The radial basis function interpolation is an effective method for approximation on scattered data. However, this interpolation method suffers from the contradiction between the accuracy and the numerical stability. With considering the distribution of the interpolation points, a bounded random shape variation scheme for the radial basis function is developed to circumvent the problem of numerical stability. In this scheme, the shape variation is bounded by the value that is determined by the maximum distance and the minimal distance which are applied to describe the average density of the interpolation centers. Within this bound, the shape of the MQ is modified through a random scheme. With applying this bounded randomly variable shape scheme, the accuracy and the stability of the MQ interpolation are balanced. Comparisons on the accuracy and the condition number of the interpolation matrix between the constant shaped MQ interpolation and this bounded randomly variable shaped MQ interpolation have been made to verify the conclusion. Furthermore, this scheme is integrated in the dual reciprocity boundary element method in the analysis of three dimensional elastic problems. Results of the numerical examples demonstrated that the developed scheme improved the accuracy of the dual reciprocity boundary element method stably.

径向基函数插值是一种对散乱数据进行逼近的有效方法。然而，这种插值方法存在精度和数值稳定性之间的矛盾。考虑到插值点的分布，提出了径向基函数的有界随机形状变化方案，以规避数值稳定性问题。在该方案中，形状变化以最大距离和最小距离确定的值为界，用于描述插值中心的平均密度。在此范围内，MQ 的形状通过随机方案进行修改。通过应用这种有界随机变量形状方案，MQ 插值的准确性和稳定性得到平衡。对常形MQ插值和有界随机变量MQ插值的插值矩阵的精度和条件数进行了比较，验证了结论。此外，该方案被集成到双互易边界元方法中，用于三维弹性问题的分析。数值算例的结果表明，所开发的方案稳定地提高了双互易边界元法的精度。