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Journal ArticleDOI

Diesel Injector Dynamic Modelling and Estimation of Injection Parameters from Impact Response Part 2: Prediction of Injection Parameters from Monitored Vibration

01 Oct 1996-Vol. 210, Iss: 4, pp 303-312

AbstractPart 2 of this paper presents the experimental and analytical procedures used in the estimation of injection parameters from monitored vibration. The mechanical and flow‐induced sources of vibration in a fuel injector are detailed and the features of the resulting vibration response of the injector body are discussed. Experimental engine test and data acquisition procedures are described, and the use of an out‐of‐the‐engine test facility to confirm injection dependent vibration response is outlined. Wigner‐Ville distribution (WVD) analysis of non‐stationary vibration signals monitored on the injector body is used to locate regions of vibration in the time‐frequency plane which are responsive to injection parameters. From the data in these regions, estimates of injection timing and fuel pressure are obtained. Accurate estimation of injection parameters from externally monitored vibration is shown to pave the way for the detection and diagnosis of injection system faults. Moreover, it is demonstrated that the technique provides an alternative method for the set‐up, checking and adjustment of fuel injection timing. Table 1 caption: Test engine specification Fig. 1 caption: Injector vibration versus cylinder pressure, line pressure and needle lift Fig. 2 caption: Bench‐top test rig layout and data acquisition system Fig. 3 caption: Injector vibration and needle motion from bench‐top testing Fig. 4 caption: Engine test layout and data acquisition system Fig. 5 caption: Time‐frequency analysis of injector vibration Fig. 6 caption: Time‐frequency analysis of injector vibration at 3000 r/min Fig. 7 caption: Timing of the fuel injection process Fig. 8 caption: Comparison of needle lift and vibration derived injection timing Fig. 9 caption: Comparison between injection line pressure and injector vibration Fig. 10 caption: Relationship between injector vibrtation and line pressure

Topics: Injector (52%)

Summary (3 min read)

INTRODUCTION

  • The injection process plays one of the most influential roles in the performance and emission control of a diesel engine.
  • Obtaining accurate values for injection parameters is the key to the specification, set-up, adjustment and diagnosis of injection equipment.
  • This in turn permits enhanced performance such as reductions in fuel consumption and pollutant emissions, and increases in power output.
  • A non-intrusive measurement approach, which does not influence injection characteristics, is attractive because it may permit more accurate estimates of injection parameters.
  • The layout of the paper is as follows: Section 2 analyses injector vibration; Section 3 describes the test methods used in the vibration measurement; Section 4 details the.

2 INJECTOR VIBRATION

  • There are two sources of injector body vibration associated with the injection process: impacts due to the needle hitting its backstop and seat (that is mechanical excitation), and the flow of high-pressure fuel within the galleries and chambers of the injector (that is fluid flow excitation).
  • Aside from the nature of the excitation sources, the monitored vibration is also influenced by the dynamic properties of the injector body.

2.1 Mechanical excitation

  • Part 1 developed a theoretical correlation between the impacts and fuel injection parameters.
  • The amplitude of the first collision in the opening impact series was shown to be related to the fuel injection pressure, and the energy of the opening impact series was shown to be related to the fuel injection rate.

2.2 Fluid flow excitation

  • The presence of flow induced vibration response is confirmed in Fig. 1 which overlays monitored body vibration upon cylinder pressure, line pressure and needle lift traces.
  • From this figure it can be seen that there is a vibration response commencing prior to the opening of the needle (at a time corresponding to the onset of high-pressure fuel supply) and continuing until the needle is fully retracted, at which point it becomes swamped by the high-amplitude impact response.
  • There are no mechanical impacts, only the flow of fuel within the injector.

3 INJECTOR VIBRATION MEASUREMENT

  • Due to the complex nature of the injector body, its mounting assembly and its interaction with the cylinder head, it is difficult to derive a mathematical model relating the internal vibration sources to an external surface-mounted monitoring transducer.
  • For this reason, an experimental investigation of the relationship between monitored vibration and fuel injection was adopted in this study.
  • Two types of experimental set-up were used: a working engine test rig, and a bench-top rig providing an out-of-the-engine injection test facility.
  • The test engine was a Ford FSD-425 production unit fitted with a Bosch V injection system and coupled to a hydraulic dynamometer.
  • The purpose of the bench-top rig was to isolate those components of monitored vibration which were due to the injection process from those components associated with combustion, piston slap and other engine sources.

