Feb 2, 1998 - 20 Cross-correlations between selected cylinder pairs as a function of equiv- .... P2. Cylinder pressure prior to combustion. P3. Cylinder pressure at the end .... With the development of gas turbine engines for aircraft, interest shifted from ...... U H. 900. -. U. 700. 600. (a). J. L. 600 700 800 900 ...
APPLICATION OF DETERMINISTIC CHAOS THEORY TO CYCLIC VARIABILITY IN SPARK-IGNITION ENGINES
A Thesis Presented to The Academic Faculty by
Johney Boyd Green, Jr.
In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mechanical Engineering
Georgia Institute of Technology November 2000 Copyright © 2000 by Johney Boyd Green, Jr.
APPLICATION OF D E T E R M I N I S T I C CHAOS T H E O R Y TO CYCLIC VARIABILITY IN SPARK-IGNITION ENGINES
Approved:
C
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Pandeli Durbetaki
G. Stuart Daw \^rx
1/
Prateen V. Desai
cT
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bam VyShelt on W**
"jt
/if
/
ZL
y
illiam/f. Weprer /
. ^
.
William L. Ditto
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Date Approved
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DEDICATION
The author dedicates this work to the memory of his mother (Emma Green) and aunt (Barbara Reed). You are dearly missed. May you both rest in peace.
L Li
ACKNOWLEDGEMENTS
The author would first like to thank God for his grace, mercy, and love. The author expresses sincere gratitude to his mentors and advisors, Dr. Pandeli Durbetaki of the Georgia Institute of Technology and Dr. C. Stuart Daw of the Oak Ridge National Laboratory, for their guidance, support, and encouragement. Further, he expresses his appreciation to his colleagues Dr. Charles E. A. Finney, Dr. Robert M. Wagner, and Jeffery S. Armfield for their assistance and friendship throughout the course of this work. The author gratefully acknowledges Dr. Frank Connolly and Tony Davis of the Ford Motor Company for many interesting discussions and suggestions. In addition, he would like to thank the management and staff of the Oak Ridge National Laboratory for their continued support. The author expresses appreciation to Dr. William J. Wepfer, Cr. Prateen V. Desai, Dr. Sam V. Shelton, and Dr. William L. Ditto for serving as members of the dissertation committee. The author would also like to thank the staff of the graduate office in the Woodruff School of Mechanical Engineering for their patience and guidance. Finally, he thanks his wife (Tonya S. Green), father (Johney Green, Sr.), family, and friends for all of their love and support.
IV
TABLE OF C O N T E N T S
DEDICATION
iii
ACKNOWLEDGEMENTS
iv
LIST OF TABLES
x
LIST OF FIGURES
xi
LIST OF SYMBOLS
xvii
LIST OF ABBREVIATIONS
xxiv
SUMMARY
xxvi
I
INTRODUCTION
1
II
BACKGROUND
4
2.1
Historical Perspective
4
2.2
Indicators of Cyclic Variability
6
2.3
Physical Mechanisms Behind Cyclic Variability
7
2.4
Traditional Statistical Measures of Cyclic Variability
9
2.5
Recent Discoveries
11
2.6
The Daw et al. Model
14 v
III
Intake and Compression Phase
15
2.6.2
Combustion Phase
16
2.6.3
Exhaust Phase
17
EXPERIMENTAL METHODS
20
3.1
Experimental Systems
20
3.1.1
Kohler Engine
20
3.1.2
Quad-4 Engine
23
3.1.3
Crown Victoria Engine
28
3.1.4
Expedition Engine
29
3.2
3.3
IV
2.6.1
Data Acquisition System
32
3.2.1
Kohler Engine
32
3.2.2
Quad-4 Engine
34
3.2.3
Crown Victoria Engine
35
3.2.4
Expedition Engine
36
Experimental Procedures
37
3.3.1
Kohler Eng:ne
37
3.3.2
Quad-4 Engine
38
3.3.3
Crown Victoria Engine
39
3.3.4
Expedition Engine
40
DATA ANALYSIS
41
4.1
Reduction of Experimental Data
41
4.1.1
41
Cylinder Pressure
4.2
4.3
V
4.1.2
Indicated Work
43
4.1.3
Heat Release
45
Traditional Analysis
47
4.2.1
Histograms
48
4.2.2
Coefficient of Variability
49
4.2.3
Lowest Normalized Value
50
4.2.4
Autocorrelation
50
4.2.5
Cross-correlation
51
4.2.6
Stationarity
52
Nonlinear Analysis
53
4.3.1
Poincare Sectioning
55
4.3.2
Bifurcation Diagrams
56
4.3.3
Mutual Information
56
4.3.4
Return Maps
58
4.3.5
Data Symbolization
58
4.3.6
Symbol-Sequence Histograms
61
4.3.7
Modified Shannon Entropy
63
4.3.8
Symbol Synchrograms
64
4.3.9
Time Irreversibility
65
4.3.10 Surrogate Data Sets
66
DISCUSSION OF RESULTS
68
5.1
68
Trends in Cyclic Variability under Lean Fueling
vii
VI
5.2
Multi-Cylinder Synchronization under Lean Fueling
5.3
Cyclic Variability at High Exhaust Gas Recirculation Levels
5.4
Issues of Data Set Length
102
5.5
Comparison of Different Combustion Measurements
108
5.6
Selection of Symbolization Parameters
119
5.7
Model Discrimination
122
...
95
N E W CYCLIC VARIABILITY MODEL
130
6.1
Model Description
130
6.1.1
Intake and Compression Phase
132
6.1.2
Combustior Phase
133
6.1.3
Exhaust Phase
136
6.2 VII
80
Model Validation
,
137
INVESTIGATION OF CONTROL
145
7.1
Control Algorithm
145
7.2
Control Implementation
146
VIII CONCLUSIONS
155
IX
159
RECOMMENDATIONS
A P P E N D I X A - COMBUSTION ANALYSIS SOURCE CODE
162
A P P E N D I X B - DATA SYMBOLIZATION SOURCE CODE
181
viii
REFERENCES
195
VITA
202
LIST OF TABLES
1
Kohler engine specifications
22
2
Quad-4 engine specifications
27
3
Crown Victoria engine specifications
29
4
Ford Expedition engine specifications
30
5
Summary of frequency distribution statistics for heat release time series. 72
6
Mean K-S values for three data sets at an ECR rate of 9%
7
Mean K-S values for three cycle-resolved combustion measurements. . 112
8
Symbol-sequence statistics for the Crown Victoria engine, the Daw et al. model, and the modified Daw et al. model
x
105
140
LIST OF FIGURES
1
Combustion efficiency curve is assumed to be an exponential sigmoidal function of equivalence ratio
2
18
Cross-section schematic of the Kohler Magnum 12 showing the intake manifold and cylinder head
21
3
Schematic of the General Motors Quad~4 engine cylinder head
24
4
Cylinder and intake configuration for the Quad-4 engine.
Cylinder
location is denoted by "C" for physical location and "F ; ' for location in firing order 5
26
Schematic of the Ford Motor Company Crown Victoria engine showing cylinder geometry with air intake, exhaust, and fuel injection.
6
. . . .
28
Ford Expedition engine cylinder and intake manifold configuration. Cylinder location is denoted by "C" for physical location and "F" for location in firing order
7
31
Cumulative probability distribution of the K-S statistic for 200 realizations of the SI engine model at lean and stoichiometric fueling conditions. 54
8
9
Time series values (circles) are discretized into symbols (0 or 1) based on their location relative to the partition (dashed line)
60
Example symbol-sequence histogram
62
XI
sured with the (a) coefficient of variation in 1MEP
(COVIMEP)
and (b)
lowest normalized value (LNV) 11
69
Experimental heat release probability histograms at equivalence ratios of 0.91 (top), 0.59 (middle), and 0.53 (bottom)
12
Autocorrelation functions of experimental Quad-4 heat release data at equivalence ratios of 0.96 (top), 0.76 (middle), and 0.69 (bottom). . .
13
74
Return maps for three engines at three equivalence ratios for approximately 3000 contiguous engine cycles
15
73
Mutual information functions of experimental Quad-4 heat release data at equivalence ratios of 0.96 (top), 0.76 (middle), and 0.69 (bottom).
