A Sensor Fault Diagnosis Scheme
for a DC/DC Converter
used in Hybrid Electric Vehicles
Hiba Al-SHEIKH
Ghaleb HOBLOS
Nazih MOUBAYED
2
Overview

Examined power converter system

Hardware prototype

Converter Modelling

Proposed residual-based fault diagnosis scheme

Bank of extended Kalman filters

Generalized likelihood ratio test

Tuning using receiver operating characteristic curve

Conclusion and future perspectives
3
Recent advances in power electronics encouraged the
Power converters are intensively used in HEVs
development of new initiatives for Hybrid Electric Vehicles
• convert power at different levels
(HEVs) with advanced multi-level power electronic systems.
• drive various load
• electric drives
4
Intensive use of power converters in modern hybrid vehicles
Need for efficient methods of condition monitoring and fault diagnosis
Reliability of the automotive electrical power system
5
Common Electrical Faults in Electric Drive Systems
Machine AC Side
• high power
• relatively low voltage
Sensors
Power Converters
Controller
Connectors/
DC Bus
high current
increase thermal and electric stresses
on the converter components and
monitoring sensors
6
Common Electrical Faults in Electric Drive Systems
Machine AC Side
Sensors
• AC current sensor
• DC bus voltage sensor
Power Converters
Controller
Connectors/
DC Bus
Sensor faults in a DC/DC power
converter system used in HEV
7
Fault Diagnosis Techniques for Power Converters
Knowledge-based
methods
Fault diagnosis
methods
Analytical model-based
methods
Observer-based
Signal-based methods
For HEV applications where converters operate under variable load
conditions, model-based diagnosis is of particular interest.
7
8
Examined Power Converter System
9
DC Main System
DC
Distribution
AC
Distribution
Automotive Electrical System
10
Power Converters
 DC/DC Choppers
 DC/AC Inverters
 AC/DC Rectifiers
Automotive Electrical System
11
12
13
Examined Power Converter System
Battery
UC
Energy Storage System
Multi-port DC bus
Inverter
DC/DC
Converter
AC Drive
Parallel DC-linked Multi-input DC/DC Converter
consisting of two bidirectional half-bridge cells
PM
14
Bidirectional DC/DC Converter Topologies
Isolated topologies
boost-half bridge
half-bridge
full-bridge
Non-isolated topologies
SEPIC
cuk
buck-boost
15
Examined Power Converter System
Converter Parameters
Parameter
Symbol
Value
Design Requirements
Input Capacitance
Input Capacitor ESR
Inductance
Inductor ESR
Output Capacitance
Output Capacitor ESR
Transistor ON resistance
Cin
RCin
L
RL
Co
RCo
RON
80µF
100mΩ
146µH
5mΩ
5mF
80mΩ
1mΩ
Source voltage
DC-link voltage
Rated Power
Switching frequency
Source voltage ripple
DC-link voltage ripple
Inductor current ripple
200V
300V
30kW
15kHz
2% p/p
4.5% p/p
±10%
16
Examined Power Converter System
s
(duty cycle)
State variables 𝑣𝐶𝑖𝑛 , 𝑖𝐿 , 𝑣𝐶𝑜
17
0.02
0.04
0.06
0.08
0.1
in
0
1
194
600
y =i
Cin
196
x =v
198
1
200
200
0
0.02
0.04
0.06
0.08
0.1
0
0.02
0.04
0.06
0.08
0.1
o
350
0
0.02
0.04
0.06
0.08
0.1
300
250
2
0
200
0
400
y =v
2
x =i
L
600
400
400
Co
3
150
300
200
x =v
200
100
time (sec)
Observed variables
during healthy boost operation
0
0.02
0.04
0.06
0.08
time (sec)
State variables
during healthy boost operation
0.1
18
Hardware Prototype of Converter System
19
Hardware Prototype
Experimental test bench
Hardware prototype of
bidirectional DC/DC converter
20
Hardware Prototype
Measurement of sensor 1 (measuring load voltage 𝒗𝒐 )
Measurement of sensor 2 (measuring source current 𝒊𝒊𝒏 )
21
Hardware Prototype
Sensor 2
Sensor 1
22
Modelling of Power Converter
23
Converter State-Space Model

The examined converter is a nonlinear and time-varying system
Battery
UC
Multi-input DC bus
Inverter
DC/DC
Converter
Boost operation
PM
24
Converter State-Space Model

