Reconstructing Full-Field Flapping Wing Dynamics from Sparse Measurements

Abstract

Flapping insect wings deform during flight. This deformation benefits the insect's aerodynamic force production as well as energetic efficiency. However, it is challenging to measure wing displacement field in flying insects. Many points must be tracked over the wing's surface to resolve its instantaneous shape. To reduce the number of points one is required to track, we propose a physics-based reconstruction method called System Equivalent Reduction Expansion Processes (SEREP) to estimate wing deformation and strain from sparse measurements. Measurement locations are determined using a Weighted Normalized Modal Displacement (NMD) method. We experimentally validate the reconstruction technique by flapping a paper wing from 5-9 Hz with 45 • and measuring strain at three locations. Two measurements are used for the reconstruction and the third for validation. Strain reconstructions had a maximal error of 30% in amplitude. We extend this methodology to a more realistic insect wing through numerical simulation. We show that wing displacement can be estimated from sparse displacement or strain measurements, and that additional sensors spatially average measurement noise to improve reconstruction accuracy. This research helps overcome some of the challenges of measuring full-field dynamics in flying insects and provides a framework for strain-based sensing in insect-inspired flapping robots.

Optimal Sensor Placement for Reliable Virtual Sensing Using Modal Expansion and Information Theory

“…Following these works, the modal expansion and filtering techniques were applied for strain/stress virtual sensing [ 3 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ] and fatigue estimation [ 16 , 17 , 18 , 19 , 20 , 21 ] for a number of structures using limited number of displacement/strain physical sensors. In particular, modal expansion techniques have been used in mechanical and aerospace systems for shape and/or strain reconstruction using sparse displacement and/or strain measurements [ 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ] or fusing acceleration and strain measurements [ 30 ]. The aforementioned studies cover a number of applications, including components of mechanical structures [ 1 , 2 ], components of civil structures such as railway bridges [ 20 ], wind turbine jacket substructures [ 11 ], truss structures [ 12 ], wind turbine towers [ 7 , 8 , 9 , 10 , 16 , 25 ], wind turbine blades [ 27 , 28 ], offshore structures [ 11 ], components of industrial structures [ 17 , 21 ], roller coaster [ 18 ], rotating [ 26 ] and underwater structures [ 13 ], as well as biologicaly inspired wing structures for robotic applications [ 29 ].…”

“…In particular, modal expansion techniques have been used in mechanical and aerospace systems for shape and/or strain reconstruction using sparse displacement and/or strain measurements [ 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ] or fusing acceleration and strain measurements [ 30 ]. The aforementioned studies cover a number of applications, including components of mechanical structures [ 1 , 2 ], components of civil structures such as railway bridges [ 20 ], wind turbine jacket substructures [ 11 ], truss structures [ 12 ], wind turbine towers [ 7 , 8 , 9 , 10 , 16 , 25 ], wind turbine blades [ 27 , 28 ], offshore structures [ 11 ], components of industrial structures [ 17 , 21 ], roller coaster [ 18 ], rotating [ 26 ] and underwater structures [ 13 ], as well as biologicaly inspired wing structures for robotic applications [ 29 ]. Recently, it is suggested to use virtual sensing in isolated linear components of linear and nonlinear models of structures [ 31 , 32 , 33 , 34 ] considering the forces at the interface between the analyzed linear component and the rest of the structure as unknown forces.…”

Wing structure and neural encoding jointly determine sensing strategies in insect flight

“…Prior studies have considered optimal strain sensing strategies in insect wings [ 23 , 43 – 46 ]. Although using different sensing tasks and optimization criteria, taken together, they show that remarkably few sensors are needed to detect or identify patterns of strain on the wing.…”