Conditional value at risk for damage identification in structural digital twins

Given measurements from sensors and a set of standard forces, an optimization based approach to perform damage identification in structures is introduced. The key novelty lies in letting the loads and measurements to be random variables. Subsequently, the conditional-value-at-risk (CVaR) is minimized subject to the elasticity equations as constraints. CVaR is a risk measure that leads to minimization of rare and low probability events which the standard expectation cannot. The optimization variable is the (deterministic) strength factor which appears as a coefficient in the elasticity equation, thus making the problem nonconvex. Due to uncertainty, the problem is high dimensional and, due to CVaR, the problem is nonsmooth. An adjoint based approach is developed with quadrature in the random variables. This approach would enable the implementation of risk-averse digital twins. Numerical results are presented in the context of a plate, a large structure with trusses similar to those used in solar arrays or cranes, and a footbridge.