The examined converter is a nonlinear and time-varying system
Battery
UC
Multi-input DC bus
Inverter
DC/DC
Converter
Buck operation
PM
25
Converter State-Space Model

The examined converter is a nonlinear and time-varying system

The converter state-space model is obtained in three steps:
1.
2.
3.
Piece-wise linear state-space model
Continuous-time nonlinear state-space model
Discrete-time nonlinear state-space model
26
Converter State-Space Model
1.
During each switching configuration, the converter is linear and
possesses a piece-wise switched linear state-space model
Boost mode
Buck mode
Switching configuration 1 (T1 ON; D2 OFF)
Switching configuration 1 (T2 ON; D1 OFF)
Switching configuration 2 (T1 OFF; D2 ON)
Switching configuration 2 (T2 OFF; D1 ON)
27
Converter State-Space Model
1.
During each switching configuration, the converter is linear and
possesses a piece-wise switched linear state-space model
𝐣
𝐣
𝐣
𝐣
𝒙 = 𝐀 𝐢 𝒙 + 𝐁𝐢 𝒖
𝒚 = 𝐂𝐢 𝒙 + 𝐃𝐢 𝒖
Operation
Mode
j=1
(Boost)
j=2
(Buck)
Switching
State
i=1
T1
D1
T2
D2
ON
OFF
OFF
OFF
i=2
i=1
i=2
OFF
OFF
OFF
OFF
OFF
ON
OFF
ON
OFF
ON
OFF
OFF
28
Converter State-Space Model
2.
Averaged continuous-time model
𝐣
𝐣
𝐣
𝐣
Operation
Mode
j=1
(Boost)
Switching
State
i=1
T1
D1
T2
D2
ON
OFF
OFF
OFF
i=2
i=1
i=2
OFF
OFF
OFF
OFF
OFF
ON
OFF
ON
OFF
ON
OFF
OFF
𝒙 = 𝐀𝐚𝐯 𝒙 𝒙 + 𝐁𝐚𝐯 𝒙 𝒖
where
𝒚 = 𝐂𝐚𝐯 𝒙 𝒙 + 𝐃𝐚𝐯 𝒙 𝒖
j=2
(Buck)
𝐣
𝐣
𝐣
𝐀𝐚𝐯 = 𝐀𝟏 𝑑 + 𝐀𝟐 1 − 𝑑
𝐣
𝐣
𝐣
𝐁𝐚𝐯 = 𝐁𝟏 𝑑 + 𝐁𝟐 1 − 𝑑
𝐣
𝐣
𝐣
𝐂𝐚𝐯 = 𝐂𝟏 𝑑 + 𝐂𝟐 1 − 𝑑
𝐣
𝐣
𝐣
𝐃𝐚𝐯 = 𝐃𝟏 𝑑 + 𝐃𝟐 1 − 𝑑
averaged using 𝒅 as
control variable
29
Converter State-Space Model
2.
Averaged continuous-time model
𝐣
𝐣
𝐣
𝐣
𝒙 = 𝐀𝐚𝐯 𝒙 𝒙 + 𝐁𝐚𝐯 𝒙 𝒖
𝒚 = 𝐂𝐚𝐯 𝒙 𝒙 + 𝐃𝐚𝐯 𝒙 𝒖

where
𝐣
𝐣
𝐣
𝐀𝐚𝐯 = 𝐀𝟏 𝑑 + 𝐀𝟐 1 − 𝑑
𝐣
𝐣
𝐣
𝐁𝐚𝐯 = 𝐁𝟏 𝑑 + 𝐁𝟐 1 − 𝑑
𝐣
𝐣
𝐣
𝐂𝐚𝐯 = 𝐂𝟏 𝑑 + 𝐂𝟐 1 − 𝑑
𝐣
𝐣
𝐣
𝐃𝐚𝐯 = 𝐃𝟏 𝑑 + 𝐃𝟐 1 − 𝑑
The continuous-time model is nonlinear
 The duty cycle is a function of the state variables, 𝒅 = 𝑓(𝒙)
 𝑓 is obtained from the converter dynamics during steady state
30
Converter State-Space Model
.

