamental frequency analysis, which has been successfully applied to various fields,
such as the spectral envelope extraction, speech modeling, music analysis, time scaling, frequency
scaling, fast Fourier transform (FFT) filter banks, and so on. Thus STFT analysis has been
formulated to examine the engine performances in the frequency domain analysis. Several case
studies are conducted with respect to engine performances on idle speed stability, air/fuel ratio and
exhaust emissions. STFT also has potentials to be extended to conduct any other automotive engine
performance analyses.
Keywords 1
Time–frequency analysis, idle speed control (ISC), air/fuel (A/F) ratio control, exhaust
emissions, short-time Fourier transform (STFT)
1. Introduction necessary. The clustering based approach has been
applied to extract unique features via STFT analysis
under various pulsed loads, so as to further identify the
Both short-time Fourier transform (STFT) and load transient events as well as shunt faults and series
wavelet transforms are broadly applied in engineering arcing faults [3]. The low-complexity adaptive STFT
and science. STFT uses the sum of complex in terms of the chirp rate has been introduced. It shows
exponentials to represent signals, which leads to a superiority over other schemes in low signal-to-noise
systematic analysis and synthesis methodology. ratio (SNR) environments on the instantaneous
Meanwhile it could manifest the latent and obscure frequency estimation. At the same time, Principal
signal properties beyond the straightforward time Component Analysis (PCA) is used to replace the
domain analysis. There are numerous recent real world difference operator to enhance robustness in
applications of STFT. The STFT estimator of Micro- calculating [4]. A STFT based blind source separation
Doppler parameters has been proposed. It outperforms algorithm is designed for separating closely spaced
the existing algorithms which can reach the Cramer- multipath signals under Gaussian noises. It aims to
Rao lower bound of the frequency-modulated signal compensate for the multipath effect and complex noise
parameters. The Micro-Doppler signature can also be in practical wireless communication systems. It
applied to the UAV rotor blade analysis [1-2]. performs the better separation of multipath signals [5].
Electrification of future warships could be The spatio-temporal STFT block is proposed to
unavoidable, thus time-frequency feature extraction is simplify the computational complexity and improve
IVUS 2022: 27th International Conference on Information Technology, May 12,
2022, Kaunas, Lithuania
EMAIL: zhengmao_ye@subr.edu (Z. Ye); radian_belu@subr.edu (R. Belu);
hang_yin@subr.edu (H. Yin); habib_mohamadian@subr.edu (H. Mohamadian)
ORCID: 0000-0001-8897-574X (Z. Ye); 0000-0002-5892-3225 (R. Belu);
0000-0002-4600-5881 (H. Yin); 0000-0002-2099-2292 (H. Mohamadian)
©️ 2022 Copyright for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
the learning capability of classical 3D convolutional 2. Discrete time short-time Fourier
neural networks via a STFT kernel at the low frequency
nodes. With fewer parameters and lower costs, it transform (STFT)
provides better performance than some other state-of-
the-art methods [6]. Time-frequency analysis is applied In the discrete time domain, the transforming data
to industrial applications of system-on-chip design, sequence can be divided into overlapped frames.
where the startup transient current and voltage supply Fourier transform is carried out in each frame. The
to the induction motor as well as robot link vibration magnitude and phase for each point in time and
signals are well monitored. Both STFT and Discrete frequency will be recorded. The complex spectrogram
Wavelet Transform (DWT) are suitable to early in each frame will be collected and formulated as a
abnormality diagnosis [7]. DWT is another practical matrix. The discrete time STFT is expressed as (1).
approach to solve complex nonlinear problems. (1)
X n ( ) = m=- x(m)W (m - nR)e
+ - j m
Essentially it is designed to conduct analysis between
the time domain and frequency domain, however it can where x(m) is the input signal sequence with the time
also be easily extended to spatial domain analysis. index m; W(m) is the window function of the selected
Some case studies in time domain, frequency domain, length M; R is the selected hop size between
and spatial domain are conducted, where integration of successive windows in samples; Xn(ω) is the discrete-
DWT and Nonlinear Component Analysis (NCA) has time Fourier transform (DTFT) of the windowed data
been applied for discrete wavelet denoising with around the center time (nR), where DTFT is simply
satisfied results [8]. formulated as (2).
