Estimating Local Compliance in a Beam From Bending Measurements Part II. Optimal Estimation of Local Compliance


  • Friend K. Bechtel
  • Chin S. Hsu
  • Timothy C. Hanshaw


Local E, compliance, bending, Kalman, estimation, optimum, ARMA, state-space


We present a method for optimally estimating local elasticity properties along a beam where each estimate is specific to an increment in a subdivision of the beam's length. Previous research indicates that knowledge of localized elasticity values can improve the estimation of strength. Immediate application is expected in the machine stress-rated (MSR) lumber production process. A sequence of bending measurements on overlapping bending spans, as commonly obtained in the MSR process, serves as input to the estimation method.

The sequence of bending measurements is modeled as an autoregressive moving average (ARMA) random process. Autoregression coefficients are estimated from a priori information and refined as additional data are obtained. Moving average weight coefficients come from span functions computed by methods in Part I. A Kalman filter, defined from coefficients of the ARMA process, is applied to the measurements, and local estimates are obtained.

Estimated local elasticity results are presented for both a simulated and a real wood beam. One set of experiments shows that as a modeled correlation coefficient is decreased from an artificially high value, the result evolves from local elasticity estimates that appear much the same as measured elasticity, but without an obvious noise component, to local estimates having more detail. This leads naturally to a suggestion for a practical, non-disruptive introduction of the estimation method to a MSR production line. Grade yield improvement is likely an immediate benefit along with a capability for further research into the estimation method and grading algorithms.


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