Design and Analysis of Optimization Experiments with Internal Noise to Maximize Alignment of Carbon Nanotubes

在过去的几十年里，碳纳米管（CNT）由于其独特的电学，机械和光学特性而成为科学研究的前沿。然而，将这些特性从纳米级材料转移到工业规模的产品通常需要CNT的对齐（在同一方向上的取向）。 排列的重要结果之一是改善导电性，这是电化学水处理中非常理想的性质，并且与改善饮用水质量的研究工作密切相关。因此，确定可扩展的和具有成本效益的实验条件，最大限度地对齐CNT是一个重要的研究问题。该研究旨在建立设计和分析有效实验的统计方法，当一个或多个输入因素容易产生内部噪声时，确定最大化CNT对齐的条件。拟议的研究包括三个任务，特别侧重于解决存在的内部噪声和复杂的响应面的因素所带来的挑战。(i)开发一种贝叶斯方法来优化有噪声输入的响应面。这种方法允许实验者结合联合收割机的输出数据，可控输入，不可控的输入从不同的来源，是一种自然的方式，将专家知识的分析，并提供了一个自然的框架，优化设计的实验与噪声输入。(ii)有噪声输入的优化实验的有效设计。该研究将侧重于开发一个综合的设计策略，这是一个无模型和贝叶斯模型为基础的优化设计相结合。无模型设计将解决内部噪声和复杂响应面带来的挑战。(iii)在共同主要研究者的实验室中演示和验证所开发的方法。一系列的实验将计划应用开发的统计方法，试图确定触发对齐的CNT的因素，并确定其最佳水平，以最大限度地对齐。建议的框架将允许实验者有效地捕捉从输入变量到输出变量的不确定性的传输，通过结合来自不同来源的数据，并通过利用无模型和基于模型的实验设计的组合，有效地探索复杂的响应面。从材料科学家的角度来看，所提出的方法将提供更准确的不确定性量化，从而对实验室实验确定的最佳工艺条件进行更可靠的预测。

Over the past several decades, carbon nanotubes (CNT) have risen to the forefront of scientific research due to their unique electrical, mechanical and optical properties. However, transferring these properties from nanoscale materials to industrial-scale products often requires alignment (orientation in the same direction) of CNT. One of the important consequences of alignment is improved conductivity, a highly desirable property in electro-chemical water treatment and closely associated with research endeavors to improve quality of drinking water. Therefore, identification of scalable and cost-effective experimental conditions that maximize alignment of CNT is an important research problem. This is addressed in the project.The proposed research aims to establish statistical methodologies for designing and analyzing efficient experiments that determine conditions for maximizing alignment of CNT, when one or more input factors are prone to internal noise. The proposed research consists of three tasks, with particular focus on addressing the challenges arising from presence of factors with internal noise and complexity of the response surface. (i) Developing a Bayesian approach to response-surface optimization with noisy inputs. Such an approach allows the experimenter to combine data on output, controllable input, and uncontrollable input from different sources; is a natural way of incorporating expert knowledge into the analysis; and provides a natural framework for optimal design of experiments with noisy inputs. (ii) Efficient design of optimization experiments with noisy inputs. The research will focus on developing a comprehensive design strategy, which is a combination of model-free and Bayesian model-based optimal designs. The model-free design will address the challenges arising from internal noise and complex response surface. (iii) Demonstration and validation of the developed methodologies in the co-PI's lab. A series of experiments will be planned to apply the developed statistical methodology in an attempt to identify factors that trigger alignment of CNT and also to identify their optimum levels to maximize alignment. The proposed framework will allow an experimenter to effectively capture the transmission of uncertainty from input variables to output variables by combining data from different sources, and by utilizing a combination of model-free and model-based experimental designs for efficient exploration of complex response surfaces. From a material scientist's perspective, the proposed method will provide a much more accurate quantification of uncertainty, resulting in more reliable predictions about optimal process conditions as determined from laboratory experiments.