Detection and reconstruction of pitch rate sensor fault
A method of reconstructing a detected faulty signal. A pitch sensor fault is detected by a processor. A signal of the detected faulty pitch sensor is reconstructed using indirect sensor data. The reconstructed signal is output to a controller to maintain stability.
1. A method of reconstructing a detected faulty signal comprising the steps of:
detecting a pitch sensor fault in a pitch sensor, by a processor, by:
obtaining sensory data from at least one non-faulted sensor other than the pitch sensor; and
determining a virtual sensor value as a function of the sensory data from the at least one non-faulted sensor, wherein determining the virtual sensor value as a function of the sensory data from the at least one non-faulted sensor is determined utilizing a pitch dynamics of a vehicle model and is represented by the following formula:
[
θ
.
v
θ
¨
v
]
=
[
0
1
-
K
θ
(
I
y
+
m
s
H
RC
2
)
-
C
θ
(
I
y
+
m
s
H
RC
2
)
]
[
θ
v
θ
.
v
]
+
[
0
m
s
H
RC
(
I
y
+
m
s
H
RC
2
)
]
[
-
v
.
x
+
v
y
ψ
.
+
g
sin
(
θ
v
+
Θ
r
)
]
;
where θ v is a pitch angle of the sprung mass, respectively; {dot over (θ)} v is a vehicle pitch rate; H PC 2 represents a distance between a center of gravity and a pitch center; l y represents moments of inertia about a y axis of a body coordinate system; v y is a lateral velocity; {dot over (v)} x represents a rate of change in a longitudinal velocity; {dot over (ψ)} is a yaw rate; Θ r is a road grade angle; m s is a sprung mass; g is a gravitational acceleration; C θ is a pitch damping; and K θ is a stiffness coefficient for pitch;
reconstructing, by a processor, a signal of the detected faulty pitch sensor using indirect sensor data not from the faulted pitch sensor;
outputting the reconstructed signal to a controller; and
controlling a vehicle control system with the controller to mitigate a vehicle instability condition.
2. The method of claim 1 wherein detecting the pitch sensor fault by the processor comprises the steps of:
obtaining sensory data from a faulted pitch sensor, the faulted pitch sensor dedicated to monitor a pitch instability condition;
generating a residual as a function of the sensory data from the faulted pitch sensor and the virtual sensor value from the at least one non-faulted sensor;
comparing the residual to a threshold; and
detecting the sensor pitch fault in response to the residual exceeding the threshold.
3. The method of claim 2 wherein an observer used to estimate a pitch state with an unknown input is represented by the following equations:
x
^
θ
[
k
+
1
]
=
E
θ
x
^
θ
[
k
]
+
F
θ
y
θ
[
k
:
k
+
L
]
;
and
u
^
θ
[
k
]
=
[
B
θ
D
θ
]
-
1
[
x
^
θ
[
k
+
1
]
-
A
θ
x
^
θ
[
k
]
y
θ
[
k
]
-
C
θ
x
θ
k
]
where E θ and F θ are the observer gain matrices for the pitch observer, where B θ and D θ are bound gain parameters, where x θ k is an estimate pitch state, and where û θ [k] is an estimate of an unknown input.
4. The method of claim 2 wherein the threshold includes an adaptive threshold.
5. The method of claim 4 wherein the adaptive threshold is estimated based on a current driving condition and dynamic region.
6. The method of claim 5 wherein the current driving conditions and dynamic region are determined using the vehicle model and sensory data.
7. The method of claim 4 wherein the adaptive threshold for the pitch rate is determined utilizing the following equation:
T d θ =max( T θ ( k ), T θ ( k− 1) . . . , T θ ( k−W θ )),
where T θ is a respective instantaneous threshold, and where W θ is a length of the time window during the pitch sensing operation to calculate the threshold.
8. The method of claim 7 wherein the instantaneous adaptive threshold is determined utilizing the following equation:
T {dot over (θ)} =B d θ +B d θ |a x |,
where a x is the longitudinal acceleration, B d θ determines a fixed static bound for the threshold,
where the constant B d θ adds a function of the longitudinal excitations to the threshold.
9. The method of claim 2 wherein determining a virtual sensor value of the pitch rate as a function of the sensory data from the at least one non-faulted sensor is determined utilizing the following equation:
{circumflex over ({dot over (θ)})} −ij ={circumflex over ({dot over (θ)})} v−ij +R ({circumflex over (θ)} v−ij ,{circumflex over (ϕ)} v−ij ){circumflex over ({dot over (Θ)})} r−ij
where {circumflex over ({dot over (θ)})} −ij is the estimated vehicle pitch rate in the form of a virtual sensor, {circumflex over ({dot over (θ)})} v−ij is the estimated body pitch rate calculated using respective vehicle sensors not indexed by ij subscript, R is the rotation matrix describing orientation of vehicle sprung mass with respect to frame reference coordinate system, {circumflex over (θ)} v−ij is the is the estimated vehicle pitch angle, {circumflex over (ϕ)} v−ij is the is the estimated vehicle roll angle, and {circumflex over ({dot over (Θ)})} r−ij is the estimated rate of change of the road grade angle, all calculated using vehicle sensors not indexed by ij subscript.
10. The method of claim 2 wherein generating the residual as a function of the sensory data from the faulted pitch sensor and the virtual sensor value from the at least one non-faulted sensor is determined by the following equation:
R {dot over (θ)}−ij =|{dot over (θ)} s −{circumflex over ({dot over (θ)})} −ij |
wherein {circumflex over ({dot over (θ)})} −ij is the virtual sensor value and {dot over (θ)} s measured value from the pitch rate sensor.
11. The method of claim 2 wherein detecting the sensor fault in response to the residual exceeding the threshold further comprises the step of determining whether the fault persists for a period of time.
12. The method of claim 11 wherein determining whether the fault persists for the period of time further comprises the steps of:
incrementing a fault count each time the residual exceeds the adaptive threshold;
detecting the fault when the fault count exceeds a predetermined count threshold.
13. The method of claim 12 wherein the fault count is reset to zero in response to a residual not exceeding the adaptive threshold.
14. The method of claim 1 wherein reconstructing the signal of the detected faulty sensor using indirect sensor data is determined using the following equation:
{circumflex over ({dot over (θ)})}=w −ij θ −ij
where {circumflex over ({dot over (θ)})} is the reconstructed pitch rate signal, and w −ij represent weight factors.
15. The method of claim 1 wherein controlling the vehicle system with the controller to mitigate a vehicle instability condition includes controlling a vehicle braking system with the controller.
16. The method of claim 1 wherein controlling the vehicle system with the controller to mitigate a vehicle instability condition includes controlling a powertrain control system with the controller.
17. The method of claim 1 wherein controlling the vehicle system with the controller to mitigate a vehicle instability condition includes controlling a vehicle traction control system with the controller.
18. The method of claim 1 wherein controlling the vehicle system with the controller to mitigate a vehicle instability condition includes controlling a steering system with the controller.