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Cold Engine Emissions Optimization Using Model Based
Calibration
Clive Tindle
General Motors Holden Ltd
ABSTRACT
Emissions calibration development of gasoline engines is becoming increasingly demanding for the calibration engineer,
due to a number of factors: reduced time for development programs, lower exhaust tailpipe emissions, and challenges to
reduce catalyst cost. To meet this demand, the technological complexity of the gasoline engine has increased with the
introduction of continuously variable intake and exhaust camshafts, and more recently the introduction of fuel injection
strategies on direct injection engines, such as double injection. With these technologies, engine data generation and
calibration optimization must be handled using a model based approach and design of experiments (DOE).
This paper focuses on the application of design of experiments methods and optimization of two-stage statistical
response models to develop an engine calibration to current worldwide standards, using MATLAB®
and Model Based
Calibration Toolbox. The model based methods used have been shown to be capable of producing calibration values for
the main actuators. Examples are presented which relate to recent applications during vehicle development. These show
that the use of model based methods is no longer a luxury, but a necessity in engine calibration.
INTRODUCTION
Virtually all the harmful pollutants emitted by modern gasoline powered vehicles are emitted during the initial engine start
and warm-up phases before catalyst light-off. Traditionally, faster catalyst light-off was achieved through retarding of
ignition timing and fuelling strategies which encouraged lower light-off temperatures. In response to more stringent
legislated emissions standards, changes in exhaust system architecture such as catalyst size, precious metal loadings
and placement have had an important role in reducing harmful pollutants. Their benefits can often be limited due to
vehicle packaging and cost restraints. At the same time, new engine technologies have been introduced to reduce engine
out emissions. Variable valve timing allows flexible control of internal exhaust gas recirculation (EGR), which can help
reduce nitrogen oxides (NOx) emissions [1]. In addition, if valve events are timed in such a manner that encourages
exhaust gas backflow into the intake ports, fuel preparation can be improved resulting in lower hydrocarbon emissions
(HC) [2 and 3]. Direct fuel injection introduces more degrees of freedom into the system and if used effectively can be an
emissions-reducing device. Semi-stratified charge combustion is realized through a double injection strategy which injects
some of the fuel during the compression stroke. The benefits are a reduction in cycle to cycle torque fluctuations and the
ability to further retard spark timing compared to homogeneous combustion [4]. The challenge to the engineer is to
optimize these high degree of freedom systems in a manner which produces the most efficient engine operation.
Model based calibration refers to the process of using DOE methods, statistical modeling and optimization to generate an
engine calibration. Figure 1 (courtesy of The MathWorks Inc.) shows a pictorial representation of the subtasks involved in
the process. The experimental plan is devised through application of advanced DOE methods. Statistical modeling uses
data collected from the experimental plan to produce accurate response models. High quality engine calibrations are then
developed through optimization of these models and system and calibration verification.
Traditional calibration methods have focused on optimizing a single variable at a time on the engine test bed which often
negates the interaction between other input variables. With higher degrees of freedom this becomes a very time
consuming and inefficient process. Introduction of the model based calibration approach has made it possible to optimize
all degrees of freedom simultaneously to enable a complete systems approach. This paper demonstrates the application
of model based calibration and discusses the best approach for each subtask based on recent experience at General
Motors Holden Ltd. This process has resulted in a successful emissions calibration that satisfied the programs objectives.

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Figure 1. Model-Based Calibration process using Mathworks tools
DESIGN OF EXPERIMENTS
In this section, the options available when designing an appropriate experiment are discussed. Experience has shown
that careful selection of appropriate design and of input variable range are the key contributing factors to success in the
model based process [5].
DOE SELECTION
Before selecting a DOE, it is important to consider the type of model that will be fitted to the data. The type of model
selected will influence the number of points required to be tested and will also determine to what extent the curvature of a
given response can best be modeled. For example, if a response feature can be described adequately using a quadratic
model, and we know that three test points are required to generate the coefficients of such a model, then it may seem
pointless to test at more than three levels for each input variable. If the requirement is to improve modeling of the
curvature of the response, then deviation from a quadratic model will be necessary and more than three levels are
required for each factor.
