Ellipsoidal Model-Based Dynamic Load Identification for Uncertain Structures with Parameter Correlations

Accurate load identification serves as a fundamental requirement for achieving lightweight and efficient structural designs. This paper presents a dynamic load identification method for structures with parameter uncertainties, integrating the ellipsoidal model with shape functions. The approach explicitly accounts for correlations among uncertain structural parameters, leading to improved identification accuracy and more compact load bounds. The method first establishes an ellipsoidal model for the uncertain parameters, representing their feasible domain as a compact ellipsoidal set. This model is then incorporated into the dynamic load identification framework. Convex optimization theory and the Lagrangian multiplier method are employed to derive analytical expressions for the load bounds. Shape functions are utilized to describe the temporal variation of the load, reducing the ill-posedness of the inverse problem, while central finite difference approximations are applied to compute load sensitivities with respect to the uncertain parameters. The efficacy of the proposed method is validated through a numerical example involving a 21-bar truss structure, demonstrating its advantages in both identification accuracy and boundary compactness compared to conventional interval methods.