  Given measurements from sensors and a set of standard forces, an optimization
based approach to identify weakness in structures is introduced. The key
novelty lies in letting the load 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. 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.