14
71
76
Symbol-sequence histograms for three engines at three equivalence ratios for approximately 3000 contiguous engine cycles. Forward-time histograms are plotted with solid lines (
), reverse-time histograms
with broken lines (--•--) 16
78
Expedition heat release return maps for all eight cylinders at stoichiometric (0 = 1.00) fueling conditions
17
Expedition heat release return maps for all eight cylinders at very lean ((f) = 0.66) fueling conditions
18
81
82
Quad-4 heat release return maps for all four cylinders at moderately lean ( = 0.68) fueling conditions
XI1
84
19
Quad-4 heat release return maps for all four cylinders at very lean ((f) — 0.59) fueling conditions
20
85
Cross-correlations between selected cylinder pairs as a function of equivalence ratio for the Fcrd Expedition
21
Cross-correlations for all cylinder pairs of the Quad-4 engine with correlation intervals of (a) 0 and (b) 1
22
91
Multi-variate symbol-sequence histograms for selected cylinder pairs of the Quad-4 engine at an equivalence ratio of 0.54
24
88
Multi-variate symbol-sequence histograms for selected cylinder pairs of the Expedition engine at an equivalence ratio of 0.66
23
86
91
Symbol synchrograms of Expedition heat release data for (a) uncorrelated (F-0,F-3) and (b) anti-correlated (F-0.F-1) cylinder pairs at an equivalence ratio of 0.66
25
93
Symbol synchrograms of Quad-4 heat release data for (a) uncorrelated (F-l,F-3) and (b) anti-correlated (F-2,F-3) cylinder pairs at an equivalence ratio of 0.54
26
94
Modified Shannon entropy as a function of (a) EGR rate and (b) equivalence ratio using an 8-level symbolization
27
Return maps of experimental Quad-4 heat release data at E G R rates of 9% (top), 16% (miodle), and 25% (bottom)
28
96
98
Return maps of experimental Quad-4 heat release data at equivalence ratios of 0.84 (top), 0.73 (middle), and 0.65 (bottom)
xin
99
29
Symbol-sequence histograms of experimental Quad-4 heat release data at E G R rates of 9% (top), 16% (middle), and 25% (bottom). Forwardtime histograms are plotted with solid lines (
), reverse-time his-
tograms with broken lines ( - - - - ) 30
100
Symbol-sequence histograms of experimental Quad-4 heat release data at equivalence ratios of 0.84 (top), 0.73 (middle), and 0.65 (bottom). Forward-time histograms are plotted with solid lines ( time histograms with broken lines (
31
), reverse-
)
101
Effect of data set length on the finite sampling error as reflected in the symbol-sequence histograms. Results are show on (a) a linear scale and (b) a logarithmic scale
32
104
Illustration of stationary and non-stationary behavior for (a) 13500 cycles and (b and c) 3000 cycles of heat release data at an EGR rate of 9%
33
107
Return maps of cylinder pressure data from the Quad-4 engine at an equivalence ratio of 0.69 using (a) peak cylinder pressure and (b) cylinder pressure at 10 degrees ATDC
34
109
Symbol-sequence histograms using (a) peak cylinder pressure and (b) cylinder pressure at 10 degrees ATDC for the Quad-4 engine at an equivalence ratio of 0.39. The data were symbolized using a symbolset size of 8 and a sequence length of 2
xiv
110
35
Return maps of heat release (a, b, and c) , IMEP (d, e, and f), and peak cylinder pressure (g, h, and i) at equivalence ratios of 0.98, 0.81, and 0.69
36
114
Symbol-sequence histograms of heat release (a, b, and c), IMEP (d, e, and f), and peak cylinder pressure (g, h, and i) at equivalence ratios of 0.98, 0.81, and 0.69
37
116
Experimental bifurcation sequences of (a) heat release (b) IMEP, and (c) peak cylinder pressure
38
118
Modified Shannon entropy as a function of symbol-sequence length at four equivalence ratios using a symbol-set size of 8
39
121
Return maps for the Crown Victoria engine at an equivalence ratio of 0.59 and four model data sets for approximately 3000 contiguous engine cycles
40
126
Symbol-sequence histograms for the Crown Victoria engine at an equivalence ratio of 0.59 and four model data sets for approximately 3000 contiguous engine cycles
41
127
Confidence intervals for the time irreversibility statistic using surrogate data sets from the Daw et al. LGRP and NND models
129
42
Ideal constant volume combustion engine cycle
131
43
Finite heat release combustion engine cycle
131
xv
44
Return maps for the Crown Victoria engine at an equivalence ratio of 0.59 (top), the Daw et al. model (middle), and the modified Daw et al. model (bottom)
45
139
Symbol-sequence histograms for the Crown Victoria engine at an equivalence ratio of 0.59 (top), the Daw et al. model (middle), and the modified Daw et al. model (bottom)
46
141
Return maps for the Quad-4 engine at an EGR rate of 16% (top) and the modified Daw et al. model (bottom.)
47
142
Symbol-sequence histograms for the Quad-4 engine at an EGR rate of 16% (top) and the modified Daw et al. model (bottom)
144
48
Block diagram of the simple proportional control algorithm
147
49
Block diagram of the predictive symbolic control algorithm
148
50
Control of period-2 dynamics in the Daw et al. model using the predictive symbolic control algorithm is illustrated with a return map.
51
. 150
Return maps and probability histograms for the Daw et al. model at an equivalence ratio of 0.71 using no control (a and d), simple proportional control (b and e), and predictive symbolic control (c and f)
52
151
Symbol-sequence histograms for the Daw et al. model at an equivalence ratio of 0.71 using (a) no control, (b) simple proportional control, and (c) predictive symbolic control. Solid lines ( original symbol series and broken lines (
) represent the 95 percent
confidence limits for 200 shuffled surrogate series
xvi
) represent the
152
Combustion Analysis A
Piston area
C
Constant-pressu ;e specific heat
P
Cv
Constant-volume specific heat
1
Connecting rod ength
m
Mass
P
Pressure
Pint
Mean cylinder pressure during the intake process
Pref
Reference absolute intake manifold pressure
Pfl,abs
Absolute cylinder pressure
P*,rel
Relative cylinder pressure
Qn
Net heat release
R
Ideal gas constant
r
Half of the stroke length
T
Temperature
U
Internal energy
V
Volume
xvii
W
Work
7
Specific heat ratio
9
Crank angle position
0EVO
Crank angle position where the exhaust valve opens
0WC
Crank angle position where the intake valve closes
Combustion Modeling (|r)
Ratio of air to fuel mass at stoichiometric conditions
a
Mass fraction burned parameter
an
Empirical ARMA coefficient
B
Bore of the cylinder
bk
Empirical ARMv\ coefficient
Ci
Empirical residual gas fraction constant
C2
Empirical residual gas fraction constant
et
Noisy parametric perturbations
F
Residual gas fraction
F0
Nominal residual gas fraction
f
Static nonlinear transform
g
Nonlinear function
k
Burning angle constant xviii
m
Mass fraction burned parameter
ma
Mass of air in tt e cylinder
ma;new
Mass of air inducted into the cylinder
m am
M i d p o i n t between cf)n a n d cf)\
0new
Injected equivalence r a t i o
(f)0
Nominal equivalence ratio
0U
Combustion efficiency location parameter
Control Algorithm hr
Heat release value
hr
Symbolic heat release value
xxi
PV
Predicted symbolic value
p
Probability value
e
Equivalence ratio error parameter
0 act
Injected equivalence ratio
(j)nom
Nominal equivalence ratio
0Pert
Equivalence ratio perturbation
Nonlinear Analysis F
Forward-time symbol-sequence histogram frequencies
Hs
Modified Shannon entropy
i
Vector index
j
Vector index
L
Sequence length
MI
Mutual information
m
Embedding dimension
Ncyc
Data set length
Nseq
Number of possible sequences Number of sequences with a non-zero frequency
n
Symbol-set size
p
Probability value
R
Backward-time symbol-sequence histogram frequencies xxii
Tf
Symbol-sequence histogram Euclidean norm statistic
T,
Time irreversibility Euclidean norm statistic Vector Vector Embedding time lag
Traditional Analysis ACF
Autocorrelation function
CCF
Cross-correlation function
IMEP
Average indicated mean effective pressure
IMEPmin
Minimum indicated mean effective pressure
Kurt
Kurtosis of a time series
N
Number of elements in a time series
Skew
Skewness of a time series
x
Mean of a time series
y
Mean of a time series
a
Standard deviation of a time series
a2
Variance of a tine series
T
Embedding time lag
xxm
ABDC
After bottom dead center
APTC
Advanced Propulsion Technology Center
ARMA
Autoregressive moving-average
ATDC
After top dead center
BBDC
Before bottom dead center
BTDC
Before top dead center
cov
Coefficient of variation
EGO
Exhaust gas oxygen
EGR
Exhaust gas recirculation
EOC
End of combustion
EVC
Exhaust valve closing
EVO
Exhaust valve opening
EWMA
Exponentially weighted moving average
GE
General Electric
GTL
Gas Turbine Laboratory
IMEP
Indicated mean effective pressure
IVC
Intake valve closing
IVO
Intake valve, opening
K-S
Kolmogorov-Smi::nov xxiv
LNV
Lowest normalized value
LPP
Location of peak cylinder pressure
MBT
Maximum brake torque
MSE
Modified Shannon entropy
NND
Noisy nonlinear dynamics
ORNL
Oak Ridge National Laboratory
PC
Personal computer
RTCAM
Real-Time Combustion Analysis Module
SOC
Start of combustion
SRL
Scientific Research Laboratory
TDC
Top dead center
UEGO
Universal exhaust gas oxygen
XXV
SUMMARY
The purpose of this research is to use concepts from deterministic chaos theory to develop an improved understanding of cycle-to-cycle variations in spark-ignited (SI) internal combustion engines. It is conjectured that prior-cycle effects such as residual unburned fuel are important deterministic causes of cyclic variability in engines. These prior-cycle effects are expected to be more evident during lean fueling and when high levels of exhaust gas residual (EGR) are present. Chaotic time-series analysis methods such as Poincare sectioning, mutual information, data symbolization, symbol sequence histograms, time irreversibility, modified Shannon entropy, and return maps are used to analyze cycle-resolved combustion data from multi- and single-cylinder research engines at idle conditicns. Traditional statistical measures are also compared with the results yielded by nonlinear time-series analysis. The overall results suggest that cyclic variability has at least some nonlinear deterministic structure. Based upon the experimental results and consideration of the physical mechanisms involved, an improved nonlinear model is proposed for cyclic variability. Confirmation of deterministic structure also implies that it may be possible to diagnose and predict future undesirable combustion events I such as misfire). Approaches are suggested to extend the EGR tolerance and/or lean operating limit of SI engines utilizing closed-loop control to reduce cyclic variability.