1


 Cin RiCin
Rin
A av x   
LRiCin


0


1
C R
 in iCin
RCin
B av x   
 LR
iCin


0


Rin
0

Cin RiCin

 RL RiCin  f x RON RiCin  1  f x RCo RiCin 
1  f x 

LRiCin
L 

1  f x 

0

Co


Rin RCin
0
1  f x RCo
L
1

Co








 1

Cav x    RiCin

 0
 1
RCin

0
D av   RiCin
RiCin

1  f xRCo 1
 0



 RCo 
0
31
Converter State-Space Model
3.
The continuous-time model is discretized using first order hold with
sampling period 𝑇 = 1𝜇 seconds.

Including process noise and measurement noise, the discrete-time statespace model becomes
𝐣
𝐣
𝒙 𝑘 + 1 = 𝐀 𝐝 𝒙 𝒙 𝑘 + 𝐁𝐝 𝒙 𝒖 𝑘 + 𝒘 𝑘
𝐣
𝐣
𝒚 𝑘 = 𝐂𝐝 𝒙 𝒙 𝑘 + 𝐃𝐝 𝒙 𝒖 𝑘 + 𝒗 𝑘

𝒘 and 𝒗 are white Gaussian, zero-mean, independent random processes
with constant auto-covariance matrices Q and R.
32
Proposed Fault Diagnosis Algorithm
33
Fault Diagnosis of Converter Sensor Faults
Sensor 2
Sensor 1
Model-Based Residual Approach
34
Fault Diagnosis of Converter Sensor Faults
Input
variables
Power Converter
System
Residual
Generation
Residuals
Residual
Evaluation
Fault/No fault
Output
variables
35
Residual Generation using
Bank of Extended Kalman Filters
36
The Extended Kalman Filter (EKF)
Converter input
signals
Converter statespace model
+
+
Sensor measured
signals
+
Estimates of the
measured signals
-
Residual signals
“Innovations”
37
The Extended Kalman Filter (EKF)

Recursive application of prediction and correction cycles

At the end of sampling period, the nonlinearity of the converter system
is approximated by a linear model around the last predicted and
corrected estimate
38
The EKF Algorithm
Initialization
𝑘 = 0, 𝐱 0|0 = 𝑬 𝐱(𝟎) and P 0|0 = P(0)
Prediction Cycle
𝐱(𝑘 + 1|𝑘) = 𝐀𝐝 x(𝑘|𝑘) x(𝑘|𝑘) + 𝐁𝐝 x(𝑘|𝑘) 𝑢(𝑘)
𝐏(𝑘 + 1|k) = 𝐀𝐣 (𝑘)𝐏(𝑘|𝑘)𝐀𝐓𝐣 (k) + 𝐐
𝐲 𝑘 + 1|𝑘 = 𝐂𝐝 x 𝑘 + 1 𝑘 𝐱(𝑘 + 1|𝑘) + 𝐃𝐝 𝑢(𝑘)
where 𝐀𝐣 (𝑘) is the jacobian matrix of 𝐀𝐝 x(𝑘|𝑘) x(𝑘|𝑘)
Correction Cycle
A new measurement is obtained 𝑦 𝑘 + 1
𝐱(𝑘 + 1|𝑘 + 1) = 𝐱(k + 1|𝑘) + 𝐊 𝑘 + 1 𝐫(𝑘 + 1)
𝐏 𝑘 + 1|𝑘 + 1 = I − 𝐊 𝑘 + 1 𝐂𝐣 𝑘 + 1 𝐏 𝑘 + 1|𝑘
where 𝐊(𝑘 + 1) = 𝐏(𝑘 + 1|𝑘)𝐂𝐣𝐓 (𝑘 + 1) 𝐂𝐣 𝑘 + 1 𝐏 k + 1 𝑘 𝐂𝐣𝐓 (k + 1) + 𝐑
𝐫 𝑘 + 1 = 𝐲 𝑘 + 1 − 𝐲 𝑘 + 1|𝑘
𝐂𝐣 (𝑘) is the jacobian matrix of 𝐂𝐝 x(𝑘|𝑘) x(𝑘|𝑘)
−1
𝒌 increments
Prediction and correction repeat with corrected estimates used to predict new estimates
39
Residuals Generated by the Bank of EKF
Observer 1
Observer 2
300
Residual r2 ey1
Residual r1 ey1
400
300
200
Instant of fault
100
200
100
0
0
0
0.01
0.02 0.03
time (s)
0.04
0.05
-100
100
50
0
-50
0
0.01
0.02
0.03
time (s)
0.04
0.05
0
0.01
0.02
0.03
time (s)
0.04
0.05
4
Residual r2 ey2
Residual r1 ey2
150
0
0.01
0.02 0.03
time (s)
0.04
0.05
2
0
-2
-4
Standardized residuals with fault on sensor 1 occurring at 0.03s
40
Residuals Generated by the Bank of EKF
Observer 1
Observer 2
2
0
-2
-4
2000
1500
1000
500
0
0
0.01
0.02 0.03
time (s)
0.04
0.05
0
2500
2500
2000
2000
Residual r2 ey2
Residual r1 ey2
2500
Residual r2 ey1
Residual r1 ey1
4
1500
1000
500
0
0.01
0.02 0.03
time (s)
0.04
0.05
0.04
0.05
1500
1000
Instant of fault
500
0
0
0.01
0.02 0.03
time (s)
0.04
0.05
0
0.01
0.02 0.03
time (s)
Standardized residuals with fault on sensor 2 occurring at 0.03s
41
Residuals Generated by the Bank of EKF
Advantage of Kalman Filtering

