基于神经网络的代用建模,用于 MEMS 加速计的高效不确定性量化和校准

IF 2.8 3区 工程技术 Q2 MECHANICS International Journal of Non-Linear Mechanics Pub Date : 2024-09-12 DOI:10.1016/j.ijnonlinmec.2024.104902
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引用次数: 0

摘要

本文探讨了微机电系统(MEMS)电容式加速度计的随机表征和不确定性量化所固有的计算挑战。马尔可夫链蒙特卡罗 (MCMC) 算法等传统方法往往受到高保真(如有限元)模拟所需的计算强度的限制。为了克服这些限制,我们建议使用基于监督学习的代理模型,特别是人工神经网络,来有效地近似 MEMS 电容式加速度计的响应。我们的方法包括利用从初始高保真有限元分析 (FEA) 中获得的数据来训练代用模型,从而在离线阶段生成丰富的数据集。代用模型复制了有限元分析在各种制造参数下预测加速度计行为的精度,从而在不影响精度的情况下降低了在线计算成本。这样就能对复杂的 MEMS 设备进行广泛而高效的随机分析,为其特性分析提供灵活的框架。在估算加速度计的灵敏度时,我们展示了该框架的一个关键应用,其中考虑到了未知的机械偏移、过蚀和厚度变化。我们采用 MCMC 方法,根据器件对瞬态电压信号的响应,估计器件未知制造参数的后验分布。代用模型可将制造参数映射到器件响应,进而映射到灵敏度测量,这种集成极大地增强了后向和前向不确定性量化,在获得精确结果的同时,显著提高了表征过程的效率和有效性。这一过程允许仅使用电压信号重建器件灵敏度,而无需直接的机械加速度刺激。
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Neural networks based surrogate modeling for efficient uncertainty quantification and calibration of MEMS accelerometers

This paper addresses the computational challenges inherent in the stochastic characterization and uncertainty quantification of Micro-Electro-Mechanical Systems (MEMS) capacitive accelerometers. Traditional methods, such as Markov Chain Monte Carlo (MCMC) algorithms, are often constrained by the computational intensity required for high-fidelity (e.g., finite element) simulations. To overcome these limitations, we propose to use supervised learning-based surrogate models, specifically artificial neural networks, to effectively approximate the response of MEMS capacitive accelerometers. Our approach involves training the surrogate models with data derived from initial high-fidelity finite element analyses (FEA), providing rich datasets to be generated in an offline phase. The surrogate models replicate the FEA accuracy in predicting the behavior of the accelerometer under a wide range of fabrication parameters, thereby reducing the online computational cost without compromising accuracy. This enables extensive and efficient stochastic analyses of complex MEMS devices, offering a flexible framework for their characterization. A key application of our framework is demonstrated in estimating the sensitivity of an accelerometer, accounting for unknown mechanical offsets, over-etching, and thickness variations. We employ an MCMC approach to estimate the posterior distribution of the device’s unknown fabrication parameters, informed by its response to transient voltage signals. The integration of surrogate models for mapping fabrication parameters to device responses, and subsequently to sensitivity measures, greatly enhances both backward and forward uncertainty quantification, yielding accurate results while significantly improving the efficiency and effectiveness of the characterization process. This process allows for the reconstruction of device sensitivity using only voltage signals, without the need for direct mechanical acceleration stimuli.

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来源期刊
CiteScore
5.50
自引率
9.40%
发文量
192
审稿时长
67 days
期刊介绍: The International Journal of Non-Linear Mechanics provides a specific medium for dissemination of high-quality research results in the various areas of theoretical, applied, and experimental mechanics of solids, fluids, structures, and systems where the phenomena are inherently non-linear. The journal brings together original results in non-linear problems in elasticity, plasticity, dynamics, vibrations, wave-propagation, rheology, fluid-structure interaction systems, stability, biomechanics, micro- and nano-structures, materials, metamaterials, and in other diverse areas. Papers may be analytical, computational or experimental in nature. Treatments of non-linear differential equations wherein solutions and properties of solutions are emphasized but physical aspects are not adequately relevant, will not be considered for possible publication. Both deterministic and stochastic approaches are fostered. Contributions pertaining to both established and emerging fields are encouraged.
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