xx vi
INTRODUCTION
Many researchers have explored the phenomenon of cyclic dispersion in internal combustion engines (e.g., Young (1981) and Ozdor et al. (1994)). Cycle-to-cycle variations are a concern because of their adverse effects on emissions, fuel economy, peak power, and overall engine efficiency. The effects of cyclic variability are even more pronounced at idle and fuel-lean or high exhaust gas recirculation (EGR) conditions. A reduction in oxides of nitrogen (NOx) and unburned or partially burned hydrocarbons (HC) is expected if the region of stable, lean combustion can be extended. As it stands now, operation near the fuel-lean limit results in oscillations between misfire or slow burning combustion events and fast burning combustion events. These oscillations produce higher HC emissions when a misfire occurs and increased NOx emissions when the fast burning, high temperature and pressure combustion is generated (Atkinson et al. 1995). Hence, a reduction in the cyclic variation in internal combustion engines near the lean limit would be very significant and beneficial to the automotive industry. Many researchers have suggested that cyclic variability is caused by factors such as turbulent fluid flow, temperature gradients, fuel and air mixing, spark timing, and nonuniform spark discharge. While many of these factors appear to be largely 1
"random" in nature (e.g., Barton et al. (1970), Young (1981), Heywood (1988), O/dor et al. (1994), Jones et al. (1997), and Roberts et al. (1997)), some researchers believe that cyclic variation may exhibit temporal patterns that are inherently complex and nonlinear, but nevertheless deterministic (e.g., Kantor (1984), Daily (1987), Martin et al. (1988), Daw et al. (1996), Finney ct al. (1998), Green et al. (1998), and Green et al. (1999)). Here and in the subsequent discussion the term "random" is used to refer to physical processes that are so high in dimensionality that they approach the classical statistical notion of independent identically distributed events. It is the premise of the proposed research that engine cyclic variability is due to the interaction of a multitude of stochastic and nonlinear deterministic components. It is further conjectured that, in some cases, a few components dominate over the rest so that low-dimensional structure (dimension of five or less) can be observed in the global combustion dynamics (i.e., averaged over the cylinder volume) (Finney 1995). At small scales (i.e., over spatial distances much smaller than the cylinder) the combustion dynamics are still expected to be high-dimensional.
Residual gas
exchange between succeeding cycles is conjectured to be one of the most important deterministic components. In this investigation, nonlinear time series analysis methods were used to investigate dynamic engine measurements.
Conventional analyses were also directly
compared with the nonlinear time series results to demonstrate the improved discrimination produced by the more sophisticated tools. Based upon the experimental
2
ear model is proposed for cyclic variability. The diagnostic information obtained from the model was used to develop a closed-loop control strategy that exploits the deterministic structure present in the engine data.
3
BACKGROUND
2.1
Historical Perspective
Cyclic variability in combustion (also known as cyclic dispersion) has been observed since the early evolution of spark-ignition engines. Cyclic dispersion was observed in 1893 by Clerk in indicator diagrams; he attributed the cyclic variability to exhaust residuals or partially atomized fuel (Clerk 1893). This explanation for cyclic variability was also given by Jones (1909) and Homans (1911). More systematic investigations of this phenomenon began around 1956 (Young 1981). With the development of gas turbine engines for aircraft, interest shifted from abnormal combustion (e.g., knock) to systematic investigations of cyclic variation in normal combustion (Vichnievsky 1955). Prior to 1956, studies of cycle-to-cycle variations were "survey-type" aimed at discerning the effects of engine and operating variables on cyclic dispersion in combustion and pressure formation (Young 1981). Advances in data acquisition made more sophisticated investigations of cyclic dispersion possible. One particularly important development was the oscilloscope. This device allowed researchers to examine numerous cycles of pressure data in real time or from magnetic tape recordings (Finney 1995). Curry (1963) made one of the first 4
studies that coupled instrumentation with a computer, allowing him to acquire measurements from more than two thousand cycles at a time, as opposed to an oscilloscope that captured measurements twenty cycles at a time. With the recent advances in computing power and in sophisticated data acquisition systems, researchers are now able to use more advanced data analysis techniques. Examples of more recent investigations are Martin et al. (1988), Griinefeld et al. (1994), and Atkinson et al. (1994, 1995). Martin et al. (1988) examined cyclic variation using conditional grouping, heat release data, and indicated mean effective pressure (IMEP). They proposed that several burn modes may exist under fuel-lean conditions and that prior cycle effects become more obvious as the air-fuel ratio is increased. Griinefeld et al. used the Raman scattering method to show that cycle-bycycle variations in the IMEP are dominated by the cyclic fluctuations of the equivalence ratio and the residual gas content under lean-burn conditions. The research of Atkinson et al. (1994, 1995] produced an ignition control strategy that reduced cyclic dispersion. They used the location of peak cylinder pressure (LPP) at maximum brake torque (MBT) as the desired operating condition for the control technique. The approach takes the average of twenty previous LPP values and compares the difference between that value and the desired LPP to determine the suitable direction of spark timing adjustment. Application of this strategy resulted in lower values of the coefficient of variation in indicated mean effective pressure, demonstrating reduced cyclic variability.
5
2.2
Indicators of Cyclic Variability
Over the years, several indicators of cyclic variability have been developed. Matekunas (1983) and Heywood (1988) noted that the cycle-to-cycle variations can be described by the changes in two different categories of indicators: those derived from in-cylinder pressure measurements and those related to microscale combustion features. Indicators derived from pressure measurements include: peak pressure, crank angle at which peak pressure occurs, maximum rate of pressure rise, crank angle at which the maximum rate of pressure rise occurs, and indicated mean effective pressure (IMEP) of the individual cycles. Pressure measurements can also be used to determine global combustion features such as: maximum rate of heat release, maximum rate of mass burning, flame development angle, and combustion duration.
More detailed flame
descriptors, such as flame radius, flame front area, flame volume, and flame speed, are typically based on optical measurements. The above indicators of cyclic dispersion have been examined by several researchers (Soltau 1960; Pundir et al. 198:.; Matekunas 1983; Belmont et al. 1986; Hamai et al. 1986; Heywood 1988; Stone et al. 1992; Weaver and Santavicca 1992). The results of these studies have shown that the in-cylinder peak pressure, the crank angle at which the in-cylinder peak pressure occurs, the IMEP, the flame radius, and the displacement of the flame kernel center from the spark gap center are reliable indicators of cyclic combustion variability. The first three are the simplest to acquire and most commonly employed. In-cylinder peak pressure displays the most cyclic dispersion at MBT, which is a practical operating point of engines (Ozdor et al. 1994). Ozdor et al.
6
lates well with the initial flame kernel development and that IMEP is an excellent indicator of combustion instabilities.
2.3
Physical Mechanisms Behind Cyclic Variability
Factors that influence cyclic combustion variation can be placed in four basic groups: chemical, mixing, turbulence, a:id spark-related. Chemical factors are associated with variables that govern the global composition of the pre-ignition mixture (Young 1981). Variables that fall under this category are fuel type, mixture equivalence ratio, and fraction of dilutents. The influence of the fuel type has been studied by such authors as Young (1981), Hey wood and Vilchis (1984), and Stone et al. (1992). Fuel type affects the initial flame kernel development and turbulent flame propagation through its impact on laminar flame speed (Ozdor et al. 1994). Studies on the effect of overall equivalence ratio have been carr: ed out by several researchers (Pundir et al. 1981; Sher and Keck 1986; Ho and Santavicca 1987; Hill 1988; Hill and Kapil 1989). Young, in his literature review, stated that minimum variation in combustion variability occurs at stoichiometric or slightly rich fuel mixtures. Young (1981), Matsui et al. (1979), Sher and Keck (1986), and Kalghatgi (1985) have found that a high fraction of dilutents increases cyclic dispersion. Research on the dependence of cyclic variability on mixture equivalence ratio and spatial inhomogeneity has been carried out by several authors (Soltau 1960; Patterson 1966; Matthes and McGill 1976; Matsui et al. 1979; Pundir et al. 1981; Hamai
7
et al. 1986; Sztenderowitz and Heywood 1990b). Ozdor et al. summarized the results of these investigations by stating that the influence of mixture equivalence ratio and spatial inhomogeneity was unresolved and hypothesized that the non-uniformity in residual gas should "manifest itself in the same manner as the A/F ratio inhomogeneity.
. . ".
Cyclic cylinder charging refers to variations in the mass of the mixture contained within the cylinder and primarily influences pressure-related parameters such as peak in-cylinder pressure and IMEP (Ozdor et al. 1994). Matekunas (1983) and Sztenderowitz and Heywood (1990a) have made attempts to explain the reasons for cyclic dispersion in IMEP, maximum in-cylinder pressure, and angle of maximum in-cylinder pressure. For example, they felt thai, IMEP fluctuations were primarily due to variations in the amount of fuel burned per cycle. Ozdor et ah suggested that further studies in this area were needed due to the lack of experimental data on the cyclic dispersion in the in-cylinder trapped fuel mass and the factors governing it. This shortage of experimental data "hampers any qualitative, not to mention quantitative, conclusion" (Ozdor et al. 1994). In-cylinder turbulence has been regarded as one of the most significant factors influencing cyclic dispersion by many who have studied the phenomena (Namazian et al. 1980; Young 1981; Johansson 1993). In-cylinder turbulence has two important features: turbulence intensity and overall flow pattern. These two elements influence combustion speed and completion by affecting quenching, flame stretching, flame kernel convection, flame kernel development, and flame propagation.
