Design of a probabilistic health monitoring system using embedded piezoelectric patch sensors

This paper proposes a probabilistic model for the placement of sensors that considers uncertain factors in the sensing system to find the best arrangement of sensor locations. Traditional procedures for structural health monitoring (SHM) usually rely on simplified behavior and deterministic factors from structure's response. Incorporating the sources of uncertainty (e.g., loading condition, material properties, and geometrical parameters) in the design of sensor network will enhance the safety and extend the useful life of the complex mechanical systems. The proposed method is defined in a reliability-based design optimization framework to search for the sufficient number of sensors for failure detection using Genetic Algorithm. The optimal arrangement is found as the one that minimizes the number and size of sensor patches and maximizes the expected probability for failure detection. This design concept involves a new failure diagnosis indicator, named detectability, formulated based on the Mahalanobis Distance (MD). MD distribution is used as a measure of the quality of the obtained sensor configuration suitable for many sensing/actuation SHM processes, while considering the uncertainties such as those from structure properties and operation condition. The MD classifier categorizes large sets of testing data by comparing the distances of the mean with the distribution of available training data sets. Statistical evaluation of failure detectability can be obtained by comparing the distribution of MD for different failure modes. Kriging modeling, used for metamodel-based design optimization, is applied for surrogate modeling of the stochastic performance of system to reduce computational cost. The surrogate model is constructed by correlating the sensor output to the vibration pattern of the structure and sensor variable inputs (e.g., size and location). Direct finite element analysis (FEA) evaluates the sensor output with respect to the input variables. Consequently, the constructed kriging model enables the estimation of sensor output for any arbitrary sensor arrays. As a case study, a rectangular panel with a size of 40 cm x 30 cm is considered that is fastened using eight screw joints. The harmonic vibration force is applied to the center of the plate and its varied vibration pattern is used to detect the joint failure. Eight different combinations of join failure are defined as health statuses (failure modes), and different size and layouts of the piezoelectric sensors are considered to detect the health status. The results verify the capabilities of the new method for failure diagnosis of screw joints in a panel with high sensitivity of fault detection.