Free tools and strategies for the generation of 3D finite element meshes: Modeling of the cardiac structures

The Finite Element Method is a well-known technique, being extensively applied in different areas. Studies using the Finite Element Method (FEM) are targeted to improve cardiac ablation procedures. For such simulations, the finite element meshes should consider the size and histological features of the target structures. However, it is possible to verify that some methods or tools used to generate meshes of human body structures are still limited, due to nondetailed models, nontrivial preprocessing, or mainly limitation in the use condition. In this paper, alternatives are demonstrated to solid modeling and automatic generation of highly refined tetrahedral meshes, with quality compatible with other studies focused on mesh generation. The innovations presented here are strategies to integrate Open Source Software (OSS). The chosen techniques and strategies are presented and discussed, considering cardiac structures as a first application context. © 2013 E. Pavarino et al.

Método numérico-analítico generalizado para estimação do campo eletromagnético de linhas de transmissão de energia elétrica utilizando a teoria dos elementos finitos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Análise da resolução do modelo de Hughes em sondagens magnetotelúricas

Na maioria dos métodos de exploração geofísica, a interpretação é feita assumindo-se um modelo da Terra uniformemente estratificado. Todos os métodos de inversão, inclusive o de dados eletromagnéticos, exigem técnica de modelamento teórico de modo a auxiliar a interpretação. Na literatura os dados são geralmente interpretados em termos de uma estrutura condutiva unidimensional; comumente a Terra é assumida ser horizontalmente uniforme de modo que a condutividade é função somente da profundidade. Neste trabalho uma técnica semi-analítica de modelagem desenvolvida por Hughes (1973) foi usada para modelar a resposta magnética de duas camadas na qual a interface separando as camadas pode ser representada por uma expansão em série de Fourier. A técnica envolve um método de perturbação para encontrar o efeito de um contorno senoidal com pequenas ondulações. Como a perturbação é de primeira ordem a solução obtida é linear, podemos então usar o princípio da superposição e combinar soluções para várias senoides de forma a obter a solução para qualquer dupla camada expandida em série de Fourier. Da comparação com a técnica de elementos finitos, as seguintes conclusões podem ser tiradas: • Para um modelo de dupla camada da Terra, as camadas separadas por uma interface cuja profundidade varia senoidalmente em uma direção, as respostas eletromagnética são muito mais fortes quando a espessura da primeira camada é da ordem do skin depth da onda eletromagnética no meio, e será tanto maior quanto maior for o contraste de condutividade entre as camadas; • Por outro lado, a resistividade aparente para este modelo não é afetada pela mudança na frequência espacial (v) do contorno; • Em caso do uso da solução geral para qualquer dupla camada na Terra cuja interface possa ser desenvolvida em série de Fourier, esta técnica produziu bons resultados quando comparado com a técnica de elementos finitos. A linerização restringe a aplicação da técnica para pequenas estruturas, apesar disso, uma grande quantidade de estruturas pode ser modelada de modo simples e com tempo computacional bastante rápido; • Quando a dimensão da primeira camada possui a mesma ordem de grandeza da estrutura, esta técnica não é recomendada, porque para algumas posições de sondagem, as curvas de resistividade aparente obtidas mostram um pequeno deslocamento quando comparadas com as curvas obtidas por elementos finitos.

Estudo do fenômeno de instabilidade de estruturas cilíndricas de paredes finas submetidas ao carregamento de pressão externa

Thin walled cylindrical shells are widely used in many areas of industry, including civil, mechanical, nuclear, marine, petroleum and aerospace engineering. The wide application of thin cylindrical shells and the importance of instability phenomenon are the motivation basis to this study, since these factors have a great importance in engineering projects. It is presented a detailed study about the instability of cylindrical shells based on theoretical calculation, which results are compared with finite elements method calculation. The loading and boundary conditions analyzed are based on the most common types verified in real engineering projects and refer respectively to lateral (external) pressure and cylinders with simply supported edges. The calculation based on the finite elements method was executed with ANSYS 13.0 software. The results obtained with this calculation are in good agreement with the analytical theory presented in the technical note NACA No 1341 (BATDORF, 1947) considering a wide range of applicability. On the other hand, the analytical method presented in the book Theory of Elastic Stability (TIMOSHENKO; GERE, 1936) has a very restrict applicability and has presented considerable deviations in a great sort of the analyzed cases

A coupling technique for non-matching finite element meshes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Optimal reactive power flow via the modified barrier Lagrangian function approach