3.1 Bench-top injector tests

  • Only one injector (the test injector) is mounted in the bench-top cylinder head.
  • The other three injectors, used to maintain representative loading of the injection pump, are mounted together in a dummy cylinder head with associated fuel collection vessels.
  • This separation of the test injector from the load injectors is further to ensure its vibration isolation.
  • Fuel levels can be adjusted via the injection pump rack setting in the usual way, and the pump speed can be varied by the closed-loop.

I I

  • Two-channel data acquisition from the bench-top rig was made with a computer-controlled 12-bit device sampling simultaneously at 65 kHz.
  • From the bench-top tests, several aspects of injector vibration response were confirmed.
  • This conclusion is reinforced by the directly measured needle acceleration traces shown in Figs 3(a2) and 3(b2).
  • The inserts within Figs 3(a2) and (b2) show the acceleration waveforms as predicted by the model developed in Part 1.
  • These can be seen to exhibit quite a good correlation with their measured equivalents, further validating the accuracy of the model.

3.2 Engine injector tests

  • Before conducting a test, the engine was run to normal operating temperature, and then a constant speed test was performed at four load settings between 35 and 130 Nm.
  • A wide range of operating conditions, and consequently of fuel injection characteristics, was covered.
  • In the same manner as for the bench-top rig, the incoming data was gated in software to give 1024-point segments.

It can be seen that during injection, vibration energy

  • The opening impact responses are seen to attenuate is spread over a wide range of frequencies from around gradually with time and the two higher frequency response ridges have all but disappeared by the time that the injector closing impact occurs.
  • Figure 6 shows WVD analysis results for differing engine loads at a speed of 3000 r/min.
  • Furthermore, it is more difficult to distinguish the injector closing response in the lowfrequency region.
  • The needle opening is governed by a large and repeatable fuel pressure front, but the needle closing is governed by the residual pressure in the injector, and this is likely to vary quite considerably from injection to injection.
  • If the residual fuel pressure is low, it is likely that a large amplitude body response will result.

5 ANALYSIS OF THE INJECTION PROCESS

  • Having identified within the WVD analysis those regions of frequency response which contain injection related information, bounds can be placed upon the frequency range of interest.
  • With these bounds it is possible to set a bandpass filter so that envelope analysis can be used as an alternative means of extracting the appropriate high-frequency information from the monitored vibration data.

5.1 Extraction of timing information from monitored

  • It can be seen that the values of the injection events obtained from the monitored vibration time signature are highly consistent with those obtained by direct needle lift mea- surement.
  • The vibration-derived timing of the needle opening and fully open events is nearly identical to the equivalent needle lift information, and the vibrationderived band of the closing event timing neatly contains the directly measured trace.
  • It can be seen from the closing impact bands depicted in Fig. 8 that averaging of the band limits does, in the majority of instances, give a timing value for the needle closing event which is very close to that obtained by needle lift measurement.

5.2 Extraction of fuel pressure information from

  • Injector vibration is caused by a combination of mechanical impacts and high-pressure fluid flow within the injector body.
  • This vibration response can be detected using an accelerometer mounted either on the injector body, or on the injector fixing saddle.
  • An engine-isolated bench-top rig was used to demonstrate that injector vibration response is not contaminated by engine-related vibration sources such as combustion noise and piston slap.
  • Wigner-Ville distribution analysis was applied to the highly non-stationary vibration signals monitored on an injector body and this showed that the highfrequency body response contains regions of information which describe the injection process.

Q IMechE 1996

  • The proposed vibration-based non-intrusive approach to the analysis of diesel fuel injection systems could provide a powerful alternative to the conventional intrusive fuel line pressure and the needle lift measurement techniques that are commonly used.
  • In addition, this technique has important implications in the field of diesel engine condition monitoring.
  • Deviations from the demonstrated good condition relationships between monitored vibration and fuel injection parameters will be likely to indicate a change in condition.

