Affiliations: Shock, Noise, and Vibration Group, Northrop Grumman
Shipbuilding, Pascagoula, MS, USA | Department of Mechanical Engineering, Mississippi
State University, Mississippi State, MS, USA
Abstract: Design of mechanical systems often necessitates the use of dynamic
simulations to calculate the displacements (and their derivatives) of the
bodies in a system as a function of time in response to dynamic inputs. These
types of simulations are especially prevalent in the shock and vibration
community where simulations associated with models having complex inputs are
routine. If the forcing functions as well as the parameters used in these
simulations are subject to uncertainties, then these uncertainties will
propagate through the models resulting in uncertainties in the outputs of
interest. The uncertainty analysis procedure for these kinds of time-varying
problems can be challenging, and in many instances, explicit data reduction
equations (DRE's), i.e., analytical formulas, are not available because the
outputs of interest are obtained from complex simulation software, e.g. FEA
programs. Moreover, uncertainty propagation in systems modeled using nonlinear
differential equations can prove to be difficult to analyze. However, if (1)
the uncertainties propagate through the models in a linear manner, obeying the
principle of superposition, then the complexity of the problem can be
significantly simplified. If in addition, (2) the uncertainty in the model
parameters do not change during the simulation and the manner in which the
outputs of interest respond to small perturbations in the external input forces
is not dependent on when the perturbations are applied, then the number of
calculations required can be greatly reduced. Conditions (1) and (2)
characterize a Linear Time Invariant (LTI) uncertainty model. This paper seeks
to explain one possible approach to obtain the uncertainty results based on
these assumptions.
Keywords: Uncertainty, sensitivity analysis, model simulation, transient uncertainty
