Measurement of welding residual stresses of reactor vessel by inherent strain method. Application of robust estimation (M-estimation)

The objective of this study is to ensure the safety of nuclear reactors. A number of accidents occurred from the welded zones of the reactor vessel or the coolant pipes have been reported at sites around the world. One of the main causes is welding residual stress. It is therefore very important to know the welding residual stress in order to maintain the safety of the plants. Welded joints in nuclear reactors have complex shapes, and the welding residual stresses have complex three-dimensional distributions. In this study, the mock-up is idealized and manufactured for the welded joint at the pipe penetration part of actual reactor vessel. The inherent strain method is applied to accurately measure the welding residual stress of the joint. The inherent strain method is an analytical method which solves an inverse problem using a least squares method. The least squares method is the maximum likelihood estimation method, if the errors of data satisfy a normal distribution, and the fitting model has no approximation error. But these assumptions are hardly satisfied. The robust estimation method intends to improve the estimation accuracy, by weighting to the data, even if the data and the model are incomplete. In this study, Biweight method and adaptable Biweight method from the robust estimation methods are applied to the inherent strain method. In these methods, all measured data are used with the same weight 1 in the first analysis. The calculation is repeated, adjusting the weights based on the residuals of last calculation. The theory of the inherent strain method incorporated with such robust estimate method is developed. The welding residual stress of the above joint is analyzed by Biweight method and adaptable Biweight method. As a result, high-accurate estimation is achieved. (author)