Data Preprocessing for Automotive Engine Tune-up
Chi-man VONG, Io-weng CHAN, Chio-pang CHANG, Wai-kei LEONG
{cmvong, da11229, da11220, da11324}@umac.mo
Department of Computer and Information Science, Faculty of Science and Technology, University of Macau
Abstract: Data preprocessing [4, 6, 7] is an important procedure for mathematical modelling.
Mathematical model estimated based on a training data set results better if the data set has been properly
preprocessed before passed to the modelling procedure. In the paper, different preprocessing methods on
automotive engine data are examined. The preprocessed data sets using different preprocessing methods
are passed to neural networks for models estimation. The generalizations of these estimated models could
be verified by applying test sets, which determine the effects of different preprocessing methods. The
results of preprocessing methods for automotive engine data are shown in the paper.
Key words: Automotive engine setup, PCA, CCA, Kernel PCA, Kernel CCA, Data preprocessing
1. Introduction
Mathematical modelling [1, 2, 3] is very common in many applications because of its capability of
estimating an unknown and complex mathematical model covering the application data. However, as
there is a natural law – GIGO (Garbage In Garbage Out). No matter how good the modelling tool is. If
garbage data is passed in, then garbage results are returned. Hence data preprocessing is a must for high
accuracy of modelling results. Traditional statistical methods concentrate on data redistribution and data
sampling in order to provide consistency within the data. However, most statistical methods are not
capable to handle high data dimensionality. To overcome this problem, dimensionality reduction is
usually applied. However, reducing some input features may cause information loss because the input
features themselves are highly (and perhaps nonlinearly) correlated. Under this situation, several
preprocessing methods from machine learning, support vector machines (SVM) and statistics are
compared to verify their ability to handle the issues of high dimensionality and nonlinear correlation.
In the comparison, a testing application of automotive engine tune-up is selected since it involves a
moderate number of dimensions (> 30) and the input features are nonlinearly correlated.
2. Data Preprocessing
Formally, data preprocessing is a procedure to clean and transform the data before it is passed to other
modelling procedure. Data cleaning involves removing the noise and outliers in the data set, while data
transforming tries to reduce the irrelevant number of inputs, i.e., reducing dimensionality of the input
space. As data cleaning is very straightforward of applying standard process of “zero mean and unit
variance”, the concentration is put on data transforming. The following subsections introduce the
common data transformation methods [6, 7].
2.1 Principal Component Analysis
A well-known and frequently used technique for dimensionality reduction for input space is linear
Principal Component Analysis (PCA). Suppose one wants to map vectors x  Rn into lower dimensional
vectors z  Rm with m < n. One proceeds then by estimating the covariance matrix:
ˆ 
Σ
xx
where x 
1
N
1 N
( x k  x)( x k  x) T

N  1 k 1
(1)
N
x
k 1
k
and xk is a vector = the kth data point in training set and computes the eigenvalue
decomposition
ˆ u u
Σ
xx i
i i
(2)
where ui is the ith eigenvector of Σ̂ xx and i is the ith eigenvalue of Σ̂ xx . By selecting the m largest
eigenvalues and the corresponding eigenvectors, one obtains the m transformed variables (score
variables):
z i  u Ti ( x  x)
(3)
The remaining n–m variables are neglected as they are no longer important. Note that the transformed
variables are no longer real physical variables.
2.2 Kernel Principal Component Analysis
Linear PCA always performs well in dimensionality reduction when the input features are linearly
correlated. However, for nonlinear case, PCA cannot give good performance. Hence PCA is extended to
nonlinear version under SVM formulation. This nonlinear version is called Kernel PCA (KPCA). KPCA
involves solving the following system of equations in :
Ωα  α
where
(4)
Ω kl  K ( xkT , xl ) k, l = 1,…,N.
The kernel function K is chosen as RBF (Radial Basis Function), i.e., K(x, y) = exp(-||x-y||/22), with  the
user predefined standard deviation. The vector of variables  = [1 ; … ; N] is an eigenvector of the
problem and  R is the corresponding eigenvalue. In order to obtain the maximal variance one selects
the eigenvector corresponding to the largest eigenvalue. The transformed variables become
N
zi ( x)    i ,l K ( xl , x)
(5)
l 1
where i = [i1 ; … ; iN] is the eigenvector corresponding to the ith largest eigenvalue, i = 1, 2, …,p, and
p is the largest number such that eigenvalue p of the eigenvector p is nonzero. One more point to note is
that the eigenvectors i should satisfy the normalization condition of unit length:
αTi α i 
1
i
, i  1,2,...., p
(6)
where 1  2  … p > 0, i.e., nonzero.
2.3 Canonical Correlation Analysis
In canonical correlation analysis (CCA), one is interested in finding the maximal correlation between
project variables zx = wTx and zy = vTy, where x  Rn, y Rm denote given random vectors with zero mean.
CCA also involves an eigenvalue problem for which the eigenvectors w, v are solved:
1
1
2

C xx C xy C yy C yx w   w

1
1
2

 C yy C yxC xx C xy v   v
(6)
where Cxx = E[xxT], Cyy=E[yyT], Cxy = E[xyT] and the eigenvalues 2 are the squared canonical
correlations.
Only one of the eigenvalue equations needs to be solved since the solutions are related by
Cxy w  xCxx w

