Damage Detection and Sensor Placement Strategies for Structures Under Frequency-Domain Dynamics

Abstract

Identification and monitoring of damage have a growing importance in the maintenance of structures. With advances in high performance computing, numerical modeling tools are becoming more common in anomaly detection and structural damage localization. However, many methods presuppose that sufficiently many experimental data points are obtained. As these monitoring schemes are applied to higher risk, more detailed, and aging structures, a key challenge is the gathering of sufficient information through sensors such that modern damage estimation mechanisms can identify and diagnose anomalies with certainty. To that end, we formulate a simultaneous inversion and optimal experimental design (OED) framework for models described by a set of discretized partial differential equations (PDEs). Abstractly, we construct and solve the corresponding (potentially nonlinear) inverse problem to attain a parameter estimator. Then, to devise the next best sensor placement, we linearize the OED problem around the newly determined estimator to generate the Fisher Information Matrix (FIM) for the next best sensor placement problem. In this manner, we let information gleaned from our measurements guide our sensor placement process: given a current estimated damage state with up-to-date sensor information, find the next best sensor using the FIM and update the damage estimator.We will also explore three different strategies to enhance the framework. First, we introduce a Modified Error in Constitutive Equations (MECE) functional as a damage estimator. Using MECE will quasi-convexify the damage estimation problem, making the problem more resilient from being trapped in local minima. Next, we formulate a decision-centric, utility maximization framework for the OED problem. Mutual information (or relative entropy) is chosen as the utility criteria so that sensor locations maximize the information about the structural parameters. We provide a discussion on how prior knowledge can be incorporated. Finally, we develop a novel PDE-constrained optimization approach for generalized stress inversion. Given digital image correlation measurements on a structure, this method aims to infer body’s original stress field.We will demonstrate all developed capabilities using a combination of numerical and experimental models of varying complexities. We show that these approaches can recover accurate parameter estimators (using a set number of sensors) in the presence of noisy measurements.