8
Ozdor et al. summarized the findings of several investigators regarding turbulence. As for turbulence intensity, Ozdor et al. noted that it caused variations in flame stretching, local quenching, and flame kernel convection. Overall in-cylinder flow pattern influences initial flame kernel development and turbulent flame propagation with flame kernel convection aid convection of the fully developed flame. It has been reported that minimum engine cyclic variations occur in the presence of intensive swirl coupled with tumble or squish (Ozdor et ai. 1994). Spark and spark plug-related factors can ha.ve a significant effect on the initial flame kernel development stage. These factors induce cyclic dispersion by perturbing the ignition process. Spark variability is influenced by a number of parameters including ignition timing, gas discharge characteristics, gap design, and gas flow in the vicinity of the spark plug. Recent studies are summarized by (Ozdor et al. 1994).
2.4
Traditional Statistical Measures of Cyclic Variability
As previously mentioned, experimental indicators such as peak pressure, IMEP, crank angle of peak pressure, and maximum rate of heat release are used to characterize cyclic variability. Traditional measures of cyclic variability are based on the statistical distributions of these indicators. Heywood (1988) presented a measure of cyclic variability defined as the coefficient of variation in IMEP
(COVJMEP);
it is the standard
deviation in IMEP divided by the mean IMEP converted to a percentage. Soltau (1960) defined variability as the average difference in peak pressure between each cycle and the mean cycle. Patterson (1966) used frequency histograms to estimate the
9
rate of pressure rise. Barton et al. (1970) used skewness and kurtosis to determine the distribution of the magnitude and timing of peak pressure and the magnitude and timing of the maximum pressure rise rate. Recently another statistic has been developed to measure cyclic variability (Hoard and Rehagen 1997). They suggested the lowest normalized value (LNV) as a measure of the tendency toward misfire. The LNV statistic is defined as the minimum IMEP value in a set of data divided by the mean IMEP value of the cata converted to a percentage. Hoard and Rehagen (1997) suggest that another statistical measure of cyclic variability is needed since the COVIMEP
measures the roughness of combustion whereas the LNV measures misfire
tendency. The previously mentioned methods assume that changes in cyclic variability can be measured in terms of univariate statistics and that the cyclic descriptors can be treated as independent random variables. Because of the latter assumption, such methods ignore temporal correlations that may exist in the data. Other investigators such as Barton et al. (1970), Belmont et al. (198G), and Johansson (1994) have attempted to measure correlations between successive measurements using autocorrelation or Fourier analysis. In their autocorrelation analysis, Barton et al. stated that peak in-cylinder pressure was a random parameter and had no cycle-to-cycle determinism. In the study carried out by Belmont et al.. they concluded that there was
a strong "memory" effect between cycles revealed by autocorrelation techniques. Johansson discovered a correlation between the duration of the early flame development and turbulence using Fourier analysis.
2.5
Recent Discoveries
Recent investigations of cyclic dispersion have demonstrated the importance of the so-called prior-cycle effect. Martin et al. (1988), in their study, examined difFerent burn modes in a lean-burn single-cylinder engine. Their results suggested that priorcycle effects exist and that, the nature of cyclic variability may range from completely stochastic to a combination of deterministic and stochastic processes. Stevens el al. (1992) developed a control strategy that uses information from previous cycles to predict future cycles. The results indicate that some prior-cycle effects are present in peak cylinder pressure and IMEP data that make it possible to accurately predict some of their future values. Recently, Griinefeld et al. (1994) reported strong evidence that deterministic prior-cycle effects in IMEP exist and attributed the variability to oscillations in the equivalence ratio and effects of residual gases on the fresh charge. Some investigators have proposed that prior-cycle effects may be a manifestation of nonlinear interactions between cycles. Chew et al. (1994) asserted that observations of in-cylinder pressure measurements "conclusively" demonstrated deterministic chaos. They surmised that the intake runner influenced the charge conditions and developed a model to account for this effect. In another study, Finney et al. (1994) presented experimental observations of deterministic prior-cycle effects in a SI engine
11
using a chaotic time series analysis technique. They used a predictability factor based on a maximum-likelihood estimator of the Kolmogorov entropy to show that shortterm deterministic effects exist in cylinder pressure traces. In 1995, Finney performed a study that echoed these results. He applied various nonlinear time series analysis techniques to pressure data and found discernible levels of deterministic prior-cycle effects in a variety of engine configurations and measurement variables. More systematic parametric studies carried out by other researchers have also demonstrated that cyclic variability in SI engines exhibit patterns that can be explained as the result of noisy nonlinear combustion instabilities (Daw et al. 1996; Letellier et al. 1997; Daw et al. 1997; Wagner et al. 1998b; Daw et al. 1998). These studies indicate that combustion instabilities are dominated by the effects of residual cylinder gas (prior-cycle effects) and noisy perturbations of engine parameters. Evidence of the coupling between deterministic and stochastic effects in combustion instabilities has been observed in bifurcation diagrams of experimental heat release data (Wagner et al. 1998a; Wagner 1999; Wagner et al. 1999). Researchers have also utilized other advanced nonlinear analysis techniques such as return maps, modified Shannon entropy, and symbolic time-series analysis to analyze temporal patterns in dynamic measurements of engine combustion variables (Daw et al. 1996; Daw et al. 1998; Finney et al. 1998; Green et al. 1998; Green et al. 1999). These techniques focus primarily on characterizing the predictability and the occurrence of repeating temporal patterns. Typically, temporal behavior is quantified using standard, cycleresolved engine combustion measurements, such as IMEP and heat release.
12
tor (1984) introduced a simple engine model focusing on dynamical instability in the combustion process in SI engines. The Kantor model featured combustion oscillations stimulated by the temperature of the intercyclic residual gas. Slight changes in residual gas temperature strongly affected succeeding cycles through the Arrhenius combustion rate term. Daily (1987, 1988) further studied Kantor's model and suggested that activation energy was an important parameter involved in chaotic behavior. Wagner et al. (1993) suggested an improved version of the Kantor model and demonstrated control of cyclic variability using a simplified feedback strategy to perturb ignition timing in each cycle. Daw et al. (1996) made further improvements to the Kantor model, proposing a physically oriented model that explains important characteristics of cyclic combustion variations in spark-ignited engines. A key feature of the Daw et al. model is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Data generated by the Daw et al. model had good agreement with experimental heat release data. An important motivation for using concepts from nonlinear dynamics to characterize and possibly control cyclic variability is the dramatic success these methods have produced in other applications. Examples of such applications are given by Daw etal. (1995), Schiff etal. (1994), Roy et al. (1992), Garfinkel et al. (1992), and Ditto et al. (1990). The pulsed combustor application described by Daw et al. (1995) is particularly similar to cyclic engine combustion.
13
As mentioned previously, researchers at the Oak Ridge National Laboratory developed the physically oriented Daw et al. (1996) spark-ignited engine model that captures important characteristics of cyclic combustion variations.
The main feature
of the model is the interaction between stochastic fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Prior-cycle or "memory" effects are accounted for by residual fuel and air trapped in the cylinder after combustion and passed on from one cycle to the next. The simplicy of the model allows rapid simulation of thousands of engine cycles, permitting detailed analysis of cyclic variability for diagnostics and control. The model was utilized in this investigation to gain a better understanding of the dynamics observed experimentally in cycle-resolved combustion data. The Daw et al. model can also be described as a noisy nonlinear dynamics model since it couples stochastic fluctuations in engine parameters with nonlinear deterministic interactions between successive engine cycles. Stochastic effects are modeled as noisy perturbations to engine parameters such as injected equivalence ratio or the residual gas fraction. The random fluctuations in engine parameters represent high dimensional elements of the combustion process (e.g., fuel and air mixing, fuel vaporization, and wall wetting). Nonlinear behavior in the model is captured witli a sigmoidal combustion efficiency function. The shape of this curve captures the effect that small changes in equivalence ratio have on heat release rate near the lean limit (Glassman 1987). The model is discrete in time, with each cycle represented as a
14
single combustion event. The details of the model are described in Sections 2.6.1 through 2.6.3.
2.6.1
Intake and Compression Phase
After the intake phase and during the compression process, the total mass of fuel and air in the cylinder prior to ignition is equivalent to the residual mass from the previous cycle plus the new fuel and air inducted during the intake phase: mf[i] =
mf)res[i] + mf)new[i]
(1)
ma[i] =
ma)res[i] + majnew[i]
(2)
where rrif[i] and ma[i] are the mass of fuel and air in the cylinder immediately preceding spark, mf)res[i] and majresri] are the masses of unreacted air and fuel remaining from the previous cycle, and mf)new[i] and ma)new[i] are the masses of fuel and air inducted into the cylinder. The masses of fuel and air inducted into the cylinder are subject to two constraints. The first constraint is based on the assumption that the injected equivalence ratio 0 new has a mean value 4>0 and a Gaussian distribution with standard deviation o^. Physically, the fluctuations in the injected equivalence ratio arise from vaporization or turbulence effects, and the model simulates the fluctuations by generating a new random number for each cycle: 0new[i]~N(0o,crJ)
15
(3)
as: =
m f , new [i]
x
VF
m a ; new[i]
where (^)
/A
is the ratio of air 1,0 fuel mass at stoichiometric conditions, which cor-
responds to complete combustion with no excess combustion products. The second constraint on the masses of fuel and air inducted into the cylinder is: ^
=
mffi]
+
Wf
mji] Wa
where Wf and wa are the average molecular weights of fuel and air, and nt is the total number of moles in the cylinder prior to ignition. Equation 5 is based upon the assumption that the total number of gas moles in the cylinder is constant. This restricts the amounts of new fuel and air that can be inducted into the cylinder and ensures that they are reduced m proportion to the amount of residual gas retained from the previous cycle. This constraint is justified by assuming that the contents of the cylinder behave as an ideal gas with constant input pressure and temperature.
