On Board Diagnosis for Three-Way Catalytic Converters · on a simplified phenomenological model of...
Transcript of On Board Diagnosis for Three-Way Catalytic Converters · on a simplified phenomenological model of...
On Board Diagnosis for Three-Way Catalytic Converters
Ing. Stefania Santini
Università di Napoli Federico IIDipartimento di Informatica e Sistemistica
GRACE Group for Research on Automotive Control Engineering
Università del SannioFacoltà di Ingegneria
On Board Diagnosis
On Board Diagnosis for Three-Way Catalytic Converters
On Board Diagnosis (OBD)is an integral part of the
emission control system and alerts the driver of failures in
the vehicle equipment via a warning light
λλλλλλλλ--SENSORSENSOR
THREETHREE--WAY CATALYTIC CONVERTER (TWC)WAY CATALYTIC CONVERTER (TWC)
MISFIREMISFIRE
FUEL SYSTEMFUEL SYSTEM
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NCOH2
22
O
IntakePort
FuelInjector
Fuel
Air
ExhaustPort
HCCONOx
OBD for Catalyst Deterioration
! The monitoring strategy is based on a simplified phenomenological model of the TWC and the oxygen sensor
! Pre- and post-catalyst sensorsmeasure the oxygen content in the exhaust gas
! This indirectly gives an indicationof the catalyst conversion efficiency
GRACEOn Board Diagnosis for Three-Way Catalytic Converters
A/F
Con
vers
ion
Effic
ienc
y (%
)
13 13.5 14 14.5 15 15.50102030405060708090100
HC
NOx
CO
Stoichiometry
4 22 2 3 2CeO Ce O O →← +
= CeO2
= Ce2O3
= O2
Oxygen Storage
On Board Diagnosis for Three-Way Catalytic Converters
Monitoring the Oxygen Storage Mechanism
"if an excess of O2 participates in the the combustion it will be chemically stored (up to a certain capacity);"if a deficit of O2 exists, then the catalyst will give up oxygen (as long as some is available) to allow reactions to happen
! During its life, the TWC loses this beneficial peculiarity, whichcan thus be considered as an indirect index of the aging processand the consequent deterioration of the component
! The oxygen-storage is a key mechanism that enhances the catalyst activity helping catalyzed oxidation-reduction reactions:
On Board Diagnosis for Three-Way Catalytic Converters
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Monitoring the Oxygen Storage Capacity
Some experimental results investigate the relationship between:
#oxygen storage capacity (OSC)#aging process#pollution production (THC)
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On Board Diagnosis for Three-Way Catalytic Converters
Experimental set-up
! Measurements of the OSC for different catalysts were performed by ELASIS using:
a target test vehicle, FIAT Nuova Punto 16v 35 g/ft3 Pd/Rd 5:1 400 cpsi TWCpre- and post-converter oxygensensors
! Experiments were conducted always in the same vehicle conditionsin order to compare the results for different TWCs
! The on-board computer monitors many engine variables such as mass air flow, engine speed, manifold pressure
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On Board Diagnosis for Three-Way Catalytic Converters
Estimating the OSC
OSC of a converter has been indirectly estimated measuring theoxygen level at the inlet and the outlet of the TWC while
crossing from rich to lean conditions (oxygen chemiadsorption) and vice versa (oxygen release)
165 170 175
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NEW TWC165.4 165.6 165.8 166
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Vol
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time [sec]
rich -> leanV
olt
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AGED TWC
On Board Diagnosis for Three-Way Catalytic Converters
Time delay between pre- and post-converter λλλλλλλλ-sensors signals vs. OSC
The different levels of deterioration for TWCs are achieved by running the vehicle on the test bench for a fixed amount of
kilometers, or warming the catalyst in a furnace, thus inducting thermal deactivation.GRACE
On Board Diagnosis for Three-Way Catalytic Converters
0
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OSC [mg]
Tim
e de
lay
[sec
]
new
5K km80K km
1270°C 16h
1300°C 32h1300°C 64haged
OSC vs. THC emissions on ECE cycle
The measure of the OSC has been related to the corresponding amount of THC for catalysts with different degrees of aging
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On Board Diagnosis for Three-Way Catalytic Converters
0
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HC emission [g/km]
OSC
[mg]
0,480,4
new
5K km80K km
1270°C 16h 1300°C 32h1300°C 64h aged
On Board Diagnosis for Three-Way Catalytic Converters
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European Drive Cycle (ECE)
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cle
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ph)
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Model-Based Diagnosis Strategy
Model of the borderline catalyst
Model of TWC + Model of λλλλ sensor
DecisionProcedure
Uses deviations
from prediction
Fault
Supervisor
Inputs
Plant
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On Board Diagnosis for Three-Way Catalytic Converters
ky
ky
TWC Model
GRACE
On Board Diagnosis for Three-Way Catalytic Converters
λTP
n
fm!