Summarized in Table 1 is the effect of the number of input variables (called factors) on the number of tests for a full
factorial and central composite design (CCD).
Table 1. Summary of tests required for different designs.
# of input variables
Quadratic – Full
Factorial
Quadratic/Cubic
CCD*
3 27 15
8 6561 273
*CCD uses 1 center point only
Depending upon the number of input variables in the experiment it may or may not be practical to use a full factorial DOE.
Considering three input variables, either a full factorial approach or a central composite design could be used. However,
to run a full factorial with eight input variables would involve running 6,561 tests, which in almost all instances would be
unpractical due to time and resource constraints. For the same reasons, it may also not be practical to run a CCD with
273 points. Figure 2 shows the CCD layout for three and eight variables, with Variable 2 plotted against Variable 1.
Other experimental designs offer more flexibility in terms of choosing the number of points. The limitation or overhead with
the CCD is that it is based on a 28
factorial design with the addition of star and center points. The axial distance of the star
points from the center point, known as the ‘alpha’ ratio, increases with the number of input variables. If the star points are
to fall within the variable ranges (known as an inscribed star point design), then the factorial points become concentrated
around the centre of the design space.
Data ModelingExperiment Design
Calibration Implementation
Data Collection

3. 3
Comparison of 3 and 8 variable CCD
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Variable 1
Variable2
3 Variable CCD
8 Variable CCD
Star
Point
Figure 2 – CCD layout for three and eight variables.
This concentration is undesirable from a modeling standpoint, as large areas without test points exist within the design
space. A more flexible design that takes into consideration the number and type of terms in the model is the optimal
design. This design is computer-based and offers good flexibility especially with constrained design spaces [6]. The
minimum number of points in an optimal design is equal to the number of terms in the model. Table 2 below summarizes
some options when choosing an optimal design compared to a CCD.
Table 2. Comparison of optimal and CCD
DOE Model Minimum # of terms
CCD Cubic 273
Optimal Cubic 165
Clearly, there are savings on the number of test points using comparable models. However, although fewer DOE test
points will save critical test bed testing time, it is worth remembering that the model fit may deteriorate as a result. To
decide how many test points are required, analysis of a statistic known as Prediction Error Variance (PEV) can be used.
Figure 3 shows PEV for a typical design. The aim is to achieve a small PEV; values greater than 1 magnify the predicted
error of the model chosen before any data has been collected [7].
Figure 3. PEV for a typical design.
The dark red areas show PEV > 1. These areas are at the edge of the design space, so deterioration in model accuracy
can be expected. If necessary, extra points can be added through design augmentation, with a space-filling design to
reduce PEV. Alternatively, if the optimum solution ends up in an area where PEV is high, a second DOE can be
conducted with revised input variable ranges.

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To summarize, a full factorial design with three levels or a CCD is adequate for cases using three or fewer input variables.
As the number of input variables increases, the full factorial design becomes impractical, and other options must be
exploited. A CCD becomes less flexible as the number of input variables increases due to the concentration of points
towards the center of the design space (within inscribed star points). Both optimal and space-filling designs are best
suited for a high number of input variables, given limitations on the number of tests that can be conducted.
SCREENING EXPERIMENTS FOR INPUT VARIABLE SELECTION AND RANGE SETTING
Failure to select appropriate variables and ranges for the DOE can result in tests being run at unstable operating points
and optimum values being found at the edge of the design space. These issues may appear trivial at first, especially if the
DOE is going to be used on an existing application that has history. Even so, it is easy to make the DOE either too
complex, by adding variables which have no effect on the responses, or too simple, by missing one or more key variables.
For a new application that has additional complexity, the same mistakes are easier to make as there is no previous
application knowledge. A general approach used by statisticians is to run a screening experiment with as many relevant
input variables as possible over reasonably large ranges. Analysis of this data will narrow down the relevant input
variables and give a good indication of their ranges. An additional benefit is that relevant data from the screening
experiment can also be used for model fitting, by augmenting the base design or for the purposes of model validation. In
our experience, screening experiments have been used in such cases but have only been necessary for systems with
large degrees of freedom.
