The foundations of predictive computational science involve the development of methods that address all of the sources of uncertainty in the prediction of events in the physical universe: 1) the system of logic that is of sufficient depth to rigorously manage and
quantify uncertainty; 2) the uncertainty in observational data; 3) the uncertainty in model selection and how to cope with model inadequacy; 4) uncertainty in model parameters; and 5) uncertainty due to discretizations of proposed mathematical models. To these issues one must add the development of efficient computational methods to handle uncertainties and to solve often large stochastic systems, including parallel sampling methods, stochastic solvers, and methods for statistical inverse analysis. This presentation describes general Bayesian approaches that address all of these sources of uncertainty through use of the Occam Plausibility Algorithm, OPAL, an adaptive process
that enables selection of plausible models among sets of model classes while also addressing model inadequacies through model validation processes. Applications of these methods to models of tumor growth in living tissue, coarse-graining of molecular models, and other areas are discussed.
Challenges in Bayesian Uncertainty Quantification and Propagation for Structural Dynamics Simulations
Prof. Costas Papadimitriou | University of Thessaly | Greece
Bayesian analysis provides a logical framework for quantifying and propagating uncertainties in structural dynamics simulations, integrating physics-based models and experimental/monitoring data. The framework can also be used to optimally allocate experimental resources for maximizing the information contained in the data for the purpose of uncertainty quantification and propagation (UQ+P). Bayesian tools such as Laplace asymptotic
approximations and sampling algorithms require a moderate to very large number of system re-analyses to be performed. Computational demands may become excessive, depending on the model complexity, the time required to perform a simulation, and the number of model runs. The process of data-driven UQ+P is important for structural health diagnosis,
and decision making for cost-effective system design and maintenance actions that meet performance/safety requirements.
This lecture will cover selected theoretical and computational developments of a Bayesian UQ+P framework for structural dynamics simulations. Theoretical challenges related to model embedded uncertainty and model prediction uncertainty will first be addressed for properly quantifying the uncertainty in the structural model parameters. Then computational challenges encountered in large-order finite element (FE) models of hundreds of
thousands or millions degrees of freedom, and/or localized nonlinear actions activated during system operation, will be addressed. Efficient model reduction techniques, consistent with the model parameterization, will be presented to drastically speed up computations within the Bayesian UQ+P framework. Finally, a computationally efficient asymptotic approximation will be proposed to simplify information-based utility functions used for optimizing the placement of sensors in a structure. The structure of the approximation provides insight into the use of the prediction error spatial correlation to avoid sensor clustering, as well as the effect of the prior uncertainty on the optimal sensor configuration. Applications will focus on the use of the framework for FE model selection/calibration, as well as structural health monitoring using vibration measurements.