Apparatus for estimating lateral forces of railroad vehicles
The present disclosure relates to an apparatus and a method for estimating a lateral force applied to a bogie due to contact between a wheel and a rail when a railroad vehicle drives in a curved section, the apparatus including: a lateral velocity estimation observer configured to calculate a lateral velocity estimate by estimating a lateral velocity based on a vertical acceleration, a lateral acceleration, a yaw velocity, and a wheel angular velocity of the railroad vehicle; and a lateral force estimation observer configured to calculate a lateral force estimate, by estimating a lateral force applied to a bogie of the railroad vehicle based on a steering angle of the railroad vehicle, a vertical force applied to the railroad vehicle, and a lateral velocity estimate calculated by the lateral velocity estimation observer.
1. An apparatus for estimating a lateral force of a railroad vehicle, the apparatus comprising:
a lateral velocity estimation observer configured to calculate a lateral velocity estimate by estimating a lateral velocity based on a vertical acceleration, a lateral acceleration, a yaw velocity, and a wheel angular velocity of the railroad vehicle; and
a lateral force estimation observer configured to calculate a lateral force estimate by estimating a lateral force applied to a bogie of the railroad vehicle based on a steering angle of the railroad vehicle, a vertical force applied to the railroad vehicle, and a lateral velocity estimate calculated by the lateral velocity estimation observer,
wherein the lateral velocity estimation observer includes:
a vertical velocity calculator configured to calculate a vertical velocity of the railroad vehicle by averaging a front wheel angular velocity and a rear wheel angular velocity measured by a wheel sensor; and
a lateral velocity estimator configured to calculate the lateral velocity estimate based on the vertical acceleration, the lateral acceleration, and the yaw velocity measured by a body sensor and further based on a vertical velocity calculated by the vertical velocity calculator.
2. The apparatus of claim 1 , wherein:
the lateral velocity estimation observer calculates the lateral velocity estimate using a Kalman filter; and
the lateral force estimation observer calculates the lateral force estimate using an extended Kalman filter.
3. The apparatus of claim 1 , wherein the lateral velocity estimate ({circumflex over (v)} y (k)) is calculated by the following equation:
{circumflex over (v)} y ( k )=[0 1 ]{circumflex over (x)} ( k|k ),
where {circumflex over (v)} y (k) is a lateral velocity estimate of the railroad vehicle estimated in kth step and {circumflex over (x)}(k|k) is a state variable estimate in kth step.
4. The apparatus of claim 1 , wherein the lateral force estimate ({circumflex over (F)} yƒ (k),{circumflex over (F)} yr (k)) is calculated by the following equation:
[
F
^
yf
(
k
)
F
^
yr
(
k
)
]
=
[
0
0
0
1
0
0
0
0
0
1
]
X
^
(
k
❘
k
)
,
where {circumflex over (X)}(k|k) is a state variable estimate in kth step, {circumflex over (F)} yƒ (k) is an estimate of lateral force applied to a front wheel bogie in kth step, and {circumflex over (F)} yr (k) is an estimate of lateral force applied to a rear wheel bogie in kth step.
5. A method for estimating a lateral force of a railroad vehicle, the method comprising:
calculating a vertical velocity estimate by estimating a lateral velocity based on a vertical acceleration, a lateral acceleration, a yaw velocity and a wheel angular velocity of the railroad vehicle;
and
calculating a lateral force estimate by estimating a lateral force applied to a bogie of the railroad vehicle based on a steering angle of the railroad vehicle, a vertical force applied to the railroad vehicle, and a lateral velocity estimate,
wherein the lateral velocity estimate is calculated by a lateral velocity estimation observer that includes:
a vertical velocity calculator configured to calculate a vertical velocity of the railroad vehicle by averaging a front wheel angular velocity and a rear wheel angular velocity measured by a wheel sensor; and
a lateral velocity estimator configured to calculate the lateral velocity estimate based on the vertical acceleration, the lateral acceleration, and the yaw velocity measured by a body sensor and further based on a vertical velocity calculated by the vertical velocity calculator.
6. The method of claim 5 , wherein the lateral velocity estimate is calculated by using a state variable estimated in kth step calibrated by using an estimation error with respect to an output variable between a kth state variable estimate predicted in k−1th step and a value measured in kth step, as in the following equation:
{circumflex over (v)} y ( k )=[0 1 ]{circumflex over (x)} ( k|k ),
where {circumflex over (v)} y (k) is a lateral velocity estimate of the railroad vehicle estimated in kth step; and {circumflex over (x)}(k|k) is a state variable estimate in kth step.
7. The method of claim 5 , wherein the lateral force estimate is calculated by calculating an estimate of lateral force applied to a front wheel bogie and an estimate of lateral force applied to a rear wheel bogie in kth and by applying a state variable estimate in kth step to the following equation:
[
F
^
yf
(
k
)
F
^
yr
(
k
)
]
=
[
0
0
0
1
0
0
0
0
0
1
]
X
^
(
k
❘
k
)
,
where {circumflex over (X)}(k|k) is a state variable estimate in kth step, {circumflex over (F)} yƒ (k) is an estimate of lateral force applied to a front wheel bogie in kth step, and {circumflex over (F)} yr (k) is an estimate of lateral force applied to a rear wheel bogie in kth step.