Mechanical and Civil Engineering Seminar

This seminar discusses robust-to-uncertainties design applications that adopt a probabilistic approach to incorporate the associated uncertainties into the optimization problem formulation. This leads to performance objectives described by multidimensional, probabilistic integrals. To facilitate high modeling flexibility estimation of these integrals through stochastic simulation is considered. This setting creates an associated high computational burden for the resultant optimization, especially for problems involving complex numerical models. To alleviate this burden the seminar will first briefly discuss some advanced stochastic simulation techniques and will then focus on integration of surrogate modeling principles. Kriging is adopted as the underlying metamodel to approximate the system model response and its predictive capabilities (ability to provide measure of uncertainty for approximated response) are fully exploited within the proposed framework. Discussion will extend to both single-objective and multi-objective optimization problems, though the emphasis will be on the former. Formulation of the metamodel in the so-called augmented space is considered, composed of both the design variables and the uncertain model parameters. This means that the metamodel is simultaneously used to support both the uncertainty propagation (evaluation of probabilistic integral), and the design optimization (search for local minima). Metamodel accuracy is adaptively controlled through a sequential approximate optimization approach, with different implementation principles depending on the nature of the problem (single or multi –objective design). Rather than building by default high-accuracy metamodel over the entire domain of interest an iterative procedure is established; at each iteration an adaptive design of experiments is performed (exploiting information from the previous iteration), a new metamodel is formulated and the optimization design problem is solved. Comparing solutions between subsequent iterations provides information for convergence as well as for regions of interest (either in the design or uncertain parameter space) that the metamodel accuracy needs to be improved. Through this iterative approach, an adaptive control for the accuracy of the metamodel is achieved minimizing the number of simulations for the expensive system model. Applications considered extend to the suspension design for a quarter car model riding on a rough road, and (time permitting) design of viscous dampers for seismic retrofitting based on life-cycle cost objectives and risk aversion principles.