DynSyst_Special_Topics: Convex Optimization Based Approach for High Fidelity Uncertainty Propagation Through Nonlinear Dynamic Systems

这项研究工作的主要重点是通过非线性动力系统的准确不确定性传播的问题，随机强迫项和设计的数据同化算法，以确定最佳的和多假设的估计的实际物理现象。所提出的研究工作的一个主要特点是提出的不确定性演化问题作为一个凸优化问题，保证收敛。Fokker-Planck-Kolmogorov方程（FPKE）和Chapman-Kolmogorov方程（CKE）将用于确定由于初始或边界条件，模型参数和强迫函数的概率不确定性而导致的状态pdf的演变。通过准确地表征与过程和测量模型相关的不确定性，所提出的研究提供了系统设计的低复杂度的数据同化算法与显着改善标称性能。拟议的研究工作将侧重于通过严格的分析、模拟和设计，证明这些新想法在准确预测复杂物理现象（例如有毒物质在大气中的扩散）方面的适用性和可行性。从一个或多个来源地点释放的危险材料会产生羽流，羽流在当地气象条件下扩散和传播。任何用来表示污染物扩散的模型都是许多假设和简化的反映，以允许确定一个易于处理的模型。由于缺乏对当地气象条件的了解或建模过程中的许多假设而产生的不确定性可能对准确估计有毒羽流产生深远的不利影响。应用所提出的方法，通过大气中的有毒物质的扩散将提供政府机构，如环保署或国土安全部的手段，以控制或监测有害空气污染物的排放。一个广泛的计划，将研究计划纳入教育和推广计划将到位，涉及研究生，本科生和高中生以及在科学和工程领域代表性不足的少数民族

The main focus of this research work is on the problem of accurate uncertainty propagation through nonlinear dynamical systems with stochastic forcing term and the design of data assimilation algorithms to determine optimal and multi-hypothesis estimates of the actual physical phenomenon. A main feature of the proposed research work is to pose the uncertainty evolution problem as a convex optimization problem with guaranteed convergence. The Fokker-Planck-Kolmogorov equation (FPKE) and Chapman-Kolmogorov equation (CKE) will be used to determine evolution of state pdf due to probabilistic uncertainty in initial or boundary conditions, model parameters and forcing function. By accurately characterizing the uncertainty associated with both process and measurement models, the proposed research offers systematic design of low-complexity data assimilation algorithms with significant improvement in nominal performance. The proposed research effort will focus on demonstrating, through rigorous analysis, simulation and design, the applicability and feasibility of these new ideas in accurate forecasting of complex physical phenomenon such as the dispersion of toxic material through atmosphere. Release of hazardous material from one or multiple source locations creates a plume, which is diffused and transported by local meteorological conditions. Any model used to represent the dispersion of a pollutant is a reflection of numerous assumptions and simplifications to permit determination of a tractable model. The uncertainties resulting from the lack of knowledge of local meteorological conditions or numerous assumptions in the modeling process can have a profoundly detrimental effect on the accurate estimate of the toxic plume. The application of the proposed methodologies to the dispersion of toxic material through the atmosphere will provide governmental agencies such as EPA or DHS means to control or monitor the emission of harmful air pollutants.An extensive plan to integrate the research plan into an educational and outreach plan will be put in place that involves graduate, undergraduate as well as high-school students and under-represented minorities in science and engineering fields