Automotive engine control is an important and (2)
X ( ) = m=- x(m)e
+ - j m
challenging field of scientific research. Almost all the
research outcomes however are limited to time domain The nature of STFT is determined by the shape of
data analysis. For instance, the A/F ratio excursion window functions. Typical window functions W(m)
from stoichiometry (14.7) deteriorates the fuel include the rectangular window, triangular window,
economy, exhaust emissions and vehicle driveability. Gaussian window, Chebyshev window, Hamming
The time delay constant and fraction of injected fuel window, Hann window, Kaiser window, Blackman
into engine cylinders are two parameters to model the window, as well as the FlatTop window. The
wall wetting phenomenon, where the linear least rectangular window produces the narrowest bandwidth
square model has been applied to solve the engine which is seldom used in practice due to the leakage
transient fuel control problem in the time domain [9]. effect. The FlatTop window and the Hamming window
Engine idle speed stability control has been well- will generate the largest and smallest bandwidth in
recognized as a complicated highly nonlinear problem practical implementation, respectively. In case that
in automotive industry. All existing classical, modern, critical temporal features and fast frequency
and intelligent control theories have been applied to modulation are needed, wide bandwidths should be
engine idle speed control. The two key control applied (e.g. FlatTop window). Conversely narrow
variables of the target idle speed and coolant bandwidths should be applied to focus on those
temperature are both varying over the time [10]. frequency features (e.g. Hamming window).
Nonparametric frequency response identification via The spectrogram is the visual representation of the
STFT is also presented to design robust linear signal strength in terms of the frequency spectrum. It is
controllers, together with the mixed sensitivity formulated as the magnitude squared of the STFT in
function optimization. It is applied to engine idle speed (3), which is relevant to the power spectral density of
control using dynamometer testing. It generates much the function. A narrow-band spectrogram corresponds
better delay margins. However its role in idle speed to the long length M of the window frame, while a
control is quite limited [11]. In order to optimize the wide-band spectrogram in turn corresponds to the short
overall performance of gasoline direct injection length M of the window frame. Each spectrogram
powertrain systems, both fuel economy and exhaust covers the list of amplitudes of the window frame size.
gas aftertreatment have to be taken into account. When The kth amplitude is associated with the actual
the lean burn technology is employed to reduce fuel frequency k.
consumption, exhaust emission levels would increase
on the other hand. Fuel injection control and exhaust
Spectrogram =| X () |2 =| STFT ( x,W ) |2 (3)
n
emission control approaches are still dominated by the STFT computation can be conducted via M-point
time domain data analysis [12-13]. In this preliminary fast Fourier transform (FFT) in each window frame.
study, time–frequency analysis of automotive engine Each window frame has to be zero-padded to avoid
performances will be conducted across diverse case aliasing effects. Thus (M-R) zeros will be padded at the
studies. STFT has been applied by using the 3D end of input signal sequence via zero-padding. In fact
spectrogram representation to reveal hidden properties the FFT stems from discrete Fourier transform (DFT),
beyond the classical time domain analysis. which is regarded as a special case of the DTFT for
finite causal signals. The M-point DFT is defined as
(4), where WM represents the M-th root of unity in (5).
(4)
X (i ) = k =0 x(k )WMik (0 i M )
M -1
WM = e- j 2 / M (5)
The simplest FFT scheme is to split the M-point
data sequence into two separate (M/2)-point data
sequences in terms of the even number and odd
number, which is (M/2)/log2(M) times faster than DFT.
x(2k + 1)W (2k +1)i (6)
M /2-1 M /2-1
X (i) = k =0
x(2k )W 2ki + M k =0 M
= +W k =0 xo (k )WMki/2
M /2-1 M /2-1
k =0
xe (k )Wki
M /2
i
M
= DFT {xe (k )} + WMi DFT {xo (k )} (0 i M )
Without loss of generality, being a generalized
cosine window, numerical simulations with respect to
the Blackman window (a0 = 0.42, a1 = 0.5, a2 = 0.08)
has been selected in the following sessions via the
(M/2) point FFT scheme.
