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

这项研究的主要工作集中在具有随机强迫项的非线性动力系统中的精确不确定性传播问题和数据同化算法的设计，以确定对实际物理现象的最优和多假设估计。所提出的研究工作的一个主要特点是将不确定性演化问题归结为一个保证收敛的凸优化问题。Fokker-Planck-Kolmogorov方程(FPKE)和Chapman-Kolmogorov方程(CKE)将被用来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的演化。通过准确地描述与过程模型和测量模型相关的不确定性，所提出的研究提供了低复杂性数据同化算法的系统设计，名义性能显著提高。拟议的研究工作将集中于通过严格的分析、模拟和设计来证明这些新想法在准确预测复杂物理现象方面的适用性和可行性，例如有毒物质在大气中的扩散。从一个或多个来源释放有害物质会产生烟羽，并根据当地的气象条件扩散和运输。任何用来表示污染物扩散的模型都反映了许多假设和简化，以便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模拟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烟羽产生深远的不利影响。将拟议的方法应用于有毒物质在大气中的扩散，将为诸如EPA或国土安全部等政府机构提供控制或监测有害空气污染物排放的手段。将实施一项广泛的计划，将研究计划整合到教育和推广计划中，涉及研究生、本科生和高中生以及科学和工程领域代表性不足的少数族裔

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