Evaluating applied force reduced-order models: validation

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Abstract
Reduced-order modelling describes a powerful set of techniques for dramatically reducing the cost of dynamic simulations in complex engineering systems, with broad application for designing and understanding nonlinearity. For Reduced-Order Models (ROMs) to be useful in an industrial context, an analyst must have a high degree of confidence that the results reported by the ROM are reflective of the full-order system. Typically, some full-order results are required to demonstrate the accuracy of a particular ROM. For large and complex systems, this will significantly undercut the initial computational motivations for creating said ROM in the first place. This work presents a novel, full-order simulation-free validation method for applied force ROMs of conservative, geometrically nonlinear systems. This is achieved by testing prospective results to see if they could exist in a series of larger ROMs. If they can, then the smaller ROM has sufficiently approximated the relevant section of the full-order invariant manifold. This allows potential reduction bases to be rapidly tested and a valid, ideally small, basis chosen. This is especially valuable in an applied force context where any low-frequency mode could be required in the reduction basis. A two degree-of-freedom ROM, describing a 100,000 degree-of-freedom finite element model of a curved double arch exhibiting internal resonance, is constructed and fully validated in under 15 min on a desktop computer. Refining the mesh such that there are 1,000,000 degrees-of-freedom increases this time to 170 min. Equivalent full-order simulation validation would take days. Furthermore, no a priori assumption is made about the nature or even the presence of the internal resonance, which is not the case for other reduced-order approaches. This is an important step towards accessible and automatable reduced-order modelling software.
Funding Information
  • University of Bristol

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