Online energy-based error indicator for the assessment of numerical and experimental errors in a hybrid simulation

Hybrid simulation is an effective structural test technique combining the numerical simulation of substructures with predictable behavior, and experimental testing of complex components that are difficult to model. Consequently, hybrid simulation is prone to both numerical and experimental errors. In this paper, the dominant sources of numerical and experimental errors that can contaminate the results of a hybrid simulation are examined. It is shown that linearized analytical stability and accuracy limits for algorithms and test procedures used in a hybrid simulation may fail to adequately predict the results due to errors and nonlinearities of actual tests. An alternative approach based on monitoring the energy balance of the structural system is proposed to capture the effects of both experimental and numerical errors. This method extends an existing experimental error indicator to also account for (a) errors resulting from modification of experimental measurements by iterative corrections in numerical integrators or other signal correction procedures, and (b) numerical errors in the integration algorithm including equilibrium errors and kinematic relations between displacement, velocity and acceleration. The effectiveness of the proposed energy error indicator in predicting severity of errors is demonstrated through numerical and experimental simulations using various integration procedures.