Abstract
Realistic mathematical modeling of phenomena is an important issue in engineering. Models are commonly based on strong theoretical foundations, but validated by comparison with experimental data. On some occasions, these parameters can be measured directly from experiment; but, in other cases, methodologies are needed to infer the parameters from experimental observations. This inference should reflect the inherent uncertainty in measurements associated with the phenomena. In this work, a methodology is proposed to probabilistically characterize model parameters predicting the response of a magneto-rheological (MR) damper. The methodology is illustrated by an examination of the hyperbolic tangent (HT) damper model. This mathematical model predicts the force produced by an MR damper due to the relative displacement and velocity between the two ends of the device. Traditionally, the parameters in the HT damper model are treated as deterministic parameters and are fit to experimental data by minimizing an objective function, which measures the error between model and experiment. Here, the model parameters are treated as random variables. Bayes' inference is used to estimate the probability density function (PDF) of the parameters given a set of experimental data. Gibbs sampling, using the Metropolis Hasting algorithm, is used to determine samples of this PDF. The results of this approach are illustrated by: (1) using the probabilistic parameters to simulate the damper response and (2) comparing the simulated responses to both experimental data and the damper response predicted using a deterministic set of parameters. The strength of this modeling approach is that it has the potential to be used to explore correlations between parameters, to estimate the relative contributions of individual parameters and to help compare multiple models for the same device. While the techniques presented here are well established in the literature, their application as a tool for modeling structural control devices is novel.