Stochastic Inverse Methods to Identify non-Gaussian Model Parameters in Heterogeneous Aquifers

La modelación numérica del flujo de agua subterránea y del transporte de masa se está convirtiendo en un criterio de referencia en la actualidad para la evaluación de recursos hídricos y la protección del medio ambiente. Para que las predicciones de los modelos sean fiables, estos deben de estar lo más próximo a la realidad que sea posible. Esta proximidad se adquiere con los métodos inversos, que persiguen la integración de los parámetros medidos y de los estados del sistema observados en la caracterización del acuífero. Se han propuesto varios métodos para resolver el problema inverso en las últimas décadas que se discuten en la tesis. El punto principal de esta tesis es proponer dos métodos inversos estocásticos para la estimación de los parámetros del modelo, cuando estos no se puede describir con una distribución gausiana, por ejemplo, las conductividades hidráulicas mediante la integración de observaciones del estado del sistema, que, en general, tendrán una relación no lineal con los parámetros, por ejemplo, las alturas piezométricas. El primer método es el filtro de Kalman de conjuntos con transformación normal (NS-EnKF) construido sobre la base del filtro de Kalman de conjuntos estándar (EnKF). El EnKF es muy utilizado como una técnica de asimilación de datos en tiempo real debido a sus ventajas, como son la eficiencia y la capacidad de cómputo para evaluar la incertidumbre del modelo. Sin embargo, se sabe que este filtro sólo trabaja de manera óptima cuándo los parámetros del modelo y las variables de estado siguen distribuciones multigausianas. Para ampliar la aplicación del EnKF a vectores de estado no gausianos, tales como los de los acuíferos en formaciones fluvio-deltaicas, el NSEnKF propone aplicar una transformación gausiana univariada. El vector de estado aumentado formado por los parámetros del modelo y las variables de estado se transforman en variables con una distribución marginal gausiana.Zhou ., H. (2011). Stochastic Inverse Methods to Identify non-Gaussian Model Parameters in Heterogeneous Aquifers [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/12267Palanci

Three-dimensional Hydraulic conductivity upscaling in groundwater modelling

Groundwater numerical simulation is a tool nowadays routinely used in water resources evaluation. The accuracy of groundwater flow and transport simulations relies very much on the ability to properly characterize the spatial variability of hydraulic conductivity. One of the problems that this characterization faces is the disparity between the sample support and the support used in the discretization of the numerical model. While it is possible to generate realizations of conductivity at the measurement support scale, it is too demanding to perform numerical simulations with such a level of discretization. The need to change of support calls for upscaling techniques. We refer to the scale at which hydraulic conductivity can be characterized as the fine scale, and the scale of the numerical discretization as the coarse scale. This thesis proposes a three-dimensional hydraulic conductivity upscaling algorithm geared to its use with a finite difference code. Because finite difference codes use the interblock conductivity to compute the groundwater flow between blocks, the algorithm aims at computing the hydraulic conductivity representative of the volume between block centres as direct input to the groundwater flow solver, thus avoiding unnecessary averaging rules between neighboring block conductivities. This is particularly important since at the coarse scale hydraulic conductivities will, in general, have to be represented by full tensors, and the averaging of tensors is not a trivial task. The anisotropic spatial correlation of the hydraulic conductivities at the fine scale, even when these conductivities are considered isotropic at this scale, will induce flow anisotropy at coarser scales. Determining the interblock upscaled conductivity tensor is done by isolating the fine scale hydraulic conductivities that make up the interblock of interest plus a sufficiently large skin surrounding it, and then solving the groundwater flow equation using several boundary conditions. The symmetric 3D tensor that is capable to best reproduce the average fluxes through the interblock, given the average hydraulic head gradient, for the different boundary conditions is computed by a simple optimization and retained as the interblock conductivity tensor at the coarse scale. The algorithm has been verified in three synthetic experiments. Hydraulic conductivity at the small scale is considered isotropic to flow in all cases, but displaying different spatial heterogeneity: isotropic spatial correlation, anisotropic correlation, and a sand/shale distribution. In all three cases the upscaled models reproduce very well the average flows between blocks as computed at the fine scale. The speed of the algorithm depends very much on the size of the skin selected to perform the small scale simulations to determine each of the interblock conductivity tensor. The larger the skin, the better the final reproduction of the average flows; however, we found that a skin about half the size of the upscaling block gives good results in the three examples.Zhou ., H. (2009). Three-dimensional Hydraulic conductivity upscaling in groundwater modelling. http://hdl.handle.net/10251/13715Archivo delegad

A full divergence-free of high order virtual finite element method to approximation of stationary inductionless magnetohydrodynamic equations on polygonal meshes

In this present paper we consider a full divergence-free of high order virtual finite element algorithm to approximate the stationary inductionless magnetohydrodynamic model on polygonal meshes. More precisely, we choice appropriate virtual spaces and necessary degrees of freedom for velocity and current density to guarantee that their final discrete formats are both pointwise divergence-free. Moreover, we hope to achieve higher approximation accuracy at higher "polynomial" orders k_{1} \geq 2, k_{2} \geq 1, while the full divergence-free property has always been satisfied. And then we processed rigorous error analysis to show that the proposed method is stable and convergent. Several numerical tests are presented, confirming the theoretical predictions

A Rough-Set-basedClustering Algorithm for Multi-stream

AbstractThe paper propose a rough-set-based clustering algorithm for multiple data stream, which solve the problem that existing clustering algorithm for multiple data streams can not take into account conflicts between clustering quality and efficiency. Firstly, the algorithm calculates the distance between data stream to determine the initial equivalence relations, and calculates the similarity between the initial equivalence relation to determine the initial cluster. In the second place, the similarity between the initial clusters is used to merge the initial clusters. Finally, k-means clustering algorithm is called to dynamically adjust the clustering results, and then real-time clustering structure is obtained. In conclusion Experimental results demonstrated that the algorithm has higher efficiency and clustering quality

On the α\alpha-spectral radius of hypergraphs

For real $\alpha\in [0,1)$ and a hypergraph $G$, the $\alpha$-spectral radius of $G$ is the largest eigenvalue of the matrix $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$, where $A(G)$ is the adjacency matrix of $G$, which is a symmetric matrix with zero diagonal such that for distinct vertices $u,v$ of $G$, the $(u,v)$-entry of $A(G)$ is exactly the number of edges containing both $u$ and $v$, and $D(G)$ is the diagonal matrix of row sums of $A(G)$. We study the $\alpha$-spectral radius of a hypergraph that is uniform or not necessarily uniform. We propose some local grafting operations that increase or decrease the $\alpha$-spectral radius of a hypergraph. We determine the unique hypergraphs with maximum $\alpha$-spectral radius among $k$-uniform hypertrees, among $k$-uniform unicyclic hypergraphs, and among $k$-uniform hypergraphs with fixed number of pendant edges. We also determine the unique hypertrees with maximum $\alpha$-spectral radius among hypertrees with given number of vertices and edges, the unique hypertrees with the first three largest (two smallest, respectively) $\alpha$-spectral radii among hypertrees with given number of vertices, the unique hypertrees with minimum $\alpha$-spectral radius among the hypertrees that are not $2$-uniform, the unique hypergraphs with the first two largest (smallest, respectively) $\alpha$-spectral radii among unicyclic hypergraphs with given number of vertices, and the unique hypergraphs with maximum $\alpha$-spectral radius among hypergraphs with fixed number of pendant edges