Two-Step Correction and Decoupled Sequential Framework for Uncertainty-Oriented Dynamic Force Reconstruction

Dynamic force reconstruction is an approach to determine external forces acting on aircraft structures based on measurable responses, which is essential for enhancing structural safety and reliability. However, existing methods typically assume zero initialization and low noise conditions while ignoring the heterogeneous uncertainties inherent in engineering applications. This paper proposes an uncertainty-oriented dynamic force reconstruction method that integrates a two-step correction strategy and a decoupled sequential framework. First, based on the inverse Newmark method, tendency components (reconstruction errors) caused by initialization errors and measurement noises are derived and eliminated through a baseline correction (first step) followed by a feedback correction (second step). This two-step method calibrates the force reconstruction model and provides a reference for uncertainty-oriented reconstruction. Next, for uncertainty-coupled dynamic systems, heterogeneous uncertainties are quantified by nonprobabilistic models and decoupled through dimensionality reduction. To enhance computational efficiency, the uncertainty-oriented reconstruction problem is reformulated into an alternating optimization of center and radius terms within a sequential inversion framework. Eventually, its feasibility is validated through numerical and experimental examples. Results demonstrate that the two-step correction strategy achieves reconstruction accuracy exceeding 95% under different loading cases, while the decoupled sequential framework improves the efficiency of uncertainty-oriented reconstruction by an order of magnitude.