ANALYSIS OF DIESEL ENGINE COMBUSTION USING IMAGING AND BLIND SOURCE
SEPARATION
K. Bizon1, S. Lombardi1, G. Continillo1,2, E. Mancaruso2, B. M. Vaglieco2
1 Università del Sannio, Benevento, Italy
2 Istituto Motori C.N.R, Naples, Italy
OUTLINE
Introduction
Experimental setup & procedure
Independent component analysis
Analysis of crank-angle resolved measurements
Cycle-to-cycle variations analysis
Comparison with other methods
Summary & conclusions
OBJECTIVE OF THE WORK
First attempt of application of independent
component analysis (ICA) to 2D images of combustion- related luminosity acquired from an optically accessible Diesel engine
Identification of the leading independent structures (independent components, ICs) and:
study of the transient behavior of the flame during a single cycle
analysis of the cycle-to-cycle variability
Assessment of the alternative decompositions (e.g.
proper orthogonal decomposition, POD)
INTRODUCTION
The fast development of optical systems has made
available measurements of distributed in-cylinder variables but the measurements interpretation is not always easy due to the huge amount of data, and to the variety of
coupled phenomena taking place in the combustion chamber
This has lead to the increasing interest in the application of sophisticated mathematical tools, e.g. proper orthogonal decomposition (POD) has become a popular reduction and analysis tool. It has contributed to the knowledge of many physical phenomena, but it cannot separate
independent structures, i.e. all POD modes contain some element of all structures found in all of the fields
Alternative decompositions can be considered, e.g.
independent component analysis (ICA) can be expected
to provide a more powerful insight with respect to POD
OUTLINE
Introduction
Experimental setup & procedure
Independent component analysis
Analysis of crank-angle resolved measurements
Cycle-to-cycle variations analysis
Comparison with other methods
Summary & conclusions
EXPERIMENTAL ENGINE
Direct injection four-stroke diesel engine with a single cylinder and a multi-valve production head
The research engine features only two valves and utilizes a classic extended piston with a UV grade crown window
Single cylinder diesel engine
Engine type 4-stroke
Bore 8.5 cm
Stroke 9.2 cm
Swept volume 522 cm3
CC volume 21 cm3
Compression ratio 17,7:1 Common rail injection system Injector type Solenoid driven Nozzle Microsac, single
guide Holes
number 6
Cone angle 148°
Hole
diamete r
0.145 mm
Rated flow 400 cm3/30 s
OPTICAL SETUP
High-speed digital complementary metal oxide semiconductor (CMOS)
camera, controlled by a trigger signal generated by a delay unit linked to
the engine encoder, in combination with a 45° UV/visible mirror located
inside the piston
EXPERIMENTAL PROCEDURE & RESULTS
Engine speed of 1000 rpm, continuous-
mode operation, using commercial Diesel fuel
Injection pressure fixed at 600 bar and no EGR
Typical CR injection strategy of pre, main and post injections (PMP) starting at -9°, -4° and 11° CA with duration of 400, 625 and 340 μs
Cylinder pressure recorded at 0.1 CA°
increments by means of a pressure transducer
ROHR calculated using the first law, perfect gas
approach
CMOS high-speed camera: frame rate of 4 kHz and exposure time of 166 μs
888 images of the in-cylinder luminosity field, collected from -4° to 30.5° CA, with CA increment of 1.5°, over N= 37
consecutive fired cycles
The original spatial mesh of 529×147 is clipped to 120×120 pixels framing the combustion chamber
- 4 0 - 3 0 - 2 0 - 1 0 0 1 0 2 0 3 0 4 0
C r a n k a n g l e [ d e g r e e s ] 0
1 0 2 0 3 0 4 0 5 0 6 0
Combustion pressure [bar]
0 1 0 2 0 3 0
Drive current [Ampere]
0 4 0 8 0 1 2 0 1 6 0
Rate Of Heat Release [kJ/kg/°]
OUTLINE
Introduction
Experimental setup & procedure
Independent component analysis
Analysis of crank-angle resolved measurements
Cycle-to-cycle variations analysis
Comparison with other methods
Summary & conclusions
POD VS. ICA
Proper orthogonal decompositon
Extracts dominant structures -
orthonormal and optimal in the L2 sense
Relatively simple eigenvalue problem to solve
Fields of application: turbulent flows, model reduction, image processing, PIV data & flame luminosity from SI &
Diesel engines
Independent component analysis
Extracts a set of mutually independent signals from the mixture of signals, i.e.
permits to separate the data into underlying
informational components
Optimization problem
maximizing some measure of the independence
Fields of application:
neuroimaging, spectroscopy, combustion engines
(separation of vibration
sources)
POD VS. ICA
Proper orthogonal decompositon
Extracts dominant structures -
orthonormal and optimal in the L2 sense
Relatively simple eigenvalue problem to solve
Fields of application: turbulent flows, model reduction, image processing, PIV data & flame luminosity from SI &
Diesel engines
Independent component analysis
Extracts a set of mutually independent signals from the mixture of signals, i.e.
