This work presents an extended Sequential Monte Carlo sampling algorithm embedded with a Variational Bayes step to approximate the Prediction PDF, and thereby, the Prior PDF for the next iteration of the Bayesian Filtering procedure. Known as the Variational Bayes - Sequential Ensemble Monte Carlo (VB-SEMC) sampler, this algorithm seeks to address the case whereby the State-evolution model does not have an inverse function. When this happens, analytical form of the Prediction PDF could not be determined as it is the composite function of the current Posterior PDF and the inverse State-evolution function. To approximate the Prediction PDF from the Prediction samples, a Gaussian Mixture Model is adopted whose covariance matrix is determined via Principle Component Analysis (PCA).

As a form of verification, a numerical example involving the identification of inter-storey stiffness within a 2DOF Shear Building model is presented whereby the stiffness parameters degrade according to a simple State-evolution model whose inverse function can be derived. The VB-SEMC sampler is implemented alongside the SEMC sampler and the results will be compared on the basis of the accuracy of the estimates, the Coefficient of Variation (COV), and computational time. Following which, a second example is presented based on a Non-linear time-series model whose State-evolution model does not yield an inverse function. The VB-SEMC sampler will be implemented and the results of the estimates will be compared against the true evolution model.