An Elman Model Based on GMDH Algorithm for Exchange Rate Forecasting

This paper centres on a new GMDH (group method of data handling) algorithm based on the k-nearest neighbour (k-NN) method. Instead of the transfer function that has been used in traditional GMDH, the k-NN kernel function is adopted in the proposed GMDH to characterise relationships between the input and output variables. The proposed method combines the advantages of the k-nearest neighbour (k-NN) algorithm and GMDH algorithm, and thus improves the predictive capability of the GMDH algorithm. It has been proved that when the bandwidth of the kernel is less than a certain constant C, the predictive capability of the new model is superior to that of the traditional one. As an illustration, it is shown that the new method can accurately forecast consumer price index (CPI).

The complete bibliography, which provides a comprehensive list of articles and books on the theory and application of the Group Method of Data Handling (GMDH) algorithm from 1970 to 1982, was published in the book [12]. In this book three types of algorithms were described: the original GMDH algorithm (by Stanley J. Farlow), algorithm of adaptive learning networks related to GMDH (by Roger Barron, A.N. Mucciardi, F.G. Cook, Y.N. Croing and Andrew R. Barron) and modified GMDH algorithm (by Y. Sawaragi, Y.S. Ikeda and others). These three types of algorithms for modelling by sifting many models-candidates according to external criteria, as it appears, were applied to solution of many practical problems successfully. It was shown by papers published in the considered book [12] and in the many other papers [11].

Radio propagation measurement were acquired at the 900 MHz and 1800 MHz frequency bands from six (6) live base stations (BS1 to BS6) in Kaduna town, Nigeria using an Asus Zenfone enhanced with a network monitoring software (Network Cell Info Lite). The receive signal strength (RSS) measurements were taken from the BSs at a distances of 200 m apart (in dB) until the signal faded out and the measurements were taken for twelve (12) calendar months which covered all seasons of the year, the corresponding path loss were calculated which were subsequently used to develop a propagation path loss prediction model with the Group Method of Data Handling (GMDH) algorithm. However, the results obtained shows very small variations between the model fit (which was the best fit curve from the measured data) and the predictions (which is the forecast). Hence, since the variations between the model fit and the predictions are not wide, with sometime the values of prediction being better than that model fit, the GMDH model is showing good prediction for Kaduna metropolis.

Summary Many methods have been developed to determine the solution gas/oil ratio (Rs), starting with experiments, followed by empirical correlations establishments, and recently with machine learning applications receiving much interest due to their ability to produce precise results compared with empirical correlations. In this paper, the group method of data handling (GMDH) and the enhanced GMDH based on discrete differential evolution (GMDH-DDE) are used for the first time to estimate the Rs and to provide a correlation to the laboratory measured Rs from bubblepoint pressure (Pb), oil API gravity (API), gas-specific gravity (γg), and reservoir temperature (T) without crude oil properties. These two methods are compared with backpropagation neural networks (BPNN). The reason for using the hybrid GMDH (GMDH-DDE) is to overcome the drawbacks of the GMDH, such as the method used to calculate neuron weights (i.e., quadratic polynomial transfer function), which seems to have inaccuracies. Also, in selecting model inputs, the GMDH tends to choose the most appropriate inputs for the model; however, the selection criteria are not straightforward and may affect the final results. Furthermore, the GMDH has a multicollinearity problem, affecting model coefficient stability and overfitting problems, etc. A total of 420 data sets from the Mpyo oil field were used, with 70% used for training and 30% used for testing. According to the findings, the GMDH-DDE outperformed both the GMDH and BPNN. In comparison with the GMDH and BPNN, the GMDH-DDE has a higher correlation coefficient (R), lower root-mean-square error (RMSE), and lower mean absolute error (MAE). During training, R, RMSE, and MAE were 0.9849, 0.090, and 0.010, respectively, and during testing, R = 0.9603, RMSE = 0.290, and MAE = 0.017. The second-best technique (GMDH) produces R, RMSE, and MAE values of 0.9611, 0.122, and 0.032 in training, and R = 0.9438, RMSE = 0.349, and MAE = 0.055 in testing. Furthermore, the GMDH-DDE used less computational time (1.32 seconds) compared with the GMDH (2.01 seconds) and BPNN (4.96 seconds), proving that the GMDH-DDE has accurate and fast convergence compared with the GMDH and BPNN. These findings show that the GMDH-DDE and GMDH can be adopted as alternative methods for predicting the Rs.