λFG
O2 storage
λFG AFR in the feedgasλTP AFR at the tailpipen engine speed
fuel mass flow rate fm!
Models of a warmed-up TWC are usually based on the hypothesis that:
# the catalyst dynamics are dominated by the oxygen storage phenomenon
# the other phenomena occur on a much shorter time scale
This allows description of the catalyst activity only in terms of the oxygen buffer dynamics using thepre- and post-catalyst AFR (Air Fuel Ratio) and a transport delay
( )
( )
<⋅
−⋅⋅⋅
≥⋅
−⋅⋅⋅
=1 )(123.0
1 )(123.0
FGRFGf
FGLFGf
fmC
S
fmC
S
λθλ
λθλθ
!
!!
A Simplified TWC Dynamical Model
Nonlinear dynamicmodel describing the
TWC activity in terms of the oxygen buffer dynamics and
a transport delay
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fraction of oxygen stored in the TWC
AFR of the gas modified by oxygen dynamics
On Board Diagnosis for Three-Way Catalytic Converters
AFR at the tailpipe
( )( )
( ) ( )
( ))()(
,1
,1
1 )(11 )(1
ntt
ff
fltTP
FGfltFG
fltfltFG
flt
FGRFGFG
FGLFGFGFG
cor
cor
∆λλ
λλλτ
λλλτ
λ
λθλαλλθλαλ
λ
−=
+−=
<⋅−−≥⋅−−
=
!
percentage of oxygen stored/released
])1(1[)(f
)1()(f8
R
8L
θ−−=θ
θ−=θ
TWC Model against Experimental Data
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AF
R [\
]
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AF
R [\
]
640 645 650 655 660 665 670 675 6800.8
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Time [sec]
AF
R [\
]
Blu (dash) line: UEGO tailpipe sensor measurements
Red (dash-dot) line: AFR model output
The model has been identified through a least-square algorithm using data from an ECE drive cycle
Validation range Identification range Validation range
760 780 800 820 840 8600.8
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Time [sec]
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R [\
]
Validation range
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On Board Diagnosis for Three-Way Catalytic Converters
A Post-Catalyst λλλλλλλλ-sensor Model
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On Board Diagnosis for Three-Way Catalytic Converters
The simple model of the nonlinear λλλλλλλλ-sensor is based on its static characteristic:
This curve was identified
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1
λTP [\]
sens
or s
igna
l [V
olt]
sensor delay
)]([)( lpost tftV ∆λ −=
The λλλλλλλλ-sensor Model against Experimental Data
Blu (dash) line: sensor measurements
Red (dash-dot) line: model output
The model has been identified through a least-square algorithm using data from an ECE drive cycle
Identification range Validation range
890 895 900 905 910 915 9200
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igna
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olt]
Validation range
310 315 320 325 330 3350
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olt]
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or s
igna
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olt]
740 745 750 755 760 7650
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or s
igna
l [V
olt]
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GRACE
On Board Diagnosis for Three-Way Catalytic Converters
The Monitoring Algorithm
#The decision procedure is based on the deviations of the measured signal from the predicted model output
#The diagnostic algorithm works on the amplitude of the oscillations of both the actual and the simulated signals
#It implements a stochastic analysis in order to provide a statistical confidence in the TWC's condition
GRACE
On Board Diagnosis for Three-Way Catalytic Converters
2out
12
2
TP1
11
1
1
xy
xs
Kx
ssx
=+
=
+=
τ
λτ
τ
Cumulative Sum Algorithm
GRACE
On Board Diagnosis for Three-Way Catalytic Converters
The on-line decision procedure is based on a CUSUM which uses observations from the plant and the output of the model
