Published

2022-02-07

Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study

Predicción de ondulación geoide con Redes Neuronales Artificiales (base radial y regresión generalizada), regresión lineal múltiple y métodos de interpolación: estudio comparativo

DOI:

https://doi.org/10.15446/esrj.v25n4.91195

Keywords:

Generalized regression neural network, Radial basis function neural network, Multiple linear regression, Interpolation methods (en)
red neuronal de regresión generalizada; red neuronal de base radial; regresión lineal múltiple; métodos de interpolación; determinación geoide (es)

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The present work aimed to develop a prediction model to estimate geoid undulation and to compare its efficiency with other methods including radial basis function neural network (RBFNN), generalized regression neural network (GRNN), multiple linear regression (MLR) and, ten different interpolation methods. In this study, the k-fold cross-validation method was used to evaluate the model and its behavior on the independent dataset. With this validation method, each of a k number of groups has the chance to be divided into training and testing data. The performances of the methods were evaluated in terms of the root mean square error (RMSE) mean absolute error (MAE), Nash–Sutcliffe efficiency coefficient (NSE), and correlation coefficient (R2) and using graphical indicators. The evaluation of the performance of the datasets obtained using cross-validation was done in two ways. If we accept the method having the minimum error result as the most appropriate method, the natural neighbor (NN) method in the DS#5 dataset gave better results than the other methods (RMSE=0.14173  m, MAE=0.09729 m, NSE=0.98986, and R2=0.99011. On the other hand, it has been observed that, the GRNN method exhibited the best performance, on average, with RMSE=0.18539 m, MAE=0.13676 m, NSE=0.98229, and R2=0.98249.

Este estudio evalúa los métodos diferentes de predicción de ondulación geoide donde se incluye dos tipos de Redes Neuronales Artificiales -la red neuronal de base radial y la red neuronal de regresión generalizada- al igual que métodos convencionales donde se incluyen la regresión lineal múltiple y diez técnicas diferentes de interpolación. En este trabajo, la validación cruzada de K iteraciones se usó para evaluar el modelo y su comportamiento en un conjunto de datos independiente. Con este método de evaluación, cada grupo de números k tiene la posibilidad de dividirse entre datos de entrenamiento y datos de evaluación. El desempeño de los métodos se evaluó en términos de la raíz del error cuadrático medio (RMSE, del inglés root mean square error), el error absoluto medio (MAE, mean absolute error), el coeficiente de eficiencia Nash-Sutcliffe (NSE, Nash–Sutcliffe efficiency coefficient) y el coeficiente de correlación (R2, correlation coefficient) a través de indicadores gráficos. La evaluación del desempeño de los grupos de datos obtenidos con la validación cruzada se realizó en dos vías. Cuando el método que tiene el resultado de mínimo error es aceptado como el método más apropiado, el vecino natural ofrece mejores resultados que otros métodos (RMSE = 0.142 m, MAE = 0.097 m, NSE = 0.98986, and R2 = 0.99011). Por otro lado, se observó que en promedio la red neuronal de regresión generalizada presentó un mejor desempeño (RMSE = 0.185 m, MAE = 0.137 m, NSE = 0.98229, and R2 = 0.98249).

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APA

Konakoglu, B. and Akar, A. (2022). Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study. Earth Sciences Research Journal, 25(4). https://doi.org/10.15446/esrj.v25n4.91195

ACM

[1]
Konakoglu, B. and Akar, A. 2022. Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study. Earth Sciences Research Journal. 25, 4 (Feb. 2022). DOI:https://doi.org/10.15446/esrj.v25n4.91195.

ACS

(1)
Konakoglu, B.; Akar, A. Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study. Earth sci. res. j. 2022, 25.

ABNT

KONAKOGLU, B.; AKAR, A. Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study. Earth Sciences Research Journal, [S. l.], v. 25, n. 4, 2022. DOI: 10.15446/esrj.v25n4.91195. Disponível em: https://revistas.unal.edu.co/index.php/esrj/article/view/91195. Acesso em: 16 jan. 2025.

Chicago

Konakoglu, Berkant, and Alper Akar. 2022. “Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study”. Earth Sciences Research Journal 25 (4). https://doi.org/10.15446/esrj.v25n4.91195.

Harvard

Konakoglu, B. and Akar, A. (2022) “Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study”, Earth Sciences Research Journal, 25(4). doi: 10.15446/esrj.v25n4.91195.

IEEE

[1]
B. Konakoglu and A. Akar, “Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study”, Earth sci. res. j., vol. 25, no. 4, Feb. 2022.

MLA

Konakoglu, B., and A. Akar. “Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study”. Earth Sciences Research Journal, vol. 25, no. 4, Feb. 2022, doi:10.15446/esrj.v25n4.91195.

Turabian

Konakoglu, Berkant, and Alper Akar. “Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study”. Earth Sciences Research Journal 25, no. 4 (February 7, 2022). Accessed January 16, 2025. https://revistas.unal.edu.co/index.php/esrj/article/view/91195.

Vancouver

1.
Konakoglu B, Akar A. Geoid undulation prediction using ANNs (RBFNN and GRNN), multiple linear regression (MLR), and interpolation methods: A comparative study. Earth sci. res. j. [Internet]. 2022 Feb. 7 [cited 2025 Jan. 16];25(4). Available from: https://revistas.unal.edu.co/index.php/esrj/article/view/91195

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