# Optimal Estimation of Grain Orientation in an Anisotropic Weld by Ultrasonic Techniques

[Doktorsavhandling]

Grain orientation in an anisotropic weld highly influences ultrasound paths and thus is a significant parameter when making simulations of ultrasonic testing of anisotropic welds. Though each weld is thought to be unique in its structure, the common procedure in modeling is to prescribe the grain orientation in a weld based on limited experience. An effort of estimating the grain orientation in an anisotropic weld is described in this thesis. The whole task mainly consists of two sub-problems, the forward modeling and the inversion with an optimization scheme. By forward modeling, an ultrasonic non-destructive testing process is simulated, which is based on the weld model with prescribed grain orientation. Experimental data then are employed in inversion with an aim at minimizing the difference between the simulated results and the experimental data. In the inversion, the grain orientation is taken as variables. The forward model presented in this thesis is composed of a weld model, a 2D ray tracing algorithm, a transmitter model and a receiver model. The weld model is established by analyzing the macrograph of an anisotropic weld. In order to describe ultrasound paths through the weld model, a 2D kinematic ray tracing algorithm is adopted. In addition, a transmitter model is developed with a truncated traction distribution along the upper boundary of a half-space. In modeling the receiver, the electromechanical reciprocity principle is utilized. The inversion calculation is realized with optimization techniques. Two different optimization methods are at first used to perform nonlinear inversion on a stratified structure as a simpler test case. Both a gradient-based algorithm and a genetic algorithm are utilized and evaluated. Finally a multi-objective genetic algorithm is adopted to fulfill the inversion of grain orientations in the weld model. As an essential part of the inversion, ultrasonic experiments with P and SV waves are performed. Calculations with synthetic data and experimental data are executed. The results achieved demonstrate that it is still a challenge to determine grain orientations in an anisotropic weld with inversion. A successful estimation demands more research work in the future.

**Nyckelord: **anisotropic weld model, 2D ray tracing, ultrasonic probe model, nonlinear optimization, multi-objective genetic algorithm

Denna post skapades 2007-11-13. Senast ändrad 2013-09-25.

CPL Pubid: 61725