The decision rule is designed to test, on the sequence of the plant observations (independent random variables), the following two hypotheses:
when the plant is “good”
when the plant is “bad”
1 1
0 0
value thearound is mean theif value thearound is mean theifµµ
HH
{ }ky
It is computed on-line as the average of the corresponding sequence of the model observations where the model mimics the borderline catalyst behaviour
{ }ky
CUSUM: Decision Test
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On Board Diagnosis for Three-Way Catalytic Converters
DECISION TEST:
#if the decision gives a result , the sampling and the test keep on going
#fault is declared for the first observation sample that gives andecision
0H
1H
0µ
1µ
Let
CUSUM: Decision
GRACEOn Board Diagnosis for Three-Way Catalytic Converters
log-likehood ratio for the observations from y1 to yk
Sufficient statistic
•Newman Pearson Lemma, see for example:
Basseville, M., I. V. Nikiforov, Detection of Abrupt Changes: Theory and Applications, Prentice Hall Inc., Englewood Cliff, NY, 1993;
Srinath, M. D., P. K. Rajasekaran, and R. Viswamathan, Introduction to Statistical Signal Processing with Applications, Prentice Hall Inc., Englewood Cliff, NJ, 1996.
Threshold to be selected
∑=
=k
iik sS
1 )()(
ln0
1
i
ii yp
yps
µ
µ=
The decision is given by*:
≥<
hSHhSH
kk
k
if hypothesis if hypothesis
step at the1
0
CUSUM: Gaussian Distribution
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On Board Diagnosis for Three-Way Catalytic Converters
When monitoring the malfunction by the comparing the Sk level with a fixed threshold, one must wait a long time for the failure to be detected !
grows when the plant is “bad” and decreases when it is “good”
For a gaussian distribution with variance and probability density
the Cusum index is:
2σ22
21)( σ
µ
µ πσ
−−=
y
eyp
)(1
202 ∑=
−−=k
i
dik ydS µ
σ
Modified CUSUM
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On Board Diagnosis for Three-Way Catalytic Converters
To have reasonable alarm settings, we use as decision index:
The detection rule compares the CUSUM Sk to amoving threshold mk+h modified on-line
wherehmSg kkk ≥−= jk Smkj1
min≤≤
=
CUSUM Optimality
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On Board Diagnosis for Three-Way Catalytic Converters
#Extended theoretical studies have investigated the optimality of CUSUM algorithms in terms of detectability and false alarms rates
#It is known that the CUSUM algorithm is optimal when it is tuned with the true values of the parameters before and after the change
#The loss of optimality is a consequence of the lack of a priori information about µ0 and µ1
#In our case, this is avoided by the knowledge of the model (which provides the µ1 value) and the plant behaviour (which shows a mean value µ0 approximately equal to zero when the TWC is working properly)
The χ2 Test
GRACEOn Board Diagnosis for Three-Way Catalytic Converters
#The sufficient statistic can be easily computed and used in practical applications under the hypothesis that data are governed by a Gaussian distribution
#An on-line χ2 test of the Gaussian nature of the sequence of plant observations {yk} is developed
#The test selects windows of Gaussian distributed data and only on these windows the CUSUM decision procedure is applied
#The test helps to determine the degree of statistical confidence in approximating a generic observed distribution with a Gaussian distribution
Constructing the χ02 Index (1)
GRACEOn Board Diagnosis for Three-Way Catalytic Converters
Given N observations yi (N is the width of the window), let us construct aparticular Gaussian bell:
∑=
=N
iiy
NY
1
1 ∑= −
−=N
i
iY N
Yy
1
2
1)(σ
22)(
21)( Y
Yy
YY eyp σ
πσ
−−=
Constructing the χ02 Index (2)
GRACEOn Board Diagnosis for Three-Way Catalytic Converters
We define:
