<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0121-1129</journal-id>
<journal-title><![CDATA[Revista Facultad de Ingeniería]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Fac. ing.]]></abbrev-journal-title>
<issn>0121-1129</issn>
<publisher>
<publisher-name><![CDATA[Universidad Pedagógica y Tecnológica de Colombia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0121-11292022000100204</article-id>
<article-id pub-id-type="doi">10.19053/01211129.v31.n59.2022.14037</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks]]></article-title>
<article-title xml:lang="es"><![CDATA[Determinación del diámetro interior de tuberías a presión para sistemas de agua potable utilizando redes neuronales artificiales]]></article-title>
<article-title xml:lang="pt"><![CDATA[Determinação do diâmetro interno de tubulações de pressão para sistemas de água potável usando redes neurais artificiais]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[García-Ubaque]]></surname>
<given-names><![CDATA[Cesar-Augusto]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ladino-Moreno]]></surname>
<given-names><![CDATA[Edgar-Orlando]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[García-Vaca]]></surname>
<given-names><![CDATA[María-Camila]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Distrital Francisco José de Caldas  ]]></institution>
<addr-line><![CDATA[Bogotá Distrito Capital]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Distrital Francisco José de Caldas  ]]></institution>
<addr-line><![CDATA[Bogotá Distrito Capital]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Católica de Colombia  ]]></institution>
<addr-line><![CDATA[Bogotá Distrito Capital]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2022</year>
</pub-date>
<volume>31</volume>
<numero>59</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0121-11292022000100204&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0121-11292022000100204&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0121-11292022000100204&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The fifth-degree polynomial equation determines the diameter in pressurized drinking water systems. The input variables are Q: flow (m3/s), H: pressure drop (m); L: pipe length (m); &#949;: roughness (m), &#977;: kinematic viscosity (m2/s), and &#425;k: sum of minor loss coefficients (dimensionless). After applying the energy equation for a hydraulic system composed of two tanks connected to a pipe of constant diameter and accepting the Colebrook-White and the Darcy-Weisbach equations, an undetermined expression is obtained since more unknowns than equations are established. This problem is solved by implementing a nested loop for the coefficient of friction and the diameter. This article proposes an Artificial Neural Network (ANN) implementing the Levenberg-Marquardt backpropagation method to estimate the diameter from the log-sigmoidal transfer function under stationary flow conditions. The training signals set consists of 5,000 random data that follow a normal distribution, calculated in Visual Basic (®Excel). The statistics used for the network evaluation correspond to the mean square error, the regression analysis, and the cross-entropy function. The architecture with the best performance had a hidden layer with 25 neurons (6-25-1) presenting an MSE equal to 5.41E-6 and 9.98E+00 for the Pearson Correlation Coefficient. The cross-validation of the neural scheme was carried out from 1,000 independent input signals from the training set, obtaining an MSE equal to 6.91E-6. The proposed neural network calculates the diameter with a relative error equal to 0.01% concerning the values &#8203;&#8203;obtained with ®Epanet, evidencing the generalizability of the optimized system.