A designated set of shape functions are created for cylindrical shell structures. The 1D Chebyshev polynomial is applied along the axial direction and the 1D harmonic basis along the circumferential direction. A 2D orthogonal space is formed on the cylindrical domain by combining the above two 1D bases and is used to develop the expansion function. A finite element model is not required for the expansion technique, nor are the boundary conditions or external forcing functions. Using these generated shape functions, the dynamic time response at some points on cylindrical shells structure can be expanded to obtain the information at a larger number of points. Only the measurement data, geometry, and coordinates of measured points are needed. The developed polynomial expansion technique is also extended to a Data Consistency Assessment Function (DCAF), which can assess the consistency of the data set and identify the inconsistent points. The inconsistent points can also be modified by using the polynomial expansion method. A cylindrical shell structure in either air or water medium is used to experimentally demonstrate the use of the developed shape functions for polynomial expansion and data consistency assessment and modification.

为圆柱壳结构创建一组指定的形状函数。一维Chebyshev多项式沿轴向应用，一维谐波沿周向应用。通过组合上述两个一维基数，在圆柱域上形成一个二维正交空间，并用于扩展展开函数。扩展技术不需要有限元模型，边界条件或外部强迫函数也不需要。使用这些生成的形状函数，可以扩展圆柱壳结构上某些点的动态时间响应，以获得更多点的信息。仅需要测量数据，几何形状和被测点的坐标。所开发的多项式扩展技术也已扩展到数据一致性评估函数（DCAF），该函数可评估数据集的一致性并识别不一致的点。也可以使用多项式展开法来修改不一致的点。空气或水介质中的圆柱壳结构用于通过实验证明所开发的形状函数用于多项式展开以及数据一致性评估和修改。