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)因其独特的电学、力学和光学性质而上升到科学研究的前沿。然而，将这些性质从纳米材料转移到工业规模的产品通常需要碳纳米管的取向(取向相同)。对齐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工作密切相关。因此，确定可扩展且经济的实验条件以最大化碳纳米管的比对是一个重要的研究问题。该研究旨在建立统计方法来设计和分析有效的实验，以确定当一个或多个输入因素容易产生内部噪声时使CNT对齐最大化的条件。拟议的研究包括三项任务，特别侧重于解决因存在具有内部噪声的因素和响应面的复杂性而产生的挑战。(I)开发一种贝叶斯方法来优化具有噪声输入的响应面。这种方法允许实验者组合来自不同来源的输出、可控输入和不可控输入的数据；是将专家知识纳入分析的自然方式；并为具有噪声输入的实验的优化设计提供了自然的框架。(2)具有噪声输入的优化实验的有效设计。研究将集中于开发一种综合的设计策略，这是无模型和基于贝叶斯模型的优化设计的组合。无模型设计将解决内部噪声和复杂响应面带来的挑战。(3)在共同PI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CNT对齐的因素，并确定它们的最佳水平，以最大限度地对齐。建议的框架将允许实验者通过组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来有效地探索复杂的响应面，从而有效地捕捉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，建议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做出更可靠的预测。

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.