de Mooij Cornelis, Martinez Marcias
Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands.
Department of Mechanical and Aerospace Engineering, Clarkson University, 8 Clarkson Av., Potsdam, NY 13699, USA.
Sensors (Basel). 2024 May 31;24(11):3562. doi: 10.3390/s24113562.
Two shape-sensing algorithms, the calibration matrix (CM) method and the inverse Finite Element Method (iFEM), were compared on their ability to accurately reconstruct displacements, strains, and loads and on their computational efficiency. CM reconstructs deformation through a linear combination of known load cases using the sensor data measured for each of these known load cases and the sensor data measured for the actual load case. iFEM reconstructs deformation by minimizing a least-squares error functional based on the difference between the measured and numerical values for displacement and/or strain. In this study, CM is covered in detail to determine the applicability and practicality of the method. The CM results for several benchmark problems from the literature were compared to the iFEM results. In addition, a representative aerospace structure consisting of a twisted and tapered blade with a NACA 6412 cross-sectional profile was evaluated using quadratic hexahedral solid elements with reduced integration. Both methods assumed linear elastic material conditions and used discrete displacement sensors, strain sensors, or a combination of both to reconstruct the full displacement and strain fields. In our study, surface-mounted and distributed sensors throughout the volume of the structure were considered. This comparative study was performed to support the growing demand for load monitoring, specifically for applications where the sensor data is obtained from discrete and irregularly distributed points on the structure. In this study, the CM method was shown to achieve greater accuracy than iFEM. Averaged over all the load cases examined, the CM algorithm achieved average displacement and strain errors of less than 0.01%, whereas the iFEM algorithm had an average displacement error of 21% and an average strain error of 99%. In addition, CM also achieved equal or better computational efficiency than iFEM after initial set-up, with similar first solution times and faster repeat solution times by a factor of approximately 100, for hundreds to thousands of sensors.
对两种形状传感算法，即校准矩阵（CM）法和逆有限元法（iFEM），在准确重建位移、应变和载荷的能力以及计算效率方面进行了比较。CM通过使用针对每个已知载荷工况测量的传感器数据以及针对实际载荷工况测量的传感器数据，对已知载荷工况进行线性组合来重建变形。iFEM通过基于位移和/或应变的测量值与数值之间的差异最小化最小二乘误差泛函来重建变形。在本研究中，详细介绍了CM以确定该方法的适用性和实用性。将文献中几个基准问题的CM结果与iFEM结果进行了比较。此外，使用具有减缩积分的二次六面体实体单元对一个具有NACA 6412横截面轮廓的扭曲和锥形叶片组成的代表性航空航天结构进行了评估。两种方法均假定为线弹性材料条件，并使用离散位移传感器、应变传感器或两者的组合来重建全位移和应变场。在我们的研究中，考虑了表面安装传感器和分布在整个结构体积内的传感器。进行这项对比研究是为了满足对载荷监测日益增长的需求，特别是对于从结构上离散且不规则分布的点获取传感器数据的应用。在本研究中，CM方法被证明比iFEM具有更高的精度。在所研究的所有载荷工况上进行平均，CM算法实现的平均位移和应变误差小于0.01%，而iFEM算法的平均位移误差为21%，平均应变误差为99%。此外，在初始设置之后，CM的计算效率也与iFEM相当或更高，对于数百到数千个传感器，首次求解时间相似，重复求解时间快约100倍。
