Effect of mesh distortion on the accuracy of high order vorticity-velocity CFD approaches

The numerical solution of the incompressible Navier-Stokes equations offers an alternative to experimental analysis of fluid-structure interaction (FSI). We would save a lot of time and effort and help cut back on costs, if we are able to accurately model systems by these numerical solutions. These advantages are even more obvious when considering huge structures like bridges, high rise buildings or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the Kinematic Laplacian Equation (KLE) to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ordinary differential equations (ODE) time integration schemes, allowing us to tackle each problem as a separate module. The current algortihm for the KLE uses an unstructured quadrilateral mesh, formed by dividing each triangle of an unstructured triangular mesh into three quadrilaterals for spatial discretization. This research deals with determining a suitable measure of mesh quality based on the physics of the problems being tackled. This is followed by exploring methods to improve the quality of quadrilateral elements obtained from the triangles and thereby improving the overall mesh quality. A series of numerical experiments were designed and conducted for this purpose and the results obtained were tested on different geometries with varying degrees of mesh density.

Multi-node TOA-DOA cooperative LOS-NLOS localization : enabling high accuracy and reliability

This dissertation investigates high performance cooperative localization in wireless environments based on multi-node time-of-arrival (TOA) and direction-of-arrival (DOA) estimations in line-of-sight (LOS) and non-LOS (NLOS) scenarios. Here, two categories of nodes are assumed: base nodes (BNs) and target nodes (TNs). BNs are equipped with antenna arrays and capable of estimating TOA (range) and DOA (angle). TNs are equipped with Omni-directional antennas and communicate with BNs to allow BNs to localize TNs; thus, the proposed localization is maintained by BNs and TNs cooperation. First, a LOS localization method is proposed, which is based on semi-distributed multi-node TOA-DOA fusion. The proposed technique is applicable to mobile ad-hoc networks (MANETs). We assume LOS is available between BNs and TNs. One BN is selected as the reference BN, and other nodes are localized in the coordinates of the reference BN. Each BN can localize TNs located in its coverage area independently. In addition, a TN might be localized by multiple BNs. High performance localization is attainable via multi-node TOA-DOA fusion. The complexity of the semi-distributed multi-node TOA-DOA fusion is low because the total computational load is distributed across all BNs. To evaluate the localization accuracy of the proposed method, we compare the proposed method with global positioning system (GPS) aided TOA (DOA) fusion, which are applicable to MANETs. The comparison criterion is the localization circular error probability (CEP). The results confirm that the proposed method is suitable for moderate scale MANETs, while GPS-aided TOA fusion is suitable for large scale MANETs. Usually, TOA and DOA of TNs are periodically estimated by BNs. Thus, Kalman filter (KF) is integrated with multi-node TOA-DOA fusion to further improve its performance. The integration of KF and multi-node TOA-DOA fusion is compared with extended-KF (EKF) when it is applied to multiple TOA-DOA estimations made by multiple BNs. The comparison depicts that it is stable (no divergence takes place) and its accuracy is slightly lower than that of the EKF, if the EKF converges. However, the EKF may diverge while the integration of KF and multi-node TOA-DOA fusion does not; thus, the reliability of the proposed method is higher. In addition, the computational complexity of the integration of KF and multi-node TOA-DOA fusion is much lower than that of EKF. In wireless environments, LOS might be obstructed. This degrades the localization reliability. Antenna arrays installed at each BN is incorporated to allow each BN to identify NLOS scenarios independently. Here, a single BN measures the phase difference across two antenna elements using a synchronized bi-receiver system, and maps it into wireless channel’s K-factor. The larger K is, the more likely the channel would be a LOS one. Next, the K-factor is incorporated to identify NLOS scenarios. The performance of this system is characterized in terms of probability of LOS and NLOS identification. The latency of the method is small. Finally, a multi-node NLOS identification and localization method is proposed to improve localization reliability. In this case, multiple BNs engage in the process of NLOS identification, shared reflectors determination and localization, and NLOS TN localization. In NLOS scenarios, when there are three or more shared reflectors, those reflectors are localized via DOA fusion, and then a TN is localized via TOA fusion based on the localization of shared reflectors.

Towards greater accuracy in individual-tree mortality regression

Background mortality is an essential component of any forest growth and yield model. Forecasts of mortality contribute largely to the variability and accuracy of model predictions at the tree, stand and forest level. In the present study, I implement and evaluate state-of-the-art techniques to increase the accuracy of individual tree mortality models, similar to those used in many of the current variants of the Forest Vegetation Simulator, using data from North Idaho and Montana. The first technique addresses methods to correct for bias induced by measurement error typically present in competition variables. The second implements survival regression and evaluates its performance against the traditional logistic regression approach. I selected the regression calibration (RC) algorithm as a good candidate for addressing the measurement error problem. Two logistic regression models for each species were fitted, one ignoring the measurement error, which is the “naïve” approach, and the other applying RC. The models fitted with RC outperformed the naïve models in terms of discrimination when the competition variable was found to be statistically significant. The effect of RC was more obvious where measurement error variance was large and for more shade-intolerant species. The process of model fitting and variable selection revealed that past emphasis on DBH as a predictor variable for mortality, while producing models with strong metrics of fit, may make models less generalizable. The evaluation of the error variance estimator developed by Stage and Wykoff (1998), and core to the implementation of RC, in different spatial patterns and diameter distributions, revealed that the Stage and Wykoff estimate notably overestimated the true variance in all simulated stands, but those that are clustered. Results show a systematic bias even when all the assumptions made by the authors are guaranteed. I argue that this is the result of the Poisson-based estimate ignoring the overlapping area of potential plots around a tree. Effects, especially in the application phase, of the variance estimate justify suggested future efforts of improving the accuracy of the variance estimate. The second technique implemented and evaluated is a survival regression model that accounts for the time dependent nature of variables, such as diameter and competition variables, and the interval-censored nature of data collected from remeasured plots. The performance of the model is compared with the traditional logistic regression model as a tool to predict individual tree mortality. Validation of both approaches shows that the survival regression approach discriminates better between dead and alive trees for all species. In conclusion, I showed that the proposed techniques do increase the accuracy of individual tree mortality models, and are a promising first step towards the next generation of background mortality models. I have also identified the next steps to undertake in order to advance mortality models further.

Post processing of multiple GPS receivers to enhance baseline accuracy

Inexpensive, commercial available off-the-shelf (COTS) Global Positioning Receivers (GPS) have typical accuracy of ±3 meters when augmented by the Wide Areas Augmentation System (WAAS). There exist applications that require position measurements between two moving targets. The focus of this work is to explore the viability of using clusters of COTS GPS receivers for relative position measurements to improve their accuracy. An experimental study was performed using two clusters, each with five GPS receivers, with a fixed distance of 4.5 m between the clusters. Although the relative position was fixed, the entire system of ten GPS receivers was on a mobile platform. Data was recorded while moving the system over a rectangular track with a perimeter distance of 7564 m. The data was post processed and yielded approximately 1 meter accuracy for the relative position vector between the two clusters.