independent residuals

with white Gaussian, zero-mean and unit-covariance characteristics
 in case of faultless operation

with altered statistical characteristics
 in case of sensor faults
Statistical change detection approaches
42
Residual Evaluation using
Generalized Likelihood Ratio Test
43
Residuals Evaluation Approaches

Statistical data processing

Correlation

Pattern recognition

Fuzzy logic

Fixed threshold

Adaptive threshold
Likelihood ratio tests
Generalized Likelihood Ratio
(GLR) Test
Stochastic envirmonent
44
Residuals Evaluation using GLR Test
Statistical Hypothesis Testing Problem
Ho and H1


sensor is faultless
residuals are Gaussain
with 𝜇0 = 0 and 𝜎02 = 1


sensor is faulty
𝜇0 is altered into 𝜇1
and 𝜎02 into 𝜎12
45
Residuals Evaluation using GLR Test
Statistical Hypothesis Testing Problem
Ho and H1

Maximizing the likelihhod ratio


 
L e yi


 p e yi ; ˆ 1 , H 1
 ln 
 p e yi ; ˆ o , H o
𝜇1 is the Maximum Likelihood Estimate (MLE) of 𝜇1
𝜇0 is the MLE of 𝜇0


46
GLR Algorithm
At every time step t
Apply the GLR statistic on the recent W residual values
Evaluate 𝐺𝐿𝑅𝑡 (𝑘) for
all 1 ≤ 𝑘 ≤ 𝑊 using
k  x (k ) 
GLRt k    t

2  
2
Yes
Is residual
variance known?
No
Evaluate 𝐺𝐿𝑅𝑡 (𝑘) for
all 1 ≤ 𝑘 ≤ 𝑊 using
2
k   xt (k )  
 
GLRt k   ln 1  
2    t (k )  


Generate a detection function
𝑔 𝑡 = 𝑚𝑎𝑥 𝐺𝐿𝑅𝑡 (𝑘) for each residual
Decide H1
(fault)
Yes
Is 𝑔(𝑡) > 𝛾?
No
Decide H0
(No fault)
47
Detection Function Generated by GLR Test
Residual r1 ey1
Residual r2 ey2
5
300
200
instant of fault
0
100
0
0
0.01
0.02
0.03
0.04
0.05
-5
0
0.01
GLRt for r1 ey1
0.02
0.03
0.04
0.05
GLRt for r2 ey2
30
20
 unknown
20
10
10
0
 unknown
0
0.01
0.02
0.03
0.04
0.05
0
0
0.01
GLRt for r1 ey1
0.02
0.03
0.04
0.05
GLRt for r2 ey2
30
20
 known
20
10
10
0
 known
0
0.01
0.02 0.03
time (s)
0.04
0.05
0
0
0.01
0.02 0.03
time (s)
Detection function with fault on sensor 1
0.04
0.05
48
Detection Function Generated by GLR Test
Residual r1 ey1
Residual r2 ey2
5
2000
0
1000
instant of fault
0
-5
0
0.01
0.02
0.03
0.04
0.05
0
0.01
GLRt for r1 ey1
0.03
0.04
0.05
0.02 0.03 0.04
GLRt for r2 ey2
0.05
GLRt for r2 ey2
4
40
 unknown
 unknown
2
0
0.02
20
0
0.01
0.02 0.03 0.04
GLRt for r1 ey1
0.05
3
0
0
0.01
40
 known
2
 known
20
1
0
0
0.01
0.02 0.03
time (s)
0.04
0.05
0
0
0.01
0.02 0.03
time (s)
Detection function with fault on sensor 2
0.04
0.05
49
Tuning using Receiver Operating
Characteristic Curve
50
ROC Analysis
1) residualAn evaluation
tool to measure the performance of(1,the
1
based GLR test.
true positives rate (fpr)
+ optimal 𝛾
as 𝛾 increase
(0, 0)
0
false positives rate (tpr)
1
51
ROC Analysis
Three ROC Plots:
 W = 30