A new approach called the Modified Barrier Lagrangian Function (MBLF) to solve the Optimal Reactive Power Flow problem is presented. In this approach, the inequality constraints are treated by the Modified Barrier Function (MBF) method, which has a finite convergence property: i.e. the optimal solution in the MBF method can actually be in the bound of the feasible set. Hence, the inequality constraints can be precisely equal to zero. Another property of the MBF method is that the barrier parameter does not need to be driven to zero to attain the solution. Therefore, the conditioning of the involved Hessian matrix is greatly enhanced. In order to show this, a comparative analysis of the numeric conditioning of the Hessian matrix of the MBLF approach, by the decomposition in singular values, is carried out. The feasibility of the proposed approach is also demonstrated with comparative tests to Interior Point Method (IPM) using various IEEE test systems and two networks derived from Brazilian generation/transmission system. The results show that the MBLF method is computationally more attractive than the IPM in terms of speed, number of iterations and numerical conditioning. (C) 2011 Elsevier B.V. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Longitudinal bar buckling behavior

Reinforced concrete columns might fail because of buckling of the longitudinal reinforcing bar when exposed to earthquake motions. Depending on the hoop stiffness and the length-over-diameter ratio, the instability can be local (in between two subsequent hoops) or global (the buckling length comprises several hoop spacings). To get insight into the topic, an extensive literary research of 19 existing models has been carried out including different approaches and assumptions which yield different results. Finite element fiberanalysis was carried out to study the local buckling behavior with varying length-over-diameter and initial imperfection-over-diameter ratios. The comparison of the analytical results with some experimental results shows good agreement before the post buckling behavior undergoes large deformation. Furthermore, different global buckling analysis cases were run considering the influence of different parameters; for certain hoop stiffnesses and length-over-diameter ratios local buckling was encountered. A parametric study yields an adimensional critical stress in function of a stiffness ratio characterized by the reinforcement configuration. Colonne in cemento armato possono collassare per via dell’instabilità dell’armatura longitudinale se sottoposte all’azione di un sisma. In funzione della rigidezza dei ferri trasversali e del rapporto lunghezza d’inflessione-diametro, l’instabilità può essere locale (fra due staffe adiacenti) o globale (la lunghezza d’instabilità comprende alcune staffe). Per introdurre alla materia, è proposta un’esauriente ricerca bibliografica di 19 modelli esistenti che include approcci e ipotesi differenti che portano a risultati distinti. Tramite un’analisi a fibre e elementi finiti si è studiata l’instabilità locale con vari rapporti lunghezza d’inflessione-diametro e imperfezione iniziale-diametro. Il confronto dei risultati analitici con quelli sperimentali mostra una buona coincidenza fino al raggiungimento di grandi spostamenti. Inoltre, il caso d’instabilità globale è stato simulato valutando l’influenza di vari parametri; per certe configurazioni di rigidezza delle staffe e lunghezza d’inflessione-diametro si hanno ottenuto casi di instabilità locale. Uno studio parametrico ha permesso di ottenere un carico critico adimensionale in funzione del rapporto di rigidezza dato dalle caratteristiche dell’armatura.

Studies of spatial clustering of inertial particles in turbulence

We present studies of the spatial clustering of inertial particles embedded in turbulent flow. A major part of the thesis is experimental, involving the technique of Phase Doppler Interferometry (PDI). The thesis also includes significant amount of simulation studies and some theoretical considerations. We describe the details of PDI and explain why it is suitable for study of particle clustering in turbulent flow with a strong mean velocity. We introduce the concept of the radial distribution function (RDF) as our chosen way of quantifying inertial particle clustering and present some original works on foundational and practical considerations related to it. These include methods of treating finite sampling size, interpretation of the magnitude of RDF and the possibility of isolating RDF signature of inertial clustering from that of large scale mixing. In experimental work, we used the PDI to observe clustering of water droplets in a turbulent wind tunnel. From that we present, in the form of a published paper, evidence of dynamical similarity (Stokes number similarity) of inertial particle clustering together with other results in qualitative agreement with available theoretical prediction and simulation results. We next show detailed quantitative comparisons of results from our experiments, direct-numerical-simulation (DNS) and theory. Very promising agreement was found for like-sized particles (mono-disperse). Theory is found to be incorrect regarding clustering of different-sized particles and we propose a empirical correction based on the DNS and experimental results. Besides this, we also discovered a few interesting characteristics of inertial clustering. Firstly, through observations, we found an intriguing possibility for modeling the RDF arising from inertial clustering that has only one (sensitive) parameter. We also found that clustering becomes saturated at high Reynolds number.

