US 6,983,220 B1
Method for estimating compliance at points along a beam from bending measurements
Friend K. Bechtel, Mead, Wash. (US); Chin Shung Hsu, deceased, late of Pullman, Wash. (US), by Ning Wang, legal representative; and Timothy Charles Hanshaw, Pullman, Wash. (US)
Assigned to Kierstat Systems LLC, Mead, Wash. (US)
Filed on Dec. 14, 2002, as Appl. No. 10/318,711.
Int. Cl. G06F 17/18 (2006.01)
U.S. Cl. 702—179 20 Claims
OG exemplary drawing
 
4. A computer-implemented method of obtaining a local compliance estimate at a point of estimation on an elongated beam, from a sequence of “m” measured compliance values at “m” measurement points spaced along the beam, each measured compliance value being obtained by applying a bending span to a length segment of the beam, the length segment including the point of estimation and having unknown local compliance values along its length, the length segment and measured compliance value being identified with a corresponding measurement point on the beam; thereby defining a sequence of corresponding “m” measured compliance values, “m” measurement points, “m” bending spans and “m” length segments; the method comprising the following steps:
representing each measured compliance value minus an estimated mean value common to the measured compliance sequence as being the output from a state-space representation of a dynamic system, the state-space representation comprising a vector state equation and a scalar output equation, the state equation containing a state matrix, a state vector, and an input vector with at least one component being a white random noise source, the state equation describing how the state vector with component state variables changes from one measurement point to the next, the local compliance values from the corresponding length segment minus the common estimated mean value being represented by the state variables, the output equation having an output matrix specific to a corresponding bending span and having a measurement white random noise source independent of input vector noise, the output equation specifying for each measurement point the dynamic system output as a linear combination of the state variables plus measurement noise;
using a priori information to initialize a Kalman filter by initializing estimates of the state vector, input vector covariance matrix, measurement noise variance, and state vector covariance matrix;
applying the Kalman filter recursively to the sequence of “m” measured compliance values minus the common estimated mean value;
computing from the Kalman filter a sequence of “m” state vector estimates, one corresponding to each member of the measured compliance value sequence; and
obtaining the local compliance estimate at the point of estimation as the common estimated mean value plus a selected component from a selected state vector estimate in the sequence of “m” state vector estimates.