Uncertainty Quantification in Dynamical Systems using Monte Carlo Methods (UQDyn)

Engineering structures such as multi-story buildings, bridges or dams are subjected to extreme dynamic loads during their lifetime. These include earthquakes, thermal loads in the event of a fire, severe wind loads on tall structures and wave loads on dams, among others. Structural failures due to these loads cause large-scale loss of life and property. An adequate understanding of how structures fail is therefore essential to mitigate the adverse effects of these loads by engineering design.

Predicting the performance of dynamically excited structures is challenging because of the inherent uncertainties in the applied loads and the structural model. These uncertainties can be systematically analysed using probability theory, where the uncertainty associated with the load and structural system parameters are represented by means of appropriate probabilistic models, such as random variables, stochastic processes or random fields. These uncertainty models are incorporated into the general framework of physics-based modelling of the structural system and propagated to the output response. The uncertainty in structural performance is then quantified by means of second-order statistics, probability density functions, probability of exceedance, etc.

Uncertainty quantification in structural dynamics includes a plethora of computationally challenging problems such as assessment of first-passage probability of large engineering system, response sensitivity analysis, online estimation of dynamic states in instrumented structures, and problem of mathematical model updating based on measured structural responses under diagnostic and (or) operating loads.  The Monte Carlo simulation techniques have emerged as the most robust and widely accepted tool for this class of problems. In this project, we develop reliable and efficient Monte Carlo methods for tackling some of the afore-mentioned challenges.