A Survey of Image-based Relighting Techniques

Image-based Relighting (IBRL) has recently attracted a lot of research interest for its ability to relight real objects or scenes, from novel illuminations captured in natural/synthetic environments. Complex lighting effects such as subsurface scattering, interreflection, shadowing, mesostructural self-occlusion, refraction and other relevant phenomena can be generated using IBRL. The main advantage of image-based graphics is that the rendering time is independent of scene complexity as the rendering is actually a process of manipulating image pixels, instead of simulating light transport. The goal of this paper is to provide a complete and systematic overview of the research in Imagebased Relighting. We observe that essentially all IBRL techniques can be broadly classified into three categories (Fig. 9), based on how the scene/illumination information is captured: Reflectance function-based, Basis function-based and Plenoptic function-based. We discuss the characteristics of each of these categories and their representative methods. We also discuss about the sampling density and types of light source(s), relevant issues of IBRL.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

Experimental and numerical analysis of reinforced concrete elements subjected to blast loading

El hormigón es uno de los materiales de construcción más empleados en la actualidad debido a sus buenas prestaciones mecánicas, moldeabilidad y economía de obtención, entre otras ventajas. Es bien sabido que tiene una buena resistencia a compresión y una baja resistencia a tracción, por lo que se arma con barras de acero para formar el hormigón armado, material que se ha convertido por méritos propios en la solución constructiva más importante de nuestra época. A pesar de ser un material profusamente utilizado, hay aspectos del comportamiento del hormigón que todavía no son completamente conocidos, como es el caso de su respuesta ante los efectos de una explosión. Este es un campo de especial relevancia, debido a que los eventos, tanto intencionados como accidentales, en los que una estructura se ve sometida a una explosión son, por desgracia, relativamente frecuentes. La solicitación de una estructura ante una explosión se produce por el impacto sobre la misma de la onda de presión generada en la detonación. La aplicación de esta carga sobre la estructura es muy rápida y de muy corta duración. Este tipo de acciones se denominan cargas impulsivas, y pueden ser hasta cuatro órdenes de magnitud más rápidas que las cargas dinámicas impuestas por un terremoto. En consecuencia, no es de extrañar que sus efectos sobre las estructuras y sus materiales sean muy distintos que las que producen las cargas habitualmente consideradas en ingeniería. En la presente tesis doctoral se profundiza en el conocimiento del comportamiento material del hormigón sometido a explosiones. Para ello, es crucial contar con resultados experimentales de estructuras de hormigón sometidas a explosiones. Este tipo de resultados es difícil de encontrar en la literatura científica, ya que estos ensayos han sido tradicionalmente llevados a cabo en el ámbito militar y los resultados obtenidos no son de dominio público. Por otra parte, en las campañas experimentales con explosiones llevadas a cabo por instituciones civiles el elevado coste de acceso a explosivos y a campos de prueba adecuados no permite la realización de ensayos con un elevado número de muestras. Por este motivo, la dispersión experimental no es habitualmente controlada. Sin embargo, en elementos de hormigón armado sometidos a explosiones, la dispersión experimental es muy acusada, en primer lugar, por la propia heterogeneidad del hormigón, y en segundo, por la dificultad inherente a la realización de ensayos con explosiones, por motivos tales como dificultades en las condiciones de contorno, variabilidad del explosivo, o incluso cambios en las condiciones atmosféricas. Para paliar estos inconvenientes, en esta tesis doctoral se ha diseñado un novedoso dispositivo que permite ensayar hasta cuatro losas de hormigón bajo la misma detonación, lo que además de proporcionar un número de muestras estadísticamente representativo, supone un importante ahorro de costes. Con este dispositivo se han ensayado 28 losas de hormigón, tanto armadas como en masa, de dos dosificaciones distintas. Pero además de contar con datos experimentales, también es importante disponer de herramientas de cálculo para el análisis y diseño de estructuras sometidas a explosiones. Aunque existen diversos métodos analíticos, hoy por hoy las técnicas de simulación numérica suponen la alternativa más avanzada y versátil para el cálculo de elementos estructurales sometidos a cargas impulsivas. Sin embargo, para obtener resultados fiables es crucial contar con modelos constitutivos de material que tengan en cuenta los parámetros que gobiernan el comportamiento para el caso de carga en estudio. En este sentido, cabe destacar que la mayoría de los modelos constitutivos desarrollados para el hormigón a altas velocidades de deformación proceden del ámbito balístico, donde dominan las grandes tensiones de compresión en el entorno local de la zona afectada por el impacto. En el caso de los elementos de hormigón sometidos a explosiones, las tensiones de compresión son mucho más moderadas, siendo las tensiones de tracción generalmente las causantes de la rotura del material. En esta tesis doctoral se analiza la validez de algunos de los modelos disponibles, confirmando que los parámetros que gobiernan el fallo de las losas de hormigón armado ante explosiones son la resistencia a tracción y su ablandamiento tras rotura. En base a los resultados anteriores se ha desarrollado un modelo constitutivo para el hormigón ante altas velocidades de deformación, que