3. Idle speed stability comparisons Figure 1: Engine idle speed signals and zero crossing
between 2 typical engines rates during startup and steady state
In Figure 2, the window frame and hop size being
When the engine is idling, a target rotational speed adopted are 1024 and 512 sample points, respectively.
has to be maintained in order to keep running without 3D spectrogram is mostly depicted as a heat map based
stalling out. The automotive engine idle speed could on a decibel scale (dB) of the intensity. All intensity
range from 600 rpm to 1000 rpm. The low engine idle values will be described by the false color. For
speed is helpful to reduce fuel consumption, but example, red color is much stronger than blue color in
meanwhile it can also generate stability problems. The dB. During the engine startup, the magnitude of the
goal of engine idle speed control is to stabilize and case B on the right (luxury engine) is much less than
smooth the engine at the low idle speed against various that of the case A on the left (economy engine),
uncertainties and external loads such as cylinder to indicating that the luxury engine being tested runs at
cylinder variations, air conditioner, power steering, AC relatively low idle speed, which will benefit fuel
alternator and water pump. economy. On the other hand, the frequency variation
In this session, time–frequency analysis of of the case B (luxury engine) is much higher than that
automotive engine idle speed stability is presented. of the case A (economy engine). It indicates that during
Two typical 4-cylinder engines for the luxury vehicle the transient process, control algorithms and
(Mercedes) and economy vehicle (Ford) are selected commands delivered by an Engine Electronic Unit
for comparison purposes. Rather than measuring the (ECU) of the luxury engine plays the better role than
engine speed along with time, some experiments are those of the economy engine. In the steady state of
conducted to collect the audio signals at engine startup engine idling, the magnitude of the case B (luxury
and at steady state of idling. For each engine, it is engine) is still much less than that of the case A
convenient to measure the audio signals in two diverse (economy engine), manifesting that the luxury engine
cases of startup and idling. After normalization, 2 sets being tested requires the relatively low idle speed,
of time domain signals are plotted in Figure 1, together which will benefit fuel economy. Conversely however,
with the related zero crossing rates, which is the simple the frequency variation of the case B (luxury engine) is
means to describe the smoothness of the idle speed much smaller than that of the case A (economy engine).
quality using the number of zero-crossings within a It indicates that during the steady state of engine idling,
time window being applied. Obviously the idle speed the luxury engine produces the smoother idle speed
quality at the steady state should be much smoother operation than the economy engine.
than that during the quick startup. The focus of the When two 4-cylinder engines of the luxury vehicle
context, however, is to extract some features in the (Mercedes) and economy vehicle (Ford) with the same
frequency domain, such that other properties can be displacement are chosen, based on time–frequency
captured using time–frequency analysis on idle speed analysis of engine idle speed stability issues at both the
quality. Accordingly discrete time STFT is employed transient state and steady state, it can be found out that
where outcomes from multiple cases could compare the luxury engine being tested operates at relatively
with each other to reveal hidden characteristics based lower idle speed but runs smoother than the economy
on 3D spectrogram plots, covering cases of both startup engine. As a result, the luxury engine requires the
and steady states of idling for two engines from the fewer amount of fuel consumption but it provides more
luxury and economy vehicles. comfortable condition during idling. In Figure 3, the
window frame and hop size have been switched to 512 combustion process. The A/F ratio in the
and 256 sample points, respectively. The conclusions stoichiometric mixture is defined as 14.7
being drawn are actually the same. Thus in all (stoichiometry). When the A/F ratio is lower than the
subsequent sessions being discussed, resolutions in stoichiometry, the rich air fuel mixture is formed.
time domain and frequency domain will be no longer When the A/F ratio is higher than the stoichiometry,
emphasized. the lean air fuel mixture is formed. Lean burn simply
means the burning of fuel with an excess of air inside
the combustion chamber.
The rich air fuel mixture gives rise to incomplete
combustion inside. The incomplete combustion also
results in the low combustion temperature, thus it leads
to low levels of NOx. At the same time, however, extra
amounts of CO and HC will be generated. On the other
hand, the lean air fuel mixture corresponds to the
excess air. The excess air in a lean-burn engine in turn
will emit much less amount of CO and HC. The
complete combustion with the sufficient amount of
oxygen leads to the high combustion temperature over
time, thus it produces high levels of NOx.
It is clearly shown that the A/F ratio plays a
dominant role in the fuel economy, amount of exhaust
emissions (NOx, CO and HC) as well as the power
output. In this case, it is necessary to conduct time-
frequency analysis of the A/F ratio in lean burn
engines. For the exhaust aftertreatment system of lean
burn engines, the Lean NOx Trap (LNT) is required to
manage the amount of NOx. Because the LNT has its
Figure 2: Comparisons of 3D spectrogram plots on maximum capacity limit. Periodic NOx storage (lean
idle speed quality (Case 1) burn) and NOx purge (rich burn) cycles are necessary
(e.g. storage: 60 sec and purge: 2-3 sec in each cycle).
