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In this paper, a new computational framework based on the topology derivativeconcept is presented for evaluating stochastic topological sensitivities ofcomplex systems. The proposed framework, designed for dealing with highdimensional random inputs, dovetails a polynomial dimensional decomposition(PDD) of multivariate stochastic response functions and deterministic topologyderivatives. On one hand, it provides analytical expressions to calculatetopology sensitivities of the first three stochastic moments which are oftenrequired in robust topology optimization (RTO). On another hand, it offersembedded Monte Carlo Simulation (MCS) and finite difference formulations toestimate topology sensitivities of failure probability for reliability-basedtopology optimization (RBTO). For both cases, the quantification ofuncertainties and their topology sensitivities are determined concurrently froma single stochastic analysis. Moreover, an original example of two randomvariables is developed for the first time to obtain analytical solutions fortopology sensitivity of moments and failure probability. Another 53-dimensionexample is constructed for analytical solutions of topology sensitivity ofmoments and semi-analytical solutions of topology sensitivity of failureprobabilities in order to verify the accuracy and efficiency of the proposedmethod for high-dimensional scenarios. Those examples are new and make itpossible for researchers to benchmark stochastic topology sensitivities ofexisting or new algorithms. In addition, it is unveiled that under certainconditions the proposed method achieves better accuracies for stochastictopology sensitivities than for the stochastic quantities themselves.

A polynomial dimensional decomposition framework based on topology  derivatives for stochastic topology sensitivity analysis of high-dimensional  complex systems and a type of benchmark problems