Sensitivity study of dynamic systems using polynomial chaos

Abstract

Global sensitivity has mainly been analyzed in static models, though most physical systems can be described by differential equations. Very few approaches have been proposed for the sensitivity of dynamic models and the only ones are local. Nevertheless, it would be of great interest to consider the entire uncertainty range of parameters since they can vary within large intervals depending on their meaning. Other advantage of global analysis is that the sensitivity indices of a given parameter are evaluated while all the other parameters can be varied. In this way, the relative variability of each parameter is taken into account, revealing any possible interactions. This paper presents the global sensitivity analysis for dynamic models with an original approach based on the polynomial chaos (PC) expansion of the output. The evaluation of the PC expansion of the output is less expensive compared to direct simulations. Moreover, at each time instant, the coefficients of the PC decomposition convey the parameter sensitivity and then a sensitivity function can be obtained. The PC coefficients are determined using non-intrusive methods. The proposed approach is illustrated with some well-known dynamic systems.

Uncertainty and global sensitivity analysis of neutron survival and extinction probabilities using polynomial chaos

“…An alternative method, which is based upon GPC, has been proposed in Sudret (2008) and used to solve time independent structural mechanics problems (Blatman and Sudret, 2010;Crestaux et al, 2009) and also dynamical problems (Sandoval et al, 2012). To calculate the sensitivity indices from the polynomial chaos coefficients we must first re-order the expansion in (40) and collect terms involving an equal number of dimensions.…”

Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations

“…First, PCEs are more than just an approximation of the simulator, they allow for a fully probabilistic prediction of what the simulator would produce. In fact, the full randomness of the response is contained within the set of the expansion coefficients (Haro Sandoval et al, 2012). Second, with the use of PCEs the mean and variance of the output QoI are available in closed-form .…”

“…Note that some input parameters of SWI models (such as dispersivity and hydraulic conductivity) can vary within large ranges and it would be of great interest to consider the entire uncertainty range of these parameters. Moreover, possible interactions between different input parameters can be taken into account by evaluating the sensitivity indices of a given parameter while all other parameters are simultaneously varying (Haro Sandoval et al, 2012). Both of these objectives can be accomplished through the use of global SA.…”

Metamodel-Based Sensitivity Analysis: Polynomial Chaos Expansions and Gaussian Processes

“…Younes et al [65]; Brown et al [14]; Sandoval et al [45]. Recent extensions to problems with dependent input parameters can be found in Sudret and Caniou [60]; Munoz Zuniga et al [40].…”