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 (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


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:


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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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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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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

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

time [sec]

Vol

t

lean -> rich

180 190 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

time [sec]

Vol

t

rich -> lean

NEW TWC165.4 165.6 165.8 166

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

time [sec]

lean -> rich

Vol

t

141.5 142 142.5 143

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

time [sec]

rich -> leanV

olt

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AGED TWC


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


0

2

4

6

8

10

12

14

18,7 19 68 168 860 900 1250

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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0

200

400

600

800

1000

1200

1400

0,07 0,09 0,12 0,18 0,23 0,32 0,5

HC emission [g/km]

OSC

[mg]

0,480,4

new

5K km80K km

1270°C 16h 1300°C 32h1300°C 64h aged


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European Drive Cycle (ECE)

0 200 400 600 800 1000 12000

10

20

30

40

50

60

70

80

Vehi

cle

spee

d (m

ph)

Time (sec)

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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ky

ky

TWC Model

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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


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

450 460 470 480 490 5000.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Time [sec]

AF

R [\

]

520 540 560 580 600 6200.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Time [sec]

AF

R [\

]

640 645 650 655 660 665 670 675 6800.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

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

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Time [sec]

AF

R [\

]

Validation range

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A Post-Catalyst λλλλλλλλ-sensor Model

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The simple model of the nonlinear λλλλλλλλ-sensor is based on its static characteristic:

This curve was identified

0.8 0.9 1 1.1 1.2 1.30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

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

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time [sec]

sens

or s

igna

l [V

olt]

Validation range

310 315 320 325 330 3350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time [sec]

sens

or s

igna

l [V

olt]

510 515 520 525 530 5350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time [sec]

sens

or s

igna

l [V

olt]

740 745 750 755 760 7650

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Time [sec]

sens

or s

igna

l [V

olt]

Validation range

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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

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2out

12

2

TP1

11

1

1

xy

xs

Kx

ssx

=+

=

+=

τ

λτ

τ

Cumulative Sum Algorithm

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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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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


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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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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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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#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


#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)


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)


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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#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


#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


#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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2 4 6 8 10 120

10

20

30

40

50

60

70

80

90

100

threshold

Pro

babi

lity

of F

alse

Ala

rm [%

]

2 4 6 8 10 120

10

20

30

40

50

60

70

80

90

100

threshold

Pro

babi

lity

of C

orre

ct D

etec

tion

[%]

The optimal value for the threshold is 7

0 20 40 60 80 1000

10

20

30

40

50

60

70

80

90

100

Probability of False Alarm [%]

Pro

babi

lity

of C

orre

ct D

etec

tion

[%]

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


200 300 400 500 600 700 8000

1

2

3

4

5

6

7

8

9Indice catalizzatore

tempo [s]

200 300 400 500 600 700 8000

0.2

0.4

0.6

0.8

1

1.2

1.4Indice catalizzatore

tempo [s]

200 300 400 500 600 700 8000

0.005

0.01

0.015

0.02

0.025

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 · on a simplified phenomenological model of...

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