An inverse elastic method of crack identification based on sparse strain sensing sheet

Reliable damage detection over large areas of structures can be achieved by spatially quasi-continuous structural health monitoring enabled by two-dimensional sensing sheets. They contain dense arrays of short-gauge sensors, which increases the probability to have sensors in direct contact with damage (e.g. crack opening) and thus identify (i.e. detect, localize, and quantify) it at an early stage. This approach in damage identification is called direct sensing. Although the sensing sheet is a reliable and low-cost technology, the overall structural health monitoring system that is using it might become complex due to large number of sensors. Hence, intentional reduction in number of sensors might be desirable. In addition, malfunction of sensors can occur in real-life settings, which results in unintentional reduction in the number of functioning sensors. In both cases, reduction in the number of (functioning) sensors may lead to lack of performance of sensing sheet. Therefore, it is important to explore the performance of sparse arrays of sensors, in the cases where sensors are not necessarily in direct contact with damage (indirect sensing). The aim of this research is to create a method for optimizing the design of arrays of sensors, that is, to find the smallest number of sensors while maintaining a satisfactory reliability of crack detection and accuracy of damage localization and quantification. To achieve that goal, we first built a phase field finite element model of cracked structure verified by the analytical model to determine the crack existence (detection), and then we used the algorithm of inverse elastostatic problem combined with phase field finite element model to determine the crack length (quantification) and location (localization) by minimizing the difference between the sensor measurements and the phase field finite element model results. In addition, we experimentally validated the method by means of a reduced-scale laboratory test and assessed the accuracy and reliability of indirect sensing.