A hybrid binary grey wolf optimizer for selection and reduction of reference points with extreme learning machine approach on local GNSS/leveling geoid determination
Introduction
Advances in satellite technologies have enabled us to reach a large amount of data about the earth we live on. It is possible to obtain high accuracy positions from satellites, especially for positioning purposes. While heights obtained by GNSS techniques are geometrically defined ellipsoid heights, orthometric or normal heights that are better suited to the physical earth are used in engineering studies [1], [2], [3], [4], [5]. For this reason, geoid determination in which conversion from ellipsoid height to orthometric height is applied is an important issue [6], [7], [8], [9].
Today, many different methods are used in geoid determination studies, depending on the size of the study area and available data. In the literature, there are many different geometric and gravimetric geoid determination methods, mainly astro-geodetic, gravimetric, and GNSS/leveling [6], [8], [10], [11], [12], [13], [14]. One of these, GNSS/leveling geoid has very important for more accurate geoid in engineering applications instead of national or global geoid with high accuracy. For a high-accuracy GNSS/leveling geoid, reference points that reflect the topographic characteristics of the land, distributed appropriately to the project area, are needed. It is clear that the more geoid reference points, the better the modeling can be. However, too many reference points extend the duration of land surveys, which is a factor affecting the cost of projects. One of the main goals is to determine the minimum number of GNSS/leveling geoids with the same accuracy with optimization in the selection of model points. In this study, the optimization issue in local GNSS/leveling geoid determination with ELM is examined. For this purpose, the effect of different algorithms, different reference numbers, and distribution on local GNSS/leveling geoid modeling with ELM was investigated in a sample study area.
Doganalp and Selvi [15] investigated interpolation methods for local geoid determination. In this study, the accuracies of local geoids modeled with Polynomial interpolation, Least-squares collocation method (LSC), Multiquadric (MQ) interpolation method, and Thin Plate Spline (TPS) method for strip area projects are examined.
Erol B and Erol S [16] investigated Learning-based computing techniques in determining local geoids. Multivariable polynomial regression using least squares adjustment (MPRE), ANN, Adaptive network-based fuzzy inference system (ANFIS), and Wavelet neural networks (WNN) methods were used for modeling by using Istanbul metropolitan triangulation network data. The accuracy of each model was calculated by related test points.
Cakır and Yılmaz [1] studied the usability of polynomials, radial basis functions, and multilayer perceptron neural network methods in determining local geoids. Geoid height values of the test points were calculated by using the local geoids obtained from these methods in the test network of the Kayseri region, and the differences between them were interpreted.
Rabah and Kaloop [17] determined the geoid for Egypt by using the minimum curvature surface technique, and the obtained results were compared with the EGM2008 model.
Karaarslan et al. [18] implemented a local geoid determination study for the Trabzon region. The results obtained from Weighted average interpolation, Polynomial surface regression, and Multiquadratic interpolation methods were compared.
Mitas and Mitasova [19] presented the basic principles and mathematical relations of spatial interpolation methods, and 2-dimensional, 3-dimensional, and 4-dimensional interpolations of elevation were explained with examples in GIS studies.
Optimization is the process of optimizing the objective function under current constraints [20]. The Particle swarm optimization (PSO) algorithm is a population-based heuristic optimization algorithm proposed by Eberhart and Kennedy in 1995, inspired by the pattern of social behaviors of bird and fish swarm in finding food, interactions, and achieving goals [21]. Although the PSO algorithm has been proposed to solve continuous problems [22], [23], it has been modified and used to solve binary [24], [25], [26] and discrete optimization problems [27], [28].
Tree-Seed Algorithm (TSA) is a proposed population-based meta-heuristic algorithm, inspired by the relationship between tree and seed [29]. TSA has been used in optimization problems such as constrained optimization [30], [31], optimal power flow [32], traveling salesman problem [33], training ANN [34], and so forth.
The Artificial Bee Colony (ABC) algorithm inspired the foraging behavior of real honeybees and was proposed by Karaboga in 2005 [35]. The ABC algorithm focuses on the social behavior of three different bees in the colony (working bees, stalking bees, and scout bees) to discover nectar and collect it in the hive. This swarm-based algorithm has been applied in many areas [36], [37], [38], [39], [40].
The hunting approaches as a group and the social hierarchy in the pack are so important for the grey wolves to live in nature together. Mirjalili et al. was inspired by the social behaviors of these grey wolves in the pack for proposing the GWO algorithm [41]. GWO is a state-of-the-art meta-heuristic algorithm that has been used widely so as to solve optimization problems such as optimal power flow [42], [43], wind speed forecasting [44], pattern recognition [45], feature selection [46], unit commitment [47], parameters estimation [48], [49] in recent years and continues to be developed by many researchers. Binary [50], discrete [51], and multi-objective [52] versions of the GWO have been proposed in the literature.