2.6.2
Combustion Phase
The net efficiency of the combustion process r]c is modeled as a function of the incylinder equivalence ratio which is given by:
*-SB-(F). 16
^>
where r] c m a x is the maximum fraction of fuel burned during the combustion process, (f>\ is the equivalence ratio corresponding to a combustion efficiency of 0.1?7C)max, (f)u is the equivalence ratio corresponding to a combustion efficiency of 0.9r/crnax, and (f)m is equal to ^'+^u. The function defined by Equation 7 generates a smooth curve with values from 0 to ?7C)rnax with a knee centered at m and provides the essential nonlinearity for the model dynamics. An example combustion efficiency curve is illustrated in Figure 1. The heat released during each combustion event is a function of combustion efficiency and is proportional to the fraction of fuel burned during the combustion process and can be expressed as: Q[i] oc 77c[i]mf[i]
2.6.3
(8)
Exhaust Phase
The primary physical mechanism for cycle-to-cycle coupling (i.e., determinism) is the residual fraction F of unburned fuel and air that remains in the cylinder after combustion. The residual fraction has an effect on the initial conditions of the following cycle, thus altering the following cycle's charge. The remaining air and fuel in the
L7
Equivalence ratio
Figure 1: Combustion efficiency curve is assumed to be an exponential sigmoidal function of equivalence ratio.
18
mf,res[i + l] =
F[i]m f [i]{l-77 c [i]}
ma>res[i + l] -
F [ i ] j m a [ i ] - (^\
(9) r/ c [i]m f [i]|
(10)
Fluctuations in F associated with variations in rhe exhaust process are modeled by letting it vary stochastically each cycle: F[i]~jV(F 0 ,
W-Sw}
(18)
where 0X is the initial crank angle position, Of is the hnal crank angle position, and A0 is the crank angle sampling interval in radians. This expression yields gross or net IMEP based upon the limits of the summation.
4.1.3
Heat Release
In this investigation, net heat release as a function of crank angle position was calculated using a technique based upon the first law of thermodynamics (Stone 1992). The heat release analysis presented by Stone is a simplified version of the heat release analysis presented by Heywood (1988). This approach is equivalent to the combustion pressure method developed by Rassweiler and Withrow (Rassweiler and Withrow 1980; Grimm and Johnson 1990). The Rassweiler and Withrow approach compares the total pressure rise due to combustion to the pressure rise due to piston motion. The first law applied to a control volume within the combustion chamber with no mass transfer across the system boundary is given by: 5Qa = dU + SW
(19)
where 5Qn is the differential of the net heat released by combustion, dU is the differential change in internal energy, and 8W is the differential of the work due to piston 45
and products of combustion and that there is a uniform temperature, the differential change in internal energy can be expressed as: dU = mc v dT
(20)
where m is the mass within the control volume, cv is the constant-volume specific heat, and dT is the differential change in temperature. The ideal gas equation of state in differential form is: m d T = ^ (PdV-f VdP) R
(21)
where R is the ideal gas constant which is equal to the difference between the constantpressure (cp) and constant-volume (cv) specilic heats for an ideal gas. Substituting Equation 21 into Equation 20 and substituting the relationship between cp and cv for R yields: dU = —^— Cp
(PdV + VdP)
(22)
Cv
Noting that SW = PdV and that the specific heat ratio is defined as 7 = ^-p-, Equation 19 can now be expressed as: SQn = -^— (PdV + VdP) + PdV 7~f
(23)
Expressing Equation 23 on an incremental angle basis results in the net heat release rate:
^sJLpdV d9
7 - 1
d0 4(5
+
_ L 7 - 1
V
^
(24)
d X j) l0 g2P( x i, x j) - Y
Xj = l Xj = l
x;=L
N
P(Xi)l0£2P(Xi) ~ Y x
j
P( X j) l0 ^P( X j) =:
l
(35) where x; is the time series value at time t, xj is the time series value at time t + r, p(xi) is the individual probability density for x;, p(xj) is the individual probability density for Xj, and p(x;,Xj) is the joint probability density for x, and Xj. The probability functions p are calculated by binning the data and constructing histograms. If the time series value at Xj is statistically independent of the time series value at Xj then p(xj,Xj) = p(x,)p(xj) and the mutual information is zero (Weigend and Gershenfeld 1993; Abarbanel 1996). The time lag where the first minimum of the mutual information function occurs corresponds to the embedding dimension for phase space reconstruction (Fraser and Swinney 1986). Mutual information was used in this investigation to verify and characterize the occurrence of temporal coupling in cycle-resolved combustion data. 57
4.3.4
Return Maps
Return maps provide a simplified projection of the phase space trajectory into a two-dimensional space. This approach can be very effective for observing lean fueling combustion variations because the global dimensionality appears to be consistent with a low-dimensional map. The construction process involves plotting some characteristic combustion measure (e.g., IMEP, heat release, or peak cylinder pressure) at cycle (i) versus some succeeding cycle (e.g., i + 1) as points in a plane. With each new cycle, the current point "maps" into the next, building up a composite statistical picture of how cycles are interrelated. Martin et al. (1988) used return maps to show that discernible cycle-to-cycle patterns exist in IMEP data under fuel-lean conditions. Information extracted from return maps is used in this investigation to gain a better understanding of the underlying deterministic structure of integrated combustion parameters.
4.3.5
Data Symbolizcition
This investigation utilizes the symbol-statistics approach to time series analysis suggested by Tang et al.
(1995) which is analogous to the technique employed by
Lehrman and Rechester (1997). Although this method is motivated by symbolicdynamics theory, it is not completely rigorous, mainly because generating partitions are undefined in the presence of noise (a generating partition is a division of the data space which yields a perfect symbolic description of the time-series structure). For a more detailed information on the theoretical basis and development of symbolization
58
and Daw et al. (1998). Data symbolization involves the conversion of a data series of many possible values into a symbol series of only a few distinct values. This "coarse-graining" has the practical effect of producing low-resolution data from high-resolution data.
Only
large-scale features are captured, and the effects of dynamic and measurement noise on statistical algorithms are reduced. In the practical sense; for studying engine dynamics, only a qualitative description, such as "stronger" combustion or "weaker" combustion, might be desired, with many of the intermediate levels neglected. The key step in symbolizing time series measurements involves transforming the original time series values into a stream of discretized symbols. This discretization is accomplished by partitioning the range of data values into a finite number of regions (usually ranging from two to ten) and then assigning a symbol to each measurement based upon which region it falls into. For example, the simplest scheme is to assign symbolic values of 0 or 1 to each observation depending on whether it is above or below some critical value. For the results presented here, partitions are defined such that the individual occurrence of each symbol is equiprobable (i.e., the likelihood of observing a single measurement in any given region is the same). A simple illustration of data symbolization is shown in Figure 8 for an artificial time series of 20 records. Time series values (circles) below the partition (dashed line) are assigned a symbolic value of 0, and time series values above the partition are symbolized as 1. The partition is defined such that the resulting symbol series has
59
1 11J.IU O^JulVO
O X)
6 c/3
0 1 1 0 1 1 0 0 0 1 1 1 0 0
1 1 0 1 0 0
Symbol series Figure 8: Time series values (circles) are discretized into symbols (0 or 1) based on their location relative to the partition (dashed line).
60
is included in Appendix B.
4.3.6
Symbol-Sequence Histograms
Once a time series is symbolized, the relative frequencies of all possible sequences of consecutive symbols over a finite interval provide an efficient measure of temporal patterns in the data. A simple way to summarize the relative frequencies of each possible symbol sequence is to assign a unique number that identifies each sequence, thus making it possible to plot frequency versus sequence number in a plot called a symbol-sequence histogram. The number of possible sequences can be expressed as: N seq = n L
(36)
where n is the number of symbols or symbol-set size (e.g., 0 or 1 for n = 2) and L is the sequence length. A convenient numerical representation of each symbol sequence is achieved by converting the base-n sequence into a base-10 equivalent number, which is called the sequence code. For example, a symbol sequence of 1 0 1 (depicted as bold circles in Figure 8), with n = 2 and L = 3 (which yields a total of 8 possible sequences for n L = 2 3 ), has a sequence code of 5 (from 1 x 2 2 + 0 x 2 1 + 1 x 2°). Because of the equiprobable partitioning convention, the relative frequency of each sequence for random data will be equal (i.e., 1/8 in this example) Thus any significant deviation from equiprobable sequences is indicative of time correlation and determinism. A simple illustration of a symbol-sequence histogram is depicted in Figure 9, created from the example time series of Figure 8. Sequence 1 0 1 with a sequence id
O
4/18 o
3/18
o
,
g °- 08 ' f 0.06 >
0
0.1 -
0.1 -
Tirr = 0.0210
Oi
(K3)Kohierat = 0.73
-0.99 0.1 i
u
A.*
.
