Comparative Analysis of Bayesian Regularization and Levenberg-Marquardt Training Algorithms for Prediction of the Geoid Undulation Values Using Artificial Neural Network

Although it is very difficult and time consuming to find orthometric heights used in engineering applications with classical leveling measurements, conversion from ellipsoid heights determined by GNNS technique to orthometric heights is easier. However, the geoid undulation values with certain accuracy must be known for this transformation. In this context, this study evaluates the application of Bayesian Regularization (BR) and Levenberg-Marquardt (LM) training algorithms of artificial neural networks (ANNs) in the modeling and prediction of geoid undulation values. The neural network models were developed using data from a set of measurements (414 C3 points) made for Rize, Turkey. The data set was divided into two parts. The first part was used to train the network (373 C3 points, 90% of the whole data set). The remaining 41 C3 points were used for testing process. The optimal number of neurons required for the hidden layer was determined after examining several topologies wherein the neurons were varied from 5 to 25 for each of the algorithms. Based on the statistical and graphical results, the LM algorithm gave the best accuracy. For the BR algorithm, the least RMSE, MAE and R2 values of 5.95 cm, 6.80 cm, and 0.99929 were obtained, respectively. The least RMSE, MAE and R2 values of 5.27 cm, 4.88 cm, and 0.99945 were recorded for the LM algorithm. Comparing to the results of the both algorithms, the LM algorithm reveals a more accurate model fitting and a more efficient predicting ability.