Development of Corrosion Monitoring System using Inverse Analysis

开发了基于反分析的海滨结构腐蚀监测系统。提出了一种新的反分析方法。为了缓解该反问题的不适定性，提出将腐蚀识别问题转化为0-1整数问题，将腐蚀识别问题视为缺陷和正常表面的两个离散表面电阻值。将阻力系数作为概率变量处理，放宽了对离散值的严格约束。通过对一个简单算例的求解，验证了该方法的有效性，并提出了一种新的边界元分析方法，该方法利用多极展开快速求解目标区域内的问题。数值模拟验证了本技术的能力。在这种方法中，多极展开被应用到非目标边界上的边界积分方程，并在保证高项误差界的项处截断展开。该方法通过引入多极矩作为未知量代替非目标区域的未知量，减少了计算量。为了证明该方法的有效性，进行了一些例子分析。当需要求解目标区域的解时，特别是在大尺寸的边值问题中，这种方法可以快速、精确地得到目标区域的解，静磁分析在结构的腐蚀检测和无损检测中具有重要意义。本文提出了一种新的边界积分法，它不需要对服从拉普拉斯方程的静电场域中的电流密度分布进行计算和积分。

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.