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El diámetro en sistemas a presión de agua potable es posible determinarlo mediante una ecuación polinómica de quinto grado. Como variables de entrada se tiene: Q: caudal (m3/s), H: pérdida de carga (m); L: longitud de la tubería (m); &#949;: rugosidad (m), &#120599;: viscosidad cinemática (m2/s) y &#425;k: sumatoria de coeficientes de pérdidas menores (adimensional). Aplicado la ecuación de la energía para un sistema hidráulico compuesto por dos tanques conectados con una tubería de diámetro constante y aceptando la ecuación de Colebrook-White y la ecuación de Darcy-Weisbach se obtiene una expresión subdeterminada debido a que se establecen más incógnitas que ecuaciones. Este problema se soluciona implementando un bucle anidado para el coeficiente de fricción y el diámetro. Este artículo propone una Red Neuronal Artificial (RNA) implementando el método de Retropropagación Levenberg-Marquardt para estimar el diámetro a partir de la función de transferencia log-sigmoidal, esto bajo condiciones estacionarias de flujo. El conjunto de las señales de entrenamiento está conformado por 5,000 datos aleatorios que siguen una distribución normal, calculados en Visual Basic (®Excel). Los estadísticos utilizados para la evaluación de la red corresponden al error medio cuadrático, el análisis de regresión y la función de entropía cruzada. La arquitectura que demostró un mejor redimento correspondió a una capa oculta con 25 neuronas (6-25-1) presentando un MSE igual a 5.41E-6 y 9.98E+00 para el Coeficiente de Correlación de Pearson. La validación cruzada del esquema neuronal se realizó a partir de 1,000 señales de entrada independientes del conjunto de entrenamiento obteniendo MSE igual 6.91E-6. La red neuronal propuesta calcula el diámetro con un error relativo igual a 0.01% con respecto a los valores obtenidos a partir de ®Epanet, evidenciando la capacidad de generalización del sistema optimizado.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo O diâmetro em sistemas de água potável pressurizada pode ser determinado por meio de uma equação polinomial de quinto grau. Como variáveis de entrada temos: Q: vazão (m3/s), H: perda de carga (m); L: comprimento do tubo (m); &#949;: rugosidade (m), &#977;: viscosidade cinemática (m2/s) e &#425;k: soma dos coeficientes de perdas menores (adimensional). Aplicando a equação de energia para um sistema hidráulico composto por dois tanques conectados por uma tubulação de diâmetro constante e aceitando a equação de Colebrook-White e a equação de Darcy-Weisbach, obtém-se uma expressão subdeterminada, pois se estabelecem mais incógnitas do que equações. Este problema é resolvido implementando um loop aninhado para o coeficiente de atrito e o diâmetro. Este artigo propõe uma Rede Neural Artificial (RNA) implementando o método Backpropagation de Levenberg-Marquardt para estimar o diâmetro a partir da função de transferência log-sigmoidal, isto sob condições de fluxo permanente. O conjunto de sinais de treinamento é composto por 5.000 dados aleatórios que seguem uma distribuição normal, calculados em Visual Basic (®Excel). As estatísticas utilizadas para a avaliação da rede correspondem ao erro quadrático médio, à análise de regressão e à função de entropia cruzada. A arquitetura que apresentou melhor rendimento correspondeu a uma camada oculta com 25 neurônios (6-25-1) apresentando um MSE igual a 5,41E-6 e 9,98E+00 para o Coeficiente de Correlação de Pearson. A validação cruzada do esquema neural foi realizada a partir de 1.000 sinais de entrada independentes do conjunto de treinamento, obtendo-se MSE igual a 6,91E-6. A rede neural proposta calcula o diâmetro com um erro relativo igual a 0,01% em relação aos valores obtidos do ®Epanet, mostrando a capacidade de generalização do sistema otimizado.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Artificial Neural Network]]></kwd>
<kwd lng="en"><![CDATA[Colebrook-White]]></kwd>
<kwd lng="en"><![CDATA[Darcy-Weisbach]]></kwd>
<kwd lng="en"><![CDATA[Levenberg-Marquardt]]></kwd>
<kwd lng="en"><![CDATA[pipeline hydraulics]]></kwd>
<kwd lng="es"><![CDATA[Colebrook-White]]></kwd>
<kwd lng="es"><![CDATA[Darcy-Weisbach]]></kwd>
<kwd lng="es"><![CDATA[hidráulica de tuberías]]></kwd>
<kwd lng="es"><![CDATA[Levenberg-Marquardt]]></kwd>
<kwd lng="es"><![CDATA[red neuronal artificial]]></kwd>
<kwd lng="pt"><![CDATA[Colebrook-White]]></kwd>
<kwd lng="pt"><![CDATA[Darcy-Weisbach]]></kwd>
<kwd lng="pt"><![CDATA[Levenberg-Marquardt]]></kwd>
<kwd lng="pt"><![CDATA[rede neural artificial]]></kwd>
<kwd lng="pt"><![CDATA[tubulação hidráulica]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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