Maestría en Matemática Aplicada

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    Implementación de un sistema predictivo con redes neuronales para el control del comportamiento de la planta Festo MPS-PA
    (Universidad Técnica de Ambato. Facultad de Ingeniería en Sistemas, Electrónica e Industrial. Maestría en Matemática Aplicada, 2021) Soria Mejía, Daysi Maribel; Benalcázar Palacios, Freddy Geovanny
    In the present research work, the implementation of a Dynamic Matrix Predictive Controller (DMC) with Neural Networks was carried out for the level control process (liquid) of a Festo Compact Workstation plant of the hydraulics and pneumatics laboratory of the Technical University of Ambato. The dynamics of the plant was found through the training of a feedforward neural network, the training and testing data used were obtained by conducting an experiment that consists of applying different step inputs to the plant and the response of the system to said input. The algorithm implemented was that of a dynamic matrix predictive controller, for which it is necessary to know the mathematical model of the level process represented as a transfer function, said mathematical model was built using the exponential regression method by least squares.
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    Modelo matemático de la producción de la empresa Salinerito en la Provincia Bolívar
    (Universidad Técnica de Ambato. Facultad de Ingeniería en Sistemas, Electrónica e Industrial. Maestría en Matemática Aplicada, 2021) Sánchez Verdezoto, Carlos Alfredo; Benalcázar Palacios, Freddy Geovanny
    EXECUTIVE SUMMARY The present research work is descriptive, predictive and longitudinal with a trend. The objective was to develop a mathematical model for the production of the company Confites El Salinerito in the Bolívar province, from the production values in the period from January 2017 to July 2020, the data were obtained directly from the company. To achieve the research objectives, the methodology proposed by Box-Jenkins was applied, which describes the characteristics of the time series in terms of trend, seasonality and stationarity; The free software RStudio version 4.0.1 was applied for the estimation of the parameters, the processing and the analysis of the data. It was concluded that the mathematical model that most accurately adjusts to the production values of the company was SARIMA (1, 1, 1) (1, 1, 1) 12, the same one that allowed making the monthly production forecasts for the period from August 2020 to January 2021. The results obtained by the developed model and the methodology used by the company to establish its monthly production were also compared.
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    Modelo matemático para determinar la calidad de servicio en el transporte público urbano en la ciudad de Ambato
    (Universidad Técnica de Ambato. Facultad de Ingeniería en Sistemas, Electrónica e Industrial. Maestría en Matemática Aplicada, 2021) Toscano Ramos, Orlando Ruben; Benalcázar Palacios, Freddy Geovanny
    This research is quantitative, descriptive and correlational. The objective was to build a mathematical model that allows determining the quality of the urban public transport service in the city of Ambato in the period 2020 - 2021. The data were obtained through the survey technique with its instrument the questionnaire, the same as applied to 400 users who use public transport in the city of Ambato. To achieve the objectives proposed in the research, the binary logistic regression model was applied, which helps to classify and predict the quality of the urban public transport service in the city of Ambato The variables involved in this research were: as a dependent variable the quality of the service and as predictive or independent variables: the waiting time, the treatment of the user, the current state of the units and the way of driving of the carrier. For the processing and analysis of the data, the Microsoft Excel 2016 program and the free software RStudio version 4.0.1 were used. It is concluded that the constructed logistic regression model correctly adjusts to the predictor variables, the decision frontier yielded by the model was 0.6142 or 61.42%, which is used to determine the quality of the safe and unsafe service. The model correctly classifies 308 observations, of which 205 observations are classified as safe, representing 51.25% of the total data, while 103 observations were classified as unsafe, which is equivalent to 25.75%. With the analysis carried out, it was determined that the urban public transport of the city of Ambato is moderately safe, for which the pertinent authorities should place emphasis on improving the quality of the service.