W = 50

W = 70

For each W, 𝛾 is varied from 0 to 𝛾𝑚𝑎𝑥

For each 𝛾, a test set of 1000 simulations is used

Healthy and faulty trials

During faulty trials, different fault amplitudes were injected

At the end of every trial, the detection function 𝑔 𝑡 is generated
using 𝐺𝐿𝑅𝑡 and compared the corresponding 𝛾

At the end of the 1000 trials, the tpr and fpr are calculated and
the corresponding point is located on the ROC curve.
52
ROCCurve
curve (Observer
1) r1ey1 r e
ROC
for1/ Residual
Residual
1 y1
ROCCurve
curve (Observer
2) r2ey2 r2ey2
ROC
for2/ Residual
Residual
1
X: 0
Y: 1
X: 0.002894
Y: 1
X: 0.0152
Y: 0.9942
0.98
X: 0
Y: 1
truepositive
positiverate
rate
true
truepositive
positiverate
rate
true
1
X: 0.01333
Y: 1
X: 0.0304
Y: 1
0.9
0.8
0.96
W=30
W=50
W=70
0.94
0
5
10
false positive rate
15
28.05
28.08
1
28.1
0.99
21.24
21.56
W=50
0.7
W=70
0.6
-0.005
20
false positive rate
W=30
0
0.005
0.01
-3
x 10
20.31
19.8
1 17.88 35.31
35.32
optimal
point for 𝜸=28.05 and 𝑾=70
optimal
point (0,1)
17.63
34.83
0.015
0.02
0.025
false
positive
false positive
rate rate
17.39
31.43
16.35
30.66
0.03
14.9
0.035
29.71
0.04
14.8
14.49
optimal
point for 𝜸=35.31 and 𝑾=70
optimal
point (0,1)
0.8
35.33
0.6
28.11
0.4
0.98
28.13
0.2
28.14
0.97
-1
0
1
2
3
4
5
6
7
-3
x 10
28.16
28.17
0
35.34
35.35
-1
0
1
2
3
4
5
6
7
-3
x 10
53
Conclusion and Future Perspectives
54
Proposed Fault Diagnosis Algorithm
Input
variables
Power Converter
System
Bank of Kalman
Filters
Output
variables
Residual
Generation
Residuals 𝒓𝟏 , 𝒓𝟐
Tuning of W
ROC curve
Tuning of 𝜸
GLR Test
Detection function 𝒈(𝒕)
Decision 𝒈(𝒕) ≷ 𝜸
Fault/No fault
Residual
Evaluation
55
Conclusion
“Combining several disciplines to achieve an
efficient comprehensive fault diagnosis scheme”
sensor faults
Battery
UC
DC/DC DC bus
Inverter
Converter
PM
56
Conclusion
+
Model-based
Residual
generation
GLR Test
+
ROC Curves
Power Converter
Process
57
« Study on power converters used in hybrid vehicles with monitoring and
diagnostics techniques »
17th IEEE MELECON’14 Mediterranean Electrotechnical Conference
« Power electronics interface configurations for hybrid energy storage in
hybrid electric vehicles »
17th IEEE MELECON’14 Mediterranean Electrotechnical Conference
« Modeling, design and fault analysis of bidirectional DC-DC converter for
hybrid electric vehicles »
23rd IEEE ISIE’14 International Symposium on Industrial Electronics
« Condition Monitoring of Bidirectional DC-DC Converter for Hybrid Electric
Vehicles »
22nd MED’14 Mediterranean Conference on Control & Automation
58
« A Sensor fault diagnosis scheme for a DC/DC converter
used in hybrid electric vehicles »
9th IFAC Symposium on Fault Detection, Supervision and Safety for
Technical Processes SAFEPROCESS'15
59
Future Perspectives
Future work will utilize the proposed model-based approach
to detect/diagnose component faults in the converter such
as



open-circuited transistor
short-circuited diode
degraded capacitor
60
Thank you