H
0.02 -
0 -
0 -0
(Ql)Quad-4at = 0
10
20 30 40 50 Sequence code
60
1
V
0.02 -
;'.
/1' H% iAAv A rv l':\ •/ 1\J V ¥/ U! W »
0
p*10
0
10
K. , , ' L I
V\\
1 T... i,:>) 40 50 60
20 30 Sequence code
(Q2)Quad-4al = 0.84
T,„ = 0.0295
kvH/V*VK
03
X
X
Heat release [i]
Heat release [i]
Heat release [i]
C-5 (F-5)
C-4(F-1)
C-6 (F-4)
^-. +
+
i>
r.iV.Ai • • • • • .
SB-1*
*'-V. .*•"
S&PZ*S*W?^&#&V>100 50 p
TV:;.: ' •
y,
i^^SSS^^i
0 -50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05
^w^^s^Qii:.
Equivalence ratio 2100 (c) 1900 1700 1500 3 ITi
£
D.
1300
. . . . _ • • •.rftj.'ii.vA
M
fc-
u c
•a
'.'.Vj*. :V »Vv>
~>,
„'m:vv. .-:•.
U
*«££ *?} V - v • '• 500 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Equivalence ratio
Figure 37: Experimental bifurcation sequences of (a) heat release (b) IMEP, and (c) peak cylinder pressure. 118
many misfires which are usually followed by a high-energy combustion event. There is a strong presence of detcrmiristic structure and the dynamics depicted in the final stage are the same as those observed in Figure 35c. All of the combustion measurements previously mentioned are able to identify patterns in combustion dynamics with high levels of noise.
However, the results
of the qualitative and quantitative analyses indicate that heat release measurements provide more details about the underlying deterministic structure of cyclic combustion variations than IMEP and peak cylinder pressure measurements. As a result, heat release measurements were emphasized in this investigation.
5.6
Selection of Symbolization Parameters
It should be recognized that the choice of symbolization parameters can effect the dynamical features that are revealed. Binary partitions are useful for detecting the onset of period-2 oscillations (or bifurcations), but a higher level of symbolization is required to distinguish period-2 dynamics from period-4 or period-8 dynamics. A higher level of symbolization is also useful for model discrimination. Daw et al. (1998) and Finney et al. (1998) demonstrated
this principle using data from heat release
experiments and data generated by a noisy period-2 logistic map. The logistic map is a form of a quadratic map and is related as x 1+1 = Axj(l — xj) where A is an adjustable feedback parameter. The noisy period-2 logistic map and the experimental heat release data have underlying dynamics that are very different. But with Gaussian noise added to its feedback parameter, the logistic map produced data that appeared to
119
exhibit dynamics nearly identical to those observed in symbol-sequence histograms of experimental heat release data created using a binary partition. Using a higher partition to generate the symbol-sequence histograms, it was much easier to distinguish between the two data sets. For these reasons, a symbol-set size of 8 was used to symbolize data in this investigation. In addition to symbol-set size, a suitable sequence length must also be identified for data symbol]zation. One approach useful for selecting a suitable sequence length involves using the minimum value of the modified Shannon entropy, Hs (see Equation 37) (Daw el al. 1998; Finney et al. 1998). For random data H^ should equal 1, whereas for nonrandom data it should be between 0 and 1 with lower values of Hs suggesting increased deterministic structure. The value of Hs is a function of sequence length and usually reaches a minimum value as sequence length is increased from one. This trend is illustrated in Figure 38 using heat release data from the Quad-4 engine at four equivalence ratios. As equivalence ratio decreases, the bifurcation progresses and the deterministic features of the dynamics become more evident even in the presence of significant levels of dynamic noise. The minimum value of Hs represents the set of symbolization parameters which best distinguishes the data from a random sequence. Sequences that are too short do not provide enough information about some of the important deterministic features. Sequences that are too long are subject to data, depletion and affected more by dynamic noise. Thus, it can be argued that the sequence length value that produces the minimum value of H s is the best choice for the given data and symbol-set size.
120
o ^H •I—I
c
(U
c o c cS
c/3 X) 0) LC
-a o
2
3
4
5 6 7 Sequence length
8
10
Figure 38: Modified Shannon entropy as a function of symbol-sequence length at four equivalence ratios using a symbol-set size of 8.
121
In this investigation, a symbol-sequence length of 2 was used since it is optimal or nearly optimal for a wide variety of experimental conditions for various engines and provides a moderate number of possible sequences (64 for nL = 82).
5.7
Model Discrimination
Several of the cyclic combustion variability models that have been proposed for sparkignition engines can be grouped into two major categories: linear Gaussian random processes (LGRP) and noisy nonlinear dynamics (NND). Both of these approaches presume that the cyclic variability models should include both deterministic and random elements. The LGRP model further assumes that the deterministic component is inherently linear in that the next combustion event is a linear function of prior combustion events. Also, cyclic combustion variations are assumed to be influenced linearly by stochastic or random effects. A general form for this type of relationship is the autoregressive moving-average (ARMA) model which is usually defined as: N :
Yt = ^
K a
n^t~n + ^2
n=l
b e
k t"k
(44)
k=0
where yt represents some measure of a cycle resolved combustion event, such as heat release, and et are the noisy perturbations such as fluctuations in as-injected equivalence ratio. Usually, the et are assumed to be Gaussian in nature. The ARMA fitting process uses linear least squares to determine the coefficients an and b^ from experimental data. See Belmont et al. (1986) for a discussion of an ARMA treatment of cyclic variability data.
122
The standard ARMA model can be modified to include nonlinear transformations of the combustion output y t to another observable z t .
Symbolically this can be
expressed as: zt = f(y t )
(45)
where f is a static (i.e., one-to-one) nonlinear transform of the linear combination of past combustion events and noisy perturbations.
This type of transform could
be caused by oscillations in the as-injected equivalence ratio resulting from noisy fluctuations
in the intake air. Note that in spite of the above nonlinear transform,
the modified ARMA process str 1 fits the LGRP category, because the basic dynamics still depend only linearly on the past (i.e., there is no nonlinear memory). NND models are inherently different from LGRP models because they explicitly allow for a nonlinear relationship between past and future combustion events. Such models are generally written as yt = g ( y t - i , e t )
(46)
where g is a nonlinear function and the effects of noisy perturbations are included in the function. Equation 46 takes into account nonlinear memory effects. One of the first NND models was proposed by Martin et al. (1988). In that investigation, the nonlinearity was introduced in the form of an abrupt transition between stochastic and random behavior when misfires occurred.
The Daw et al.
model is a more
detailed and physically descriptive NND model (see Section 2.6). The nonlinearity in the Daw et al. model is based upon the effect of residual gas on flame speed and subsequent combustion events rear the lean combustion limit. 123
Research in the area of dynamic-systems theory has shown that time irreversibility can be employed to discriminate between models, even in the presence of high noise levels (Diks et al. 1995). Specifically, processes consistent with a LGRP are inherently time reversible (Weiss 1975). Processes consistent with NND, however, are inherently time irreversible. It should be possible to decide which class of models is more appropriate, since experimental combustion measurements are time irreversible under lean fueling conditions and at high EGR levels. Surrogate data sets from the LGRP and NND models were constructed so they could be compared with experimental data. Three approaches were employed to represent LGRP models: (i) an ARMA model, (ii) the model of Daw et al. with residual effects disabled and driven with linearly hltered anti-correlated noise, and (iii) a data transformation technique of Schreiber and Schmitz (1996). To create the ARMA model, experimental data were fit using a second-order model and then surrogate data were generated by driving the model with Gaussian noise. The Schreiber-Schmitz surrogates that were produced had the same autocorrelation and data distribution characteristics as the experimental data. Surrogate data sets from the ARMA model, the Schreiber-Schmitz data transformation, and the LGRP version of the Daw et al. model were provided by C.E.A. Finney of the University of Tennessee (Finney 2000). The standard version of the Daw et al. model was used to simulate a NND model. Matt Kennel of the University of California, San Diego, provided the surrogate data sets generated by the NND version of the Daw et al. model (Kennel 1996).
124
The aforementioned surrogate data sets were fit to heat release data from the Crown Victoria engine at an equivalence ratio of 0.59 (see Figure 14). Model data sets of approximately 3000 cycles each were generated to simulate the experimental data. The ARM A and the Schreiber-Schinitz surrogates are statistically based models and the LGRP and NND surrogates of the Daw et al. model are physically based models with parameters set to the approximate conditions of the experimental data. Figure 39 depicts return maps for the experimental and model data, and Figure 40 depicts the corresponding symbol-sequence histograms created using an 8-level symbolization and a sequence length of 2 cycles. The return maps in Figure 39 indicate that the the LGRP models and the NND model exhibit certain features that appear in the experimental date under lean fueling conditions. For example, the general return map patterns have the characteristic "crescent" shape opening to the left. However, on careful examination, note that the NND return map reveals a definite asymmetry about the diagonal, while the LGRP return maps appear at least qualitatively symmetric. The ARMA model return map looks ellipsoidal and symmetric about the diagonal, but does not exhibit the qualitative shape of the experimental data. In the symbol-sequence histograms illustrating the forward- and reverse-time realizations of each data set (Figure 40), only the NND model exhibits the same qualitative time irreversibility as the experimental data, and its T-irr value is closer to that of the experimental data than those of the other models. These trends are reproducible over a range of lean fueling conditions and suggest that models which
125
Crown Vic at (|) = 0.59
^t
• » > • • •
/
*^VI
Heat release [i] Daw et al. model
,—1
+
1—1
0)
rrl
^ * W M i U ^ t
"^B
'-?9 i^B* 7mi • • • •
.
