Influence surfaces for reconstructing individual point loads and positions from multi-contact measurements on a single force plate

Force plates are the gold standard for measuring ground reaction forces, but their reliance on equilibrium equations limits them to single-contact measurements. When multiple point loads act simultaneously, conventional force plates yield only the combined force and center of pressure. The individual load contributions cannot be separated. This paper applies influence surface theory to extend force plate analysis beyond equilibrium-based methods. Instead of evaluating global force and moment balances, influence surfaces characterize how loads at different positions contribute to structural responses at individual supports. This enables load identification for multiple simultaneous contacts, with the number of separable loads determined by the available sensor count. The influence surfaces are trained from measurement data using Gaussian Process Regression, capturing the real plate behaviour without requiring finite element modelling. To reduce complexity, the inverse problem is addressed sequentially. First, load positions are estimated. Second, the horizontal force components are determined. The method is validated on a 2.5 m × 1.0 m force plate using static tests with known load positions. The approach successfully reconstructs individual load positions and three-dimensional forces for two simultaneous contacts. Walking trials are included as a demonstration of the methodology under realistic conditions.