Parameter Optimization Method for Identifying the Optimal Nonlinear Parameters of a Miniature Transducer with a Metal Membrane

This study proposes a parameter optimization method for identifying the optimal nonlinear parameters of a miniature transducer with a metal membrane. Specifically, a nonlinear lumped parameter model (LPM) of a miniature transducer that accounts for predicted displacement in a manner that is consistent with the displacement measured by a high-precision capacitance micro-displacement sensor is proposed. To avoid application of the proposed optimization method to an ill-posed problem, this paper proposes a constrained equation that is derived from the relationships of nonlinear parameters. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is used to minimize the objective function in order to obtain an appropriate solution from the proposed nonlinear LPM. The numerical simulation results and a discussion of the experiments are presented. The numerical simulation verification demonstrated that the presented method can estimate the suitable nonlinear parameters for the displacement with errors. With regard to empirical verification, the empirical investigations showed that the proposed method could accurately assess the nonlinear parameters of a miniature transducer with a metal membrane.