Optimization of cathodic protection for complicated structures using fast multipole boundary element method and equivalent boundary condition

本文的研究工作主要包括三个部分：第一部分对复杂结构阴极保护问题的边界元法进行了综述。首先对锌牺牲阳极海水泵的边界元解法进行了实验验证。其中必须考虑极化曲线对流速和时间的依赖性。提出了一种基于“宏观极化曲线”概念的边界元法，并对一个由数千根不锈钢管和海军黄铜管夹板组成的锌牺牲阳极换热器进行了分析。应用边界元法对埋地长管道外加电流阴极保护中的外加电流和电极位置进行了优化。第二部分介绍了快速多极边界元法（FMBEM）在大型船舶外加电流阴极保护中的应用，并给出了计算实例 ...更多信息 腐蚀问题进行了研究。结果表明，这种方法可以成功地应用于腐蚀分析，通过采用以前的研究结果的潜在问题，与以下程序：（1）根细胞M^O_O的利用（这是在多极展开过程中得到的）对于无限区域问题，（2）对Bi-CGSTAB迭代法中的残差计算公式进行了修正，使之能科普极化曲线引起的非线性。为了提高管道的计算效率，本文还提出了一种适用于有限边界元法的管道单元。通过几个算例验证了FMBEM在腐蚀问题中的适用性。第三部分，提出了一种有效的阴极保护优化设计方法。为了科普存储量和计算量大的问题，采用了模糊边界元法。为了实现有效的优化，设计变量的初始值，即，每个电极的位置和电流通过求解逆问题来确定。在反问题中，待保护的金属表面上的电势和电流密度都被给定为理想值，即，保护电位及其相应的电流密度。利用有限边界元法有效地求解了反问题，并利用得到的初值，用辛方法求解了优化问题。最后通过算例验证了该方法的有效性和实用性。少

This research consists of three parts.In the first part, boundary element methods (BEM) to analyze the cathodic protection for complicated structures were reviewed. At first an experimental verification of BEM solusion was shown for an actual seawater pump with zinc sacrificial anodes. where the dependence of polarization curves on flow rate and time must be taken into account. Then, an effective BEM based on a concept "macroscopic polarization curve" was presented, and a heat exchanger having thousands of stainless steel tubes and naval brass tube-holder plates with zinc sacrificial anodes was analyzed using this method. Optimization of the impressed current and location of electrodes in impressed current cathodic protection was performed using the BEM for an underground long pipeline. An inverse and optimization problems in impressed current cathodic protection for a large ship were also solved.In the second part, application of the fast multipole boundary element method (FMBEM) to c … More orrosion problems was studied. It was found that this method can be successfully applied to corrosion analysis by employing the previous research results on the potential problems together with the following procedures ; (1) use of M^O_O of the root cell (which is obtained in the process of multipole expansion) for the infinite region problems, and (2) modification of the residual calculation formula in the Bi-CGSTAB iterative method to cope with the nonlinearity caused by polarization curves. A pipe element which is suitable to the FMBEM was also developed to increase the efficiency of calculation for pipelines. A few examples were shown to demonstrate the applicability of the FMBEM to corrosion problems.In the third part, an effective optimization technique for cathodic protection design was developed. To cope with the large amount of memory and calculation, FMBEM is applied. To achieve an effective optimization, the initial values of the design variables, i.e., the location and current of each electrode, are determined by solving an inverse problem. In the inverse problem both of the potential and the current density on the metal surfaces to be protected are given as the ideal values, i.e., the protection potential and its corresponding current density. The inverse problem is solved effectively by using FMBEM.Using thus obtained initial values, the optimization problem is solved by the symplex method. A couple of example problems were solved to demonstrate the effectiveness and usefulness of the present method. Less