Identification and evaluation of cracks in electrostatically actuated resonant gas sensors using Harris Hawk / Nelder Mead and perturbation methods

In this paper we study the static deflection, natural frequency, primary resonance of an electrostatically actuated cracked gas sensor. Besides, a novel hybrid metaheuristic algorithm is proposed to detect the location and depth of possible crack on the microcantilever systems. The gas sensor configuration consists of a microcantilever with a rigid plate attached to its end. The nonlinear effects of the electrostatic force and fringing field are taken into account in the mathematical model. The crack is represented by a rotational spring. In the first part, the effect of crack on the static and dynamic pull-in instability are studied. The equations of motion are solved by the application of the perturbation methods. Next, an inverse problem is formulated to predict the location and depth of the crack in the gas sensor. For that purpose, the weighted squared difference of the analytical and predicted frequency response is considered as the objective function. The location and depth of the crack in the microsystem are determined using the hybrid Harris Hawk and Nelder Mead optimization algorithms. The accuracy and efficiency of the proposed algorithm are compared with the HHO, DA, GOA, and WOA algorithms. Taguchi design of experiments method is used in order to tune the parameters of optimization algorithms systematically. It is shown that the proposed algorithm can predict the exact location and depth of the open-edge crack on an electrostatically actuated microbeam with proof mass.