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About PRISM

Uncertainty Quantification

Verification, validation and uncertainty quantification are central to PRISM’s predictive simulation efforts. We described the essential elements of our approach below.
Tierwise Approach. We adopt a tier-wise approach to verification and validation, as shown below.

uncertainty-fig1

In this approach, we build on the complexity of our experiments and simulations progressively. Tier 1 involves single-physics simulations and validation experiments and are typically conducted during years 1 and 2 of the program. An example of this is the measurement and simulation of fluid damping in fixed-fixed and fixed-free micro-cantilevers. Tier 2 represents coupled physics simulations and validation experiments. An example is the simulation of the pull-in phenomenon the PRISM RF-MEMS device, which involves the interaction of structural deformation, electrostatic s and fluid damping. Tier 3 represents system level simulations and validation experiments. An example of a typical Tier 3 validation effort involves the measurement and prediction of the lifetime of the PRISM device.
Overall Process. The overall uncertainty quantification process is shown below. First, a Phenomenon Identification and Ranking Table (PIRT) is developed which identifies the main physical phenomena, numerical methods and software to be tested. A Verification Test Suite (VERTS) is then developed which identifies verification tests to be performed, identifies exact solutions with which comparisons are to be made, and sets out acceptance criteria. A Validation Test Suite (VALTS) similarly identifies the validation simulations and experimental data to be used, and identifies acceptance criteria. Rigorous protocols are followed for software quality assurance.

uncertainty-fig2

In a typical validation exercise, we first perform solution verification to determine the necessary mesh and time-step sizes, and to estimate discretization error. All input parameters are identified and classified as either aleatoric or epistemic, and appropriate pdfs and parameter ranges are identified. Sensitivity analysis and effect screening are then conducted to identify the most important parameters. To allay the cost of large-scale unsteady simulation, a meta-model is constructed. A particular focus of the Center is the use of methods based on polynomial chaos for uncertainty propagation. Uncertainty in aleatoric variables is propagated by sampling the metamodel, while epistemic variables are treated by performing computations to span the expected range. Once uncertainty propagation is complete, overall uncertainty (discretization error, error in the metamodel, as well as propagated uncertainty) are rolled up to estimate an overall uncertainty in the simulation. As a final step, an assessment of the prediction accuracy is made, and is used to make decisions on the future course of action.
Coarse-Grained Model. A critical element of our uncertainty quantification effort is the development of a coarse-grained model to help provide an understanding of overall system behavior and to inform the planning of simulations and experiments. The coarse-grained model delineates the connection between system-level outputs such as device lifetime to input parameters such as device dimensions, material properties and model parameters, and helps identify the most fruitful pathways for improving our predictions. We have developed a two-dimensional coarse-grained model including elastic membrane deformation and electrostatics, with simplified models for fluid damping, dielectric charging and contact and bounce, as shown below.

uncertainty-fig3

Experimental Program. An extensive experimental program is underway conducted at Purdue's state-of-the-art Birck Nanotechnology Center to augment published data with validation-quality measurements, particularly on microstructural characterization, and to develop a first-of-its-kind validation database for uncertainty quantification in microsystems. Typical validation experiments have included the measurement of fluid damping on microcantilevers and fixed-fixed membranes across a range of Knudsen numbers, gap-versus-voltage and pull-in voltage measurements in RF-MEMS, long-range creep measurements in RF-MEMS as well as the characterization of dielectric charging in dielectrics used in MEMS applications.

uncertainty-fig4

About PRISM

PRISM leverages advances in nanoscale science and engineering to create innovative nanotechnologies addressing societal challenges and opportunities in computing, communications, the environment, security, energy independence, and health.


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Contact

Matt Potrawski
Managing Director, PRISM Center
Purdue University
Birck Nanotechnology Center
1205 W. State St., Suite 2027
West Lafayette, IN 47907-2088