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University of Huddersfield Repository
Gu, Fengshou, Ball, Andrew and Rao, K K
Diesel injector dynamic modelling and estimation of injection parameters from impact response part
2: prediction of injection parameters from monitored vibration
Original Citation
Gu, Fengshou, Ball, Andrew and Rao, K K (1996) Diesel injector dynamic modelling and
estimation of injection parameters from impact response part 2: prediction of injection parameters
from monitored vibration. Proceedings of the Institution of Mechanical Engineers Part D Journal of
Automobile Engineering, 210 (44). pp. 303-312. ISSN 0954-4070
This version is available at http://eprints.hud.ac.uk/id/eprint/6788/
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http://eprints.hud.ac.uk/

303
Diesel
injector dynamic modelling and estimation
of
injection-parameters from impact response
Part
2
:
prediction
of
injection parameters from
monitored vibration
F
Gu,
MSc
and
A
D
Ball,
BEng, PhD
School
of
Engineering,
University
of
Manchester
K
K
Rao,
MSc
Department
of
Mechanical
Engineering, University
of
Manchester Institute of Science and Technology
Part
2
of this paper presents the experimental and analytical procedures used in the estimation of injection parameters from monitored
vibration. The mechanical andflow-induced sources of vibration
in
a fuel injector are detailed and the features of the resulting vibration
response of the injector body are discussed. Experimental engine test and data acquisition procedures are described, and the use of an
out-of-the-engine test facility to confrm injection dependent vibration response is outlined.
Wigner-Ville distribution (WVD) analysis of non-stationary vibration signals monitored
on
the injector body is used to locate regions
of vibration in the time-frequency plane which are responsive to injection parameters. From the data
in
these regions, estimates of
injection timing and fuel pressure are obtained.
Accurate estimation of injection parameters from externally monitored vibration is shown to pave the way for the detection and
diagnosis of injection system faults. Moreover, it is demonstrated that the technique provides an alternative method for the set-up,
checking and adjustment
of
fuel injection timing.
Key words:
fuel
injection
timing
injector, condition monitoring, injector
v
i
b
r
a
t
i
o
n
,
1
INTRODUCTION
The injection process plays one of the most influential
roles in the performance and emission control of a
diesel engine. Obtaining accurate values for injection
parameters is the key to the specification, set-up, adjust-
ment and diagnosis of injection equipment. This in turn
permits enhanced performance such as reductions in
fuel consumption and pollutant emissions, and increases
in power output.
It is conventional to characterize the injection process
in terms of injection pressure, needle lift and injection
rate (the latter two factors contain injection timing
information). Injection pressure is usually measured
with
a
strain gauge transducer positioned in the high-
pressure
fuel
line, and needle lift is measured with a dis-
placement sensor inside the injector
(1,
2).
Part
1
described why, due to their intrusive nature, it was in-
evitable that these measurement techniques would
adversely affect the motion
of
the needle within the
injector valve and would consequently change the fuel
injection characteristics.
A
non-intrusive measurement approach, which does
not influence injection characteristics, is attractive
because it may permit more accurate estimates of injec-
tion parameters.
A
further possible advantage of such
an approach is that in-service condition monitoring
with subsequent adjustment, fault detection and diag-
nosis becomes feasible.
Fundamental to the principle of non-intrusive mea-
surement
is
the remote detection and interpretation of
The
MS
was
received
on
4 April 1994 and was accepted
for
publication
on
28
October
1995.
DO179512
Q
IMechE
1996
impact vibration, time-frequency
analysis,
injection
pressure,
some transmitted quantity which contains sufficient
information to enable the source parameter value to be
inferred. Of the possible transmitted parameters, one of
the most likely to contain the necessary information is
the vibration response of the injector body to the oper-
ation of the injector valve within it.
Specifically, injector vibration response is due to a
combination of the needle impacting and the flow of
high-pressure fuel within the body. Using modern signal
processing techniques and computational capabilities, it
appears possible to extract injection parameter informa-
tion from the non-stationary vibration signals that are
detected by a transducer when positioned on the outer
surface of an injector body.
In this study, the vibration response of
a
fuel injector
when operating in a test engine is analysed using the
Wigner-Ville distribution
(WVD),
and estimates of
injection timing and fuel pressure are obtained. The
layout of the paper is as follows: Section
2
analyses
injector vibration; Section
3
describes the test methods
used in the vibration measurement; Section
4
details the
WVD
analysis of the monitored vibration signals; and
Section
5
compares vibration-based results with those
obtained from conventional measurement.
2
INJECTOR VIBRATION
There are two sources of injector body vibration associ-
ated with the injection process: impacts due to the
needle hitting its backstop and seat (that is mechanical
excitation), and the
flow
of
high-pressure fuel within the
galleries and chambers
of
the injector (that is fluid flow
Roc
Instn
Mech Engrs
Vol210

