DIAGNOSIS OF CAM PROFILE SWITCHING OF AN AUTOMOBILE GASOLINE ENGINE
David Antory1, Paul J. King 2, R. Peter Jones1,3 and Ross McMurran1
International Automotive Research Centre, University of Warwick, Coventry, CV4 7AL, U.K.
Powertrain Electronics Controls Simulation, Jaguar Cars Limited, Coventry, CV3 4BJ, U.K.
3
School of Engineering, University of Warwick, Coventry, CV4 7AL, U.K.
1
2
Abstract: The investigation on cam profile switching (CPS) in an automotive gasoline
engine is presented. The performance of the CPS system is monitored and analysed to
allow a diagnostic technique to be developed to determine whether the engine valves
have operated to their correctly commanded position. The proposed diagnostic was
developed from tests undertaken on a gasoline engine. The proposed approach is capable
of performing accurate and reliable condition monitoring and diagnosis using Principal
Component Analysis techniques. The results of the diagnostic are presented later in the
paper.
Keywords: Automobiles, Detection, Diagnosis, Engines, Process Monitoring.
1. INTRODUCTION
Vehicles sold throughout the world are subject to an
increasing stringent set of emission thresholds. To
achieve certification, all sensors and vehicle subsystems that may affect vehicle exhaust emissions have
to be monitored by an On-Board Diagnostic (OBD)
system that is part of the Engine Management System or
any other embedded controller. This was requirement
was introduced in the US in 1988 for OBD1, for open
and short circuit faults, and 1994 for OBD2, for changes
in sensor and actuator responses, for Europe this
legislation, EOBD, was introduced on any vehicle built
after January 2000. Both sets of legislation link the
performance of the different diagnostics to emission
thresholds. In the event of component or sub-system
failure, a check engine light must be illuminated as an
indication to a driver there is a problem so corrective
action can be taken to minimise the pollution caused by
that fault. As the emissions thresholds are continually
reduced more sophisticated techniques have to be
employed to meet these increasing tightening
thresholds.
Condition monitoring and diagnosis (CMD) has already
been applied to a number of industrial systems to great
effect. CMD process can support the performance and
the robustness of any systems by monitoring their entire
operational conditions to make sure that the outcome of
the process is achieved without any significant
disturbances. While they may add complexity in terms
of understanding the technologies behind them, they can
also give an advantage to the CMD purposes. By taking
the measurement signals from the sensors and actuators
using an existence data-acquisition system, a dedicated
CMD model can be built. The use of automotive data
has recently been discussed (Mills, 2005). The model
for the CMD system is generated from the collection of
the measurement signals to represent the chosen
systems/sub-systems. This type of model falls within a
category of data-driven model. One of the popular datadriven techniques is Principal Component Analysis
(PCA). It is a well-known technique for data
compression and feature extraction. It has gained
considerable attention and has been successfully applied
in many industrial chemical and semiconductor
processes (Kourti and MacGregor, 1995; MacGregor,
2005) and recently has been applied in the automotive
engine diagnostics (Antory, 2005).
This paper presents results of a collaborative research
project between IARC and Jaguar and Land Rover on
the investigation of a Cam Profile Switching (CPS)
diagnostic for a gasoline engine. CPS allows for
different valve lift and cam durations to operate on an
engine. This has the following benefit for the driver of
improving engine torque and fuel economy, more
detailed discussion on CPS is given in Section 3. Further
background information on CPS can be found in a
number of papers (Milovanovic et al., 2005; Rask and
Sellnau, 2004; Xu et al., 2003; Alger et al., 2003;
Sellnau and Rask et al., 2003; Brüstle C. and
Schwarzenthal D., 1998).
The CMD model for CPS system was validated using
measurements signals collected from a gasoline engine
connected to a dynamometer in an engine test cell
facility. Good results were obtained and detail analysis
was performed. It was shown that the proposed
approach was capable of performing a reliable CMD
process to diagnose faults for a gasoline engine CPS
system.