Ek=Npk ; the expected number of observations belonging to the k-th interval if the distribution were actually Gaussian
Ok; the number of observations actually belonging to the k-th interval
The χ02 can be constructed as:
M intervals
For χ02< M the approximation
is acceptable, while it is unacceptable for χ0
2>> M
∑=
−=M
k k
kkE
EO
1
220
)(χ
Reduced χ02 and Degrees of Freedom
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On Board Diagnosis for Three-Way Catalytic Converters
#It is now possible to introduce a specific distribution defined in terms of degreesof freedom:
#Degrees of freedom: ψν −= M# of constraints among the samples yi
In our case mean, variance and
∑=
=M
kkON
1
νχχ
202
0~ =#The reduced is:2
0~χ
νχσχ 2][ ][ 222 == vE
Running the χ2 Test
GRACEOn Board Diagnosis for Three-Way Catalytic Converters
#If this probability is high, it is possible to be confident when supposing the data to be governed by a Gaussian distribution
#Conversely, if the probability is low, there is a significantdisagreement with the Gaussian hypothesis
#The test computes the probability of finding a value greater than or equal to the actually obtained
2~χ20
~χ
)~~( 20
2 χχ ≥p
The Threshold Choice
GRACEOn Board Diagnosis for Three-Way Catalytic Converters
#A statistical analysis has been performed in order to find the threshold value h, optimal both for the minimization of false alarm occurrence and for the maximization of correct fault detection occurrence
#The probabilities of false alarm and correct fault detection have been computed through extensive simulations
# Simulations were run 200 times for each threshold value, inserting white noise at the output of the plant
#The variance of the noise have been changed at each run
Choosing the Threshold
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On Board Diagnosis for Three-Way Catalytic Converters
2 4 6 8 10 120
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threshold
Pro
babi
lity
of F
alse
Ala
rm [%
]
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threshold
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babi
lity
of C
orre
ct D
etec
tion
[%]
The optimal value for the threshold is 7
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Probability of False Alarm [%]
Pro
babi
lity
of C
orre
ct D
etec
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thr=1thr=2
thr=3,4,5thr=6
thr=7
thr=8thr=9,10,11,12,13
Diagnosis Strategy comparedto Experimental Data (along EUDC)
gk index evolution. “Bad” TWC
GRACEOn Board Diagnosis for Three-Way Catalytic Converters
200 300 400 500 600 700 8000
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9Indice catalizzatore
tempo [s]
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tempo [s]
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0.03Indice catalizzatore
tempo [s]
gk index evolution. The TWC was aged for 16 h in a furnace
gk index evolution. The TWC was aged for 64 h in a furnace #The real-time diagnosis is performed only under particular conditions for the engine and the after-treatment system
#The algorithm runs once for each trip (single trip strategy) and it is active along a finite time horizon (diagnosis range)
#During the test duration no special excitation of the air/fuel is needed, i.e. the algorithm is not `intrusive‘
References
! Fiengo, G., L. Glielmo, S. Santini, and A. Caraceni, `A Fault Diagnosis Algorithm for Three-Way Catalytic Converters,’ Proceeding of 5th
International Symposium on Advanced Vehicle Control, Ann Arbor, Michigan, August 22-24, 2000, pp. 14—21
! Fiengo. G., L. Glielmo, and S. Santini, `On Board Diagnosis for Three-Way Catalytic Converters’, to appear on International Journal ofNonlinear Robust Control
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On Board Diagnosis for Three-Way Catalytic Converters