A Novel Approach for Diesel Particulate Filter
Diagnostic Using Resistive Sensor
Bilal Youssef
Electrical and Computer Department
Beirut Arab University, BAU – Beirut, Lebanon
bilal.youssef@bau.edu.lb
Abstract— Recent legislations for diesel vehicles require the
use of a soot sensor downstream the particulate filter to meet the
new challenging OBD requirements. This work proposes a novel
approach for DPF filter status assessment that can be integrated
in an embedded diagnostic strategy. The proposed approach is
based on a 2D graphical signature method used for nonlinear
systems diagnostic and estimation. The signature-based method is
used to generate relevant character from available resistive signal
provided by the soot sensor. Numerical results based on 100
simulations using dynamic driving cycles show that the proposed
signature’s character is correlated to the DPF status with high
isolation capabilities. The proposed work can be implemented on
the SCU for real-time diagnostic.
Keywords— Resisitive soot sensor; Diesel particulate filter;
graphical signature; On-board diagnostic.
I. INTRODUCTION
Nowadays, significant improvements of automotive engine
performance are needed. In this context, diesel engine emission
regulations are becoming increasingly stringent. Although
significant progress has been made over the past years, further
innovations regarding engine combustion, control strategies and
on-board diagnostics are needed in order to meet the future
requirements in terms of fuel consumption and pollutants
emission. In particular, the increasing concerns on human health
and ecological impact lead to ever-tighter regulations of
pollutants emissions from diesel engines. The reduction of soot
emissions is becoming very important as soot particles
negatively affect the air quality and can harm human lungs [1].
The use of diesel particulate filter (DPF) is becoming a standard
with regard to particulate matter (PM) emission reduction in
most of worldwide countries.
Despite significant progress in this area, via the introduction
of the particulate filter, there are still concerns about these
emissions, especially for on-board diagnostics throughout the
life of a vehicle [2, 3]. Indeed, over time the particulate filter
may not perform its function properly due to different types of
failures. DPF damage is mainly due to extreme temperature
gradients encountered during regeneration phase. It is the role of
the on- board diagnostic (OBD) module to detect faulty DPF and
generate alarm indicating the need to change the faulty filter.
Modern legislation trends, require the monitoring of very
low PM emissions to comply with the OBD threshold regarding
DPF-malfunction detection [4]. The classical diagnostic
approaches are based on the use of differential sensors that
978-1-5386-4449-2/18/$31.00 ©2018 IEEE
measure the difference of pressure over the filter. This approach
is limited and will not be able to detect small leakages according
to the new OBD-limits of upcoming legislation [2-4].
Recent technologies are based on direct measurements of
particulate matter emissions using soot sensors [4-6]. PM sensor
based on the resistive principles collects the soot in a cumulative
manner and provides sufficient accuracy and sensitivity that
allows to monitor small DPF leakage according to the new
OBD-limits. The diagnostic strategies based on the resistive
sensor uses the sensor loading-time as a DPF status indicator.
The model based methods compare the measured loading time
with a reference one predicted using DPF and sensor models
coupled with engine-out soot estimator. The model-free
diagnostic methods are based on the direct use of the measured
loading time without the need of mathematical models or soot
estimator. The soot sensor precision and the accuracy of the
estimator are the main factors that guide the selection of the
suitable method.
In this paper, the potential of a graphical signature generation
method [7, 8] to detect DPF malfunction is assessed using
numerical simulations. This method aims to provide a diagnostic
scheme that uses the observations given by available sensors in
order to detect internal malfunctions and to deduce system’s
parameters that are difficult to derive in analytical way. The
signature-based method is used to reconstruct unmeasured
quantities in dynamic systems and it is particularly suitable to
nonlinear systems with short available computation time. For
instance, it has been applied for real-time automotive
applications where the signature-based algorithm is
implemented in the engine control unit for torque and trapped
mass estimations [8, 9]. The signature-based diagnostic method
is proposed here to generate relevant feature enabling DPF
leakage detection. It is shown that the generated signature’s
feature is correlated to the DPF status and has high
discrimination capabilities comparing to the commonly used
sensor response-time. Therefore it can be used for model-based
and model-free diagnostic approaches.