 C yx v  yC yy v
(7)
where
x  1
y 
vT C yy v
wT C xx w
(8)
2.4 Kernel Canonical Correlation Analysis
In kernel canonical correlation analysis (KCCA), the formulation is similar to CCA except kernel trick is
applied. The kernel chosen is again RBF. Solve the following system in ,  as the projection vectors:
0
 0 c, 2   
 1c ,1  I
  
 




0   
0
 2c, 2  I   
 c ,1

(9)
where
 c ,1  M c 1 M c
 c , 2  M c  2 M c and
M c  I  1v1Tv / N
1,kl  x kT xl
 2 ,kl  y kT y l for k , l  1,..., N
v1, v 2 are lagrange multipiers
I is an identity matrix, 1v is a 1 - vector  R N
(10)
3. Automotive Engine Tune-up
Modern automotive petrol engines are controlled by the electronic control unit (ECU). The engine
performance, such as power output, torque, brake specific fuel-consumption and emission level, is
significantly affected by the setup of control parameters in the ECU. Much parameter is stored in the
ECU using a look-up table format. Normally, the car engine performance is obtained through
dynamometer tests. Traditionally, the setup of ECU is done by the vehicle manufacturer. However, in
recent the programmable ECU and ECU read only memory (ROM) editors have been widely adopted by
many passenger cars. The devices allow the non-OEM’s engineers to tune-up their engines according to
different add-on components and driver’s requirements.
Current practice of engine tune-up relies on the experience of the automotive engineer. The engineers will
handle a huge number of combinations of engine control parameters. The relationship between the input
and output parameters of a modern car engine is a complex multi-variable nonlinear function, which is
very difficult to be found, because modern petrol engine is an integration of thermo-fluid,
electromechanical and computer control systems. Consequently, engine tune-up is usually done by
trial-and-error method. Vehicle manufacturers normally spend many months to tune-up an ECU optimally
for a new car model. Moreover, the performance function is engine dependent as well. Knowing the
performance function/model can let the automotive engineer predict if a new car engine set-up is gain or
loss, and the function can also help the engineer to setup the ECU optimally.
In order to acquire the performance model for an engine, modelling techniques such as neural networks,
support vector machines, statistical regression could be employed. No matter which method is used for
modelling, the data must be preprocessed.
4. Experiment Setup
In order to compare the previous methods, a set of 300 training data is acquired through the dynamometer.
Practically, there are many input control parameters and they are also ECU and engine dependent.
Moreover, the engine horsepower and torque curves are normally obtained at full-load condition. The
following common adjustable engine parameters and environmental parameters are selected to be the
input (i.e., engine setup) at engine full-load condition.
x = < Ir, O, tr, f, Jr, d, a, p > and y = <Tr>
where
r: Engine speed (RPM) and r = {1000, 1500, 2000, 2500, …, 8000}
Ir: Ignition spark advance at the corresponding engine speed r (degree before top dead centre)
O: Overall ignition trim (  degree before top dead centre)
tr: Fuel injection time at the corresponding engine speed r (millisecond)
f: Overall fuel trim (  %)
Jr: Timing for stopping the fuel injection at the corresponding engine speed r (degree before top dead
centre)
d: Ignition dwell time at 15V (millisecond)
a: Air temperature (°C)
p: Fuel pressure (Bar)
Tr: Engine torque at the corresponding engine speed r (Nm)
After acquiring the training data, it is ready to pass to each of the previously mentioned preprocessing
methods to verify which method is best to automotive engine data. Those methods are implemented in
commercial computing package such as MATLAB under Windows XP.
5. Results
Results are separated into two parts: dimensionality reduction and pertained accuracy. Table 1 shows the
effects of dimensionality reduction of different methods, with 5% information loss, i.e., all the dimensions
contributing only 5% information in total for the training data set are discarded.
Original Dimension
Reduced Dimension
PCA
50
45
KPCA
50
41
CCA
50
46
KCCA
50
43
Table 1. Comparison of dimensionality reduction for different methods
Another result is the accuracy pertained, i.e., the generalization on unseen inputs of the models built using
the reduced dimensional data set. To compare the pertained accuracy, we need a mathematical model to
be built based on the original data set and additional four models based on the reduced data set. In total,
there are five mathematical models built. In our case, neural networks [1, 3, 8] are used as the modelling
tool because it is very mature and built inside MATLAB. The generalizations for the five models are
tested upon a common test set of 20 cases that are acquired from the dynamometer as well. Table 2 shows
the results of accuracy. From the results, it is shown that KPCA performs best among all preprocessing (or
no preprocessing) methods.
Accuracy on test set
No preprocessing
92.2%
PCA
86.3%
KPCA
93.1%
CCA
89.1%
KCCA
91.2%
Table 2. Comparison of generalization of models built upon the reduced training sets
6. Conclusions
Data preprocessing is a useful procedure for data transformation especially when the dimensionality of a
training data set is high. With lower dimensions, the computation issues are relaxed and the estimated
models based on the reduced training set may even perform better in not only the training accuracy but
also the generalization.
In this paper, different preprocessing methods are tested and the results are also compared. In the
application domain of automotive engine setup, it is verified that KPCA is the best among the methods we
test.
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