RESPONSE SURFACE CHARACTERIZATION
Response surface characterization refers to the process of modeling experimental data that has a number of input
variables. The response is “characterized” or represented by mathematical equations that can be reconstructed to
visualize a surface. This section discusses the techniques used to successfully model the experimental data. Examples of
different responses are used to help explain the approach and provide insight into engine behavior.
The DOE data points were collected on the engine dynamometer, using a standard test automation system. Common
emissions variables and combustion parameters were measured under steady state operating conditions. The purpose of
the exercise was to optimize engine behavior during the warm-up phase. In order to best characterize this, the engine’s
coolant and oil were maintained at 25 ˚C for all test points. This was achieved by using an external refrigeration plant
connected to the engine’s coolant system. All mapping tests were performed at this quasi-steady thermal condition; based
on previous studies [8], this provides more representative data than performing tests with fully warm fluids.
TWO-STAGE REGRESSION APPROACH
The two-stage model approach allows for separation of one or more of the input variables into a ‘first stage’, with the
remainder falling into the ‘second stage.’ It works best when there is prior knowledge of how a response changes with a
given input(s). For gasoline engines, a typical first-stage input would be spark timing, as the majority of responses – brake
torque, emissions, combustion stability, and so forth – can be seen to have approximate, quadratic, or cubic relationships
with spark timing. This type of approach has been shown by others in the engine mapping community to be beneficial [9]
and fits in well with how engine data has been traditionally collected for common engine mapping procedures, such as
torque model calibration.
There are two valuable benefits from the two-stage approach. First, it gives the engineer an opportunity to have a clear
understanding of the factor being varied – in this case spark, at each DOE (second stage) operating condition. This leads
to easier identification of outliers within the test data. Second, the complexity of the DOE can be reduced by one factor,
which will lead to reduced model complexity. Performing sweeps will add to the total number of test points, but the above
benefits far outweigh this disadvantage. Each spark sweep may be considered as a ‘local model’ or ‘first stage,’ and each
DOE test point as the ‘global model’ or ‘second stage.’
The Local Model
The local model is generated from data collected at fixed global settings, and one variable – spark – is varied from a
reference point, for example, maximum brake torque (MBT), towards a retarded spark condition. A mathematical model
that best describes the response’s characteristics – for example, a polynomial – can then be fitted to the data. An
example spark sweep is shown in Figure 4, with a cubic fit to engine-out hydrocarbon emissions (HC). Higher-order
polynomials might better fit the raw data points, but they would more than likely model the noise within the measurement
system and hence not be beneficial. Also shown in Figure 4 is a data outlier; without knowledge of adjacent test points,
identifying this as an outlier would be much more difficult.

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- 3 0 - 2 0 - 1 0 0 1 0 2 0 3 0
0
0 . 0 0 5
0 . 0 1
0 . 0 1 5
0 . 0 2
0 . 0 2 5
0 . 0 3
0 . 0 3 5
0 . 0 4
Spark Retard
HCemissions
Local Response Model for HC
Outlier
Towards MBT
Figure 4. Spark sweep data for derivation of local model
A cubic model applied to the data shown in Figure 4 takes on the mathematical form:
3
3
2
210 SPARKbSPARKbSPARKbbHC +++=
where, bi are the regression coefficients. The fit of the polynomial at the local stage can be assessed through analysis of,
say, the root mean square error (RMSE). This is performed after all outliers have been removed. At this stage, different
order polynomials can be compared using RMSE values. It is also important from the calibration engineer’s point of view
to scrutinize this model and perhaps think about whether this type (shape) of behavior is expected and follows the laws of
physics. This model also makes available the limitations and expectations of the engine.
