Power grid voltage integrity verification requires checking if all the voltage drops on the grid are less than a certain threshold that guarantees proper circuit operation. This thesis addresses the problem of correcting the grid when some voltage drops exceed this threshold by making minor modifications to the existing design. The method uses current constraints that capture the uncertainty about the underlying circuit behavior to find the maximum voltage drop on the grid, and then to estimate the voltage drop as a function of the metal widths on the grid. It formulates a nonlinear optimization problem and finds the required change in widths that reduces the maximum voltage drop on the grid below the threshold while keeping the total area cost at a minimum.

No description available.

Wind is the main abiotic cause of disturbance to forests in large parts of the world, particularly at temperate and boreal latitudes. In the past few decades the consequences of large wind-induced losses have been experienced at various levels, from small forest owners to large-scale, whole-society level. This is particularly relevant for areas, such as Europe, where forests are intensively managed, and the assets exposed to wind hazard are substantial. To better manage forests and commercial tree plantations to reduce the risk of wind damage, process-based, semi-mechanistic mathematical models such as ForestGALES are used. This model has been parameterised and evaluated for numerous conifer species, which constitute the major plantation types in temperate and boreal biomes. However, the geographical extent and economic importance of fast-growing broadleaved species, such as those of the Eucalyptus genus, and the lack of detailed historical data on wind damage to these species, require that tools for the estimation of the risk of wind damage to these species are developed and evaluated. This is particularly relevant in light of the projected increases of surface temperature due to climate change, and of the frequency and severity of extreme windstorms, that are expected as a consequence of climate change. Fieldwork was conducted in a semi-natural Eucalyptus globulus (Labill.) forest in the Asturias region in Northern Spain to acquire data for the parameterisation of ForestGALES for E. globulus, using a tree-pulling experiment. The behaviour of the parameterisation was investigated for different stocking densities to evaluate whether the effects of tree height, stocking density, and presence of a fresh upwind gap are consistent with the literature. This parameterisation was then used to compare the vulnerability to wind damage between E. globulus and Pinus pinaster (Ait.), the predominant plantation species in the Aquitaine region of SW France where extensive damage was experienced from storms Martin (1999) and Klaus (2009). The effects of rooting depth (2x), growth rate (2x), presence/absence of a recently created windward gap, and of the predominant wind climate in Aquitaine were investigated in this comparison. In order to aid forest managers with optimal resource allocation for practical applications of ForestGALES, and to provide forest modellers with invaluable insights for the development of robust wind damage risk models, ForestGALES was subjected to a sensitivity analysis. A generalisation of the variance-based method of Sobol’ for the case of correlated variables was used to investigate the sensitivity of the outputs of ForestGALES (the critical wind speeds for stem breakage and uprooting, and the associated probabilities of damage) to variation in its input variables. Almost all the E. globulus trees pulled in Asturias failed by overturning rather than breakage, which allowed for good confidence in the calculations of the overturning moments required for the empirical component of ForestGALES. Resistance to overturning was not significantly influenced by the presence of a tap-root. Modelling the shape of the tree crowns with an ellipsoid provided a good approximation of the geometry of the canopy, but required additional fieldwork as crown width in the four cardinal directions had to be estimated visually prior to the tests. The scarcity of detailed published data on wind damage to E. globulus made evaluating the parameterisation particularly challenging. This impediment was obviated by investigating the behaviour of the parameterisation with regards to the well-known effects of tree height, stocking density, and presence of a fresh upwind gap. The simulations showed that the parameterisation behaved as expected, with vulnerability of E. globulus stands increasing with tree height, stocking density, and the presence of a gap. High initial planting densities, an early thinning, and a final harvesting before the trees have reached a height of 20 – 25m are recommended to reduce the risk of wind damage to E. globulus. The comparison with P. pinaster showed that E. globulus trees are particularly susceptible to the presence of a recently created windward gap. Therefore, harvesting at neighbouring sites should be minimised, and preferentially performed when the neighbouring stands are still at a young age to take advantage of the fast growth rates of E. globulus. These practices would ensure that in case of wind damage any losses are recovered in a short time. These procedures can reduce the cumulative risk through the rotation, while maintaining competitive yields. The ForestGALES simulations have also highlighted that the silvicultural practices currently in place in Aquitaine expose P. pinaster trees to high levels of cumulative risk (> 20%). The sensitivity analysis of ForestGALES has highlighted the strengths of the model and the areas that require substantial improvement. The results of the analysis show that ForestGALES is able to simulate very effectively the dynamics of wind damage to forest stands, as the model architecture reflects the significant influences of tree height, stocking density, dbh, and size of an upwind gap, on the calculations of the critical wind speeds of damage. Similarly, in ForestGALES the wind climate of a site is the main driver of variation of the probabilities of damage, as it is for real forests affected by extreme storms. Conversely, when the windiness of a site is moderate, ForestGALES accounts for the larger role of tree and stand variables. The sensitivity analysis has shown that ForestGALES is particularly efficient at simulating not only the effect of the size of windward gaps on the vulnerability of a stand, but also at differentiating between recently formed stand edges and edges that have been in place since the establishment of a stand. Therefore, for practical applications of the model, tree height, dbh, stocking density, the size and nature of an upwind gap, and the local wind climate, are the variables that need to be known with a high accuracy in order to maximally reduce the uncertainty of the model predictions. The section of the model that requires further attention and research is the one dedicated to the calculation of the trees’ resistance to overturning. The sensitivity analysis has shown that rooting depth and soil type, the model input variables on which the empirical component of ForestGALES that describes the resistance to overturning is based, contribute only marginally to the variation in the outputs. This finding unequivocally identifies that efforts for future research should be aimed at studying the mechanics of root-soil interactions with regards to tree stability. The results of the sensitivity analysis have also shown that the variance-based method used in this research project is equally sensitive to the accurate description of the probability distribution functions of the scrutinised variables, as it is to their correlation structure.