304
F
GU,
A
D
BALL AND
K
K
RAO
excitation). Aside from the nature of the excitation
sources, the monitored vibration is also influenced by
the dynamic properties of the injector body.
2.1
Mechanical excitation
In Part
1
the impact behaviour of an injector was inves-
tigated numerically by modelling the needle motion as
a
two-mass vibro-impact system. The retracting backstop
impact was shown to be of lower amplitude but to
contain more high-frequency components than the sub-
sequent advancing needle seat impact. The first collision
in the needle retracting impact series indicates the
instant when the needle first reaches its fully open posi-
tion. Similarly, the first collision in the needle advancing
impact series indicates the instant when the needle first
returns to its seat.
Part
1
developed a theoretical correlation between
the impacts and fuel injection parameters. The ampli-
tude of the first collision in the opening impact series
was shown to be related to the fuel injection pressure,
and the energy of the opening impact series was shown
to be related to the fuel injection rate.
2.2
Fluid
flow
excitation
During injection, fuel flows through the internal pass-
ages and chambers of the injector with
a
sharp high-
pressure wave front. This turbulent flow impinges upon
the injector body and causes it to vibrate. The forces
involved are proportional to the dynamic head of the
fuel flow and the frequency of the resulting vibration
depends upon the sharpness of the wavefront. This
means that injection at larger fuel rates
is
more likely to
produce higher frequency and larger amplitude body
vibrations than injection at smaller rates.
The presence of flow induced vibration response is
confirmed in Fig.
1
which overlays monitored body
vibration upon cylinder pressure, line pressure and
needle lift traces. From this figure it can
be
seen that
there is a vibration response commencing prior to the
opening of the needle (at a time corresponding to the
onset of high-pressure fuel supply) and continuing until
the needle is fully retracted, at which point it becomes
swamped by the high-amplitude impact response. In
this time span, there are no mechanical impacts, only
the flow of fuel within the injector.
2.3
Injector
body
response
Due to the short duration of the collisions which com-
prise the opening and closing impact series (the dura-
tion of a collision is of the order of
a
microsecond), the
injector vibration response to this excitation is a
sequence of three series of transients, with each tran-
sient being dominated by the lower body frequencies.
Within an injection cycle, the order of the excitation
events dictates that the first transient series is due to
flow excitation, the second transient series is due to
opening impact excitation, and the third transient series
is due to closing impact excitation.
Depending upon engine operating conditions (for
example the duration of injection), an individual tran-
sient response within the train of responses may
or
may
not have decayed completely before the next transient
occurs. As shown in Part
1,
the opening and closing
impact series have different spectral contents, meaning
that their associated responses will have different spec-
tral contents too. From a time trace of monitored vibra-
tion, it may not
be
possible to detect the instant of the
closing impact if it is buried in the continuing transient
response from the opening impact series. The different
frequency contents of the two responses suggest,
10
1
I
I
1
I
I
I
I
1
1
--.**.-*.-
Cylinder pressure
Injector vibration
8
----
Line pressure
2
0
-2
Closing impact response
Fluid excitation res
I
I
I
I
1
I I
I
0
0.5
1
1.5
2
2.5
3 3.5
4
Injector vibration versus cylinder pressure, line pressure and needle
lift
Time (ms)
Fig.
1
Part
D:
Journal
of
Automobile
Engineering
Q
IMechE
1996

