A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method

An algorithm to schedule water delivery in pressurized irrigation networks

This study presents a deterministic constrained optimisation algorithm developed for using in a pressurized irrigation network. In irrigation networks —or water networks supplied by a head tank— utility managers can fully adapt the delivery times to suit their needs. The program provides a strategy for scheduling water delivery at a constant flow rate (opening and closing of hydrants, units, and subunits) to minimise energy consumption. This technique improves on earlier approaches by employing a deterministic method with little computing time. This method has been tested in the University of Alicante pressurized irrigation network, where decision-makers have identified the need to diminish the energy expenditure for watering University’s gardens.This work was supported by the research project “DESENREDA” through the 2021 call “Estancias de movilidad en el extranjero Jose Castillejo” of the Ministerio de Universidades (CAS21/00085) and for the project “Hi-Edu Carbon” Erasmus Plus Programme, Key Action KA22021, action type (2021-1-SK01-KA220-HED-000023274

Parallel approach of a Galerkin-based methodology for predicting the compressive strength of the lightweight aggregate concrete

A methodology based on the Galerkin formulation of the finite element method has been analyzed for predicting the compressive strength of the lightweight aggregate concrete using ultrasonic pulse velocity. Due to both the memory requirements and the computational cost of this technique, its parallelization becomes necessary for solving this problem. For this purpose a mixed MPI/OpenMP parallel algorithm has been designed and different approaches and data distributions analyzed. On the other hand, this Galerkin methodology has been compared with multiple linear regression models, regression trees and artificial neural networks. Based on different measures of goodness of fit, the effectiveness of the Galerkin methodology, compared with these statistical techniques for data mining, is shown.This research was supported by the Spanish Ministry of Science, Innovation and Universities Grant RTI2018-098156-B-C54, co-financed by the European Commission (FEDER funds)

Accurate integration of forced and damped oscillators

The new methods accurately integrate forced and damped oscillators. A family of analytical functions is introduced known as T-functions which are dependent on three parameters. The solution is expressed as a series of T-functions calculating their coefficients by means of recurrences which involve the perturbation function. In the T-functions series method the perturbation parameter is the factor in the local truncation error. Furthermore, this method is zero-stable and convergent. An application of this method is exposed to resolve a physic IVP, modeled by means of forced and damped oscillators. The good behavior and precision of the methods, is evidenced by contrasting the results with other-reputed algorithms implemented in MAPLE

An Octahedric Regression Model of Energy Efficiency on Residential Buildings

System modeling is a main task in several research fields. The development of numerical models is of crucial importance at the present because of its wide use in the applications of the generically named machine learning technology, including different kinds of neural networks, random field models, and kernel-based methodologies. However, some problems involving the reliability of their predictions are common to their use in the real world. Octahedric regression is a kernel averaged methodology developed by the authors that tries to simplify the entire process from raw data acquisition to model generation. A discussion about the treatment and prevention of overfitting is presented and, as a result, models are obtained that allow for the measurement of this effect. In this paper, this methodology is applied to the problem of estimating the energetic needs of different buildings according to their principal characteristics, a problem that has importance in architecture and civil and environmental engineering due to increasing concerns about energetic efficiency and ecological footprint

Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support

Estimation problems are frequent in several fields such as engineering, economics, and physics, etc. Linear and non-linear regression are powerful techniques based on optimizing an error defined over a dataset. Although they have a strong theoretical background, the need of supposing an analytical expression sometimes makes them impractical. Consequently, a group of other approaches and methodologies are available, from neural networks to random forest, etc. This work presents a new methodology to increase the number of available numerical techniques and corresponds to a natural evolution of the previous algorithms for regression based on finite elements developed by the authors improving the computational behavior and allowing the study of problems with a greater number of points. It possesses an interesting characteristic: Its direct and clear geometrical meaning. The modelling problem is presented from the point of view of the statistical analysis of the data noise considered as a random field. The goodness of fit of the generated models has been tested and compared with some other methodologies validating the results with some experimental campaigns obtained from bibliography in the engineering field, showing good approximation. In addition, a small variation on the data estimation algorithm allows studying overfitting in a model, that it is a problematic fact when numerical methods are used to model experimental values.This research has been partially funded by the Spanish Ministry of Science, Innovation and Universities, grant number RTI2018-101148-B-I00