Energy spectra unfolding of fast neutron sources using the group method of data handling and decision tree algorithms

A new algorithm for autoregresive moving average (ARMA) parameter estimation is introduced. The algorithm is based on the group method of data handling (GMDH) first introduced by the Russian cyberneticist, A. G. Ivakhnenko, for solving high-order regression polynomials. The GMDH is heuristic in nature and self-organizes into a model of optimal complexity without any a priori knowledge about the system's inner workings. We modified the GMDH algorithm to solve for ARMA model parameters. Computer simulations have been performed to examine the efficacy of the GMDH and comparison of the GMDH is made to one of the most accurate and one of the most widely used algorithms, the fast orthogonal search (FOS) and the least-squares methods, respectively. The results show that in some cases with noise contamination and incorrect model order assumptions, the GMDH performs better than either the FOS or the least-squares methods in providing only the parameters that are associated with the true model terms.

Enhanced group method of data handling (GMDH) for permeability prediction based on the modified Levenberg Marquardt technique from well log data

This study aims to determine the effect of a flood-spreading system on the morphometric characteristics of alluvial fans (AFs) in Gribayegan Fasa, Iran, and its relationship with erosion, age, texture, and type of formations. After determining the AFs using the semiautomatic method and determining their recharged watersheds, 25 morphometric characteristics were investigated. The most important morphometric characteristics were identified using principal component analysis (PCA). The group method of data handling (GMDH) neural network is used to predict erosion, soil texture, age, and formation material based on the morphometric characteristics of the fan. The results demonstrate that the semiautomatic method can effectively extract AF from the landscape. The results of AF morphometry before and after flood spreading show that the fan area, drainage basin circularity (Cirb), fan perimeter, relief ratio of the fan, fan length, minimum fan height, and maximum fan height were higher before flood spreading, and basin shape, St (soil texture), upper fan slope, fan volume, and sweep angle had higher values after the flood. In addition, the results of PCA show that fan area, fan perimeter, fan length, fan radius, fan volume, basin area, basin perimeter, main channel length, basin length, and drainage density are important factors. The results of the GMDH algorithm reveal that this method can accurately predict the formation, age, soil texture, and erosion rate using morphometric characteristics. Therefore, the R2 is 0.92 for the formation age and R2 is 0.86 for the erosion rates, formation types, and soil texture, respectively. Therefore, the most important morphometric parameters can be determined using PCA, and the conditions and processes in the basin, such as formation material, age, soil texture, and erosion rate, can be predicted with high accuracy using the GMDH algorithm.

The current study proposes a two-step approach for pore facies characterization in the carbonate reservoirs with an example from the Kangan and Dalanformations in the South Pars gas field. In the first step, pore facies were determined based on Mercury Injection Capillary Pressure (MICP) data incorporation with the Hierarchical Clustering Analysis (HCA) method. In the next step, polynomial meta-models were established based on the evolved Group Method of Data Handling (GMDH) neural networks for the purpose of pore facies identification from well log responses. In this way, the input data table used for training GMDH-type neural network consists of CALI, GR , CGR , SGR, DT, NPHI, RHOB, PEF, PHIE and VDL logs. The MICP-HCA derived pore facies were considered as the desired outputs. Moreover, multi-objective genetic algorithms (GAs) are used to the evolutionary design of GMDH-type neural networks. Training error and prediction error of neural network have been considered as conflicting objectives for Pareto multi-objective optimization. The results of this study indicate the successful implementation of GMDH neural networks for classification of pore facies in the heterogeneous gas bearing carbonate rocks of South Pars gas field.

