Uncertainty Analysis of a Multi-Sensor Fusion Measurement Chain for Blade Collision Warning in Coaxial Twin-Rotor Helicopters

A coaxial twin-rotor helicopter features a compact structure by eliminating the tail rotor. Although offering advantages in lift capability and maneuverability, the design presents challenges from its mechanical complexity and the aerodynamic interference between the counter-rotating rotors. During blade intersection, the collision risk of the blades depends not only on the blade-tip distance, but also on the intersection phase and the blade-tip position. In our study, we defined a blade collision warning parameter, d, to represent a fused safety clearance in coaxial twin-rotor helicopters, and proposed a correlated uncertainty propagation model for the measurement chain. The proposed model incorporates uncertainty sources from radar ranging, phase determination, geometric consistency, phase-synchronized triggering, sensor-point substitution, and model discrepancy through covariance terms. Experimental validation is performed on a single-rotor blade-intersection platform under controlled conditions. With the simulated blade rotated at 420 r/min, the combined standard uncertainty ranges from 0.677 to 0.996 mm over the reference warning parameter range of 99–990 mm. The event-level residual-compatibility rate is 86.8%, with localized non-compatibility observed at several reference points. Additional tests at 300 and 600 r/min demonstrated millimeter-level stability. Our uncertainty analysis identified radar ranging as the dominant contributor, followed by model discrepancy and sensor-point substitution uncertainty.