Calibration of potential drop measuring and damage extent prediction by Bayesian filtering and smoothing

A Bayesian Approach to Model Calibration and Parameter Estimation in Potential Drop Measuring

“…In the latter half both parameter estimates approach in conjunction the actual underlying parameter values, albeit, not exhibiting convergence in the sense of an asymptotic behaviour. As pointed out in [2], different reasons can account for this shortcoming which encompass the variability of the material-dependent constants of the respective dynamic model and the possible inability of the dynamic model to cover specific physical behaviour. However, by introducing the dynamic model parameters θ 1 and θ 2 as additional random variables that are updated from step to step and therefore adjustable to the true underlying parameters instead of assigning them constant values, the asymptotic behaviour of the measurement model parameter estimates is not improved.…”

“…Applying a recursive prediction and update scheme with due regard to the Markov property of states and the conditional independence of measurements and the thus ensuing implications for the choice of dynamic models [2] yields the desired effect and ensures a constant number of computations per time step. The predictive distribution of the state x k at time step k given the measurements up to time step k − 1 and the unknown parameters is given by the ChapmanKolmogorov equation as…”

“…The rationale behind this approach is the following: In [2] where the model calibration was accomplished by means of Walker's law with fixed dynamic model parameters, the contribution of an appropriately represented test-initiation phase with a suitable dynamic model to the accuracy improvement was not investigated. By modifying the Forman/Mettu equation to a degree where an almost exact compliance with the reference data is feasible depending on the material-dependent parameters, the performance of the two dynamic models can be compared.…”

“…However, the linkage between both quantities can be accomplished by a calibration curve as conceptually shown in Figure 1. A new methodology to address this problem by Bayesian filtering and smoothing has been presented in [2] and is carried on and enhanced with the present contribution.…”

“…Herein, the model calibration challenge in DCPD measuring is addressed in conjunction with parameter estimation by a Bayesian approach for fatigue-tested corner crack specimens. As opposed to [2] where solely the model calibration and state estimation is dealt with, the recursive Bayesian filtering and smoothing framework is extended to additionally infer the unknown dynamic model parameters from the cycle-dependent potential drop observations. Furthermore, two different dynamic models that depict the underlying physical process with diverging precision are utilised.…”