A Nonstationary Covariance Function Model for Spatial Uncertainties in Electrostatically Actuated Microsystems

Alwan, Aravind; Aluru, N. R.

doi:10.1615/int.j.uncertaintyquantification.2015011166

Cited by 4 publications

(6 citation statements)

References 26 publications

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“…It is seen that this form of the displacement function differs from that in Eq. (3.2) only by a linear term and it can be shown that the resulting covariance function is identical under this modification [29,32]. The final formulation is given by: We also assign prior PDFs to the unknown parameters in order to obtain their poste-rior estimates using the generated datasets.…”

Section: Resultsmentioning

confidence: 99%

“…(32) for a given set of values for d, so that the resulting random process closely matches the actual, unknown process from which the dataset is derived. A thorough discussion of this procedure may be found in [29]. We use Bayesian inference to perform the model estimation, in which we first assign prior probability density functions (PDF) to the unknown parameters and then compute the posterior PDFs under the influence of the data.…”

Section: Modeling Spatially Varying Random Fieldsmentioning

confidence: 99%

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Analysis of the Effect of Spatial Uncertainties on the Dynamic Behavior of Electrostatic Microactuators

Alwan

Aluru²

2016

Commun. Comput. Phys.

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This paper examines the effect of spatial roughness on the dynamical behaviour of electrostatic microactuators. We develop a comprehensive physical model that comprises a nonlinear electrostatic actuation force aswell as a squeeze-film damping term to accurately simulate the dynamical behavior of a cantilever beam actuator. Spatial roughness is modeled as a nonstationary stochastic process whose parameters can be estimated from profilometric measurements. We propagate the stochastic model through the physical system and examine the resulting uncertainty in the dynamical behavior that manifests as a variation in the quality factor of the device. We identify two distinct, yet coupled, modes of uncertainty propagation in the system, that result from the roughness causing variation in the electrostatic actuation force and the damping pressure, respectively. By artificially turning off each of these modes of propagation in sequence, we demonstrate that the variation in the damping pressure has a greater effect on the damping ratio than that arising from the electrostatic force. Comparison with similar simulations performed using a simplified mass-spring-damper model show that the coupling between these two mechanisms can be captured only when the physical model includes the primary nonlinear interactions along with a proper treatment of spatial variations. We also highlight the difference between nonstationary and stationary covariance formulations by showing that the stationary model is unable to properly capture the full range of variation as compared to its nonstationary counterpart.

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Section: Resultsmentioning

confidence: 99%

Section: Modeling Spatially Varying Random Fieldsmentioning

confidence: 99%

Analysis of the Effect of Spatial Uncertainties on the Dynamic Behavior of Electrostatic Microactuators

Alwan

Aluru²

2016

Commun. Comput. Phys.

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“…where Φ = {α i , ν, φ, θ} is a set of unknown parameters in the Gaussian process and Pr(Φ) and Pr(Φ|d) are the prior and posterior distributions of Φ, respectively. If prior information about the distribution of the unknown parameters exists, it can be incorporated into the prior probability density functions (PDFs) of the corresponding unknown parameters [31]. Conversely, if prior information on the parameters is absent, the uniform PDFs in the certain range can be included.…”

Section: Gaussian Process Modelingmentioning

confidence: 99%

Spatial Uncertainty Modeling for Surface Roughness of Additively Manufactured Microstructures via Image Segmentation

et al. 2019

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Despite recent advances in additive manufacturing (AM) that shifts the paradigm of modern manufacturing by its fast, flexible, and affordable manufacturing method, the achievement of high-dimensional accuracy in AM to ensure product consistency and reliability is still an unmet challenge. This study suggests a general method to establish a mathematical spatial uncertainty model based on the measured geometry of AM microstructures. Spatial uncertainty is specified as the deviation between the planned and the actual AM geometries of a model structure, high-aspect-ratio struts. The detailed steps of quantifying spatial uncertainties in the AM geometry are as follows: (1) image segmentation to extract the sidewall profiles of AM geometry; (2) variability-based sampling; (3) Gaussian process modeling for spatial uncertainty. The modeled spatial uncertainty is superimposed in the CAD geometry and finite element analysis is performed to quantify its effect on the mechanical behavior of AM struts with different printing angles under compressive loading conditions. The results indicate that the stiffness of AM struts with spatial uncertainty is reduced to 70% of the stiffness of CAD geometry and the maximum von Mises stress under compressive loading is significantly increased by the spatial uncertainties. The proposed modeling framework enables the high fidelity of computer-based predictive tools by seamlessly incorporating spatial uncertainties from digital images of AM parts into a traditional finite element model. It can also be applied to parts produced by other manufacturing processes as well as other AM techniques.

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“…However, autocorrelated measurements are not necessarily from a stationary process. Recently, different models for various nonstationary processes have been proposed in many areas of measurement science (see [3][4][5][6]). For measurements from a nonstationary process, how to evaluate the corresponding uncertainties is a critical task.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of measurement uncertainty from a nonstationary process

Zhang

2019

Meas. Sci. Technol.

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In metrology, when repeated measurements are autocorrelated, it is not appropriate to use the traditional approach to evaluate the uncertainty of the average of repeated measurements. In literature, methodologies were developed to evaluate the uncertainty of measurements from a stationary process, which demonstrated ‘statistical equilibrium’. In this paper, we discuss approaches to evaluate the measurement uncertainty when the data are from a nonstationary process. In particular, for some nonstationary processes with a time-dependent mean and a constant variance, we may be able to assess the uncertainty based on one realization. Specifically, after the effect of the time-dependent mean is removed, the residuals may show equilibrium behavior and thus can be treated as being from a stationary process. We propose approaches to evaluate the uncertainty of measurements based on one realization of such a process with practical examples presented for illustration.

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A Nonstationary Covariance Function Model for Spatial Uncertainties in Electrostatically Actuated Microsystems

Cited by 4 publications

References 26 publications

Analysis of the Effect of Spatial Uncertainties on the Dynamic Behavior of Electrostatic Microactuators

Analysis of the Effect of Spatial Uncertainties on the Dynamic Behavior of Electrostatic Microactuators

Spatial Uncertainty Modeling for Surface Roughness of Additively Manufactured Microstructures via Image Segmentation

Evaluation of measurement uncertainty from a nonstationary process

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