The paper is organized as follows. Section II presents the
considered system’s components (DPF, soot sensor and SCU)
and gives a brief description of DPF diagnostic challenges. The
signature generation procedure is described in Section III and
the mathematical preliminaries are presented. Numerical results
based on 100 simulations using two dynamic driving cycles are
shown and discussed in Section IV. Finally, some conclusive
remarks are given in Section V.
II. SYSTEM’S COMPONENTS
This section gives a brief description about the DPF
operation, malfunction and monitoring needs. The resistive soot
sensor operating principles with useful information about OBD
and SCU are also given.
continues to decrease with soot particles accumulation, until a
minimum threshold is reached. The sensor is then heated in
order to burn the soot layer and start a new cycle. Therefore,
when the sensor is placed downstream of the DPF, its output is
a function of the soot quantity getting out of the particulate filter.
A. Particulate Filter
Diesel particulate filter fulfills the role of particles trapping
by forcing the exhaust gases to pass through a porous wall.
When the DPF is fully loaded, a regeneration procedure is
performed to eliminate accumulated particles by increasing the
temperature of the exhaust gas via delayed fuel injections. The
damage of the DPF is mainly due to extreme temperature
gradients that appear in the case of poorly-controlled
regenerations
The filtration efficiency of a damaged DPF decreases
rapidly with the presence of leakages that lead to high soot
emissions downstream the filter. When the soot emissions
exceed a predefined threshold called the OBD-limit, the filter is
considered faulty and the on board diagnostic strategy must
generate a malfunction indicator light in order to replace the
filter.
Fig. 2. Soot particles are collected on ceramic in the spaces between two interdigital electrodes.
The sensor is considered fully-loaded when its resistance
reaches a lower limit far below the initial value of the ceramic
substrate. An integrated heater allows to regenerate the sensing
element by oxidation of the captured soot. An electric current,
passing through a circuit on the rear face of the sensor, provides
high temperature for soot burning. This regeneration process
takes about a minute, after which soot collection can resume. At
iso-conditions, the loading time of a sensor varies. We
considered during the study that these variations followed a
normal law of standard deviation equal to 15%.
Fig. 1. Soot partiles are trapped by the DPF and then cleaned by oxidation
during the regeneration phase. FilterLeakages occur due to high temperature
gradients..
B. Soot Sensor
The sensor is based on a well-proven resistive technology.
The soot is collected on ceramic in the spaces between two interdigital electrodes (see Fig. 2). A DC voltage is applied on the
sensing surface where soot are accumulated from the exhaust
line. The sensing principle is based on the fact that soot particles
are electrically conductive.
During operation the soot particles from the exhaust gas
creates conductive paths that connect the electrodes. Before the
establishment of these paths, the resistance between the
electrodes is that of the ceramic. When the first path is created,
the resistance begins to decrease (percolation). This decrease
continues as soot is captured and new paths are created. The
general operating principle of a resistive soot sensor is illustrated
on Fig. 3.
The sensor accumulates particulate matter (soot) that exit
downstream the filter. The resistance starts to fall when the
conductive soot made a first bridge between the electrodes. It
Fig. 3. Resistance signal decreases with soot loading, until a minimum
threshold is reached where sensor regeneration is performed.
C. Sensor Control Unit
Upcoming legislation will require the use of a soot sensor
downstream the DPF to meet the new challenging OBD-limits.
This sensor measures the soot emissions and process the
information in the SCU (Sensor Control Unit) to provide the
ECU (Engine Control Unit) with information relative to DPF
status. At the same time, The SCU may need some variables
related to the engine operating conditions from the ECU.
