Civil Engineering Departmental Seminar - Stochastic mechanics, global reliability and optimization of complex structures via physically driven probability density evolution method

Full uncertainty quantification and propagation are the basis for the reliability evaluation of complex systems, while the damage and failure from materials to structures should also be incorporated. This leads to the major difficulty lying in the coupling of randomness and nonlinearity for real-world structures and systems, which are generally high-dimensional systems. Incorporating the underlying physics of the system and the principle of preservation of probability will lead to a physically driven full probabilistic uncertainty propagation method. Some new advances will be outlined, including: (1) The generalized density evolution equation and the dimension-reduced probability density evolution equation for high-dimensional nonlinear systems based on the principle of preservation of probability; (2) The effects of randomness of structural parameters observed from experimental studies; and (3) Global reliability and design optimization of structures in the context of uncertainty. Challenging problems to be studied further will also be discussed.