An inverse problem in nondestructive evaluation of spot-welds

Abstract

In this work, we investigate the problem of determining a heat source at the bottom of a plate from thermal measurements obtained at the top. This problem arises in a novel nondestructive evaluation technique for assessing the quality of a spot-weld. We devise a simple algorithm that takes thermal images and produces estimates of the heat source. The computational approach, which uses Tikhonov regularization, is shown to be convergent. Numerical examples illustrate the behavior of the inversion algorithm.

Level-set, penalization and cartesian meshes: A paradigm for inverse problems and optimal design

“…The penalized equation (7) allows to efficiently find an approximate solution to (2) in L 2 norm [3]. Nevertheless, the gradient of the solution on the boundary has no reason to be consistent in L 2 norm because of the mesh-depending obstacle.…”

“…Going back to the optimization problem, we discuss in this subsection a preliminary approach to solve our model inverse problem (1) and (2). The resolution relies first on the definition of an adjoint problem to the direct one (2), and then on the computation of the shape derivative in order to find an appropriate velocity for the displacement of the boundary of the obstacle.…”

“…The resolution relies first on the definition of an adjoint problem to the direct one (2), and then on the computation of the shape derivative in order to find an appropriate velocity for the displacement of the boundary of the obstacle.…”

“…Inverse geometry problems arise in many different areas of research, from tomographic imaging in medical or environmental fields [1] to non-destructive control of materials [2], to name just a few. Also, as both European and international regulations on greenhouse gases emissions are growing stricter and as fuel prices are rising, the automotive and aeronautical industries, besides improvements on motors and masses of their engines, are required to look for aerodynamic ways to reduce oil consumption, particularly through an accurate shape design leading to drag reduction.…”

Quality control automated laser-ultrasonic method for solder joints of nozzles of chambers in liquid rocket engines

“…Решению проблемы НК качества паяных соединений изделий и, в частности, камер ЖРД, посвя-щен ряд работ как отечественных [1,2], так и зарубежных ученых [3,4]. Анализ научно-технической ли-тературы [5][6][7] показал, что перспективным методом НК качества паяных соединений сопел камер ЖРД является лазерно-ультразвуковой метод, который позволяет не только определить наличие дефектов, но и измерить их геометрические характеристики [8].…”