DIESEL INJECTOR DYNAMIC MODELLING. PART
2
305
Fuel Return
Tank
however, that it should be possible to differentiate
between the two events if the monitored vibration
response is transformed into
a
time-frequency represen-
tation.
PC
computer
3 INJECTOR VIBRATION MEASUREMENT
Due to the complex nature of the injector body, its
mounting assembly and its interaction with the cylinder
head, it is difficult to derive a mathematical model rela-
ting the internal vibration sources to an external
surface-mounted monitoring transducer. For this
reason, an experimental investigation of the relationship
between monitored vibration and fuel injection was
adopted in this study.
Two types of experimental set-up were used:
a
working engine test rig, and a bench-top rig providing
an out-of-the-engine injection test facility. The test
engine was
a
Ford FSD-425 production unit fitted with
a
Bosch
V
injection system and coupled to
a
hydraulic
dynamometer. The bench-top test rig comprised
a
cylin-
der head from another Ford FSD-425 engine and fitted
with an identical injection system, but driven by an elec-
tric motor. The purpose of the bench-top rig was to
isolate those components of monitored vibration which
were due to the injection process from those com-
ponents associated with combustion, piston slap and
other engine sources. In addition to the recording of
injector vibration when in the test engine, fuel line pres-
sure, needle lift and fuel consumption were recorded by
conventional methods to enable the relationship
between the injection parameters and vibration to be
investigated.
3.1
Bench-top injector tests
In addition to the internal sources of diesel injector
vibration, it is likely that other factors, particularly
combustion noise, will also excite the injector body.
During combustion, there is a sharp rise in cylinder
pressure and a consequent shock which acts upon the
cylinder head, cylinder wall and the tip of the injector
nozzle. This shock to the injector tip, and the vibration
of the cylinder head, are likely to contribute to the
vibration response
of
the injector body.
Figure
1
(in Section 2) shows that there is no severe
cylinder pressure change at the time of injector needle
opening, and it is hence unlikely that the cylinder pres-
sure makes any significant contribution to injector body
vibration. At the time of the injector needle closing,
however, the cylinder pressure rises sharply with the
onset of combustion, and it is hence unlikely that the
injector body vibration is due to needle impacts alone.
Ascertaining the sources of excitation during the needle
closing phase is not straightforward, and this difficulty
provided the motivation for the development of the
bench-top injector test rig.
Figure
2
depicts the schematic layout of the bench-
top rig, which was designed to isolate injector vibration
response from all sources aside from those inherent to
the operation of the injector. The principal components
of the rig are a variable speed electric motor driving an
injection pump, which in turn supplies fuel from a tank
to a set of four fuel injectors, one of which is mounted
in a cylinder head. To ensure close correlation with the
engine tests, the injection pump, injectors and cylinder
head are identical to those used on the engine. Supports
shrouded in damping material, and vibration isolating
mounts are employed to minimize the transmission
of
vibration from the motor and the fuel pump to the test
injector.
Only one injector (the test injector) is mounted in the
bench-top cylinder head. The other three injectors, used
to maintain representative loading of the injection
pump, are mounted together in a dummy cylinder head
with associated fuel collection vessels. This separation
of the test injector from the load injectors is further to
ensure its vibration isolation. Fuel levels can be adjust-
ed via the injection pump rack setting in the usual way,
and the pump speed can be varied by the closed-loop
II
Fuel
Supply
Tank
Q
IMechE
1996
Roc
Instn
Mech
Engrs
Vol210

306
F
GU,
A
D
BALL AND
K K
RAO
motor controller. Two-channel data acquisition from
the bench-top rig was made with a computer-controlled
12-bit device sampling simultaneously at
65
kHz. The
incoming data streams of body vibration and directly
measured needle motion readings were gated in soft-
ware into 1024-point segments.
From the bench-top tests, several aspects of injector
vibration response were confirmed. By comparing the
vibration signal in Fig. 3(al) with that in Fig. 1 (which
was obtained from an engine test) it can be seen that the
two body response waveforms are very similar. From
this similarity
it
can be concluded that combustion
shocks, piston slap and other engine operating sources
have minimal effect upon injector vibration response.
Such response
is
only a consequence of mechanical and
flow-related vibration sources within the injector. This
conclusion is reinforced by the directly measured needle
acceleration traces shown in Figs 3(a2) and 3(b2). Of
particular interest in Fig. 3 is that the upper (a1 and a2)
traces are from a high-load situation, where both
opening and closing needle impacts are apparent,
whereas the lower traces (bl and b2) are from a low-
load test in which it can be seen that there occurs no
opening impact of the needle with its backstop.
-150
I
401
I
-,
-
.
.
.,
. . .
-L"
0
0.64
1.28 1.92 2.56 3.2 3.84 4.48 5.12 5.76 6.4 7.04 7.68
Time(ms)
Fig.
3
Injector vibration'and needle
motion
from
bench-top testing
Part
D:
Journal of
Automobile
Engineering
Q
IMechE
1996