The relevant diagnostic of faulty DPF with soot emissions
that exceed the OBD-limit must be performed during
certification using a succession of three NEDC cycles (New
European Driving Cycle) and also in real conditions with
minimum frequency defined by the IUPR (In Use Performance
Ratio) standard. Therefore, the design of a robust and efficient
OBD algorithm that is suitable for both certification cycle and
real driving conditions is challengeable. The OBD threshold
limit is a fixed value, but due to physical uncertainties and
tolerances, a statistical analysis has to be considered to assess
the robustness of the diagnostic strategy in terms of false alarms
and non-detections. Hence, the main challenge of the DPF
diagnostic strategy is to detect DPF malfunction while
minimizing the false alarms rate for all possible driving
conditions. The sensor with the SCU embedded strategy must
provide a fast and accurate DPF diagnostic.
A robust DPF diagnostic strategy in real life driving
conditions has to avoid the misdetection of a faulty DPF and to
consider a good DPF as faulty. Moreover the sensor must have
sufficient accuracy and sensitivity as well as a stable lifetime
operation under the harsh environment conditions in the
exhaust line (temperature, vibrations,…)
III. GRAPHICAL SIGNATURE
The signature-based method aims to provide a diagnosticestimation scheme that uses the observations given by available
sensors in order to detect internal malfunctions and to deduce
system’s parameters that are difficult to derive in analytical way.
Data projection of measurements vector over some moving
time-window into the 2D plane is performed. This projection
provides a zoom effect enabling to detect abnormal behaviours
and to extract useful features that can be used for diagnostic
purposes.
In this work, the signature-based method is used to generate a
relevant character that is correlated to the DPF status using the
resistive signal. The different steps needed for signature
generation are recalled in the sequel of this section. The
signature generation procedure consists of simple arithmetic
operations with a low computation effort (no need for iterative
calculations or optimization algorithms).
The proposed method can be used for real-time automotive
applications where fast DPF diagnostic scheme is requested. The
signature generation procedure in a moving window of length N
is illustrated on Fig. 4.
A. Data Normalization
Consider a dynamic system where the output measurements
are taken with some fixed sampling rate. The N past
measurements y(t1), . . . , y(tN) are then used to build a
measurement vector Y.
A normalization function 𝑁𝜀 is then used in order to get a
normalized vector with components that lie in [−1, 1]:
𝑁𝜀 ∶ ℝ𝑁 → ℝ𝑁
𝑌
𝑁𝜀 (𝑌) = 𝑌̅ =
∈ [−1,1]𝑁
𝜂(‖𝑌‖∞ + 𝜀 − 1) + 1
Where the coefficient 𝜂 ∈ {0, 1} and ε > 0 is a small regularizing
coefficient while ‖𝑌‖∞ is given by:
‖𝑌‖∞ =
𝑚𝑎𝑥|𝑌𝑖 |𝑁
𝑖=1
Fig. 4. Graphical illustration of signature generation in a moving window of
length N.
B. Data Projection
A projection 𝑃𝜀 ∶ ℝ𝑁 × ℝ → ℝ2 is a function that associates
to each vector (Y, y) of ℝ𝑁 × ℝ (a set of N + 1 measures) a point
in the 2D plane ℝ2 .
The following steps define the whole procedure:
 Consider a regular polygon with N nodes (𝑄𝑖 )𝑁
𝑖=1 .
𝜋
𝑄𝑖 ∶ 𝑖𝑚𝑎𝑔𝑒 (𝑒 2𝑗(𝑖−1)𝑁 ) ; 𝑗 2 = −1.
 The normalized vector 𝑌̅ = 𝑁𝜀 (𝑌) is then computed using
the normalization map.
 The 𝑖 𝑡ℎ component of 𝑌̅ (𝑌̅𝑖 ) is then used to place a point
𝜓𝑖 (𝑌̅) on the 𝑖 𝑡ℎ segment of the regular polygon as defined
below:
1
𝜓𝑖 (𝑌̅) = [(1 + 𝑌̅𝑖 )𝑄(𝑖+1|𝑁) − (𝑌̅𝑖 − 1)𝑄𝑖 ]
2
Where, (𝑖 + 1|𝑁) = (𝑖 + 1)𝑀𝑜𝑑𝑢𝑙𝑜 𝑁.
if 𝑌̅𝑖 = 0 then 𝜓𝑖 (𝑌̅) is placed in the middle of the segment
𝑄𝑖 𝑄𝑖+1 while for 𝑌̅𝑖 = −1, 𝜓𝑖 (𝑌̅) coincides with 𝑄𝑖 and so
on.