The paper is organised as follows: The next section
discusses the condition monitoring and diagnosis
methods, followed by discussion of the experimental
data associated with this case study in Section 3. Section
4 details the implementation of the proposed method
where the process monitoring is performed and is
analysed. Finally, Section 5 summarises and concludes
the paper.
2. CONDITION MONITORING & DIAGNOSIS METHOD
This section discusses briefly the fundamental theory of
the proposed condition monitoring and diagnosis
methods.
2.1. Principal Component Analysis (PCA)
PCA is a one of the most popular data-driven method
that has gained significant interests in large industrial
processes. This is due to its simplicity and powerful
approach to capture redundant information in the
process. PCA relies on eigenvalue-eigenvector
decomposition in the data. By capturing the most
important variation in the data, a better monitoring
process can be achieved.
By forming a data matrix, X ∈ ℜ m×n , in which m
samples are stored as row vectors, of n (n << m) process
variables stored as column vectors, the application of
PCA generates a reduced set of new independent
‘artificial’ variables, principal component (PC) scores T
and PC loadings P. This transformation captures
important variation and can be written as follows:
k
X = t 1pΤ1 + t 2pT2 + L + t k pTk + E = ∑ t i pTi + E
i =1
(1)
Here, X is a sum of vector products of PC score ti,
stored as column vectors in T, and PC loading pi, stored
as column vectors in P. The determination of k (< n) is
crucial as it represents the significant variation of the
first k eigenvectors of the correlation matrix Sxx defined
as follows:
S xx =
1
X T X ∈ ℜ n×n
(m − 1)
(2)
X is scaled to zero mean-centred and unit variance to
eliminate different unit scales of the process variables. E
is the residual matrix which describes unimportant
variation and noise in the original data, X. Eq(1) shows
that the important variation stored in the estimation
k
ˆ = t pT can be used to determine the
matrix, X
∑i i
i =1
residual, E, as follows:
ˆ
E=X−X
(3)
PCA transformation produces loading vectors, pi,
which describe the coefficient of the linear relationships
between the process variables, and score vectors, ti,
which represent the variation in these variables. The
PCA model is built by determining k reduced set of PCs
that describe significant process variation.
The loading vectors, pi, are the eigenvectors of the
correlation matrix, Sxx, defined as follows:
S xx p i = λi p i
(4)
where λi is the eigenvalue associated with the
eigenvector pi of the correlation matrix, which
measures the amount of variance captured by the
{ ti , pi } pairs, which are arranged in descending order of
λi . This means that the first k pairs capture the largest
amount of variation subsequently they contain the
largest amount of information from the original data.
This transformation enhances the ability of PCA to
extract information from the original data by eliminating
redundant information. The reduced set of variables is
then used for modelling and analysis.
2.2. Monitoring Statistics
Two monitoring statistics are generated as a mean to
evaluate the performance of the PCA model. The first
monitoring statistic is the Hotelling’s T2 or T2 statistic
(in short). T2 statistic is simply the sum of normalised
squared scores divided by their variance, uses to
measure significant variation of the process. Prior to
determining the T2, the reduced set of PC score, t, is
obtained by projecting the new observed data xnew onto
the plane defined by the PCA loadings P. This process is
summarised as follows:
t = x new P
(5)
k
T 2 = t T Λ −1t = ∑
i =1
t i2
(6)
λi
Λ −1 is a diagonal matrix of the inverse of the k largest
eigenvalues λi of correlation matrix Sxx and ti is the ith
score.
The statistical thresholds for T2 are calculated using
the F-distribution written as follows:
k (m − 1)
Tα =
Fα (k , m − k )
(m − k )
2
(7)
The second monitoring statistic is known as the Q
statistic. It gives the measurement uncertainty between
the PCA model and the observed data to determine how
well the newly observed data conforms to the model.