Due to the slow operation of ANN and updating parameters of the network iteratively during the training phase, single-hidden layer feedforward neural networks, called ELM, that select the input weights and calculates the output weights analytically is proposed by Huang et al. [53]. ELM has been used commonly as a regressor such as solar radiation estimation [54], economic growth estimation [55], sensor-less wind speed prediction [56], and so forth. An also, many metaheuristic and ELM hybrids have been proposed in the literature [57], [58], [59], [60], [61], [62], [63].
As can be seen, the effects of modeling and interpolation methods on local geoid determination results were examined in the studies in the literature. What makes this study different from the studies in the literature is the investigation of the effect of reference point selection on the modeling results in the local geoid modeling process. Because the selection of reference points directly affects the model accuracy. Different models can be obtained especially according to the topography of the study area and the distribution of the points. The selection of model reference points is of vital importance in order to produce the closest model to reality. Besides, performing these operations with a small number of points saves time and cost.
In the literature, it is seen that ELM is frequently used as regressors, especially in prediction problems. ELM has been used as a hybrid with meta-heuristic approaches for different purposes in many studies. In this study, ELM and GWO (GWO + ELM) were used as a hybrid and a more accurate modeling possibility with fewer model points with this proposed approach was investigated.
The remainder of the paper is organized as follows. Section 2 provides material and methods of the related study. The experimental setup and experimental results were presented in Section 3. Finally, the work is concluded in Section 4.
Section snippets
Materials and methods
In this study, in which PSO was investigated in determining local GNSS/leveling geoid with ANN, the existing geodetic network in Burdur province was used (Fig. 1). The data used in the study are latitude, longitude, ellipsoid height () obtained from GNSS measurements at 102 points and orthometric height () values obtained from nivelman (leveling) measurements. GNSS coordinates were obtained from ITRF96 datum observation at 2005.0 epoch, whereas orthometric heights are determined according
Experimental results and discussion
102 reference points used in this study have different orthometric heights as can be seen from the views presented in Figs. 1, 2, and 3. Of the 102 reference points with different orthometric heights, 82 were separated as training data, while 20 were separated as test data. While determining the test points, 5 groups were created by giving the equal number of element properties and rounding ratio 1 in Map Info Professional 17.0.3 program according to orthometric heights. The expert determined 4
Conclusions
Modeling is an important issue in local GNSS/Leveling geoid studies as in all scientific studies. In this study, the effect of optimization with metaheuristic algorithms on the results in local geoid determination with well-known artificial intelligence techniques was investigated. It was aimed to find fewer reference points to represent the entire area without reducing the accuracy of the model. Of the 102 data, 82 were selected as training data and 20 as test data. In this study, to analyze
CRediT authorship contribution statement
Kemal Tütüncü: Supervision, Conceptualization, Writing - original draft. Mehmet Akif Şahman: Data curation, Software, Visualization. Ekrem Tuşat: Writing - original draft, Resources, Investigation.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
We would like to thank Musevitoglu Surveying Co. for the data and technical support used in this study. The authors wish to thank the Scientific Research Projects Coordinatorship at Selçuk University, and The Scientific and Technological Research Council of Turkey for their institutional supports. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
References (68)
- et al.
Polynomials, radial basis functions and multilayer perceptron neural network methods in local geoid determination with GPS/levelling
Measurement
(2014) - et al.
Influence of local geoid variation on water surface elevation estimates derived from multi-mission altimetry for Lake Namco
Remote Sens. Environ.
(2019) - et al.
Regional geoid modeling in the area of subglacial Lake Vostok, Antarctica
J. Geodyn.
(2014) - et al.
Local geoid determination in strip area projects by using polynomials, least-squares collocation and radial basis functions
Measurement
(2015) - et al.
Learning-based computing techniques in geoid modeling for precise height transformation
Comput. Geosci.
(2013) - et al.
A discrete particle swarm optimization algorithm with self-adaptive diversity control for the permutation flowshop problem with blocking
Appl. Soft Comput.
(2012) - et al.
A novel complex network community detection approach using discrete particle swarm optimization with particle diversity and mutation
Appl. Soft Comput.
(2019) TSA: Tree-seed algorithm for continuous optimization
Expert Syst. Appl.
(2015)- et al.
A modification of tree-seed algorithm using Deb’s rules for constrained optimization
Appl. Soft Comput.
(2018) - et al.
Tree-seed algorithm for solving optimal power flow problem in large-scale power systems incorporating validations and comparisons
Appl. Soft Comput.
(2018)