sólo tiene en cuenta la rotura por tracción. Este modelo parte del de fisura cohesiva embebida con discontinuidad fuerte, desarrollado por Planas y Sancho, que ha demostrado su capacidad en la predicción de la rotura a tracción de elementos de hormigón en masa. El modelo ha sido modificado para su implementación en el programa comercial de integración explícita LS-DYNA, utilizando elementos finitos hexaédricos e incorporando la dependencia de la velocidad de deformación para permitir su utilización en el ámbito dinámico. El modelo es estrictamente local y no requiere de remallado ni conocer previamente la trayectoria de la fisura. Este modelo constitutivo ha sido utilizado para simular dos campañas experimentales, probando la hipótesis de que el fallo de elementos de hormigón ante explosiones está gobernado por el comportamiento a tracción, siendo de especial relevancia el ablandamiento del hormigón. Concrete is nowadays one of the most widely used building materials because of its good mechanical properties, moldability and production economy, among other advantages. As it is known, it has high compressive and low tensile strengths and for this reason it is reinforced with steel bars to form reinforced concrete, a material that has become the most important constructive solution of our time. Despite being such a widely used material, there are some aspects of concrete performance that are not yet fully understood, as it is the case of its response to the effects of an explosion. This is a topic of particular relevance because the events, both intentional and accidental, in which a structure is subjected to an explosion are, unfortunately, relatively common. The loading of a structure due to an explosive event occurs due to the impact of the pressure shock wave generated in the detonation. The application of this load on the structure is very fast and of very short duration. Such actions are called impulsive loads, and can be up to four orders of magnitude faster than the dynamic loads imposed by an earthquake. Consequently, it is not surprising that their effects on structures and materials are very different than those that cause the loads usually considered in engineering. This thesis broadens the knowledge about the material behavior of concrete subjected to explosions. To that end, it is crucial to have experimental results of concrete structures subjected to explosions. These types of results are difficult to find in the scientific literature, as these tests have traditionally been carried out by armies of different countries and the results obtained are classified. Moreover, in experimental campaigns with explosives conducted by civil institutions the high cost of accessing explosives and the lack of proper test fields does not allow for the testing of a large number of samples. For this reason, the experimental scatter is usually not controlled. However, in reinforced concrete elements subjected to explosions the experimental dispersion is very pronounced. First, due to the heterogeneity of concrete, and secondly, because of the difficulty inherent to testing with explosions, for reasons such as difficulties in the boundary conditions, variability of the explosive, or even atmospheric changes. To overcome these drawbacks, in this thesis we have designed a novel device that allows for testing up to four concrete slabs under the same detonation, which apart from providing a statistically representative number of samples, represents a significant saving in costs. A number of 28 slabs were tested using this device. The slabs were both reinforced and plain concrete, and two different concrete mixes were used. Besides having experimental data, it is also important to have computational tools for the analysis and design of structures subjected to explosions. Despite the existence of several analytical methods, numerical simulation techniques nowadays represent the most advanced and versatile alternative for the assessment of structural elements subjected to impulsive loading. However, to obtain reliable results it is crucial to have material constitutive models that take into account the parameters that govern the behavior for the load case under study. In this regard it is noteworthy that most of the developed constitutive models for concrete at high strain rates arise from the ballistic field, dominated by large compressive stresses in the local environment of the area affected by the impact. In the case of concrete elements subjected to an explosion, the compressive stresses are much more moderate, while tensile stresses usually cause material failure. This thesis discusses the validity of some of the available models, confirming that the parameters governing the failure of reinforced concrete slabs subjected to blast are the tensile strength and softening behaviour after failure. Based on these results we have developed a constitutive model for concrete at high strain rates, which only takes into account the ultimate tensile strength. This model is based on the embedded Cohesive Crack Model with Strong Discontinuity Approach developed by Planas and Sancho, which has proved its ability in predicting the tensile fracture of plain concrete elements. The model has been modified for its implementation in the commercial explicit integration program LS-DYNA, using hexahedral finite elements and incorporating the dependence of the strain rate, to allow for its use in dynamic domain. The model is strictly local and does not require remeshing nor prior knowledge of the crack path. This constitutive model has been used to simulate two experimental campaigns, confirming the hypothesis that the failure of concrete elements subjected to explosions is governed by their tensile response, being of particular relevance the softening behavior of concrete.

