Model-Assisted Probability of Detection for Structural Health Monitoring of Flat Plates

The paper presents a computational framework for assessing quantitatively the detection capability of structural health monitoring (SHM) systems for flat plates. The detection capability is quantified using the probability of detection (POD) metric, developed within the area of nondestructive testing, which accounts for the variability of the uncertain system parameters and describes the detection accuracy using confidence bounds. SHM provides the capability of continuously monitoring the structural integrity using multiple sensors placed sensibly on the structure. It is important that the SHM can reliably and accurately detect damage when it occurs. The proposed computational framework models the structural behavior of flat plate using a spring-mass system with a lumped mass at each sensor location. The quantity of interest is the degree of damage of the plate, which is defined in this work as the difference in the strain field of a damaged plate with respect to the strain field of the healthy plate. The computational framework determines the POD based on the degree of damage of the plate for a given loading condition. The proposed approach is demonstrated on a numerical example of a flat plate with two sides fixed and a load acting normal to the surface. The POD is estimated for two uncertain parameters, the plate thickness and the modulus of elasticity of the material, and a damage located in one spot of the plate. The results show that the POD is close to zero for small loads, but increases quickly with increasing loads.