Damage Detection and Quantification Through Differentiable Numerical Solvers

Abstract

Structural health monitoring strategies typically attempt to identify and quantify damage by utilizing sensor data. This is typically referred to as the inverse problem. While sensor data of the response of dynamical systems is usually abundant, data of damage location and quantity are typically difficult to acquire, even in lab settings. This lack of labels hinders traditional supervised learning, as the inverse problem is primarily concerned with changes in certain parameters of the dynamical system (e.g., stiffness degradation). This issue necessitates some form of parametric estimation, where the underlying structure of the physics model, parameterized by “damage-sensitive” parameters, is already known. This inverse problem setup naturally lends itself to Partial Differential Equation (PDE)-constrained optimization, where the objective function is the misfit between sensor data and the predicted sensor data of the physics model, and is constrained by a PDE residual equality constraint. Several methods exist to solve this constrained optimization problem, some using non-gradient-based optimization, e.g., Bayesian optimization. In this work, we use a gradient-based optimization method, namely automatic differentiation, to determine the gradients necessary for optimization. This is possible due to the ability to represent numerical solvers as computational graphs, which can be differentiated. This method, a variant of the primal method, offers the additional benefit of incorporating physics as a hard constraint, unlike other methods, such as the penalty method. Case studies on synthetic problems related to wind turbines are presented and evaluated, and practical workarounds for memory constraints are discussed.