Response Surface Optimization in the Presence of Internal Noise With Application to Optimal Alignment of Carbon Nanotubes

Internal noise, which means fluctuation of input factors around their set values, is common in many experiments in the physical and engineering sciences. Existing methods for response surface optimization in the presence of internal noise typically adopt a two-step approach: (a) fitting a response model as a function of the set value and (b) using Monte Carlo methods to account for internal noise while optimizing the response. In this article, motivated by a problem in optimizing alignment of carbon nanotubes (CNT), we propose a Bayesian approach for response surface optimization in the presence of internal noise. A unit-free and interpretable measure to quantify the strength of internal noise is proposed. Suitable objective functions or performance measures consistent with the overall goal of optimizing the response function are identified, methods for estimating them from available experimental data are suggested, and simulations are conducted to compare them with respect to their ability to account for internal noise in the optimization problem. The loss accrued by ignoring the internal noise in the optimization problem is quantified and studied via simulation. The proposed method is demonstrated through its application in the CNT alignment problem.