Analysis of diesel engine combustion using imaging and blind source separation

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, Italy2 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


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 windowSingle cylinder diesel engine

Engine type 4-strokeBore 8.5 cmStroke 9.2 cmSwept volume 522 cm3

CC volume 21 cm3

Compression ratio 17,7:1Common rail injection system

Injector type Solenoid drivenNozzle Microsac, single

guideHoles

number6

Cone angle 148°Hole

diameter

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 gasapproach

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

-40 -30 -20 -10 0 10 20 30 40Crank angle [degrees]

0

10

20

30

40

50

60

Com

bust

ion

pres

sure

[bar

]

0

10

20

30

Driv

e cu

rren

t [A

mpe

re]

0

40

80

120

160

Rat

e O

f Hea

t Rel

ease

[kJ/

kg/°]

OUTLINE


POD VS. ICAProper 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. ICAProper 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

1 , , mt x t x t x

1 , , nt s t s t s

x = As

n m A

s = Wx1W = 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

24 2kurt 3y E y E y

xED

n m

ICA: SEPARATION OF IMAGE MIXTUREsources

independentcomponents

POD modes

mixtures

mixing

separation

OUTLINE


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

combustion 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

y1 y2

ICA: CYCLE 9

y1 y2

ANALYSIS OF ICS AND THEIR COEFFICIENTS

2° CA 9.5° CA5° CA 2° CA 9.5° CA5° CA

y1: combustion along the fuel jets; swirl

motiony2: combustion near the chamber wallsy1 y2 y1 y2

ICS 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


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

a1 peaks where an irregular combustion process takes place (less effective separation) and is low when the burning along the jets dominates

CV of a2 is at least one order of magnitude higher than the CV of a1, 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


ICA VS. POD

Independent

components

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 23

;1 1 kurt12 48

ICA PODJ J y J y J J J

J y E y y

ICA VS. 1ST AND 2ND 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

Independent

components

1st and 2nd moment

Crank angle resolved measurments

Cycyle-to-cycle variations

OUTLINE


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

Benefits of ICA can be much higher than this simple application example shows. Based on the demonstration case, more complex data can be analyzed, and what was presented here is a first and convincing example of how ICA works in an engine context

From the movie L’Atalante by Jean Vigo (1932)Dita Parlo (born as Gerda Olga Justine Kornstädt on 4th Sept 1908 in Szczecin, Poland

Documents

Analysis of diesel engine combustion using imaging and blind source separation