Estimation of surface condition from the theory of dynamic thermal stresses

The present study applies a hybrid numerical algorithm of the Laplace transform technique and the finite-difference method with a sequential-in-time concept and the least-squares scheme to predict the unknown surface condition from the theory of dynamic thermal stresses. The unknown surface condition is not given a priori and is assumed to be the function of time before performing the inverse calculation. The whole time domain is divided into several analysis sub-time intervals and then the unknown surface condition on each analysis interval can be estimated from the transient displacement measurements or the transient temperature measurements. In order to show the efficiency and accuracy of the present inverse scheme, the comparison between the present estimates, the exact solution and the previous estimated results is demonstrated. The results show that a good estimation on the unknown surface condition can be obtained only at one selected location even for the case with the measurement error. The effect of the measurement location and the measurement error will also be investigated.