The Global Model
The purpose of the global model is to combine the collection of local models (i.e. spark sweeps) to allow reproduction for
any combination of global input variables. Taking HC emissions as an example, the DOE data collection produced N
spark sweeps, or, in other words, N local cubic models of the form depicted in Figure 4. This provides N sets of values for
local model coefficients bi, which will be used to formulate the global model. The global model will encompass all global
inputs. The type of model used to describe it will depend on how the shape of the cubic used for the local model changes
over the range of each global input variable. Figure 5 shows the characteristics of the HC response model as a function of
two global inputs: air flow and intake camshaft angle. These are the characteristic that the global model is required to
replicate by fitting an appropriate model to the coefficients of all the local models. Various options for model type are
discussed later in this section. To help explain the approach, a cubic model will be used here, due to its simplicity.
2 5
3 0
3 5
4 0
4 5
5 0
5 5
6 0
6 5
7 0
- 2 5
- 2 0
- 1 5
- 1 0
- 5
0
5
1 0
- 2
- 1
0
1
2
3
4
5
6
7
8
x 1 0
- 3
Air Flow
Effect of Global Inputs on HC Emissions
Intake Cam Advance
HCEmissions

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Figure 5. Effect of global inputs on engine-out HC emissions.
Considering the two global inputs - air flow and intake camshaft angle - the resulting global model equation for b0 is as
follows.
3
10
2
9
2
8
3
7
3
65
2
4
2
32100
**
*
INCAMcAIRFLOWINCAMcINCAMAIRFLOWcINCAMc
AIRFLOWcINCAMAIRFLOWcINCAMcAIRFLOWcINCAMcAIRFLOWccb
++++
++++++=
where cn are the coefficients of the cubic model. Similar equations can be written for b1, b2, and b3. When combined, the
response characteristics at the local stage can be reproduced for any set of global conditions within the ranges set in the
DOE.
Choosing and fitting the global model requires greater skill compared to the local level. The danger is that the global
model can easily be ‘over-fitted,’ or skewed in an undesirable way, through selection of an overly complex model. The
skewing can happen due to errors within the data set, or perhaps due to discrete changes in the response. For example,
if some of the local sweeps contained data indicating that one or more of the cylinders were misfiring, then the engine-out
HC emissions for those sweeps would be unexpectedly higher than others. This random data inclusion would have to be
removed through proper screening to ensure a good data foundation for the model-building process.
It is often the case that the cubic model is not sufficient to model the bi coefficients, and a more complex model is required
to achieve a more accurate model fit. Analysis of the statistic RMSE and other statistics such as predicted sum of squares
(PRESS RMSE) [7] were used successfully to judge model fit, after the removal of data outliers. Chasing the lowest value
for RMSE may well ‘over fit’ the model, so it is sensible to also consider PRESS RMSE, which checks the model’s ability
to predict a value after removal of a data point. A more complex model, which offers more flexibility and is capable of
modeling non-linear responses, is a radial basis function (RBF) [10]. This was the chosen model applied to the data in
Figure 5, which shows only a slice of the whole model. The complete model had eight input variables in the DOE, and its
shape changes as other inputs change. Other models to describe combustion stability, brake torque, and exhaust energy
flow rate were compiled, using the same principles described above.
CALIBRATION OPTIMIZATION
An optimized calibration refers to the data set that resides in the engine control unit (ECU) in the form of look-up tables or
constants. Combined with control strategy, the optimized calibration determines the actuator positions for a given set of
engine operating conditions. It must be capable not only of controlling the engine to meet or exceed the desired emissions
targets, but also of doing so in a manner that will not compromise other vehicle attributes, such as drivability or noise and
vibration.
This is not a simple task. A common mistake would be to optimize for a single response and ignore all other outputs. For
example, the objective of the optimization might be to seek the lowest possible HC emissions, but frequently, engine
operation at the minimum results in poor combustion stability. Hence it is best to make full use of the model-based
approach study all relevant responses, and introduce constraints during such an optimization.
There is also a certain amount of trial and error in any optimization. Relating modeled engine test bed behavior to engine-
in-vehicle behavior can require several iterations, especially when combustion stability is considered. It may therefore be
necessary to carry out optimizations with different combustion stability constraints. Without a model, derivation of these
optimums would require a re-visit to the engine test bed or ad-hoc revisions based on subjective vehicle behavior.