A three-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities

We propose the use of a highly-accurate three-dimensional (3D) fully automatic hp-adaptive finite element method (FEM) for the characterization of rectangular waveguide discontinuities. These discontinuities are either the unavoidable result of mechanical/electrical transitions or deliberately introduced in order to perform certain electrical functions in modern communication systems. The proposed numerical method combines the geometrical flexibility of finite elements with an accuracy that is often superior to that provided by semi-analytical methods. It supports anisotropic refinements on irregular meshes with hanging nodes, and isoparametric elements. It makes use of hexahedral elements compatible with high-order H(curl)H(curl) discretizations. The 3D hp-adaptive FEM is applied for the first time to solve a wide range of 3D waveguide discontinuity problems of microwave communication systems in which exponential convergence of the error is observed.

Algoritmos para mineria de datos con redes de neuronas

Este trabajo propone una serie de algoritmos con el objetivo de extraer información de conjuntos de datos con redes de neuronas. Se estudian dichos algoritmos con redes de neuronas Enhenced Neural Networks (ENN), debido a que esta arquitectura tiene algunas ventajas cuando se aproximan funciones mediante redes neuronales. En la red ENN los pesos de la matriz principal varián con cada patrón, por lo que se comete un error menor en la aproximación. Las redes de neuronas ENN reúnen la información en los pesos de su red auxiliar, se propone un método para obtener información de la red a través de dichos pesos en formas de reglas y asignando un factor de certeza de dichas reglas. La red ENN obtiene un error cuadrático medio menor que el error teórico de una aproximación matemática por ejemplo mediante polinomios de Taylor. Se muestra como una red ENN, entrenada a partir un conjunto de patrones obtenido de una función de variables reales, sus pesos asociados tienen unas relaciones similares a las que se veri_can con las variables independientes con dicha función de variables reales. Las redes de neuronas ENN aproximan polinomios, se extrae conocimiento de un conjunto de datos de forma similar a la regresión estadística, resolviendo de forma más adecuada el problema de multicolionalidad en caso de existir. Las relaciones a partir de los pesos asociados de la matriz de la red auxiliar se obtienen similares a los coeficientes de una regresión para el mismo conjunto numérico. Una red ENN entrenada a partir de un conjunto de datos de una función boolena extrae el conocimiento a partir de los pesos asociados, y la influencia de las variables de la regla lógica de la función booleana, queda reejada en esos pesos asociados a la red auxiliar de la red ENN. Se plantea una red de base radial (RBF) para la clasificación y predicción en problemas forestales y agrícolas, obteniendo mejores resultados que con el modelo de regresión y otros métodos. Los resultados con una red RBF mejoran al método de regresión si existe colinealidad entre los datos que se dispone y no son muy numerosos. También se detecta que variables tienen más importancia en virtud de la variable pronóstico. Obteniendo el error cuadrático medio con redes RBF menor que con otros métodos, en particular que con el modelo de regresión. Abstract A series of algorithms is proposed in this study aiming at the goal of producing information about data groups with a neural network. These algorithms are studied with Enheced Neural Networks (ENN), owing to the fact that this structure shows sever advantages when the functions are approximated by neural networks. Main matrix weights in th ENN vary on each pattern; so, a smaller error is produced when approximating. The neural network ENN joins the weight information contained in their auxiliary network. Thus, a method to obtain information on the network through those weights is proposed by means of rules adding a certainty factor. The net ENN obtains a mean squared error smaller than the theorical one emerging from a mathematical aproximation such as, for example, by means of Taylor's polynomials. This study also shows how in a neural network ENN trained from a set of patterns obtained through a function of real variables, its associated weights have relationships similar to those ones tested by means of the independent variables connected with such functions of real variables. The neural network ENN approximates polynomials through it information about a set of data may be obtained in a similar way than through statistical regression, solving in this way possible problems of multicollinearity in a more suitable way. Relationships emerging from the associated weights in the auxiliary network matrix obtained are similar to the coeficients corresponding to a regression for the same numerical set. A net ENN trained from a boolean function data set obtains its information from its associated weights. The inuence of the variables of the boolean function logical rule are reected on those weights associated to the net auxiliar of the ENN. A radial basis neural networks (RBF) for the classification and prediction of forest and agricultural problems is proposed. This scheme obtains better results than the ones obtained by means of regression and other methods. The outputs with a net RBF better the regression method if the collineality with the available data and their amount is not very large. Detection of which variables are more important basing on the forecast variable can also be achieved, obtaining a mean squared error smaller that the ones obtained through other methods, in special the one produced by the regression pattern.