Excitation design for damage detection using iterative adjoint-based optimization-Part 1: Method development

A technique is developed to answer the important question: "Given limited system response measurements and ever-present physical limits on the level of excitation, what excitation should be provided to a system to make damage most detectable?" The solution is developed by forming an augmented system that is the union of the undamaged and damaged systems. The difference between measurable outputs of the undamaged and damaged systems then simply becomes a state in this augmented system which may be then maximized by maximizing a related and easily developed cost function. By formulating an adjoint version of the optimization problem, the gradient of this cost function with respect to the excitation may be calculated very efficiently, and a straight forward gradient ascent procedure follows. This process is demonstrated on a 2 DOF system with a nonlinear stiffness, where it is shown that an optimized excitation increases the detectability of the damage by several orders of magnitude.