A Two-Level Parameterized Model-Order Reduction Approach for Time-Domain Elastodynamics

Model-Order-Reduction Approach for Structural Health Monitoring of Large Deployed Structures with Localized Operational Excitations

“…Hence, it is informed by the library of archetype components and reference ports, and is independent of any subsequent (feasible) system assembly. For every reference port, a reduced port space is built in order to approximate the solution on the reference port joining each compatible pair of archetype components [45,40].…”

“…As detailed in the development of the two-level PR-RBC method [40], the frequency-domain equation will be used in order to build the PR-RBC reduced spaces. Since f (t; µ) → u(t; µ) is a linear time invariant system, we can simply consider the frequency-domain representation of the load to be independent of the frequency ω when forming the PR-RBC reduced spaces in the offline stage.…”

“…is below a certain threshold or if i = min(n ω , M), where M is a prefixed maximum size allowed for X RB [40].…”

“…The dimensionality of the parameter domain which describes any sufficiently rich set of possible systems -note that the parametrization characterizes material properties, geometry, boundary conditions, and also topology -precludes application of the classical pMOR approaches due to the well-known curse of dimensionality. Within the context of time-domain elastodynamics of large geometric domains with localized excitations, the recently developed two-level PR-RBC method [40] is of great interest. The latter takes advantage of domain decomposition techniques [41,42,43,44,45] and the frequency-time duality [46,47] to construct the reduced bases.…”

“…For such example, the parameters are all chosen based on literature review of actual deployed bridges. In order to overcome the previously listed challenges associated with such task, we extend the two-level PR-RBC method [40] to account for moving loads. Moreover, using the two-point correlation functions, we build time-domain-based features which are not only sensitive to the damage -already guaranteed by the definition of the correlation function -but also relatively insensitive to nuisance parameters and measurement noise.…”