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

Abstract

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.Electroacoustic measurement is characterized by multiple categories and methods [2]. Each measurement provider formulates different instruments and procedures for transducers with different dimensions. Different methods have been applied by scientists in the past, such as the added mass method [1,3] and the optimization method [4], for transducer's linear parameters estimation. When the miniature transducer is driven in the large signal domain, abnormal vibrations have been observed due to large input signal and increased voltage imposed on voice coil for its displacement [5]. The moving diaphragm that was activated by pneumatic pressure [6] demonstrated that the transducer's model parameters cannot remain linear, but the performance of the transducer can be evaluated by position-dependent parameters [7] as nonlinear parameters. In 1990, Klippel [8] proposed a dynamic measurement system and used a high-precision laser vibrometry and noise signal to measure the linear and nonlinear parameters of a transducer LPM. The nonlinear parameters generate nonlinear effects, such as harmonic and intermodulation distortion; thus, the system that was proposed by Klippel is often used for transducer development, production, quality control, and diagnostics [5,9]. Faifer et al. [10] proposed a nonlinear LPM to identify the coefficient of stiffness K m (x) and the force factor (Bl) and investigated the reduction of 2nd-3rd harmonic distortions by transducer parameter linearization. A simulation method [11] uses finite element analysis for the identification of the nonlinear parameters early, which is the meaningful way of characterizing the transducer in the product development process. In 2001, Mihelich proposed [12] a parameter optimization method for minimizing the cost function between the predicted sinusoid type of displacements and the mo...

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“…The approach to solve this problem is an optimization method of the quasi-Newton family that approximates the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, and which is implemented in Python [68][69][70][71]. MATLAB was used to calculate the Hessian matrix [72].…”