The mismatch between measured and estimated model
results in the residual, e. The Q statistic is simply the
sum squared of the residual e. This process is
summarised as follows:
e = x − tP T = x[I n − PP T ]
(8)
n
Q = e T e = ∑ e 2j
(9)
j =1
where ej is the jth residual.
The statistical thresholds for the Q statistic (Jackson and
Mudholkar, 1979) are calculated using the following
equation:
1
⎛ h0 cα 2θ 2 θ h (h − 1) ⎞ h0
Qα = θ1 ⎜
+ 2 0 20
+ 1⎟
⎜
⎟
θ
θ
1
1
⎝
⎠
(10)
where:
and
n
∑ λi ,
i = k +1
θ2 =
n
∑ λi2 ,
i = k +1
3. CAM PROFILE SWITCHING
The description of CPS system and the design of
experiment for this case study are now discussed.
3.1. System Description
Tα2 is the threshold value with α , the significance level
of confidence, typically sets into 95% or 99%, m is the
number of samples used to build the PCA model, k is the
number of PCs retained and Fα (k , m − k ) is the upper
100 α % critical point of the F-distribution with k and
(m - k) degrees of freedom.
θ1 =
The information collected from the above observations
can then be used for condition monitoring and diagnosis
purposes. This approach produced a reduced set that
often contains more robust information of the process
than the original data. Details information about PCA
can be found in (Kourti and MacGregor, 1995;
MacGregor, 2005)
θ3 =
n
∑ λ3i ,
i = k +1
h0 = 1 −
2θ1θ 3
3θ 22
cα is the normal deviate corresponding to the
(1 − α ) percentile.
To support the interpretation of the monitoring statistics,
the corresponding contribution plot for the T2 and Q
2
statistics, can be generated from TCP
= tΛ −1 P T for T2
and using Eq.(8) for Q statistics.
Volumetric efficiency (Stone, 1999) of an engine is
measure of how an engine can draw in and expel air,
basically how well the engine breathes. The more air
that can be draw into the combustion chamber the more
fuel that can be injected to maintain a desired Air Fuel
Ratio. This then results in a higher torque output from
the engine. There are a number of different approaches
to improving the volumetric efficiency one that has been
used recently by engine manufacturers is to make use of
Variable Valve Timing (VVT) to alter the phasing and
timing of the inlet and /or exhaust cams of the engine.
Cam Profile Switching or CPS allows for different valve
lifts and cam profiles to optimise the engine's volumetric
efficiency over a range of the engines operating
envelope. Typically at low engine speeds the best setting
for the valves is achieved by having a low lift and short
cam durations for high engine speed high valve lifts is
required for longer cam durations.
3.2. Design of Experiment
There are a number of different failure modes that the
OBD system will have to detect for a CPS system. In
this paper the focus has been limited to the situation
where all of the valves are in the wrong lift position for
their commanded position. Instead of the valves being
set to their Low lift position for low engine speed
operation they are locked in their High lift position.
The tests points chosen are based upon standard set of
test points which are known to cover the steady-state
conditions of the emission drive cycles for both the US
and European regulator bodies. Table 1 lists these test
conditions.
To generate each of the different test conditions the
following approach was used. Brake Mean Effect
Pressure (BMEP), which is a measure average force
applied to the crank wheel, was adjusted via an Engine
Dynamometer with the engine speed being controlled by
the throttle. The controller on the engine test bed is run
in Speed/Load mode to maintain a specific operating
condition
Compensation provides information as to how well the
EMS is controlling the Air Fuel Ratio to 14.6.
Table 1 Design of experiment
Table 3 Variance captured by PCA
Operating Condition
Test
1
2
3
4
5
6
7
8
9
10
11
Engine Speed (rpm)
2000
2000
1000
1000
1500
1500
1500
1500
2500
2000
2500
BMEP (bar)
2.0
5.0
2.0
4.0
1.0
2.62
5.0
7.5
4.0
7.5
7.5
The data was collected under two different sets of
conditions the first being a nominal (fault-free) set of
data and the second which had the fault deliberately
introduced to the CPS system. The normal set of data
was logged during steady-state operation and the failure
data was collected just at the point when the CPS failure
occurred. For the PCA model 1000 points for each test
condition were taken from both sets. The summary of
the engine variables logged is given in Table 2.
