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、力学和光学特性，已经上升到科学研究的前沿。然而，将这些特性从纳米级材料转移到工业规模产品通常需要碳纳米管的对齐（方向相同）。对准的一个重要结果是提高导电性，这是电化学水处理中非常理想的特性，与改善饮用水质量的研究密切相关。因此，确定可扩展且具有成本效益的实验条件以最大化碳纳米管的对准是一个重要的研究问题。这个问题在项目中得到了解决。当一个或多个输入因素容易产生内部噪声时，本研究旨在建立设计和分析有效实验的统计方法，以确定最大化碳纳米管对齐的条件。提出的研究包括三个任务，特别侧重于解决内部噪声因素和响应面复杂性所带来的挑战。(i)发展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将来自不同来源的输出、可控输入和不可控输入的数据结合起来；是一种将专家知识纳入分析的自然方式；并为带噪声输入的实验优化设计提供了一个自然的框架。（ii）具有噪声输入的优化实验的有效设计。研究将重点发展一种综合设计策略，即无模型优化设计和基于贝叶斯模型的优化设计相结合。无模型设计将解决内部噪声和复杂响应面带来的挑战。（iii）在联合项目负责人的实验室中演示和验证所开发的方法。将计划进行一系列实验，以应用开发的统计方法，试图确定触发碳纳米管对齐的因素，并确定其最佳水平，以最大限度地对齐。所提出的框架将允许实验者通过结合来自不同来源的数据，并利用无模型和基于模型的实验设计的组合来有效地探索复杂响应面，从而有效地捕获不确定性从输入变量到输出变量的传递。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.