Nonlinear Model Order Reduction for Behavioral Models of Emerging Technologies

自然界中的物理现象本质上是非线性的。 然而，工程师用来建模和分析这些复杂相互作用的大多数技术都是基于线性近似。直到最近，这些近似值对于大多数工程应用都是可以接受的。然而，我们现在被迫重新考虑这种方法，因为新兴的微米和纳米技术已经导致系统变得复杂，具有许多自由度和高度非线性行为。 例如，考虑芯片实验室类型系统的设计，其使用微机械学和光电子学来操纵和分析复杂流体的行为。 这些系统可以彻底改变生物化学合成和分析的方式。 然而，它们固有地难以设计，因为它们涉及相互作用的电子、光电、流体、热和机械子系统。一方面，这种多技术系统只能用具有许多自由度的公式精确建模，并且还捕获底层物理的非线性特征;并且这些模型在计算上必然是昂贵的。 另一方面，为了有效地设计这样的系统，有必要在现实的操作环境中模拟和分析它们在广泛的刺激下的行为。 这就需要能够有效模拟的模型，以便在工程产品设计流程中探索它们所表现出的行为范围。因此，必须有一种方法来降低高维非线性系统的复杂性，而不求助于线性近似，因为只有这样的解决方案才能准确描述日益复杂的微纳米多技术系统。 为了满足这些需求，本研究将发展一种非线性行为模型的提取方法，并将为非线性模型降阶提供一种通用的方法。这些方法对于降低多技术微系统的设计成本、提高其质量和可靠性至关重要。拥有可以有效模拟的精确紧凑模型将使跨越多个能源领域的复杂异构系统的鲁棒设计成为可能。这种方法不仅广泛适用于电子系统设计，而且适用于工程和物理科学融合的新兴技术，如基于纳米技术的传感器，智能材料和系统生物学。

ABSTRACT0541150Steven LevitanU of PittsburghPhysical phenomena in nature are inherently nonlinear. However, most techniques used by engineers to model and analyze these complex interactions are based on linear approximations. Until recently, these approximations were acceptable for most engineering applications. However, we are now forced to rethink this approach due the fact that emerging micro- and nano- technologies have lead to systems that are complex, with many degrees of freedom, and highly nonlinear behavior. For example, consider the design of lab-on-a-chip type systems, which use micromechanics and optoelectronics to manipulate and analyze the behavior of complex fluids. These systems could revolutionize the way that bio-chemical synthesis and analysis are performed. However, they are inherently difficult to design because they involve interacting electronic, optoelectronic, fluidic, thermal and mechanical sub-systems. On the one hand, such multi-technology systems can only be accurately modeled with formulations that have many degrees of freedom and also capture the nonlinear characteristics of the underlying physics; and these models are necessarily computationally expensive. On the other hand, to effectively design such systems, it is necessary to simulate and analyze their behavior over a broad range of stimuli in a realistic operating environment. This requires models that can be simulated efficiently in order to explore the range of behaviors that they exhibit, in an engineering product design flow.Consequently, it is essential to have a methodology to reduce the complexity of nonlinear systems of high dimensionality, without recourse to linear approximation, since only such a solution will give an accurate description for ever increasingly complex micro- and nano- multi-technology systems. To address these needs, this research will develop a methodology for extraction of nonlinear behavioral models.The results of this work will lead to a general methodology for nonlinear model order reduction. Such methodologies are essential for reducing design costs and increasing both quality and reliability of multi-technology micro systems. Having accurate compact models that can be efficiently simulated will enable the robust design of complex heterogeneous systems that span multiple energy domains. This methodology will be broadly applicable not only to electronic systems design, but also to emerging technologies at the confluence of engineering and physical sciences, such as nanotechnology based sensors, smart materials and systems biology.