Table 2 Engine variables of the CPS system
Variable Number
1
2
3
4
5
6
7
8
9
PC
Engine Variable
Engine speed (rpm)
Intake Air Flow (g/s)
Manifold Pressure (kPA)
Engine Load (g/s)
AFR Feedback
Compensation 1
AFR Feedback
Compensation 2
Oxygen Sensor 1
Oxygen Sensor 2
Throttle Opening (%)
1
2
3
4
5
6
7
8
9
Eigenvalu
e
4.4264
2.0637
1.2239
0.7254
0.3917
0.0833
0.0715
0.0131
0.0010
Variance
Captured
49.18
22.93
13.59
8.06
4.35
0.93
0.79
0.15
0.01
Total Variance
Captured
49.18
72.11
85.71
93.77
98.12
99.05
99.84
99.99
100
4. PROCESS MONITORING & ANALYSIS
The CMD model for the CPS system was built using the
nominal (fault-free) data from all 11 sets of data. This
data was transformed using PCA, Table 3 shows the
amount of variance captured by each of the 9 Principal
Components. The first 4 principal components (PCs)
capture a total of 93.77% of the original data, a CPS
model was developed based upon this reduced set. This
means that the original 9 variables can be represented by
a mapped set of 4 independent variables for the CMD
purposes.
Once the number of PCs has been identified, the next
step was to generate two monitoring statistics, Q and T2,
using Eq.(6) and (9) respectively. Each monitoring
statistic was developed with their 99% and 95%
confidence limits for Eq.(7) and (10). The resulting
model was validated on a different set of data with the Q
and T2 monitoring statistics falling below the 95% limit.
This gives confidence that the model can then be taken
forward and used to detect failure conditions.
Fig. 1 illustrates the models performance against a set of
failure data specifically using the Q statistic. This
violation can be seen over most of the operating points
1000-2000 and 8000-9000 which represented data Set 2
and Set 9 has failed to be identified at these points as
12
10
Q Statistic
Engine Speed and Engine Load are measures of the test
conditions which have been used to define the test
condition. Note that Engine Load in this case is an
inferred measurement of load calculated internally
calculated within the Engine Management System
(EMS). Air Flow is a measure of the mass airflow
through the throttle and Manifold Pressure is generated
as a function of the difference in mass airflows coming
into and exiting the manifold. Oxygen Sensor measures
the Air Fuel Ratio in the Exhaust. Air Fuel Ratio
8
6
4
2
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Sample Number
Fig. 1. Q monitoring statistic for faulty data with 99% and
95% confidence limits.
11000
they lay well below the confidence limits. This situation
can be explained as follows. It may well be that the
operating condition of (2000 rpm, 5 bar) and (2500 rpm,
4 bar) conformed to the CPS model but they may
contain high variation which violate normal operating
condition. To assist the interpretation of this situation
and also to complement the monitoring process, a T2
monitoring statistic was then used, as shown in Fig. 2.
situation, as shown in Fig. 3. The two ellipse confidence
limits are generated with 95% and 99% confidence
limits respectively. The second type detects the
abnormality using a joint monitoring of the Q and T2
statistics, as shown in Fig. 4. Here A3 represents normal
condition. A1 is the worst condition where the fault is
detected by both Q and T2 statistics. A2 and A4 are the
conditions where the fault is apparently dominant only
1100
1000
900
2
T Statistic
800
700
600
500
400
300
200
100
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
Fig. 4. A joint bivariate scatter plot of the Q and T2
monitoring statistics with 99% confidence limits.
Sample Number
2
Fig. 2. T monitoring statistic for faulty data with 99% and
95% confidence limits.