Optimization can either be performed manually through visual inspection of all response models or automatically through
use of the optimization function available within MATLAB (called fmincon). Experience has shown that the best approach
is to use a combined approach. The response models can be used as an engine test bed simulator. This is a very
powerful tool for the engineer, as engine behavior can be examined by changing one input variable at a time. Hence, a
comprehensive understanding can be built up of how the input variables affect different responses, and an expected
outcome from the optimization may be theorized.
To perform an automated optimization, the knowledge gained from visualizing the model responses manually are used to
select an objective(s). For emissions calibration, the target is to achieve catalyst light-off and minimize engine-out
emissions at the same time. For a given exhaust system architecture, the catalyst light-off is governed primarily by the
amount of heat energy generated by the engine.

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This can be described by the following simple equation:
TCmsJrgyFlowExhaustEne pΔ=
•
]/[
In most cases, minimization of engine-out HC emissions offers the biggest challenge, as this is often close to the
emissions limit: on the other hand, strategies that minimize HC emissions also aid reduction in other gaseous emissions,
such as carbon monoxide (CO).
To determine the operating requirements of the engine (i.e., speed and torque) the vehicle emissions drive cycle must be
analyzed. The engine is required to produce torque, to power the vehicle at target speed. Apart from basic vehicle design
parameters such as mass, overall gearing, and driveline losses, other factors, such as selected gear and transmission
torque converter behavior, can alter the power requirements for a given cycle. If these are considered to be optimized,
then the engine will operate at a given speed and torque to achieve the target vehicle speed. To simplify this further, the
amount of time spent at each speed and load point can be calculated and a list of speed and load points (mini map
points) that account for > 95 percent of the catalyst heating operation period can be generated.
Taking one of these mini map points as an example, and recalling that engine speed and torque are fixed, to achieve
maximum exhaust energy flow rate, mass flow rate out of the engine and exhaust gas temperature need to be maximized.
This can be achieved through increasing intake manifold pressure (opening of the throttle blade) and retarding spark
timing. Figure 6 shows the response model for exhaust energy flow rate and HC emissions as a function of exhaust mass
flow rate and spark advance. Engine torque is not constant for each surface plot in Figure 6: for clarity, an approximate
constant torque vector has been sketched on each surface plot.
The solution to the optimization problem lies on these surfaces along the vector of constant torque. To find the best
solution along this vector, the main options available for optimization depend upon whether a single or multiple objectives
are used. A single objective would simply find the maximum or minimum of a particular response, whereas two or more
objectives would produce a Pareto trade-off [11].
- 3 0
- 2 0
- 1 0
0
1 0
2 0
3 0
2 5
3 0
3 5
4 0
4 5
5 0
5 5
6 0
6 5
7 0
0
0 . 5
1
1 . 5
2
2 . 5
3
3 . 5
x 1 0
4
Exhaust Energy and HC Emissions fn(mass flow rate, spark advance)
Spark Advance
Mass Flow Rate
ExhaustEnergy
- 3 0
- 2 0
- 1 0
0
1 0
2 0
3 0
2 5
3 0
3 5
4 0
4 5
5 0
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0
0 . 0 0 5
0 . 0 1
0 . 0 1 5
0 . 0 2
0 . 0 2 5
0 . 0 3
0 . 0 3 5
Mass Flow Rate
Hydrocarbons
Approximate constant torque vector
Approximate constant torque vector
Spark Advance
Figure 6. Exhaust energy and HC emissions response models.
Single-Objective Optimization
As the models in Figure 6 would suggest, a single objective optimization is adequate to achieve the goal of obtaining
maximum exhaust gas energy flow rate while minimizing HC emissions. In fact, either one of these responses could have
been the objective for the optimization, as long as the other response was constrained not to exceed a target value. Other
constraints were applied to the optimization, such as:

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• Combustion stability <= desired target.
• Manifold vacuum => desired target.
• Model boundary constraint; the optimum needs to lie in an area where the model is valid.
These constraints were necessary because without them during the process of minimizing HC emissions, combustion
stability would have deteriorated, and manifold vacuum decreased to levels that offered insufficient brake booster
assistance.
