Artificial Neural Networks pruning approach for geodetic velocity field determination

Abstract

There has been a need for geodetic network densification since the early days of traditional surveying. In order to densify geodetic networks in a way that will produce the most effective reference frame improvements, the crustal velocity field must be modelled. Artificial Neural Networks (ANNs) are widely used as function approximators in diverse fields of geoinformatics including velocity field determination. Deciding the number of hidden neurons required for the implementation of an arbitrary function is one of the major problems of ANN that still deserves further exploration. Generally, the number of hidden neurons is decided on the basis of experience. This paper attempts to quantify the significance of pruning away hidden neurons in ANN architecture for velocity field determination. An initial back propagation artificial neural network (BPANN) with 30 hidden neurons is educated by training data and resultant BPANN is applied on test and validation data. The number of hidden neurons is subsequently decreased, in pairs from 30 to 2, to achieve the best predicting model. These pruned BPANNs are retrained and applied on the test and validation data. Some existing methods for selecting the number of hidden neurons are also used. The results are evaluated in terms of the root mean square error (RMSE) over a study area for optimizing the number of hidden neurons in estimating densification point velocity by BPANN.

Capability of Artificial Neural Network for Forward Conversion of Geodetic Coordinates $$(\phi ,\lambda ,h)$$ ( ϕ , λ , h ) to Cartesian Coordinates (X, Y, Z)

“…This assertion is well documented in literature. For example, ANN has been applied to solve most coordinate transformation problems between global and local datums (Gullu 2010;Gullu et al 2011;Lin and Wang 2006;Mihalache 2012;Tierra et al 2008Tierra et al , 2009Tierra and Romero 2014;Turgut 2010;Yilmaz and Gullu 2012;Zaletnyik 2004), for GPS height conversion (Fu and Liu 2014;Liu et al 2011;Lei and Qi 2010;Tieding et al 2010;Wu et al 2012a), in geodetic deformation modelling (Bao et al 2011;Du et al 2014a, b;Gao et al 2014;Pantazis and Eleni-Georgia 2013;Yilmaz and Gullu 2014;Yilmaz 2013), earth orientation parameters determination (Liao et al 2012;Schuh et al 2002;Yu et al 2015), precise orbital prediction (He-Sheng 2006;Li et al 2014), gravity anomaly estimation (Hajian et al 2011;Hamid and Mohammad 2013;Tierra and De Freitas 2005), geoid determination (Kavzoglu and Saka 2005;Pikridas et al 2011;Stopar et al 2006;Sorkhabi 2015;Veronez et al 2006Veronez et al , 2011, transforming from cartesian coordinates to geodetic coordinates (Civicioglu 2012) and many others.…”