Development of Corrosion Monitoring System using Inverse Analysis

开发了基于逆分析的海滨结构腐蚀监测系统。得到了以下结果：介绍了一种新的逆分析方法。为了缓和该反问题的病态性，我们提出将腐蚀识别问题简化为0-1整数问题，将缺陷表面和法向表面看作两个离散的表面电阻值。通过将阻力系数作为概率变量，缓解了对离散值的严格约束。通过算例验证了该方法的有效性。本文提出了一种利用多极展开法快速求得目标区域解的潜在问题边界元分析新方法。数值模拟验证了该方法的有效性。该方法将多极展开应用于非目标边界上的边界积分方程，并在保证高项误差界的项上截断展开。该方法通过引入多极矩代替非目标区域的未知量，减少了计算量。为了验证该方法的有效性，进行了算例分析。当只需要目标区域内的解时，特别是在大尺寸边值问题中，这种方法使我们能够快速准确地得到它们。静磁分析对结构的腐蚀检测和无损检测具有重要意义。提出了一种新的分析静磁场的边界积分方法，无需计算和积分静电场域中服从拉普拉斯方程的电流密度分布。

The Corrosion Monitoring system for seaside structure using inverse analysis was developed. The following results was obtained.A new inverse analysis method were introduced. To relax the ill-posed of this inverse problem, we proposed the corrosion identification problem is reduced to 0-1 integer problem by considering as two discrete surface resistance values of defect and normal surface. And severe constraint on discrete value is relaxed by treating resistance coefficient as probability variable. Simple example problem was solved to demonstrate the usefulness of this method.A new technique for boundary element analysis of potential problems using a multipole expansion to obtain the solution quickly only in a target region has been developed. The capability of the present technique was verified by numerical simulations. In this technique, the multipole expansion is applied to boundary integral equations on non-target boundaries, and the expansion is truncated at the term where the error bound of the higher terms is guaranteed. This technique decreases the calculation amount by introducing multipole moments as the unknown in place of the unknown in the non-target region. To demonstrate the effectiveness of the method, some example analyses were performed. When the solutions only in the target region are needed, especially in large size boundary value problems, this technique enables us to obtain them quickly and precisely.The magnetostatic analysis is important on the corrosion detection problems and the nondestructive inspection of the structures. A new boundary integral method for analyzing magnetostatic field without the calculation and the integration of current density distribution in the electrostatic field domain which obeys Laplace equation is developed.