Parameter extraction during the final test of MEMS sensors poses a highly time-critical challenge. The progressing miniaturization, test stimuli and structural complexity lead to nonlinear couplings and inhomogeneity in system differential equations, which cannot be linearized and are therefore dependent on either slow numerical solution methods or machine learning algorithms requiring many labeled data. A transfer learning approach is presented making use of high complexity ASIC-MEMS models for Monte-Carlo generation of simulated devices, which are used to pre-train neural networks on the task of parameter extraction. In a first step, it is shown that for both, high quality factor and low quality factor systems, neural networks are not only able to fit the relation between timeseries recorded during final testing and the two performance parameters natural frequency and damping factor but also to extract Brownian noise, mass, and epitaxial layer thickness. Subsequently, it is shown that the transfer learning approach is particularly useful for the determination of parameters, which cannot be measured directly during the final test and for which it is expensive to record labeled data like Brownian noise for systems in a harsh production test environment. If only very few labeled samples are available -in the performed experiments, 25 devices under test were sufficient -the transfer learning approach outperforms a neural network purely trained on measured data. These findings emphasize the practical advances of the transfer learning approach and motivate the evaluation of further applications in the field of parameter extraction in MEMS sensors.[2020-0375] Index Terms-Capacitive MEMS accelerometer, MEMS testing, neural networks, parameter extraction, transfer learning. I. INTRODUCTIONI N A broad field of applications including vehicle safety and consumer electronics micro-electro-mechanical systems (MEMS) are indispensable. Capacitive MEMS accelerometers constitute a major subcategory, integrated among others in airbags and navigation applications as well as in smartphones. The sensor performance is highly susceptible

In micro-electro-mechanical systems (MEMS) testing high overall precision and reliability are essential. Due to the additional requirement of runtime efficiency, machine learning methods have been investigated in recent years. However, these methods are often associated with inherent challenges concerning uncertainty quantification and guarantees of reliability. The goal of this paper is therefore to present a new machine learning approach in MEMS testing based on Bayesian inference to determine whether the estimation is trustworthy. The overall predictive performance as well as the uncertainty quantification are evaluated with four methods: Bayesian neural network, mixture density network, probabilistic Bayesian neural network and BayesFlow. They are investigated under the variation in training set size, different additive noise levels, and an out-of-distribution condition, namely the variation in the damping factor of the MEMS device. Furthermore, epistemic and aleatoric uncertainties are evaluated and discussed to encourage thorough inspection of models before deployment striving for reliable and efficient parameter estimation during final module testing of MEMS devices. BayesFlow consistently outperformed the other methods in terms of the predictive performance. As the probabilistic Bayesian neural network enables the distinction between epistemic and aleatoric uncertainty, their share of the total uncertainty has been intensively studied.

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