It is clearly shown that the validation set strongly
violates the T2 confidence limits, even for the points
1000-2000 and 8000-9000 missed in the Q metric.
When this situation was monitored, they failed to stay
below the T2 statistical limits due to the dominant fault
signatures in the process. It is important to note that Q
and T2 monitoring statistics are used to complement each
other in performing the detection process of any
abnormality.
10
PC2 (22.930%)
5
towards Q or T2 statistic respectively.
Once fault has been successfully detected the next step
is to determine which component of the systems (i.e.
process variables or measurement signals) is effected
most by the fault signatures. This will allow a closer
look on how those process variables behave under fault
condition, in comparison to normal operating condition.
Contribution plots for both Q and T2 statistics can be
used for this purpose.
Initially a random selection contribution plots were
investigated to determine if there was a consistent
pattern across all of the data. This was found to be the
case so attention was focussed on the section of data
7200 to 7400 (with the fault condition occurring at
approximately 7250). Fig. 5 and Fig. 6 depict the
representation of these contribution plots for Q and T2.
0
-5
-10
-15
-6
-4
-2
0
2
4
6
PC1 (49.182%)
Fig. 3. Bivariate scatter plot of the first-two PC scores with
two ellipse confidence limits (99% and 95%).
Another type of detection process can be performed
using bivariate scatter plots. Two types of scatter plots
are utilised here. The first type uses the first-two
principal component (PC) scores to detect abnormal
In Fig 6 it can be clearly seen that both Oxygen Sensor
signals (7 and 8) are the most dominant variables in the
T2 metric, with Oxygen Sensor 1 (7) reducing to 50% of
the effect of Oxygen Sensor 2 at iteration 7400. Looking
at Fig 5 the Air Fuel Compensation 1 (5) is also a
significant which suggests that after the initial loss of
control that Oxygen Sensor 1 is being slowly brought
under control. Air Fuel Compensation 2 has yet to react
to insertion of a failure of the CPS system this might be
down to calibration or sensor dynamics effects. In Fig 5
Engine Speed (1), Manifold Pressure (3) and to a lesser
extent Engine Load (4) have been effected by the
failure. This is unsurprising since there has been a
significant change in Volumetric Efficiency, and the
torque output, of the engine. Further investigation is
required to determine which of these variables are still
significant once the steady-state has been reached on the
engine test bed.
Contribution to Q Statistic
1.5
1
0.5
0
-0.5
-1
This research is funded by the Advantage West
Midlands through the Premium Automotive Research &
Development programme based at the International
Automotive Research Centre (www.iarc.warwick.ac.uk),
Warwick Manufacturing Group, University of Warwick,
Coventry, U.K. The assistance and support of Francis
McKinney and Peter Earp of Jaguar and Land Rover is
gratefully acknowledged.
-1.5
-2
REFERENCES
7200
7250
7300
Time Instance
7350
7400
8 9
6 7
4 5
3
1 2
Number of Variable
Fig. 5. Contribution to Q statistic for faulty data. Engine
Speed (1), Manifold Pressure (3) and AFR Feedback
Compensation 1 (5) shows dominant contribution.
Contribution to T Statistic
5. CONCLUSION
2
ACKNOWLEDGEMENT
0
-2
-4
-6
-8
-10
-12
-14
-16
7200
7250
7300
Time Instance
7350
7400
5
3 4
1 2
8 9
6 7
Number of Variable
2
Fig. 6. Contribution to T statistic for faulty data. Oxygen
Sensor 1 (7) and Oxygen Sensor 2 (8) are the most dominant
variables.
The application of condition monitoring and diagnosis
of cam profile switching of an automotive gasoline
engine has been presented. Using data-driven
monitoring technique, principal component model, a
total failure in both banks can be accurately detected and
diagnosed.
Further work is required to investigate other failure
modes of the cam profile switching system to see if a
complete On-Board Diagnostic can be developed using
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