Citations
More filters

Journal ArticleDOI
Abstract: Air-borne acoustic based condition monitoring is a promising technique because of its intrusive nature and the rich information contained within the acoustic signals including all sources. However, the back ground noise contamination, interferences and the number of Internal Combustion Engine ICE vibro-acoustic sources preclude the extraction of condition information using this technique. Therefore, lower energy events; such as fuel injection, are buried within higher energy events and/or corrupted by background noise. This work firstly investigates diesel engine air-borne acoustic signals characteristics and the benefits of joint time–frequency domain analysis. Secondly, the air-borne acoustic signals in the vicinity of injector head were recorded using three microphones around the fuel injector (120° apart from each other) and an independent component analysis (ICA) based scheme was developed to decompose these acoustic signals. The fuel injection process characteristics were thus revealed in the time–frequency domain using Wigner–Ville distribution (WVD) technique. Consequently the energy levels around the injection process period between 11° and 5° before the top dead centre and of frequency band 9–15 kHz are calculated. The developed technique was validated by simulated signals and empirical measurements at different injection pressure levels from 250 to 210 bars in steps of 10 bars. The recovered energy levels in the tested conditions were found to be affected by the injector pressure settings.

115 citations


Journal ArticleDOI
TL;DR: It is shown that chaotic vibrations arise from nonlinear deterministic physical systems or non-random differential or difference equations, and in numerous engineering systems there exist nonlinearities.
Abstract: By definition, chaotic vibrations arise from nonlinear deterministic physical systems or non-random differential or difference equations. In numerous engineering systems there exist nonlinearities ...

66 citations


Journal ArticleDOI
Abstract: Diesel engines injection process is essential for optimum operation to maintain the design power and torque requirements and to satisfy stricter emissions legislations. In general this process is highly dependent upon the injection pump and fuel injector health. However, extracting such information about the injector condition using needle movements or vibration measurements without affecting its operation is very difficult. It is also very difficult to extract such information using direct air-borne acoustic measurements. In this work adaptive filtering techniques are employed to enhance diesel fuel injector needle impact excitations contained within the air-borne acoustic signals. Those signals are remotely measured by a condenser microphone located 25 cm away from the injector head, band pass filtered and processed in a personal computer using MatLab. Different injection pressures examined were 250, 240, 230, 220 and 210 bars and fuel injector needle opening and closing impacts in each case were thus revealed in the time–frequency domain using the Wigner–Ville distribution (WVD) technique. The energy of 7–15 kHz frequency bands was found to vary according to the injection pressure. The developed enhancement scheme parameters are determined and its consistency in extracting and enhancing signal to noise ratio of injector signatures is examined using simulation and real measured signals; this allows much better condition monitoring information extraction.

61 citations


Journal ArticleDOI
Abstract: In this study the characteristics of AE wave transmission around and through the cylinder head of a small four-stroke fuel injection diesel engine are investigated. Two sets of measurements have been carried out, one with simulated sources at various points on the cylinder head and one with the engine running, using a nine-sensor array. Propagation of AE waves from the simulated sources to the array sensor positions indicates attenuation factors of around 8.5. It is important to be able to estimate source–sensor distance accurately and this has been done using a threshold technique to identify the arrival time of a low frequency high amplitude wave at the sensors, then to deduce the wave speed from that information and hence calculate the source–sensor distance (transmission path length). Engine running tests were carried out and analysis focused on reconstitution of injector and exhaust valve opening events using signal mapping techniques. For injector events, the attenuation factors were similar to those measured from the simulated sources. For exhaust valve-opening events the attenuation factors varied between 5 and 7 with relatively poor correlation. This difference is thought to be due to variation in the actual source position during valve opening because the exhaust valve actuation involves a cam, push rod and rocker design. The results can be used to reconstitute the timing and amplitude of the AE emitted at the source which enables much more focussed monitoring of specific components and processes identified in the signals.