 Based on the above steps, N points (𝜓𝑖 (𝑌̅ ))𝑁
𝑖=1 are obtained
that lie on each segment of the polygon. Two points 𝛷0 (𝑌̅)
and 𝛷1 (𝑌̅ ) are then defined in the interior of the polygon
according to
𝑁
1
𝛷0 (𝑌̅) = ∑ 𝜓𝑗 (𝑌̅)
𝑁
𝑗=1
𝑁
𝛷1 (𝑌̅) =
1
∑ 𝑌̅𝑗 𝜓𝑗 (𝑌̅)
𝑁
𝑗=1
Notice that 𝛷0 (𝑌̅) and 𝛷1 (𝑌̅) are respectively the center of
mass of the 𝜓𝑖 (𝑌̅) and the weighted center of mass with
weights 𝑌̅𝑖 .
 Once the two centers 𝛷0 (𝑌̅) and 𝛷1 (𝑌̅) are obtained, a
projection 𝑃𝜀 can be defined as flollows:
𝑃𝜀 ∶ ℝ𝑁 × ℝ → ℝ2
(𝑌, 𝑦) → 𝛷0 (𝑌̅) + 𝜆𝜀 (𝑌̅ , 𝑦)[𝛷1 (𝑌̅ ) − 𝛷0 (𝑌̅) ]
With 𝜆𝜀 (𝑌̅, 𝑦) is given by
𝑁
𝜆𝜀 (𝑌̅, 𝑦) =
𝑦
1
− ∑ 𝑌̅𝑖
𝜂(‖𝑌‖∞ + 𝜀 − 1) + 1 𝑁
𝑖=1
The current output y defines the relative position of the 2D
point 𝑃𝜀 (𝑌, 𝑦) on the line ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗
𝛷0 𝛷1 .
C. Signature Generation
Let us now consider the following vector of N output
measurements taken with a fixed sample time 𝛿:
𝑌(𝑡, 𝑁) = [𝑦(𝑡 − 𝑁𝛿), … . , 𝑦(𝑡 − 𝛿)]𝑇 ∈ ℝ𝑁
Fig. 5. Vehicle speed profiles for NEDC and Artemis cycles.
Using the above projection 𝑃𝜀 applied to measurements vector
[𝑦(𝑡 − 𝑖𝛿, 𝑁)]𝑚−1+𝑁
taken in a moving window of width N, the
𝑖=0
following points can be defined:
𝑃1 (𝑡, 𝑁) = 𝑃𝜀 (𝑌(𝑡, 𝑁), 𝑦(𝑡)),
𝑃2 (𝑡, 𝑁) = 𝑃𝜀 (𝑌(𝑡 − 𝛿, 𝑁), 𝑦(𝑡 − 𝛿)),
⋮
𝑃𝑚 (𝑡, 𝑁) = 𝑃𝜀 (𝑌(𝑡 − (𝑚 − 1)𝛿, 𝑁), 𝑦(𝑡 − (𝑚 − 1)𝛿)),
𝑃𝑖 (𝑡, 𝑁)𝑚
𝑖=1 represent m 2D points that form the two-dimensional
signature 𝑆𝜀 (𝑡, 𝑁) at the current time t. Once a 2D signature is
generated, relevant characters 𝐶𝑠𝑖 can be extracted by analysing
the impact of parametric changes or system’s malfunction on the
signature’s pattern.
𝑦
𝐶𝑠𝑖 = 𝐹𝑖 (𝑆𝜀𝑥 , 𝑆𝜀 )
𝑦
𝑆𝜀𝑥 , 𝑆𝜀 constitute the vectors of x-coordinate and y-coordinate
of 𝑆𝜀 (𝑡, 𝑁) respectively.
The following section shows character’s distribution for
nominal and faulty DPF for different driving cycles.
Fig. 6. Sensor responses using two consecutive NEDC cycles for nominal and
faulty cases.