Water Quality of the Beach in an Urban and not Urban Environment

Numerous studies and theories have emerged for evaluating the quality of beaches using different parameters. In recent years in the European region, one of the most important aspects when evaluating a beach is the quality of water and sand. The quality of water is represented by the amount of Intestinal Enterococcus and Escherichia coli. This parameter is essential and others to obtain the Blue Flag, indicating that the user of the beach can swim safely. The European Directive 2006/7/EC establishes the limits of E. coli and Enterococcus that may exist in bathing water. However, it should be noted that each ecosystem is unique, and therefore the characteristics a beach are not the same per example if you are in an inland sea, or an ocean, or equal if they are close to an urban or a natural area. In this paper, 1,392 beaches in Spain have been analysed, and it has been observed that in the Mediterranean, the beaches have a lower concentration of bacteria than other areas. In addition, it appears that the sandy beaches and urban beaches have a higher content of bacteria that natural and gravel beaches

A methodology for the classification of gravel beaches

Beaches are highly flexible structures that can be deformed by several reasons, some natural as wind and swell and others not, as human actions. Gravel, considered as a component of the beach is not always separated from the rest of the materials. It is a part of the coastline sedimentary balance, usually with time and spatial scales much greater than those corresponding to the stretch of the coast under study. The conceptual and experimental difficulties of studying this kind of beach have meant that nowadays they are really unknown. In this paper, methodologies to classify and determinate the most important characteristics in gravel beaches are presented. The authors have studied 34 shingle beaches in the region of Alicante (Spain) from a database with their characteristics. Obtained data corresponds to the morphology of the beach, the materials that take part in its composition and the wave energy, considering its incidence, the wave height, the local period and its influence on the coastline. At the beginning, mathematical models are generated, allowing the expression of the relationships between the slope of berm and the rest of variables. To classify the beaches, a factor analysis has been used on the experimental data matrix, considering all the variables as predictive, obtaining in this way an index for beach classification with similar characteristics. Furthermore, to determine the predictive variables that allow characterizing the 34 beaches, a discriminant analysis has been applied over several sets of variables. In each case, a predictive model of cluster belonging is created, considering a discriminant function, and with the clustering function formed by different clusters. The methodologies developed in this paper will be applied later to other beaches as classification and variable selection methods

A parallel methodology using radial basis functions versus machine learning approaches applied to environmental modelling

Parallel nonlinear models using radial kernels on local mesh support have been designed and implemented for application to real-world problems. Although this recently developed approach reduces the memory requirements compared with other methodologies suggested over the last few years, its computational cost makes parallelisation necessary, especially for big datasets with many instances or attributes. In this work, several strategies for the parallelisation of this methodology are proposed and compared. The MPI communication protocol and the OpenMP application programming interface are used to implement the algorithm. The performance of this methodology is compared with various machine learning methods, with particular consideration of techniques using radial basis functions (RBF). Different methods are applied to model the daily maximum air temperature from real meteorological data collected from the Agroclimatic Station Network of the Phytosanitary Alert and Information Network of Andalusia, an autonomous community of southern Spain. The obtained goodness-of-fit measures illustrate the effectiveness of this nonlinear methodology, and its training process is shown to be simpler than those of other powerful machine learning methods.This research was supported by the Spanish Ministry of Science, Innovation and Universities Grant RTI2018-098156-B-C54, co-financed by the European Commission (FEDER funds), and by the University of Alicante

Galerkin's formulation of the finite elements method to obtain the depth of closure

Coastal erosion and lack of sediment supply are a serious global problem. It is therefore necessary to determine the depth of closure (DoC) of a beach—key parameter in the calculation of the sand volume and the location of the beach protection elements—in a precise way. For this reason, this work generates a numerical model based on Galerkin's formulation of finite elements that provides sufficient precision for the determination of DoC with a minimum investment. Thus, after the generation of three models in which the difference was the dependent variables, the least complex has been chosen. It is composed of the variables: median sediment size, wave height and period associated with the mean flow, as well as the angle that the mean flow forms with respect to the studied profile in absolute value (α). The selected model has been compared with the most commonly used models currently in use, having an average absolute error of 0.36 m and an average MAPE of 70% over current models. In addition, it presents a high stability, since after the random disturbance of all the input variables (up to 5%), the model error remains stable, increasing the MAPE by a maximum of 7.4% and the average absolute error by 0.15 m. Therefore, it is possible to use the model to infer the DoC in other study areas where the values of the variables are similar to those studied here, although the selected method can be extrapolated to other parts of the world.This work was partially supported by the Universidad de Alicante through the project “Estudio sobre el perfil de equilibrio y la profundidad de cierre en playas de arena” (GRE15-02)