Figure 3: Comparisons of 3D spectrogram plots on idle Figure 4: 3D spectrogram plots of A/F ratio data in lean
speed quality (Case 2) burn technology
In Figure 4, the window frame and hop size have
been selected as the 256 and 128 sample points,
4. Time–frequency analysis of the respectively. The data are collected from the 6-cylinder
air/fuel ratio in lean burn engine Ford engine using lean burn technology. In the time
domain, A/F ratio is generally higher than the
The fuel economy of an internal combustion engine stoichiometry with lean burn technology, except for
can benefit from the lean burn technology. The A/F periodically switching to rich air fuel mixture for a very
ratio is the mass ratio of air to fuel in an engine short time during the purge mode in each cycle. In the
frequency domain, it shows that high A/F ratio (lean
burn) corresponds to the relatively low frequency. It duration). The lowest amount of oxygen levels instead
indicates that a majority of engine operations in each corresponds to the sudden purge operation in the rich
cycle are conducted during lean combustion, which is mode (e.g., 2-3 seconds duration). There are still a
mostly associated to the steady state operation. The low couple of local peak values of the oxygen level along
A/F ratio (rich burn) instead corresponds to the the frequency coordinates when the time coordinates
relatively high frequency. It indicates that a minority of are fixed. These peak values are actually related to
engine operations in each cycle are conducted at instantaneous responses to sudden engine operating
incomplete rich combustion, which is mostly mode switching between the lean burn and rich burn,
associated to transient state operation. In addition, which can not be directly observed based on the simple
between the relatively low frequency and relatively time domain analysis exclusively.
high frequency, the transition of the A/F ratio along the
frequency coordinate gives rise to a sharp slope across
the transition band. It is relevant to the fact that the
operating mode switching occurs twice in any single
cycle, from lean burn to rich burn, or conversely from
rich burn to lean burn.
5. Time–frequency analysis of the
exhaust gas emission levels
In Figure 5, the window frame and hop size cover
256 and 128 sample points, respectively. The data (HC,
CO, NOx, O2) are still collected from 6-cylinder Ford
engine with the lean burn technology, using diverse
types of sensors (e.g. oxygen sensors). The goal of
exhaust gas aftertreatment is to significantly improve
the air quality and avoid pollution. HC, CO and NOx
are typical exhaust emissions on which the control
algorithms are focusing. The formation mechanisms
vary case by case across different types of emissions.
Tradeoff is always needed in the exhaust emission
control system. For example, the incomplete
combustion leads to the low combustion temperature,
it generates excessive amount of CO and HC
emissions, however in turn it helps to reduce the
amount of the NOx emission at the same time.
In the time domain, similar pattern occurs Figure 5: 3D spectrogram of exhaust emission levels
periodically for every emission curves when switching (1) HC; (2) CO; (3) NOx; (4) O2
between lean air fuel mixture in the NOx storage mode
and rich air fuel mixture in the purge mode across each It has been demonstrated from all three cases of
cycle. In the frequency domain, the highest amounts of engine performance analyses that the time-frequency
HC, CO and NOx emission levels all correspond to the approach has superiority over the exclusive time
relatively low frequency, which belongs to the domain analysis. Some special latent characteristics
relatively steady operating mode. The lowest amounts have been discovered via the frequency domain
of the HC, CO and NOx emission levels instead all analysis on a basis of STFT. STFT turns out to be a
correspond to the relatively high frequency, which are promising approach, which can also be easily
associated with the transient engine operating period, expanded to data analysis of all other aspects of
at the expense of extra control actions being needed. automotive engine performance in the similar and
There are a couple of local peak values along the straightforward way.
frequency coordinates in each case of HC, CO and
NOx when time coordinates are fixed. In fact these
peak values are associated with system responses of 6. Conclusions
sudden switching between lean burn and rich burn. It
shows that the instantaneous responses to the operating The short-time Fourier transform (STFT)
mode switching control action actually lead to analysis approach has been well implemented in
additional amounts of exhaust emissions. Furthermore, automotive engine performance analysis in this study.
in the frequency domain, the highest amount of oxygen The time–frequency approach via STFT has been
levels also correspond to the relatively low frequency, applied to idle speed stability analysis, A/F ratio
which turns out to be the lean mode (e.g., 60 seconds control and exhaust emission aftertreatment in terms of
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