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采用基于双倒易边界元法和共轭梯度法的反演算法求解二维非稳态导热边界识别问题。正问题采用双倒易边界元法求解,该法避免了传统边界元法需进行区域积分的缺点,仅需纯边界积分计算。反问题的解在正问题的基础上通过共轭梯度法最小化目标函数得到。考虑了管道和空腔未知边界为正弦曲线、偏心圆、椭圆等形状时的识别情况,讨论了初值、测量误差和加热热流大小等因素对反演解精度的影响。结果表明,该方法能将各种不规则边界识别出来,对初值和测量误差不敏感,加热热流增大时反演解精度有所提高。
The inversion algorithm based on double reciprocal boundary element method and conjugate gradient method is used to solve the problem of two-dimensional unsteady thermal boundary recognition. The positive problem is solved by the double reciprocal boundary element method, which avoids the disadvantage of the traditional boundary element method for integrating the regions, only the pure boundary integral calculation is needed. The solution to the inverse problem is obtained by minimizing the objective function by the conjugate gradient method on the basis of the positive problem. Considering the unknown boundary of pipe and cavity as the shape of sinusoid, eccentric circle and ellipse, the influence of initial value, measurement error and the size of heating heat flow on the accuracy of inverse solution is discussed. The results show that this method can identify all kinds of irregular boundaries and is insensitive to the initial value and the measurement error. The accuracy of the inversion solution increases when the heating heat flux increases.