The main purpose of this paper is to propose the use of Group Method of Data Handling (GMDH) to predict software reliability. The GMDH algorithm presented in this paper is a heuristic self-organization method. It establishes the input-output relationship of a complex system using multilayered perception type structure that is similar to a feed forward multilayer neural network. The effectiveness of GMDH is demonstrated on a dataset taken from literature. Its performance is compared with that of multiple linear regression (MLR), back propagation trained neural networks (BPNN), threshold accepting trained neural network (TANN), general regression neural network (GRNN), pi-sigma network (PSN), dynamic evolving neuro-fuzzy inference system (DENFIS), TreeNet, multivariate adaptive regression splines (MARS) and wavelet neural network (WNN) in terms of normalized root mean square error (NRMSE). Based on experiments conducted, it is found that GMDH predicted reliability with least error compared to other techniques. Hence, GMDH can be used a sound alternative to the existing techniques for software reliability prediction.KeywordsSoftware reliability forecastingGroup method of Data handlingIntelligent Techniques

It is possible to construct models, which describe and predict the annual course of net N-mineralization in agricultural soils, using the Group Method of Data Handling (GMDH), a method of heuristic self-organization. The advantage of this method is that complex ecosystems can be modeled without knowing anything about their structure and with only very few data points. The three input variables most often selected by GMDH for the different models have been soil temperature, soil water content and ammonification potential. Other parameters, which have been measured but usually not selected by GMDH as suitable input parameter for models of net N-mineralization are: substrate-induced respiration, soil respiration, mineralization potential, and microbial biomass C and N.

Grinding wheel wear equation for optimization of grinding process has been given in the form of the equation representing the relationship between grinding ratio and feed rate. However the other factors (work material, wheel, wheel speed, etc.) which affect to the wheel wear, seem not to be taken into consideration. In this paper, the wheel wear equation in abrasive cut-off operation is presented, in which chemical compositions and mechanical properties in work materials, abrasive grain, grain size, grade and wheel speed are treated as independent variables together with the feed rate, using input and output data given by the experiments and GMDH (Group Method of Data Handling) algorithm with successive determination of polynomial trends. As the results, the wheel wear equation can be obtained, of which construction is rather simple and accuracy is satisfactory.

The logistic group method of data handling (GMDH)-type neural network is proposed and applied to the medical image diagnosis of lung cancer. In this logistic GMDH-type neural network algorithm, the principal component-regression analysis is used to estimate the parameters of the neural network, and the multi-colinearity, which is generated in the conventional GMDH algorithm, is protected. Therefore, accurate and stable predicted values are obtained in the logistic GMDH-type neural network. Furthermore, the polynomial and logistic neurons are used, and the neural network architectures are automatically organized so as to minimize the prediction error criterion defined as Akaike's information criterion or prediction sum of squares. The identification results show that the logistic GMDH-type neural network algorithm is useful for the medical image diagnosis of lung cancer since the optimum neural network architecture is automatically organized so as to fit the complexity of the medical images.

Large-Spatial Pattern Identification of Air Pollution by a Combined Model of Source-Receptor Matrix and Revised GMDH

Air pollution-induced issues involve public health, environmental, agricultural and socio-economic aspects. Therefore, decision-makers need low-cost, efficient tools with high spatiotemporal representation for monitoring air pollutants around urban areas and sensitive regions. Air pollution forecasting models with different time steps and forecast lengths are used as an alternative and support to traditional air quality monitoring stations (AQMS). In recent decades, given their eligibility to reconcile the relationship between parameters of complex systems, artificial neural networks have acquired the utmost importance in the field of air pollution forecasting. In this study, different machine learning regression methods are used to establish a mathematical relationship between air pollutants and meteorological factors from four AQMS (A-D) located between Çerkezköy and Süleymanpaşa, Tekirdağ. The model input variables included air pollutants and meteorological parameters. All developed models were used with the intent to provide instantaneous prediction of the air pollutant parameter NOx within the AQMS and across different stations. In the GMDH (group method of data handling)-type neural network method (namely the self-organizing deep learning approach), a five hidden layer structure consisting of a maximum of five neurons was preferred and, choice of layers and neurons were made in a way to minimize the error. In all models developed, the data were divided into a training (%80) and a testing set (%20). Based on R2, RMSE, and MAE values of all developed models, GMDH provided superior results regarding the NOx prediction within AQMS (reaching 0.94, 10.95, and 6.65, respectively for station A) and between different AQMS. The GMDH model yielded NOx prediction of station B by using station A input variables (without using NOx data as model input) with R2, RMSE and MAE values 0.80, 10.88, 7.31 respectively. The GMDH model is found suitable for being employed to fill in the gaps of air pollution records within and across-AQMS.