Method and apparatus for real-time estimation of four wheel imbalances for chassis prognosis
A system and method for determining whether a particular wheel on a vehicle is un-balanced during operation of the vehicle. The method includes providing wheel angle signals from the wheels of the vehicle and providing a vibration measurement signal from a response point on the vehicle, such as from an accelerometer on a steering column of the vehicle. The method also includes generating a regression vector using the wheel angle signals. The method also includes generating an estimated parameter vector using a recursive least squares algorithm, the regression vector and the vibration measurement signal. The method then calculates an imbalanced magnitude value of each wheel of the vehicle using the estimated parameter vector. The method uses a persistency of excitation test to determine whether the parameter vector has converged to a true value to determine whether the calculated imbalanced magnitude values are accurate.
1. A method for determining whether wheels of a vehicle are out of balance, said method comprising:
providing wheel angle signals from the wheels of the vehicle;
providing a vibration measurement signal from a response point on the vehicle;
generating a regression vector using the wheel angle signals;
generating an estimated parameter vector using a recursive least squares algorithm, the regression vector and the vibration measurement signal; and
calculating an imbalance magnitude value of each wheel of the vehicle using the estimated parameter vector.
2. The method according to claim 1 further comprising using a persistency of excitation test to determine whether the estimated parameter vector has converged to a true value to determine whether the calculated imbalance magnitude values are accurate.
3. The method according to claim 2 wherein the persistency of excitation test includes multiplying the regression vector by a test parameter vector to generate an inner product, using the regression vector, the inner product and the recursive least squares algorithm to provide an estimated test parameter vector, generating a square sum of error value using the test parameter vector and the estimated test parameter vector, and determining whether the square sum value is small enough.
4. The method according to claim 1 further comprising generating a co-variance matrix using the recursive least squares algorithm, the regression vector and the vibration measurement signal.
5. The method according to claim 1 further comprising comparing the imbalance magnitude values to a threshold to determine whether the wheels are imbalanced.
6. The method according to claim 1 wherein generating an estimated parameter vector using the recursive least squares algorithm, the regression vector and the vibration measurement signal includes using the equation:
{circumflex over (θ)} o ( k )={circumflex over (θ)} o ( k− 1)+ P ( k )φ( k ){ y o ( k )−φ T ( k ){circumflex over (θ)} o ( k− 1)}
Where {circumflex over (θ)} o (k) is the recursive least squares parameter vector, P(k) is a covariance matrix, φ(k) is the regression vector and y o is the vibration measurement.
7. The method according to claim 1 wherein determining the imbalance magnitude values includes using the equations:
| û LF |=√{square root over ( â LF 2 +{circumflex over (b)} LF 2 )}
| û RF |=√{square root over ( â RF 2 +{circumflex over (b)} RF 2 )}
| û LR |=√{square root over ( â LR 2 +{circumflex over (b)} LR 2 )}
| û RR |=√{square root over ( â RR 2 +{circumflex over (b)} RR 2 )}
Where û is the imbalance magnitude for a left front (LF), right front (RF), left rear (LR) and right rear (RR), and â and {circumflex over (b)} are measured vibration parameters.
8. The method according to claim 1 wherein the response point is on a steering column of the vehicle.
9. The method according to claim 7 wherein generating a vibration measurement includes using an accelerometer.
10. The method according to claim 1 wherein generating a vibration measurement includes using a steering wheel torque sensor.
11. The method according to claim 1 wherein providing wheel angle signals from the wheels of the vehicle includes providing wheel angle signals from automatic braking systems.
12. A method for determining whether wheels of a vehicle are out of balance, said method comprising:
providing wheel angle signals from the wheels of the vehicle;
providing a vibration measurement signal from an accelerometer on a steering column on the vehicle;
generating a regression vector using the wheel angle signals;
generating an estimated parameter vector and a co-variance matrix using a recursive least squares algorithm, the regression vector and the vibration measurement signal;
calculating an imbalance magnitude value of each wheel of the vehicle using the estimated parameter vector; and
using a persistency of excitation test to determine whether the estimated parameter vector has converged to a true value to determine whether the calculated imbalance magnitude values are accurate.
13. The method according to claim 12 wherein the persistency of excitation test includes multiplying the regression vector by a test parameter vector to generate an inner product, using the regression vector, the inner product and the recursive least squares algorithm to provide an estimated test parameter vector, generating a square sum of error value using the test parameter vector and the estimated test parameter vector, and determining whether the square sum value is small enough.
14. The method according to claim 12 wherein generating an estimated parameter vector using the recursive least squares algorithm, the regression vector and the vibration measurement signal includes using the equation:
{circumflex over (θ)} o ( k )={circumflex over (θ)} o ( k− 1)+ P ( k )φ( k ){ y o ( k )−φ T ( k ){circumflex over (θ)} o ( k− 1)}
Where {circumflex over (θ)} o (k) is the recursive least squares parameter vector, P(k) is the covariance matrix, φ(k) is the regression vector and y o is the vibration measurement.
15. The method according to claim 12 wherein determining the imbalance magnitude values includes using the equations:
| û LF |=√{square root over ( â LF 2 +{circumflex over (b)} LF 2 )}
| û RF |=√{square root over ( â RF 2 +{circumflex over (b)} RF 2 )}
| û LR |=√{square root over ( â LR 2 +{circumflex over (b)} LR 2 )}
| û RR |=√{square root over ( â RR 2 +{circumflex over (b)} RR 2 )}
Where û is the imbalance magnitude for a left front (LF), right front (RF), left rear (LR) and right rear (RR), and â and {circumflex over (b)} are measured vibration parameters.
16. A system for determining whether wheels of a vehicle are out of balance, said system comprising:
means for providing wheel angle signals from the wheels of the vehicle;
means for providing a vibration measurement signal from a response point on the vehicle;
means for generating a regression vector using the wheel angle signals;
means for generating an estimated parameter vector using a recursive least squares algorithm, the regression vector and the vibration measurement signal; and
means for calculating an imbalance magnitude value of each wheel of the vehicle using the estimated parameter vector.
17. The system according to claim 16 further comprising means for using a persistency of excitation test to determine whether the estimated parameter vector has converged to a true value to determine whether the calculated imbalance magnitude values are accurate.
18. The system according to claim 17 wherein the means for using a persistency of excitation test multiplies the regression vector by a test parameter vector to generate an inner product, uses the regression vector, the inner product and the recursive least squares algorithm to provide an estimated test parameter vector, generates a square sum of error value using the test parameter vector and the estimated test parameter vector, and determines whether the square sum value is small enough.
19. The system according to claim 16 further comprising means for generating a co-variance matrix using the recursive least squares algorithm, the regression vector and the vibration measurement signal.
20. The system according to claim 16 wherein the means for generating an estimated parameter vector using the recursive least squares algorithm, the regression vector and the vibration measurement signal includes uses the equation:
{circumflex over (θ)} o ( k )={circumflex over (θ)} o ( k− 1)+ P ( k )φ( k ){ y o ( k )−φ T ( k ){circumflex over (θ)} o ( k− 1)}
Where {circumflex over (θ)} o (k) is the recursive least squares parameter vector, P(k) is a covariance matrix, φ(k) is the regression vector and y o is the vibration measurement.