permits to separate the data into underlying
informational components
Optimization problem
maximizing some measure of the independence
Fields of application:
neuroimaging, spectroscopy, combustion engines
(separation of vibration
sources)
Given:
: random vector of temporal mixtures
: temporal (mutually independent) source signals
The mixing model can be written as:
If then matrix is invertible and the model can be rewritten as:
The ICA problem consist of calculating such that is an optimal estimation of
ICA problem can be solved by maximization of the statistical independence of the estimates
ICA: DEFINITION
t x t
1 , , x t
m
x
t s t
1 , , s t
n
s
x = As
n m A
s = Wx
1
W = A y = Wx
s
y
ICA: APPROACHES
Maximization of nongaussianity (“nongaussian is independent”)
Maximization of kurtosis (e.g. a fast-point algorithm using kurtosis called FastICA)
Maximization of negentropy (normalized version of differential information entropy)
Minimization of mutual information
Maximum likelihood estimation
Tensorial methods
Nonlinear decorrelation and nonlinear PCA
ICA: FASTICA ALGORITHM
FastICA algorithm maximizes non-gaussianity by means of a gradient method. The (non-)gaussianity is estimated by the absolute value of kurtosis defined as:
The algorithm is employed on centered (having zero mean) and whitened data (uncorrelated and have unit variances), i.e.:
- raw data
- POD eigenvectors
- POD eigenvalues (on the diagonal)
If the number of ICs is smaller than the number mixtures, the data can be reduced during the whitening using
leading POD modes
1 2 T
E
x = D E x x
4 2
2
kurt y E y 3 E y
x E D
n m
ICA: SEPARATION OF IMAGE MIXTURE
sources independent
components POD modes
mixtures m
ixi n g
se
p
ar
at
io
n
OUTLINE
Introduction
Experimental setup & procedure
Independent component analysis
Analysis of crank-angle resolved measurements
Cycle-to-cycle variations analysis
Comparison with other methods
Summary & conclusions
CRANK ANGLE RESOLVED MEASUREMENTS
PMP at -9°, -4° and 11° CA
first luminous spots due to ignition of the preinjected fuel
main injection combustion
combustion present on all jets and in the vicinity of the chamber wall
combustio n zone moves towards the bowl
wall
simultaneous ignition of postinjection
jets
maximum of post combustion
luminosity
Images of combustion luminosity for multiple injections in a cycle, at several crank angles
ICA: CYCLE 8
y
1y
2ICA: CYCLE 9
y
1y
2ANALYSIS OF IC S AND THEIR COEFFICIENTS
2° CA 5° CA 9.5° CA 2° CA 5° CA 9.5° CA y
1: combustion along
the fuel jets; swirl motion
y
2: combustion near the chamber walls
y
1y
2y
1y
2ICS VS. ENGINE PARAMETERS
SOC of PMP:
–4°, 1° & 14°
CA main inj.
post inj.
maximum luminosity of the regular combustion process near the fuel jets of the main and post
injection
3.5° CA 17° CA
8° CA
OUTLINE
Introduction
Experimental setup & procedure
Independent component analysis
Analysis of crank-angle resolved measurements
Cycle-to-cycle variations analysis
Comparison with other methods
Summary & conclusions
CYCLE-TO-CYCLE VARIATIONS
Not all jets burn with the same flame behavior; during combustion development flames are unevenly distributed along the jets’ axes
Post injection starts in a partly burning environment, where the irregular peripheral combustion influences post-injection ignition
2° CA
3.5° CA
14° CA
18.5°
CA
main injection combustion
end of main combustion
; post injection
post injection combustion
3.5°CA
ICA separates the mean combustion luminosity at each CA
from the irregular flame structure related to cycle variability
14°CA
Separation is worse when the variability is higher, i.e. at the
end of main combustion when the flames move randomly near
the bowl wall
18.5°CA
Again, the separation is better when the cyclic variability is
lower, i.e. for the CA characterized by regular combustion
typical of jet burning
ICS VS. ENGINE PARAMETERS
a
1peaks where an irregular combustion process takes place (less effective separation) and is low when the burning along the jets dominates
CV of a
2is at least one order of magnitude higher than the CV of a
1, confirming that strong deviations from the ideal combustion process are located near the bowl wall
pilot injection
fuel burning in the centre of the bowl
regular burning of the main &
post injection fuel along the jet directions
random flames near the
bowl
irregular end of combustion
OUTLINE
Introduction
Experimental setup & procedure
Independent component analysis
Analysis of crank-angle resolved measurements
Cycle-to-cycle variations analysis
Comparison with other methods
Summary & conclusions
ICA VS. POD
Independe nt
component s
POD modes
Negentropy, i.e. normalized differential information entropy, measures the
amount of information and is always higher for ICA than for POD; it is estimated as:
1 2 1 2
2 2
3
;
1 1
12 48 kurt
ICA POD
J J y J y J J J
J y E y y
ICA VS. 1 ST AND 2 ND MOMENT
Analysis of cycle variations (but not crank angle resolved
measurements!) similar conclusions for the first two statistical moments (mean & standard deviation)
Here the "signals" were, in most cases, already spatially separated
Independe nt
component s
1
stand 2
ndmoment
Crank angle resolved measurments
Cycyle-to-cycle variations
OUTLINE
Introduction
Experimental setup & procedure
Independent component analysis
Analysis of crank-angle resolved measurements
Cycle-to-cycle variations analysis
Comparison with other methods
Summary & conclusions
SUMMARY & CONCLUSIONS
A first attempt of the application of ICA to luminosity image data collected in an optical engine was done
Two independent components were found related to:
combustion along the fuel jets presenting low variability over the cycles
near the bowl walls – highly variable; this confirms quantitatively that strong deviations from the ideal combustion process are located near the bowl walls
The analysis is fast and reliable - a single computation takes less than 0.1 s on a standard sequential single processor