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

本研究工作的主要重点是在具有随机强迫项的非线性动力系统中精确的不确定性传播问题，以及设计数据同化算法以确定实际物理现象的最优和多假设估计。本文研究工作的一个主要特点是将不确定性演化问题作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的演化。通过准确表征与过程和测量模型相关的不确定性，本研究提供了低复杂度数据同化算法的系统设计，显著提高了标称性能。拟开展的研究工作将侧重于通过严格的分析、模拟和设计，证明这些新思想在准确预测有毒物质通过大气扩散等复杂物理现象方面的适用性和可行性。有害物质从一个或多个源头释放，形成羽流，由当地气象条件扩散和输送。用于表示污染物扩散的任何模型都是许多假设和简化的反映，以便确定一个可处理的模型。由于缺乏对当地气象条件的了解或在建模过程中有许多假设而产生的不确定性，可能对有毒烟羽的准确估计产生严重的不利影响。将拟议的方法应用于有毒物质在大气中的扩散，将为环境保护署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。政府将制定一项将研究计划整合到教育和推广计划中的广泛计划，该计划将涉及研究生、本科生、高中生以及科学和工程领域中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