Proceedings of IMECE 2013 The ASME 2013 International Mechanical Engineering Congress & Exposition November 15–21, 2013, San Diego, USA IMECE2013-62522 ROBUST AND DYNAMICALLY CONSISTENT REDUCED ORDER MODELS David B. Segala * Naval Undersea Warfare Center, DIVNPT 1176 Howell Street, Newport RI, 02841 Tel: 401-832-6377, Email: david.segala@navy.mil David Chelidze Department of Mechanical Engineering University of Rhode Island, Kingston, RI 02881 Tel: 401-874-2356, Email: chelidze@egr.uri.edu ABSTRACT The need for reduced order models (ROMs) has be- come considerable higher with the increasing technological advances that allows one to model complex dynamical sys- tems. When using ROMs, the following two questions al- ways arise: 1) ”What is the lowest dimensional ROM?” and 2) ”How well does the ROM capture the dynamics of the full scale system model?” This paper considers the newly devel- oped concepts the authors refer to as subspace robustness — the ROM is valid over a range of initial conditions, forc- ing functions, and system parameters—and dynamical con- sistency —the ROM embeds the nonlinear manifold–which quanitatively answers each question. An eighteen degree- of-freedom pinned-pinned beam which is supported by two nonlinear springs is forced periodically and stochastically for building ROMs. Smooth and proper orthogonal decom- positions (SOD and POD, respectively) based ROMs are dynamically consistent in four or greater dimensions. In the strictest sense POD-based ROMs are not considered coher- ent whereas, SOD-based ROMs are coherent in roughly five dimesions and greater. Is is shown that in the periodically forced case, the full scale dynamics are captured in a five- dimensional POD and SOD-based ROM. For the randomly forced case, POD and SOD-based ROMs need three dimen- sions but SOD captures the dynamics better in a lower- dimensional space. When the ROM is developed from a different set of initial conditions and forcing values, SOD outperforms POD in periodic forcing case and are equal in the random forcing case. * Address all correspondence to this author. Introduction With today’s advanced computing technologies and high performance computing centers, larger scale, more complex dynamical systems (i.e., structural dynamics and acoustics, computational oceanographic/atmospheric dy- namics, molecular dynamics and rationale drug template design) are being numerically investigated for longer time periods and across multiple temporal and spatial scales. However, with geometrical and dynamical complexities that current software packages are able to truthfully model, long time simulations and data storage requirements can of- ten become prohibitive if the system becomes excessively large. Characterizing the system for various initial condi- tions, system parameters, and/or forcing functions or in- vestigating the dynamics in a particular time scale requires multiple simulations which can be costly and time consum- ing. Therefore, the need for high fidelity reduced order models (ROMs) that provide desirable approximations to the actual long-time dynamics is paramount to investigate complex dynamical systems. However, the following two questions still remain on the topic of ROMs: 1) ”What is the lowest dimensional ROM?” and 2)”How well does the ROM capture the dynamics of the full scale system model or a perturbed version of that model?” Using the newly developed concepts of subspace ro- bustness and dynaical consistnecy the authors demostrate through a periodically and stochastically forced pinned- pinned beam with two nonlinear springs that smooth or- thogonal decompostion (SOD)-based ROMs develop both dynamically consistent and robust ROMs as compared to proper orthogonal decompostion (POD)-based ROMs. 1