The above optimization was run at different mini map points to generate a preliminary calibration before the process of
map smoothing which is discussed later.
Multi-Objective Optimization
Using more than one objective can be very useful because in the process of optimizing one objective, another response
deteriorates. When maximizing exhaust energy flow rate, it is often the case that engine-out HC emissions start to
increase as the combustion limit is approached. To understand the trade-off between these two responses – in other
words, the best compromise between minimum HC emissions and maximum exhaust energy flow rate – a multi-objective
optimization was used, with similar constraints to those used for the single objective optimization.
The normal boundary intersection (NBI) algorithm is used for a multi-objective optimization. This algorithm considers the
optimum for each individual objective and then calculates spacing between these optima for a desired number of trade-off
points. Each trade-off point is then moved in a direction normal to the line connecting the individual optima. More
information can be found in published literature [11].
Figure 7 shows an example of the NBI algorithm applied to minimize HC emissions and maximize exhaust energy flow
rate. Two Pareto curves are shown where different combustion stability limits were chosen. Accepting higher combustion
instability results in similar HC emissions and higher exhaust energy flow rates.
Derivation of an optimum calibration from a Pareto is more time-consuming, as there is more than one possible solution.
More often than not, the calibration values are similar for adjacent Pareto points, as the engine will be operating close to
an optimum condition. As a rule of thumb, the knee point (usually the middle point on the trade-off) is used as the starting
point for the vehicle calibration. The NBI algorithm was applied to different mini map points to generate a preliminary
calibration before map smoothing.
Pareto: HC Emissions and Exhaust Gas Energy
2 .4
2 .5
2 .6
2 .7
2 .8
2 .9
3 .0
3 .1
3 .2
4 2 4 4 4 6 4 8 5 0 5 2 5 4 5 6
Exhaust Energy
EngineOutHCEmissions
Stability <= 100 % Stability <= 120 %
Pareto extended by
increasing Stability limit
Figure 7. NBI Optimization showing effect of stability limits.
CALIBRATION MAP GENERATION
Regardless of whether a single or multi objective optimization is used, the model-optimized values of the actuator settings
generally require modification for one reason or another. Most frequently, the settings are modified to generate a
reasonably smooth map for the calibration to avoid steep gradients and odd transient behavior. Generating a smooth map

9. 9
can be quite involved and becomes increasingly difficult as the number of input variables increase, due to the number of
resulting maps.
Using the output of an optimization as the starting point a manual trade-off – where all responses can be viewed
simultaneously – was found to be adequate. Small adjustments on one actuator always need to be counteracted by
adjustments on other actuators, so that the optimum is maintained whenever possible and constraints are not exceeded.
VERIFICATION / VALIDATION
The verification part of the process should not be neglected, as it is important to understand how accurate the models are
at predicting engine responses. Any model is a simplification of a complex real life situation, so the process of model
verification needs to be treated subjectively. Hence, during the verification and validation process, test data repeatability
must always be considered when a new data set is compared with a given model. Quantitatively the data may not be the
same but subjectively it may be acceptable.
Calibration Verification On FTP Drive Cycle
0
10
20
30
40
50
60
70
80
90
100
0 25 50 75 100 125 150
Time [s]
NormalisedNMHC[%]
0
10
20
30
40
50
60
70
VehicleSpeed[mph]
Vehicle Speed
HC Baseline before Optimisation
HC After Optimisation
Modal Data
Figure 8 Verification using FTP Drive Cycle
Two methods have been used here for model verification: 1) presentation of new/unseen data to the model and analysis
of statistics such as PRESS RMSE: 2) vehicle emissions tests. The first method is very good for determining whether any
over-fitting has occurred. The second method is very useful for summarizing the outcome of the model-based process, as
this result is a clear statement of whether or not the process has worked. Figure 8 compares cumulative tailpipe NMHC
(non-methane hydrocarbons) emissions for two different engine calibrations, using an FTP75 drive cycle. The only
significant difference between the calibrations were that Test 1 used non-optimized intake and exhaust camshaft settings,
and Test 2 used settings produced by the approach described in this paper. The most significant part of this comparison
is the first 60 seconds. Towards the end of this period, catalyst light-off is achieved, but prior to that, most if not all
pollutants pass directly through the catalyst and are not oxidized/reduced. The optimized calibration has outperformed the
baseline calibration reducing total NMHC by approximately 15 percent.