DRASTIC model is the most widely used method for aquifer vulnerability mapping which consists of seven hydrogeological parameters. Despite of its popularity, this technique disregards the effect of regional characteristics and there is no specific validation method to demonstrate the accuracy of this method. The main goal of this research was developing an integrated GIS-based DRASTIC model using Depth to water, Net Recharge, Aquifer media, Soil media, Topography, Impact of vadose zone and Hydraulic Conductivity (DRASTIC). In order to obtain a more reliable and accurate assessment, the rates and weights of original DRASTIC were modified using Wilcoxon rank-sum non-parametric statistical test and Single Parameter Sensitivity Analysis (SPSA). The methodology was implemented for the Shahrekord plain in the southwestern region of Iran. Two different sets of measured nitrate concentrations from two monitoring events were used, one for modification and other for validation purposes. Validation nitrate values were compared to the calculated DRASTIC index to assess the efficacy of the DRASTIC model. The validation results obtained from Pearson's correlation and chi-square values, revealed that the modified DRASTIC is more efficient than original DRASTIC. The modified rate/weight DRASTIC (spline) model showed the highest correlation coefficient and chi square value as 0.88 and 72.93, respectively, compared to -0.3 and 25.2 for the original DRASTIC (spline) model. The integrated vulnerability map showed the high risk imposed on the southeastern part of the Shahrekord aquifer. In addition, sensitivity analysis indicated that the removal of net recharge parameter from the modified model caused larger variation in vulnerability index showing that this parameter has more impact on the DRASTIC vulnerability of the aquifer. Moreover, Aquifer media (A), Topography (T) and Impact of vadose zone (I) were found to have less effect and importance compared to other variables as expected. Therefore, reduced modified DRASTIC model was proposed by eliminating A, T and I parameters. Pearson's correlation coefficient and chi-square value for the reduced model were calculated as 0.88 and 100.38, respectively, which was found to be as reliable as full modified DRASTIC model.

archives@tulane.edu / 1 / Harley Hanes

No description available.

A finite element solver has been developed for performing analysis and sensitivity analysis with Poisson's equation. An application of Poisson's equation in fluid dynamics is that of poential flow, in which case Posson's equaiton reduces to Laplace's equation. The stiffness matrix and sensitivity of the stiffness matrix are evaluated by direct integrations, as opposed to numerical integration. This allows less computational effort and minimizes the sources of computational errors. The capability of evaluating sensitivity derivatives has been added in orde to perform design sensitivity analysis of non-lifting airfoils. The discrete-direct approach to sensitivity analysis is utilized in the current work. The potential flow equations and the sensitivity equations are computed by using a preconditionaed conjugate gradient method. This method greatly reduces the time required to perfomr analysis, and the subsequent design optimization. Airfoil shape is updated at each design iteratioan by using a Bezier-Berstein surface parameterization. The unstrucured grid is adapted considering the mesh as a system of inteconnected springs. Numerical solutions from the flow solver are compared with analytical results obtained for a Joukowsky airfoil. Sensitivity derivaatives are validated using carefully determined central finite difference values. The developed software is then used to perform inverse design of a NACA 0012 and a multi-element airfoil.

No description available.

