Andryas Mawardi

Design of microresonators under uncertainty

A methodology for robust design analysis of microelectromechanical systems is presented by considering the example of comb microresonators and uncertainty in parameters governing the resonant frequency and the transconductance values. Analytical models for the variability in the resonant frequency and transconductance are developed as function of the parameter uncertainty, and used as objective functions sought to be minimized in a robust design endeavor. An enumeration search over the design space is utilized to determine the optimal design of microresonators that minimize the variability subject to constraints on performance requirements. The results are presented over a wide interval of operating resonant frequency, and can be used in the robust design of microresonators.

Numerical Simulations of an Optical Fiber Drawing Process Under Uncertainty

Manufacture of optical fibers is subject to inherent uncertainty in various process and material parameters, which, in turn, leads to variability in product quality and impacts the reliability of the optical fibers in use. Analysis of the interactive effects of parameter uncertainty on the optical fiber quality is imperative in a robust-design endeavor. To this end, a methodology for simulation of optical fiber drawing process under uncertainty is presented by considering a two-dimensional (2D) numerical model of the flow, heat and mass transfer phenomena involved in the fiber drawing process. A sampling-based stochastic model is developed, and parametric analysis is presented to elucidate the effects of uncertainty in several process and material parameters on the variability of index of refraction, residual stress, maximum tension, and defect concentration. Design maps are derived from the analysis which provide for selection of furnace wall temperature as a function of the input parameter uncertainty and target maximum acceptable variability in the index of refraction, residual stress, maximum tension, and defects.

Cure Cycle Design for Thermosetting-Matrix Composites Fabrication under Uncertainty

Design of the optimal cure temperature cycle is imperative for low-cost of manufacturing thermosetting-matrix composites. Uncertainties exist in several material and process parameters, which lead to variability in the process performance and product quality. This paper addresses the problem of determining the optimal cure temperature cycles under uncertainty. A stochastic model is developed, in which the parameter uncertainties are represented as probability density functions, and deterministic numerical process simulations based on the governing process physics are used to determine the distributions quantifying the output parameter variability. A combined Nelder–Mead Simplex method and the simulated annealing algorithm is used in conjunction with the stochastic model to obtain time-optimal cure cycles, subject to constraints on parameters influencing the product quality. Results are presented to illustrate the effects of a degree of parameter uncertainty, constraint values, and material kinetics on the optimal cycles. The studies are used to identify a critical degree of uncertainty in practice above which a rigorous analysis and design under uncertainty is warranted; below this critical value, a deterministic optimal cure cycle may be used with reasonable confidence.

Optimization under uncertainty of a composite fabrication process using a deterministic one-stage approach

Abstract Process design under uncertainty has received considerable attention in recent years, and has led to the development of several modeling and solution approaches. These approaches are broadly categorized under stochastic formulations (model parameters with probability distributions), multiperiod formulations (where uncertain parameters are discretized into a number of deterministic realizations), and parametric programming formulations. This paper presents an application of the one-stage optimization problem (OSOP), a multiperiod method, to find optimal cure temperature cycle design under uncertainty for polymer-matrix composites fabrication using the pultrusion process. The process is governed by a highly non-linear system of partial differential-algebraic equations. The OSOP method is also systematically compared with a sampling-based approach in terms of computational efficiency and solution quality. Most work done so far using such deterministic methods has focused on problems where the performance objective function (often cost) and process constraints are analytic/algebraic in nature. In contrast, in materials processing simulations, evaluation of the objective function and the process constraints are based on the solution of differential-algebraic equations (DAE).

SAMS: Stochastic Analysis With Minimal Sampling—A Fast Algorithm for Analysis and Design Under Uncertainty

Design of processes and devices under uncertainty calls for stochastic analysis of the effects of uncertain input parameters on the system performance and process outcomes. The stochastic analysis is often carried out based on sampling from the uncertain input parameters space, and using a physical model of the system to generate distributions of the outcomes. In many engineering applications, a large number of samples-on the order of thousands or more-is needed for an accurate convergence of the output distributions, which renders a stochastic analysis computationally intensive. Toward addressing the computational challenge, this article presents a methodology of Stochastic Analysis with Minimal Sampling (SAMS). The SAMS approach is based on approximating an output distribution by an analytical function, whose parameters are estimated using a few samples, constituting an orthogonal Taguchi array, from the input distributions. The analytical output distributions are, in turn, used to extract the reliability and robustness measures of the system. The methodology is applied to stochastic analysis of a composite materials manufacturing process under uncertainty, and the results are shown to compare closely to those from a Latin hypercube sampling method. The SAMS technique is also demonstrated to yield computational savings of up to 90% relative to the sampling-based method.

Effects of operating parameters on the current density distribution in proton exchange membrane fuel cells

During the operation of a proton exchange membrane (PEM) fuel cell, significant variation of the local current density could exist across the cell causing sharp temperature and stress gradients in certain points, and affecting the water management, all of which severely impact the cell performance and reliability. The variation of local current density is a critical issue in the performance of PEM fuel cell, and is influenced by the operating conditions. This article presents a model-assisted parametric design with the objective of determining the operating conditions which maximize the fuel cell performance while maintaining a level of uniformity in the current density distribution. A comprehensive two-dimensional model is adopted to simulate the species transport and electrochemical phenomena in a PEM fuel cell. Numerical simulations are performed for over a wide range of operating conditions to analyze the effects of various operating parameters on the variation of local current density of the fuel cell, and to develop design windows which serve as guideline in the design for maximum power density, minimum reactant stoichiometry, and uniform current density distribution.

Examination of load-balancing methods to improve efficiency of a composite materials manufacturing process simulation under uncertainty using distributed computing

Process simulations play an important role in guiding process understanding and development, without requiring costly manufacturing trials. For process design under uncertainty, a large number of simulations is needed for an accurate convergence of the moments of the output distributions, which renders such stochastic analysis computationally intensive. This paper discusses the application of a basic distributed computing approach to reduce the computation time of a composite materials manufacturing process simulation under uncertainty. Specifically, several load-balancing methods are explored and analyzed to determine the best strategies given heterogeneous tasks and heterogeneous networks, especially when the individual task times cannot be predicted.