IV. NUMERICAL RESULTS
In this section, the potential of the signature based diagnostic
method to detect DPF malfunction is assessed using numerical
simulations. The simulation platform is designed using DPF and
sensor models coupled with an estimator of engine-out soot
emissions. In order to consider modeling uncertainty and
estimation error, relevant dispersions were added to the sensor
model (15%) and the soot estimator (30%). A suitable character
extracted from a signature of order N=100 is evaluated using
simulated data in the case of nominal and faulty filter. The
nominal filter is calibrated with a filtration rate that corresponds
to soot emissions of 4.5mg/km using NEDC driving cycle. The
faulty filter corresponds to soot emissions of 12mg/km on
NEDC cycle. Two different driving conditions are used
corresponding to NEDC and Artemis cycles. Fig. 5 shows the
vehicle speed profiles for both cases. The corresponding sensor
resistive signal using two consecutive cycles is shown on Fig.
6 and Fig. 7 for nominal and faulty DPF.
Fig. 7. Sensor responses using two consecutive Artemis cycles for nominal and
faulty cases.
Fig. 8 shows signatures with N=100 generated from resistive
signals for nominal and faulty filter using NEDC cycle. The
sensitivity of signature’s pattern to filter malfunction is clearly
visible. The signature has a high sensitivity along the vertical
axis. Therefore the following character 𝐶𝑠1 can be a good
𝑦
indicator for DPF status. Where 𝑆𝜀 constitutes the vector of ycoordinate of all points that form the signature.
𝑦
𝐶𝑠1 = 𝑆𝑢𝑚(|𝑆𝜀 |) ;
The sensor loading time and character 𝐶𝑠1 are shown on Fig. 9
and Fig. 10 using data collected from 100 simulations for
NEDC cycle. The resulting probability distribution functions
are given in Fig. 11. It is clear that signature’s character
provides higher isolation capabilities than the commonly used
sensor loading time. Therefore, a signature-based diagnostic
strategy provides higher performance compared to strategies
based on the sensor response-time. Fig. 12 and Fig. 13 show the
Fig. 10. Signature character based on data collected from 100 simulations for
NEDC cycle in nominal and faulty cases.
Fig. 8. Signature generated from resistive signal is sensitive to DPF
malfunction.
Fig. 11. Probability density functions using NEDC cycle: Signature’s character
provides higher discrimination capabilities w.r.t. sensor loading time.
Fig. 9. Sensor loading time based on data collected from 100 simulations for
NEDC cycle in nominal and faulty cases.
Fig. 12. Sensor loading time based on data collected from 100 simulations for
Artemis cycle in nominal and faulty cases.
response-time. Signature’s character is suitable for both modelbased and model-free diagnostic approaches. Character’s
computation is based only on the soot sensor resistive
measurements and uses low-cost computation operations.
Therefore the proposed work can be implemented in the SCU
for real-time diagnostic.
Fig. 13. Signature character based on data collected from 100 simulations for
Artemis cycle in nominal and faulty cases.
Fig. 15. Probability density functions NEDC & Artemis cycles: Signature’s
character provides higher discrimination capabilities than the commonly used
sensor loading time.
REFERENCES
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Fig. 14. Probability density functions using Artemis cycle: Signature’s
character provides higher discrimination capabilities w.r.t. sensor loading
time.
sensor loading time and selected character for nominal and
faulty filter using Artemis cycle. The probability distribution
functions in this case are shown on Fig. 14. The same
observation remains valid in this case. The discrimination
capabilities of signature character is even higher in the case of
mixed data corresponding to NEDC and Artemis driving cycles
(see Fig. 15).
V. CONCLUSION
In this paper, the potential of a graphical signature generation
method for DPF malfunction detection is assessed using
simulated data. The signature pattern has a high sensitivity to
DPF status. A relevant signature character can be easily
extracted and used as a DPF status indicator. Numerical results
based on 100 simulations using NEDC and Artemis cycles have
been presented and discussed. It is shown that the proposed
signature’s character is correlated to the DPF status with high
isolation capabilities comparing to the commonly used sensor
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