<p> The thesis proposes a novel method for the computation of the design sensitivity of microwave network parameters. The approach is based on the finite-element method. When combined with the iterative update method (the Broyden method) during the gradient-based optimization process, the approach requires practically no overhead for the computation of the response Jacobian, thus accelerating the optimization. </p> <p> The efficiency and accuracy of the gradient-based optimization and the tolerance analysis greatly depend on the computation of the design sensitivity. However, common commercial full-wave electromagnetic solvers do not provide sensitivity information. With them, the design sensitivities are computed from the response themselves using finite-difference or higher-order approximations at the response level. Consequently, for each design parameter of interest, at least one additional full-wave analysis is performed. </p> <p> The proposed self-adjoint sensitivity analysis (SASA) is so far the most efficient way to extract the sensitivity information for the network parameters with the finite-element method. As an improvement of the adjoint-variable method (AVM), it eliminates the additional system analyses. With one single full-wave analysis, the sensitivities with respect to all design parameters are computed. This significantly improves the efficiency of the sensitivity computations. </p> <p> When employed in gradient-based optimization, the computational overhead of the SASA can be further reduced. Instead of the finite-difference approximation, the system matrix derivatives are updated iteratively using the Broyden update. This reduces the computational overhead of the sensitivity analysis to practically zero. Further, several switching criteria between the Broyden update and the finite-difference approximation of the system matrix derivatives is proposed to guarantee the robust convergence of the optimization algorithm. This leads to our Broyden/finite-difference SASA (B/FD-SASA). </p> <p> The efficiency in terms of CPU time as well as the accuracy of the SASA is verified by several numerical examples, where the reference results are provided through the traditional finite-difference approximations. Also, the efficiency of the B/FD-SASA is validated by a filter design example and a microwave imaging example, with implementations exploiting different gradientbased optimization algorithms. </p> / Thesis / Master of Applied Science (MASc)

In practical multibody systems, various factors such as friction, joint clearances, and external events play a significant role and can greatly influence the optimal design of the system and its controller. This research focuses on the use of gradient-based optimization methods for multibody dynamic systems with the incorporation of joint friction. The dynamic formulation has been derived in using two distinct techniques: Index-1 DAE and the tangent-space formulation in minimal coordinates. It employs a two different approaches for gradient computation: direct sensitivity approach and the adjoint sensitivity approach. After a comprehensive review of different friction models developed over time, the Brown McPhee model is selected as the most suitable due to its accuracy in dynamic simulations and its compatibility with sensitivity analysis. The proposed methodology supports the simultaneous optimization of both the system and its controller. Moreover, the sensitivities obtained using these formulations have been thoroughly validated for numerical accuracy and benchmarked against other friction models that are based on dynamic events for stiction to friction transition. The approach presented is particularly valuable in applications like robotics and servo-mechanical systems where the design and actuation are closely interconnected. To obtain numerical results, a new implementation of the MBSVT (Multi-Body Systems at Virginia Tech) software package, known as MBSVT 2.0, is reprogrammed in Julia and MATLAB to ensure ease of implementation while maintaining high computational efficiency. The research includes multiple case studies that illustrate the advantages of the concurrent optimization of design and control for specific applications. Efficient techniques for control signal parameterization are presented using linear basis functions. A special focus has been made on the computational efficiency of the formulation and various techniques like sparse-matrix algebra and Jacobian-free products have been employed in the implementation. The dissertation concludes with a summary of key results and contributions and the future scope for this research. / Doctor of Philosophy / In simpler terms, this research focuses on improving the design and control of complex mechanical systems, like robots and automotive systems, by considering factors such as friction in the joints. Friction in a system can greatly affect how it performs for the desired task. The research uses a method called gradient-based optimization, which essentially means finding the most optimal parameters of the system and its controller such that they achieve a desired goal in the most optimal way. Before a model for such a system can be developed, various techniques need to be researched for incorporation of friction mathematically. A model known as Brown McPhee friction is one such model suitable for such an analysis. When optimizing any system on a computer, an iterative process needs to be performed which may prove to be very expensive in terms of computational resources required and the time taken to achieve a solution. Hence, proper mathematical and computational techniques need to be employed to ensure that the resources of a computer are utilized in the most efficient way to get the solution is the quickest way possible. Among the various novelties of this research, it is worth noting that this method that allows for simultaneous design and control optimization, which is particularly useful for applications such as robotics and servo-mechanical systems. Considering the design and control together, leads to more efficient and effective systems. The approach is tested using a software package called MBSVT 2.0, which was specifically developed as part of this research. The software is available in 3 languages: Julia, MATLAB and Fortran for universal access to people from various communities. The results from various case studies are presented that demonstrate this simultaneous design and control approach and highlights its effectiveness making the systems more robust and better performing.