基于多翼型特征的非奇异变形感知方法研究

针对传统变形感知方法在复杂翼型结构中常见的病态、奇异等问题，提出了一种基于多翼型特征的非奇异变形重构模型。依据Timoshenko梁变形理论，采用依存插值技术离散单元位移场，建立理论截面应变与测量应变的最小二乘变分函数，推导单元节点变形与测量应变的积分重构模型。该模型的位置无关性有效消除评估截面选取不当引起的奇异，增强重构模型在复杂翼型结构中的适用性。同时，针对应变传感器服役期间常见的环境扰动，以重构精度与鲁棒性为评估指标，建立自适应多目标粒子群优化模型。实验结果表明，提出的重构模型整体测量精度较高，在机翼变形量小于20 mm范围内最大绝对误差为0.26 mm,最大相对均方根误差为0.42%;当变形量增大时，绝对误差随之增大，但相对均方根误差不超过3.5%。因此基于多翼型特征的非奇异变形重构模型能够满足机翼实时重构需求，有效扩展变形感知方法在复杂结构中的应用价值。

Research on the non-singular shape sensing method based on multi-airfoil features

To solve the ill-conditioned and singular problems of complex airfoil structures in traditional deformation sensing methods, a non-singular deformation reconstruction model based on multiple airfoil features is proposed. Based on the Timoshenko beam deformation theory, the element displacement field is discretized by using the dependency interpolation technique. A least squares variational function of theoretical surface strain and measured strain is established. Then, the reconstruction model between element node deformation and measured strain is derived. The position independence of the reconstructed model effectively eliminates the singularity caused by improper selection of evaluation sections and enhances the applicability in complex structures. Meanwhile, an adaptive multiobjective particle swarm optimization model is formulated with reconstruction accuracy and robustness for overcoming environmental disturbances. Results show that the maximum absolute error is 0. 26 mm and the maximum relative root mean square error is 0. 42% when the deformation of the wing model is less than 20 mm. With the increase of deformation, the absolute error also increases. But, the relative root mean square error does not exceed 3. 5% . Therefore, the non-singular deformation reconstruction model based on multiairfoil features can meet the requirements of real-time wing reconstruction and effectively extend the application value of deformation sensing method in complex structures.