The extension curves are constructed by the geometric continuous conditions by minimizing some fairing functions based on the shortest arc-length, minimum energy and minimum curvature variationof the curves respectively.

在保持几何连续及光顺的条件下,将一条已知的三次B啨zier曲线延拓到另一条与其不相邻接的三次B啨zier曲线,其中间媒介同样是三次B啨zier曲线,可以是一条,也可以是2条,而且其形状可以由用户加以调整·同时利用几何拼接的条件构造出形状可调的延拓曲线,进而对近似于曲线弧长、曲线能量、曲率变化率的几类目标函数分别极小化,以生成各种光顺的曲线

The magnitudes of the endpoint tangent vectors are optimized in the process of Hermite interpolation so that the curvature variationof the optimized geometric Hermite curve is a minimum.

通过在Hermite插值过程中最优化端点切矢的模长,使最优几何Hermite曲线的曲率变化率最小;得到并证明了使最优几何Hermite曲线达到几何光顺的切矢角约束条件。

The method took the normalized change ratio of frequencyand the Frobenius norm of mode shape vector as the input vector of BP neural networks.

将标准化固有频率变化率和质量归一化振型向量变化量的Frobenius范数作为损伤识别神经网络输入参数,以结构中与损伤杆件相关联的节点损伤系数作为神经网络的输出参数,来判定结构损伤位置和损伤程度。