*
•
'* • *A •v
• t
Heat release [i]
Figure 46: Return maps for the Quad-4 engine at an EGR rate of 16% (top) and the modified Daw et al. model (bottom).
142
to be less bifurcated than the experimental data. Figure 47 uses symbol-sequence histograms to compare the dynamical patterns of the experimental and model data. The symbol-sequence histograms of the experimental and model data have comparable relative frequencies for most sequence codes. The experimental and model symbol-sequence histograms were also compared quantitatively using the Euclidean distance between the relative frequencies of the sequence codes. The optimal model fit resulted a T err value of 0.0334, which suggests a fairly good fit. The modified Daw et al, model also reproduced the same quantitative time irreversibility as the experimental data. The T irr statistic was 0.0942 for the model and 0.0965 for the experimental data. The model would have been able to provide an even better fit if the effect of EGR was modeled more accurately. This example, however, demonstrates that the modified Daw et al. model adequately descr" :>es the combustion dynamics of experimental data at high EGR rates.
143
0
10
20 30 40 50 Sequence code
60
0
10
20 30 40 50 Sequence code
60
0.00
Figure 47: Symbol-sequence histograms for the Quad-4 engine at an EGR rate of 16% (top) and the modified Daw et. al. model (bottom).
144
C H A P T E R VII
INVESTIGATION OF CONTROL
7.1
Control Algorithm
To demonstrate the possibilities for exploiting the deterministic component in cycleto-cycle combustion variations, a control algorithm was developed to reduce cyclic variability in the original Daw et al. model. The control strategy employs data symbolization to predict the intensity of future combustion events in a single cylinder on a cycle-to-cycle basis. The predictive symbolization strategy is similar in nature to a Markov chain. The control strategy uses data symbolization principles described in Section 4.3.5 to predict and prevent undesirable combustion events. If the control strategy predicts an undesirable combustion event, a nonlinear proportional control perturbation is made to the nominal injected equivalence ratio (f)0. The strategy uses a "library" of previously generated model data at a model condition of interest to predict future combustion events on a cycle-to-cycle basis. Data from the "library" at some condition where control is desired is symbolized and used to predict the outcome of future combustion events at the same condition. For example, assuming a data symbolization scheme of alphabet size 8 and word length 2 (which yields 64 possible sequences), 145
is given by:
PV(i)=J£jxPijj-j^TpJ
(63)
where PV(i) is the predicted symbol value after observing symbol i and pij is the is the probability of observing the word formed by the symbols i and j . The probability functions p;j are obtained from the relative frequencies observed in the symbol sequence histogram of the "library" data file. To eliminate erroneous control actions, only probability functions with values greater than the equiprobable threshold (1/64 in this example) are accounted for. If none of the probability functions have values greater than the equiprobable threshold no control action is taken. An exponentially weighted moving average filter is used to ensure that cyclic variability is not reduced by simply increasing the overall value of the nominal injected equivalence ratio (Davis 1999). A similar predictive control strategy has been used to reduce cyclic variations in a production SI vehicle by perturbing the nominal injected equivalence ratio during each engine cycle (Davis et al. 1999).
7.2
Control Implementation
Cyclic variations in the Daw et al. combustion model were reduced using a simple proportional feedback control strategy and a more sophisticated predictive symbolic control strategy. Both control strategies use deterministic information from the combustion dynamics to reduce the occurrence of undesirable combustion oscillations under lean fueling conditions by making small changes to the injected equivalence 146
Engine Model
hr[i]
oiiinpie
io
T
pert
Proportional Control
k -
hr[i-l]
+ nom
H /
EWMA Filter
-to+
act
Figure 48: Block diagram of the simple proportional control algorithm. ratio. The control actions used to reduce cyclic variations in the engine model result in little if any additional use of fuel. Some of the control strategy details will be committed in the following discussion due to proprietary concerns. Figure 48 shows a block diagram for the simple proportional feedback control strategy. The engine model produces a heat release value (hr[i]) that is differenced by the heat release value of the previous cycle (hr[i — 1]). Using the diiference between hr[i] and hr[i — 1], an appropriate linear proportional control action is taken. The resulting control action produces an equivalence ratio perturbation nom is then modified by a signal from the exponentially weighted moving average (EWMA) filter to ensure that the difference e between the injected equivalence ratio 0 act and the nominal equivalence ratio is very small over
147
Engine Model
hr[i] •
Transform Predictive Time Series to taffl Symbolic • Symbol Series Control
pert
+X+
0
+^ nom
^s^
EWMA Filter
f
K >+
T
act
X-
Figure 49: Block diagram of the predictive symbolic control algorithm. time. Finally, the value of the injected equivalence ratio act is passed to the EWMA filter and the engine model to influence the stability of the next combustion event. Figure 49 depicts a block diagram for the alternative symbolic control strategy. The strategy transforms the heat release value produced by the model (hr[i]) into a symbolic heat release value (hr[i]). The symbolization parameters used in the syrnbolization algorithm are arbitrarily selected and are chosen relative to the complexity of the combustion dynamics. Using hr[i] and symbol-sequence statistics from the "library" data set for that engine condition, the symbolic value of the next engine cycle is predicted and an appropriate nonlinear proportional control action is taken if the predicted symbolic value is different than the target symbolic value. The resulting control action produces a,n equivalence ratio perturbation $pert that modifies the nominal equivalence ratio of the next cycle (f>nom. The equivalence ratio obtained 148
to obtain the injected equivalence ratio (j)&ct. act is then passed to the EWMA filter and the engine model to influence the stability of the next combustion event. A simple application of the predictive symbolic control scheme is illustrated in Figure 50. The Daw et al. model was used to generate data representative of a period-2 bifurcation in the absence of measurement and dynamic noise. The heat release data were generated at an equivalence ratio of 0.71 without noise on any of the adjustable model parameters. The model generated 6000 cycles of data. 3000 cycles without control and 3000 cycles with control. It is apparent from the return map in Figure 50, that the control algorithm quickly removed the period-2 combustion dynamics and shifted the combustion dynamics to the fixed point (i.e., the diagonal). This was achieved using a sym')ol-sct size of 2 and a sequence length of 2 as the symholization
parameters for the predictive
symbolic control algorithm. This sym-
bolization scheme was employed since the combustion dynamics were clearly period-2 in nature. In general, a library data set containing a few thousand cycles is sufficient for adequate model control. The period-2 bifurcation also could have been eliminated by implementing the simple proportional feedback control strategy. The predictive symbolic control scheme was also used to reduce the cyclic variations caused by a noisy period-2 bifurcation. Results from the model control experiments are illustrated using return maps (Figure 51) and symbol-sequence histograms (Figure 52). In this case, model data were generated at an equivalence ratio of 0.71 with a moderate level of Gaussian noise on the injected equivalence ratio. For this
149
Control off ° Control on •
+ CD C/3
03
o • \
r ^
13 5-H
C)
•4—>
od
ffi
Heat release [i] Figure 50: Control of period-2 dynamics in the Daw et al. model using the predictive symbolic control algorithm is illustrated with a return map.
150
3 CT
X
0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00
Gaussian Variance = 0.0266
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Heat release [i]
Normalized heat release
•x
0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00
Observed —*— Gaussian Variance = 0.0082
(e)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Heat release [i]
Normalized heat release
^, o c3 0J
9cr
ca
CD
f*
Heat release [i]
0.20 Observed —e— (0 0.18 Gaussian 0.16 r Variance = 0.0045 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 .0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Normalized heat release
Figure 51: Return maps and probability histograms for the Daw et al. model at an equivalence ratio of 0.71 using no control (a and d), simple proportional control (b and e), and predictive symbolic control (c and f).
