Robustness of Modal Filters Using Piezoelectric Sensor Arrays Subject to Positioning Uncertainties

Abstract

Modal transducers allow independent sensing, actuation and control of individual vibration modes. Shaped piezoelectric layers were initially proposed to this end but an array of independent piezoelectric transducers with weighted actuation/sensing signals were shown to be easier to implement and allows reconfigurable modal filters since the weighting can be done via software. Several methodologies to determine optimal weights for a modal filter based on a given array of sensors were proposed in the literature. In a previous work, a methodology for the topology optimization of piezoelectric sensor arrays in order to maximize the effectiveness of a set of selected modal filters was presented. This was done using a genetic algorithm optimization for the selection of twelve piezoceramic sensors, from an array of thirty-six piezoceramic sensors regularly distributed over an aluminum plate, which maximize the frequency-band of a set of modal filters, each one aiming at one of the first vibration modes. It was shown that it is possible to improve the effectiveness and frequency-band of a set of modal filters with a reduced number of sensors by optimizing the topology of the sensor array. However, this optimization may also lead to a higher sensitivity of modal filters performance on design parameters. Therefore, this work presents a robustness analysis of modal filters using a topology optimized array design with a reduced number of sensors subjected to uncertainties in the weighting coefficients and sensors positioning. For the weighting coefficients uncertainties, this is done using stochastic modeling tools to build a probabilistic model of the uncertain parameters and Monte Carlo method to evaluate the realizations of modal filters performance indices. For the sensors positioning uncertainties, a sampling-based sensitivity analysis was performed. Latin Hypercube Sampling technique was used to reduce the number of samples and alleviate the computational cost of analyzing multiple topologies. It is shown that optimal filter output is less sensitive to weighting coefficients uncertainties and more sensitive to sensors positioning.