Reduced Order Modeling for Nonlinear Multi-component Models

Reduced order modeling plays an indispensible role in most real-world complex models. A hybrid application of order reduction methods, introduced previously, has been shown to effectively reduce the computational cost required to find a reduced order model with quantifiable bounds on the reduction errors, which is achieved by hybridizing the application of local variational and global sampling methods for order reduction. The method requires the evaluation of first-order derivatives of pseudo-responses with respect to input parameters and the ability to perturb input parameters within their user-specified ranges of variations. The derivatives are employed to find a subspace that captures all possible response variations resulting from all possible parameter variations with quantifiable accuracy. This paper extends the applicability of this methodology to multi-component models. This is achieved by employing a hybrid methodology to enable the transfer of sensitivity information between the various components in an efficient manner precluding the need for a global sensitivity analysis procedure, which is often envisaged to be computationally intractable. Finally, we introduce a new measure of conditioning for the subspace employed for order reduction. Although, the developments are general, they are applied here to smoothly behaving functions only. Extension to non-smooth functions will be addressed in a future article. In addition to introducing these new developments, this manuscript is intended to provide a pedagogical overview of our current developments in the area of reduced order modeling to real-world engineering models.