Model-Free Dynamic Response Prediction at Unmeasured Locations for Three-Dimensional Structures Based on Polynomial Shape Functions

Predicting the dynamic response at unmeasured locations is of great interest in the study of structural dynamic systems to address limitations of number of available sensors and inaccessibility of measurements in enclosed or hazardous environments. Dynamic response at measured points on a structure can be expanded to predict response for unmeasured points through model-based expansion, but this approach requires a correlated (or calibrated) finite element model. To avoid finite element model dependency and the need for correlation, model-free dynamic response prediction techniques have been proposed for plate-type structures and cylindrical-shell structures. However, a limitation of those techniques is that only the 1D (one-dimensional) dynamic response along one direction of the 2D (two-dimensional structure) could be studied using the developed shape functions. In this work, we present a model-free method that overcomes these limitations in order to predict the 3D dynamic response for unmeasured locations for complicated three-dimensional structures. This work develops a new model-free method based on three-dimensional Chebyshev polynomial shape functions for predicting the 3D dynamic response of the three-dimensional utility structures. The method is based on orthogonal Chebyshev polynomials as shape functions to decompose the physical dynamic response of the measurement points into a set of polynomial dynamic response. The expansion is performed within the polynomial space from measurement points to the measurement points plus the unmeasured point. Then, the expanded polynomial space is mapped back to physical space to obtain the physical dynamic response at the unmeasured point. The advantage of the proposed method is that only the measured dynamic response data and geometric coordinates of the measurement points are needed. Namely, in this advantage, the external excitation applied to the structures and the boundary condition of the structures are not required to be quantified or known. An accelerometer-based test and high-spatial-resolution 3D scanning laser Doppler vibrometer (SLDV) test on a wind turbine blade provide test data used to experimentally validate the application of the proposed method of predicting the three-dimensional dynamic response on the three-dimensional structures. Convergence studies are performed to evaluate the impact of the number of measurement points and the location of measurement points on the accuracy of the method.