Dynamic Load Identification for Stochastic Structures Using Linear Manifold Learning

This paper proposes an integrated linear manifold learning-based framework for efficient identification of dynamic loads acting on stochastic structures. The methodology addresses the critical computational bottleneck in uncertainty quantification for stochastic inverse problems by exploiting the intrinsic low-dimensional geometric structure inherent in stochastic load response spaces. The framework systematically integrates: (1) optimal Latin hypercube sampling for efficient exploration of stochastic parameter spaces; (2) regularized identification using the Green's function method with truncated singular value decomposition to generate accurate training data; (3) principal component analysis to extract low-dimensional load manifolds; (4) radial basis function interpolation to construct rapid surrogate mappings from parameters to manifold coordinates; and (5) Markov Chain Monte Carlo sampling for comprehensive uncertainty propagation. This unified approach enables complete probabilistic load characterization including probability density functions and confidence bounds, while bypassing the need for repeated computationally intensive inverse solutions. Two numerical examples, a 25-bar planar truss and a passenger car hood structure, demonstrate the method's accuracy and computational efficiency. Results demonstrate that the proposed approach achieves accuracy comparable to direct regularization methods while reducing computational time for large-scale uncertainty propagation. The method provides comprehensive probabilistic load descriptions essential for reliability-based design and assessment in practical engineering applications.