37 citations


Journal ArticleDOI
Abstract: An analysis procedure, using the time-frequency distribution, has been developed for the analysis of internal combustion engine noise signals. It provides an approach making use of advantages of both the linear time-frequency distribution and the bilinear time-frequency distribution but avoiding their disadvantages. In order to identify requirements on the time-frequency analysis and also correlate a time-frequency analysis result with noise sources, the composition of the noise signal is discussed first. With this discussion, a mathematical model has been suggested for the noise signal. An example of identifying noise sources and detecting the abnormal condition of an injector with the noise signal time-frequency distribution for a diesel engine is also provided.

30 citations


References
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01 Jan 2014
Abstract: In this second part of the paper the Wigner distribution is adapted to the case of discrete-time signals It is shown that most of the properties of this time-frequency signal representation carry over directly to the discrete-time case, but someothers cause problems These problems are associated with the fact that in general the Wigner distribution of a discrete-time signal contains aliasing contributions It is indicated that these aliasing components will not be present if the signal is either oversampled by a factor of at least two, or is analytic 1 Introduetion In part I of this paper 1) the Wigner distribution (WD) of continuous-time signals was discussed, and it was shown that this function has some very interesting properties The determination of this distribution function requires, like the spectrum, an integral of the Fourier type to be evaluated Ideally this requires the signal to be known for all time, but in practice windowing techniques can be used to relax this requirement The effects of windowing on the WD were discussed in part 1 In general two different approaches can be distinguished to compute these Fourier-type integrals The first is by means of analogue signal processing, and recently optical signal processing methods have been proposed for determining suitable approximations to the WD 2) The second approach is based on digital signal processing This opens the way to apply computationally efficient methods for evaluating the discrete Fourier transform, but requires the concept of the Wigner distribution to be transferred to the case of discretetime signals This is the aim of this part of the paper As can be expected, the WD for discrete-time signals shows much similarity with that for continuous-time signals, but in some respects it has characteristic differences To emphasize the similarities and point out the differences we will try to follow as closely as possible the same lines as in part I, and give comments only on those results that differ from that of the continuous-time counterpart 276 Phillps Journalof Research Vol35 Nos4/5 1980 Philips Journalof Research Vol35 Nos4/5 1980 277 The Wigner distribution Also the numbering of the equations is made such that corresponding equations have the same number This has the consequence that sometimes equation numbers are not successive if equations have been deleted, and that equations that do not occur in part I have a special numbering If reference is made to an equation in part I the equation is given the prefix I All sections, except sec 7, have the same topic and heading as in part I Section 7, which in part I deals with the WD of band-limited signals, now deals with the WD of finite duration sequences Equations in this section do not correspond in general with an equation of part I 2 The Wigner distribution for discrete-time signals 21 Preliminaries In this paper Weconsider in general complex valued, discrete-time signals f(n), feC, n e Z for which the (Fourier) spectrum is defined by 3) 00 F(e) = (fJdf) (e) = L f(n) e -jnlJ (2la) n=-c:o The inverse transform is given by 11 f(n) = (fJd-l F) (n) = _1_ J F(e) ejnlJ de, 21t (2lb) -11 Inner products are defined for the signals and spectra by 00 (I, g) = L f(n) g*(n) (22a) n=-oo and 11 (F, G) = _1 J F(e) G*(e) de 21t (22b) -11 respectively Norms and Parseval's relation are then the same as in eqs (123) and (124) respectively The following operators will be used The shift operator for the signals (9{f) (n) = f(n k), kEZ (25a) and for the spectrum (9'cF) (e) = F(e C), CE R, (complex) modulation in the time domain T A C M Claasen and W F G Mecklenbrauker ( At!!,!) (n) = f (n) ein!!, and in the frequency domain c;«; F) (0) = F(O) einD ceR (26a) neZ, (26b) differentiation of the spectrum 1 (fi))F) (0) = -;-F 1(0), J (27) multiplication by the running variable (Rlf) (n) = nf(n), (28) time reversal (f!JlJ)(n) = f( -nl· (29) There are several different ways to link analogue and digital signals and systems, and hence a variety of ways to define a discrete-time version of the Wigner distribution What one would like with such a definition is (1) to obtain a simple concept; (2) to retain as many as possible of the properties of the WD of continuoustime signals; (3) to find a simple relation between the discrete-time and continuous-time WD's for discrete-time signals that are obtained by sampling of analogue signals The definition which, in our opinion, best matches these requirements is the one suggested by eq (1710) 22 Definition of the Wigner distribution The cross-Wigner distribution of two discrete-time signals f(n) and g(n) is defined by 00 u-j,g(n, 0) = 2 L e-i2kDf(n + k)g*(n kl (210) k=-oo The autoWigner distribution of a signal is then given by 00 u-j(n, 0) = Wj,f(n, 0) = 2 L e-i2kDf(n+k)f*(n kl (211) k=-oo Both functions will be called a Wigner distribution (WD) Aiming at obtaining a relation similar to (1213) the WD for the spectra must be defined by 278 Philips Journalor Research Vol35 Nos4/5 1980 The Wigner distribution so that 11 wF,G(e, n)= ~ J et; F(e + C) G*(e C) dc (212)