CONCLUSION
Model-Based-Calibration development, using DOE and statistical modeling, is a key tool in developing high-technology
engines with demanding emissions and driveability constraints. Optimization of systems with large degrees of freedom
using traditional methods is impractical. Key to the success of such methods is careful execution of each subtask

10. 10
involved. Experiments need to be designed using the most appropriate design with the correct number of points, input
variables and ranges. Engine test data need to be continuously scrutinized to ensure development of accurate models.
Calibration generation from optimization results must consider multiple output variables and constraints, and trade-offs
need to be carefully selected. A combination of visual inspection, manual manipulation, and calibration map smoothing
will result in the best practical and easy-to-implement solution in the ECU. Experience is a key factor in successful
application of this process.
ACKNOWLEDGMENTS
The author would like to acknowledge the assistance of the following people at General Motors Holden Ltd. Greg Horn,
Martin Jansz, Richard Hurley, Kevin Yardley, Joshua Wood, and Julian Banfield.
Thanks also to David Sampson at The MathWorks for his continuing support of Model-Based-Calibration Toolbox.
REFERENCES
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SAE Paper No. 2002-01-1101.
2. T. Kidokoro et al. “Development of PZEV Exhaust Emission Control System.” SAE International 2003. SAE Paper No.
2003-01-0817.
3. J.J. Batteh et al. “Transient Fuel Modeling and Control for Cold Start Intake Cam Phasing.” SAE International 2006.
SAE Paper No. 2006-01-1049.
4. K. Morita et al. “Emissions Reduction of a Stoichiometric Gasoline Direct Injection Engine.” SAE International 2005.
SAE Paper No. 2005-01-3687.
5. J. Seabrook. Practical Implementation of Design of Experiments in Engine Development. Statistics for Engine
Optimization, Edited by Edwards S.P., Grove D.M. & Wynn H.P. Professional Engineering Publishing 2000. ISBN-1-
86058-201-X
6. Douglas C. Montgomery, Design and Analysis of Experiments, 5th
Edition, Wiley 2000. ISBN 0-471-31649-0
7. Model-Based Calibration Toolbox User’s Guide. The MathWorks, Inc., 2004
8. C. R. Tindle, “Comparison of Engine-Out Emissions at Different Operating Temperatures.” Internal GM publication,
August 2005.
9. S. Flint and P. Cawsey, “Use of Experimental Design and Two-Stage Modeling in Calibration Generation for Variable
Camshaft Timing Engines.” 2nd
Conference Design of Experiments in Engine Development. Expert Verlag June 2003
ISBN 3-8169-2271-6.
10. T. Morton and S. Knott, “Radial Basis Functions for Engine Mapping.” Institution of Mechanical Engineers, IMechE
Paper No. C606/022/2002 from International Conference on Statistics and Analytical Methods in Automotive
Engineering. Professional Engineering Publishing 2002. ISBN 1-86058-387-3.
11. O. Roudenko et al., “Application of a Pareto-based Evolutionary Algorithm to Fuel Injection Optimization.” Institution of
Mechanical Engineers, IMechE Paper No. C606/003/2002 from International Conference on Statistics and Analytical
Methods in Automotive Engineering. Professional Engineering Publishing 2002. ISBN 1-86058-387-3.
12. Das Indraneel, The Normal-Boundary Intersection Home Page;
http://www.caam.rice.edu/%7Eindra/NBIhomepage.html
CONTACT
Dr. Clive Tindle
Powertrain Engineering - MP302
Holden Proving Ground
Bass Highway
Lang Lang 3984
VICTORIA - AUSTRALIA
Email: clive.tindle@gm.com
Tel: +61 (0) 3 594 58382