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    Modelo matemático prospectivo para la generación de desechos hospitalarios en el cantón Ambato
    (Universidad Técnica de Ambato. Facultad de Ingeniería en Sistemas, Electrónica e Industrial. Maestría en Matemática Aplicada, 2021) Bastidas Sarabia, Liliana Rocío; Benalcázar Palacios, Freddy Geovanny
    This research is descriptive, longitudinal and projective, in order to develop a prospective mathematical model for the generation of hospital waste in the canton of Ambato, through the database of the SIPECA system of the Municipal Public Company for the Integral Management of Solid Waste from Ambato comprised in the period January 2014 to March 2020. In this research, the time series was applied, especially the SARIMA models that are built under the Box-Jenkins methodology. For the analysis and processing of the database, the free software RStudio version 4.0.1 was used and the computer code was also built. It was possible to build a mathematical model that allows to satisfactorily analyze, explain, describe and predict the production of solid hospital waste collected monthly in the Ambato canton. It is concluded that the model that meets the tests of adequacy and randomness is the SARIMA (1, 1, 1) (1, 0, 1) [12] whose forecasting equation is: ΔŶt = -0.326 Yt − 1 + 0.992 Yt − 12 + 0.7882 Ɛt − 1 + 0.8934 Ɛt − 12 + Ɛt, with this model the projections for the period April 2021 to March 2022 were generated. Based on the projections made, it was identified that the security cells for the final disposal of hospital waste occupy an excessive volume in the sanitary landfill, for which it is proposed to use technological equipment such as the autoclave, the same one that helps to treat the waste. solid hospital waste, managing to convert waste into inert waste and reducing its volume by 80%.
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    Modelo Prospectivo para Determinar la Ocupación de Camas en el Hospital IESS Puyo
    (Universidad Técnica de Ambato. Facultad de Ingeniería en Sistemas, Electrónica e Industrial. Maestría en Matemática Aplicada, 2023-03) Gavilanes Valencia, Christian Gabriel; Benalcázar Palacios, Freddy Geovanny
    La emergencia sanitaria iniciada en el año 2020 por el COVID -19 afectó en todos los ámbitos a la humanidad; encontrando un sistema sanitario fragmentado, ante esta situación se han tomado diferentes acciones, y como una manera de aportar a la reactivación se plantea un estudio investigativo bajo el tema: “Modelo Prospectivo para determinar la ocupación de camas en el Hospital IESS Puyo”, este estudio estadístico se basó en series de tiempo por ser el óptimo para predecir el comportamiento a futuro de la ocupación de camas en el hospital. Una vez construido y aplicado el programa, se seleccionó el mejor modelo SARIMA para la ocupación de camas en las áreas de hospitalización y emergencia; para ello se utilizó la metodología Box-Jenkins para analizar la serie de tiempo correspondiente a la ocupación de camas en las dos áreas del Hospital en el periodo comprendido entre enero 2018 – septiembre 2022. Las variables usadas para la construcción de los modelos matemáticos fueron como variable dependiente la ocupación de camas y como variable independiente el tiempo. Para verificar la estacionariedad de las series de tiempo se procedió a descomponer cada una de las series en sus cuatro componentes (datos observados, tendencia, estacionalidad y aleatoriedad). Se realizó el test de Dickey Fuller y se graficaron las funciones de correlación simple y parcial para comprobar la presencia de raíces unitarias utilizándose un nivel de significancia de 0.05. Los resultados alcanzados en la presente investigación son dos modelos prospectivos, el modelo SARIMA (1,1,1) (1,0,3) se ajusta adecuadamente a la serie de tiempo de ocupación de camas en el área de hospitalización del Hospital Básico IESS Puyo, cuya estimación arrojó como ecuación de pronóstico: ∆𝑌.. Para el área de emergencias se desarrolló un modelo SARIMA (1,1,1) (1,0,2), cuya ecuación de pronóstico es: ∆𝑌𝑡= = 0.759401 𝑌t-1+0.963401 𝑌 t-12+ 0.999998 𝜖𝑡−1 + 𝜖t´, dichos modelos prospectivos encontrados permiten tener un pronóstico efectivo a mediano plazo. Al comparar los datos de testeo con los obtenidos del entrenamiento se encontró que la eficacia de los modelos del área de hospitalización y emergencia fue de 87.16% y 88.61%, respectivamente. Estos parámetros van a permitir al personal del Hospital optimizar recursos y brindar una atención de calidad a los usuarios del hospital.