Sequential Monte Carlo Based Data Assimilation Framework and Toolkit for Dynamic System Simulations

Assimilating real-time sensor data into simulations is an effective approach for improving predictive abilities. However, integrating complex simulation models, e.g., discrete event simulation models and agent-based simulation models, is a challenging task. That is because classical data assimilation techniques, such as Kalman Filter, rely on the analytical forms of system transition distribution, which these models do not have. Sequential Monte Carlo methods are a class of most extensively used data assimilation algorithms which recursively estimate system states using Bayesian inference and sampling technique. They are non-parametric filters and thus can work effectively with complex simulation models. Despite of the advantages of Sequential Monte Carlo methods, simulation systems do not automatically fit in data assimilation framework. In most cases, it is a difficult and tedious task to carry out data assimilation for complex simulation models. In addition, Sequential Monte Carlo methods are statistical methods developed by mathematicians while simulation systems are developed by researchers in particular research fields other than math. There is a need to bridge the gap of theory and application and to make it easy to apply SMC methods to simulation applications. This dissertation presents a general framework integrating simulation models and data assimilation, and provides guidance of how to carry out data assimilation for dynamic system simulations. The developed framework formalizes the data assimilation process by defining specifications for both simulation models and data assimilation algorithms. It implements the standard Bootstrap Particle Filtering algorithm and a new \emph{Sensor Informed Particle Filter}, (SenSim) to support effective data assimilation. The developed framework is evaluated based on the application of wildfire spread simulation, and experiment results show the effectiveness of data assimilation. Besides the framework, we also developed an open source software toolkit named as Data Assimilation Framework Toolkit to make it easy for researchers to carry out data assimilation for their own simulation applications. A tutorial example is provided to demonstrate the data assimilation process using this data assimilation toolkit

DAKOTA, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis:version 4.0 reference manual

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a reference manual for the commands specification for the DAKOTA software, providing input overviews, option descriptions, and example specifications

An allocation based modeling and solution framework for location problems with dense demand /

In this thesis we present a unified framework for planar location-allocation problems with dense demand. Emergence of such information technologies as Geographical Information Systems (GIS) has enabled access to detailed demand information. This proliferation of demand data brings about serious computational challenges for traditional approaches which are based on discrete demand representation. Furthermore, traditional approaches model the problem in location variable space and decide on the allocation decisions optimally given the locations. This is equivalent to prioritizing location decisions. However, when allocation decisions are more decisive or choice of exact locations is a later stage decision, then we need to prioritize allocation decisions. Motivated by these trends and challenges, we herein adopt a modeling and solution approach in the allocation variable space.Our approach has two fundamental characteristics: Demand representation in the form of continuous density functions and allocation decisions in the form of service regions. Accordingly, our framework is based on continuous optimization models and solution methods. On a plane, service regions (allocation decisions) assume different shapes depending on the metric chosen. Hence, this thesis presents separate approaches for two-dimensional Euclidean-metric and Manhattan-metric based distance measures. Further, we can classify the solution approaches of this thesis as constructive and improvement-based procedures. We show that constructive solution approach, namely the shooting algorithm, is an efficient procedure for solving both the single dimensional n-facility and planar 2-facility problems. While constructive solution approach is analogous for both metric cases, improvement approach differs due to the shapes of the service regions. In the Euclidean-metric case, a pair of service regions is separated by a straight line, however, in the Manhattan metric, separation takes place in the shape of three (at most) line segments. For planar 2-facility Euclidean-metric problems, we show that shape preserving transformations (rotation and translation) of a line allows us to design improvement-based solution approaches. Furthermore, we extend this shape preserving transformation concept to n-facility case via vertex-iteration based improvement approach and design first-order and second-order solution methods. In the case of planar 2-facility Manhattan-metric problems, we adopt translation as the shape-preserving transformation for each line segment and develop an improvement-based solution approach. For n-facility case, we provide a hybrid algorithm. Lastly, we provide results of a computational study and complexity results of our vertex-based algorithm