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本文使用直接配点无网格法结合共轭梯度法对管道内壁面侵蚀状况进行了反演识别。直接配点无网格法使用节点离散求解区域,采用移动最小二乘近似构造试函数,直接配点法构造线性方程组进行导热正问题求解;反演过程采用共轭梯度法使目标函数最小化,Akima三次样条插值将连续的几何边界反演问题转化为离散点几何位置的反演,并最终将这些离散点拟合成为光滑曲线。文中选择两个典型算例对数值方法进行验证,模拟结果表明使用直接配点无网格法结合共轭梯度法进行管道内壁几何边界识别具有较高精度。
In this paper, direct matching point meshless method and conjugate gradient method were used to identify the erosion of the inner wall of the pipeline. In the direct meshing method, the discrete solver region is used. The moving least squares approximation is used to construct the trial function, and the direct matching point method is used to construct the linear equations to solve the positive heat conduction problem. Conjugate gradient method is adopted to minimize the objective function in the inversion process. Akima Cubic spline interpolation transforms the continuous geometric boundary inversion problem into an inversion of the geometric position of the discrete points, and eventually fits these discrete points into a smooth curve. In this paper, two typical examples are selected to verify the numerical method. The simulation results show that the method of direct matching point meshless method and conjugate gradient method are used to identify geometric boundary of pipeline inner wall with high accuracy.