974 citations


01 Jan 1980
TL;DR: In this second part of the paper the Wigner distribution is adapted to the case of discrete-time signals, and it is shown that most of the properties of this time-frequency signal representation carry over directly to the discrete- time case, but some cause problems.
Abstract: In this second part of the paper the Wigner distribution is adapted to the case of discrete-time signals. It is shown that most of the properties of this time-frequency signal representation carry over directly to the discrete-time case, but some.others cause problems. These problems are associated with the fact that in general the Wigner distribution of a discrete-time signal contains aliasing contributions. It is indicated that these aliasing components will not be present if the signal is either oversampled by a factor of at least two, or is analytic. 1. Introduetion In part I of this paper 1) the Wigner distribution (WD) of continuous-time signals was discussed, and it was shown that this function has some very interesting properties. The determination of this distribution function requires, like the spectrum, an integral of the Fourier type to be evaluated. Ideally this requires the signal to be known for all. time, but in practice windowing techniques can be used to relax this requirement. The effects of windowing on the WD were discussed in part 1. In general two different approaches can be distinguished to compute these Fourier-type integrals. The first is by means of analogue signal processing, and recently optical signal processing methods have been proposed for determining suitable approximations to the WD 2). The second approach is based on digital signal processing. This opens the way to apply computationally efficient methods for evaluating the discrete Fourier transform, but requires the concept of the Wigner distribution to be transferred to the case of discretetime signals. This is the aim of this part of the paper. As can be expected, the WD for discrete-time signals shows much similarity with that for continuous-time signals, but in some respects it has characteristic differences.

686 citations


Journal ArticleDOI
TL;DR: A general class of spectral estimators of the Wigner-Ville spectrum is proposed: this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the generalclass of conjoint time-frequency representations of deterministic signals with finite energy.
Abstract: The Wigner-Ville spectrum has been recently introduced as the unique generalized spectrum for time-varying spectral analysis. Its properties are revised with emphasis on its central role in the analysis of second-order properties of nonstationary random signals. We propose here a general class of spectral estimators of the Wigner-Ville spectrum: this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time-frequency representations of deterministic signals with finite energy. Classical estimators like short-time periodograms and the recently introduced pseudo-Wigner estimators are shown to be special cases of the general class. The generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo-Wigner estimators. The effective numerical implementation, by an N-point FFT, of pseudo-Wigner estimators of 2N points is indicated and various examples are given.

549 citations


Proceedings ArticleDOI
Abstract: Capteur pour la mesure du debut de l'injection sur un moteur diesel (le deplacement de l'aiguille de l'injecteur ouvre ou ferme un circuit electrique)

4 citations


01 Jan 1993
Abstract: Cylinder pressure, injection line pressure and needle lift signals were acquired over a wide range of operating conditions from a Ford York DI diesel engine and a single cylinder Hydra research diesel engine fitted with a pump-pipe-nozzle (PPN) system and a high pressure electronic unit injector (EUI) respectively. The signals were analysed for pressure rise delay (PRD). Ignition delay and PRD data was also obtained from a photographic build of the Hydra via laser illuminated high speed cine photography with a synchronised data acquisition. Illumination delays from visual analysis of the film records are compared with pressure rise delays. Pressure rise delay data is presented for both the injection systems. The influence of high pressure injection on ignition and pressure rise delays is examined. For the covering abstract see IRRD 873243.

2 citations