Uncertainty reduction in residual stress measurements by an optimised inverse solution using nonconsecutive polynomials

Abstract

Many destructive methods for measuring residual stresses such as the slittingmethod require an inverse analysis to solve the problem. The accuracy of theresult as well as an uncertainty component (the model uncertainty) dependson the basis functions used in the inverse solution. The use of a series expan-sion as the basis functions for the inverse solution was analysed in a previouswork for the particular case where functions orders grew consecutively. Thepresent work presents a new estimation of the model uncertainty and a newimproved methodology to select the final basis functions for the case wherethe basis is composed of polynomials. Including nonconsecutive polynomialorders in the basis generates a larger space of possible solutions to be evaluatedand allows the possibility to include higher-order polynomials. The paperincludes a comparison with two other inverse analyses methodologies appliedto synthetically generated data. With the new methodology, the final error isreduced and the uncertainty estimation improved.