151
0.00
0
10
20 30 40 50 Sequence code
60
(b) Simple proportional control 0.10
>-. c 0.08 1998-02-02 00:33Z'
* MAIN BEGIN WRITE(*,*) WRITE(*,*)'************* :*********** + ***************************** > WRITER,*)'* COMBPAR : CREATES PRESSURE VS. CRANK-ANGLE DEGREE *> WRITE(*,*) J * AMD CALCULATED COMBUSTION PARAMETER FILES *' WRITE(*,*) J * VERSION 4 (1997 SEPT 30) *> WRITER,*)'* mangled by ceaf 1998-01-30 for faster execution *'
165
WRITE(*,*) WRITE(*,*)COMPVER WRITE(*,*) 99 WRITE(*,*)JSPECIFY RUN MODE (0=HELP)(l=BATCH)(2=INTERACTIVE) READ(*,*)MODE IF ((MODE.LT.0).OR.(MCDE.GT.2)) THEN WRITE(* * ) ' !!!!!!!!!!!!!!!!!!!!!!!!! ! ' WRITE(*,*)'!! INVALID INPUT VALUE. !!> WRITE(*,*)'!!!!!!!!!!!!!!!!!!!!!!!!!! ' GOTO 99 ENDIF IF (MODE.EQ.l) THEN WRITE(*,*)'SPECIFY BATCH FILE NAME (.LE. 40 CHARACTERS) :J READ(*,1)BATFIL OPEN(UNIT=9,FILE==BATFIL,ACCESS= 'SEQUENTIAL',STATUS='OLD;) ENDIF IF (MODE.EQ.O) CALL HELP 100 CONTINUE nc=0 ! default do not correct heat release IF (MODE.EQ.l) THEN read(9,1,err=170,end=170)epfil READ(9,1,ERR=170,END=170)INFIL READ(9,1,ERR=170,END=170)IMPFIL READ(9,1,ERR=170,END=170)OUTFIL READ(9,:L,ERR=170,END=170)PMAXFIL READ(9,1,ERR=170,END=170)IMEPFIL READ(9,1,ERR=170,END=170)HRFIL READ(9,2,ERR=170)END=170)SPARK read(9,2,err=170,end=170)nc WRITE(*,*) WRITE(* *) (COMBPAR: BATCH)' WRITE(* *) WRITE(* *) engine parameters \epfil WRITE(* *) INPUT FILE ',INFIL WRITE(* *) MAN. PRES. FILE \ IMPFIL WRITE(* *) P-CAD OUTPUT FILE '.OUTFIL WRITE(* *) MAX. PRES. FILE \PMAXFIL WRITE(* *) IMEP FILE ',IMEPFIL WRITE(* *) HEAT RELEASE FILE > ,HRFIL WRITE(* *) SPARK TIMING ',SPARK WRITE(* *) negative correction ',SPARK
166
IF (M0DE.EQ.2) THEN WRITE(*,*)'specify +haracters) :' READ(*,l)epfil WRITE(*,*)'SPECIFY READ(*,1)INFIL WRITE(*,*)'SPECIFY READ(*,1)IMPFIL WRITE(*,*)'SPECIFY +CTERS) :' READ(*,1)0UTFIL WRITE(*,*)'SPECIFY +CTERS) :' READ(*,1)PMAXFIL WRITE(*,*)'SPECIFY READ(*,1)IMEPFIL WRITE(*,*)'SPECIFY +TERS) :' READ(*,1)HRFIL WRITE(*,*)'SPECIFY READ(*,2)SPARK write(*,*)'correct read(*,2)nc ENDIF
engine-specific parameters file path ( F WRITE(*,6000)' F WRITE(*,6000)' I WRITE(*,6000)' I WRITE(*,6000)' I +erage [deg BTDC]' WRITE(*,6000)' I +age [deg BTDC] ;
Connecting-rod length [m] ' Specific-heat ratio (gamma); Intake valve closes [deg BTDC]' Exhaust valve opens [deg BTDC]' Initial valve position for manifold pressure av Final valve position for manifold pressure aver
STOP END
180
APPENDIX B
DATA SYMBOLIZATION SOURCE CODE
181
*********1*********2*********3*********4*********5*********6*********7** *****57**0*********0*********0*********0*********0*********0*********0** *************************************************************>!|e * * * * * * * * * *
** VERSION 2 * ** DATE 1998 MAR 05 * ** PROGRAMMER JOHNEY B. GREEN JR. * ************************************************************* *********** ** THIS PROGRAM IS A FORTRAN VERSION AND UPGRADE OF BINTREE.BAS BY * ** C.S. DAW. * ** * ** Program to read discrete time series data and estimate the * ** Modified Shannon entropy of an arbitrary partioned symbol tree.* ** Results are output in the form of Shannon entropy vs. no. of * ** tree levels and/or in :;he form of observed frequency for each * ** possible string. Symbol strings are indexed with the baselO * ** equivalent of their symbolic value. The value of each string * ** is read as first value- npart~i, second value= npart~i-l, etc., * ** where i= no. of tree levels-1 and npart is the number of * ** partitions. The decimal index range is from 0 to * ** (npart~sequencelength-l). Partitioning is performed using the * ** median of the data set Ability of code to handle "infinite" * ** number of sequence codes provided by C.E.A. Finney (3/4/98). * ***************************** ******************************************* ** (C) COPYRIGHT 1998 BY J.B. GREEN JR. ** THIS PROGRAM MAY BE DISTRIBUTED FREELY WITH NO WARRANTY, GUARANTEE ** OR SUITABILITY FOR PURPOSE EXPRESS OR IMPLIED.
* * *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * ? : * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
** CONTACT AUTHOR FOR DOCUMENTATION & SUGGESTIONS ON ALTERING CODE. * ** E-MAIL ADDRESS = * ** TELEPHONE = 423-574-0724 * ** TELEFACSIMILE = 423-574-2102 * ************************************************************************ PROGRAM MSESSHM character*40 batfil character*40 infil character*40 outfil character*l typ real*8 xmin,xmax,xavg,var,stdev
182
integer*4 mode,ans real*8 femp(l:20) real*8 fstr(1:15000,1:2) real*8 fx(l:15000) real*8 HL(1:20) real*8 sa(l:15000) integer*4 index,ind integer*4 maxnl real*8 nbin real*8 nindex integer*4 nlevel integer*4 npart integer*4 npts,n integer*4 nstr integer*4 power,treelevel real*8 x real*8 xcut(l:20) integer*4 xbin(l:15000) character*40 pnam character*78 pfunc character*60 update character*40 EJG !Special Variable (SSH Filename) real*8 seqcodeCl:15000) !Array containing sequence codes real*8 curcode !Pointer for seqcode array integer*4 Unicode !Number of unique sequence codes observed real*8 prob !Probability value 1 2 3 4 5 6 7 8 9
FORMAT(A40) F0RMATCI4) FORMAT(A40,A40) FORMAT(3F8.1) F0RMAT(I4,2X,F8.6) F0RMAT(F10.2) F0RMAT(F8.2) F0RMAT(I2,2X,F12.6,2X,F:4.6) F0RMAT(J# TL'^X.'Mod. Shan. Ent, >t2H, 'Fract, Empty Bins')
* ... MAIN BEGIN *
Program id
pnam = 'SSH.SHANTREE.MEDIAN' pfunc = 'Calc. Mod. Shan. Entropy for symbol trees using the data +med. for partitioning'
183
update = ;Updated by Johney Green, 03/05/98; Original by C.S. Daw'
•Print program info write '* » * ) write [* » * ) write I*»*) write '* *) write '* *) write 14 WRITE(*,*) STOP END
* * * * * * * *
cutoff(npart,npts,sa xcut) Written by: Robert M. Wagner Subroutine returns median of a sample sa(). The subroutine first sorts the sample in ascending order and then determines the median based on whether the sample is of odd or even length. Necessary additional subroutines:
hpsort(k,ra)
SUBROUTINE cutoff(npart,npts,sa,xcut) integer*4 npart integer*4 npts.j real*8 sa(l:15000) real*8 xcut(1:20) real*8 fract integer*4 upper,lower * — sort values call hpsort(npts,sa) *-- determine cutoff values do j=l,(npart - 1) fract = (j / float(npart)) * npts + .5 upper = INT(fract + 1)
192
xcut(j) = (sa(upper) - sa(lower)) * (fract - lower) + sa(lower) enddo !j return END ************************************************************************ ***** ROUTINE HPSORT *************************************************** ************************************************************************ SUBROUTINE hpsort(n.ra)
10
INTEGER*4 n REAL*8 ra(l:*) INTEGER*4 i,ir,j,l REAL*8 rra if (n.lt.2) return l=n/2+l ir=n continue if(l.gt.l)then 1=1-1 rra=ra(l) else rra=ra(ir) ra(ir)=ra(l) ir=ir-l if(ir.eq.l)then ra(l)=rra
return endif endif i=l 20
if (j.le.ir)then if(j.It.ir)then if (ra(j).lt.ra(j+:.))j=j+l endif if(rra.lt.ra(j))then ra(i)=ra(j) i=
j
else
193
C
j=ir+l endif goto 20 endif ra(i)=rra goto 10 END (C) Copr. 1986-92 Numerical Recipes Software *K'9 , jK.
194
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Combustion
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VITA
Johney Boyd Green, Jr. was born to Johney and Emma Green in Baton Rouge, Louisiana, on October 22, 1970. After graduating from Baton Rouge High School in 1988, he attended Memphis State University. Johney graduated magna cum laude with a Bachelor of Science degree in Mechanical Engineering and qualified as an Engineer-in-Training in the State of Tennessee in 1992. He began his graduate studies at the Georgia Institute of Technology in 1992 and received a Master of Science degree in Mechanical Engineering in December of 1993. Johney worked as a summer intern at the Oak Ride National Laboratory (ORNL) from 1992 to 1994, becoming a full-time employee in June of 1995. He spent a year as a visiting researcher at Ford Motor Company's Scientific Research Laboratory in Dearborn, Michigan from 1998 to 1999. Johney was the recipient of a National Consortium for Graduate Degrees for Minorities in Engineering and Science (GEM) Fellowship and a National Science Foundation Fellowship. He earned a 1998 ORNL Technical Achievement Award for developing a process to improve combustion stability in internal combustion engines and a 2000 Black Engineer of the Year Award in the category of Outstanding GEM Alumnus. Currently, he is conducting analytical and experimental research in support of the Department of Energy's Office of Advanced Automotive Technologies in compression-ignition engines, spark-ignition engines, and emission controls.
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