Generalized Locally Weighted GMDH for Short Term Load Forecasting

Electric load forecasting is indispensable for the effective planning and operation of power systems. Various decisions related to power systems depend on the future behavior of loads. In this paper, we propose a new input selection procedure, which combines the group method of data handling (GMDH) and bootstrap method for support vector regression based hourly load forecasting. To construct the GMDH network, a learning dataset is divided into training and test datasets by bootstrapping. After constructing GMDH networks several times, the inputs that appeared frequently in the input layers of the completed networks were selected as the significant inputs. Filter methods based on linear correlation and mutual information (MI) were employed as comparison methods, and the performance of hybrids of the filter methods and the proposed method were also confirmed. In total, five input selection methods were compared. To verify the performance of the proposed method, hourly load data from South Korea was used and the results of one-hour, one-day and one-week-ahead forecasts were investigated. The experimental results demonstrated that the proposed method has higher prediction accuracy compared with the filter methods. Among the five methods, a hybrid of an MI-based filter with the proposed method shows best prediction performance.

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.

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).

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

Forecasting is one of the essential activities at the electrical power company. Inaccurate forecasting will lead to wastage of operating costs. Data mining has been widely used to solve the problem of forecasting. In this study, we propose a method using data mining technique for doing electrical load forecasting, which is a combination of wavelet transform and group method of data handling (WGMDH). The proposed algorithm is used to predict the short-term power load which aims to improve the accuracy of forecasting. The results show that by using proposed algorithm better accuracy is achieved compared with the coefficient method which is used by Indonesian Power Company in Sumatera to forecast the electrical load. The method can improve the forecasting of electricity on average above 50% per year, both for the type of similar day and daily electricity load characteristic pattern.

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.

This study introduces a method to predict scour hole geometry at downstream of a ski-jump bucket by group method of data handling (GMDH). The GMDH network was developed using evolutionary and iterative algorithms including those of genetic programming (GP), particle swarm optimization (PSO), and back propagation (BP) algorithms. Results of alternative GMDH networks were compared with those obtained using artificial neural networks, genetic programming, ANFIS, empirical equations, and regression-based equations. Performances indicated that proposed GMDH-BP produced more accurate results in comparison with other methods. Moreover, the most effective independent parameters on scour hole geometry were determined using sensitivity analysis. Finally, combination of evolutionary and iterative algorithms has been confirmed that the GMDH network is a useful soft computing tool for prediction of scour hole geometry at downstream of a ski-jump bucket.

An improved permeability estimation model using integrated approach of hybrid machine learning technique and Shapley additive explanation

The study uses the comparison of Group Method of Data Handling (GMDH)-type neural network algorithm with Vector error correction model to predict the value of FDI on the basis of accuracy of prediction and to model the determinants of FDI in Pakistan. It was estimated in the times series data during the time period 1971-2013 and the time period 2014-2018 has been utilized to predict FDI. The Augmented Dickey-Fuller (ADF) test suggests that all variables data are of I (1) and Johansen co-integration test proved nexus of the variables FDI and its determinants in the long run. Nonetheless, the error correction-term of the vector error correction model (VECM) indicates that around 3 % of cumulative disequilibrium was expunged in every year in Pakistan. This paper compares two new methods Group Method of Data Handling (GMDH) Neural Network Algorithm and Vector Error Correction Model (VECM) in an attempt to obtain the more useful one based on accuracy of analysis when making predictions. Whereas, the effectiveness of VECM is then compared with a non parametric GMDH-like type neural network. An evaluation of forecasting model accuracies in terms of FDI was done using Root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and Diebold Mariano (DM) test. The empirical outcomes are a clear indication that Group Method of Data Handling GMDH-type of neural network algorithm did very well in comparison with the vector error correction model based on forecasting.

Permeability is an important petrophysical parameter that controls the fluid flow within the reservoir. Estimating permeability presents several challenges due to the conventional approach of core analysis or well testing, which are expensive and time-consuming. On the contrary, artificial intelligence has been adopted in recent years in predicting reliable permeability data. Despite its shortcomings of overfitting and low convergence speed, artificial neural network (ANN) has been the widely used artificial intelligent method. Based on this, the present study conducted permeability prediction using the group method of data handling (GMDH) neural network from well log data of the West arm of the East African Rift Valley. Comparative analysis of GMDH permeability model and ANN methods of the back propagation neural network (BPNN) and radial basis function neural network (RBFNN) were further explored. The results of the study showed that the proposed GMDH model outperformed BPNN and RBFNN as it achieved R/root mean square error (RMSE) value of 0.989/0.0241 for training and 0.868/0.204 for predicting, respectively. Sensitivity analysis carried out revealed that shale volume, standard resolution formation density, and thermal neutron porosity were the most influential well log parameters when developing the GMDH permeability model.

Machine learning (ML) has been recognized as a feasible and reliable technique for the modeling of multi-parametric datasets. In real applications, there are different relationships with various complexities between sets of inputs and their corresponding outputs. As a result, various models have been developed with different levels of complexity in the input–output relationships. The group method of data handling (GMDH) employs a family of inductive algorithms for computer-based mathematical modeling grounded on a combination of quadratic and higher neurons in a certain number of variable layers. In this method, a vector of input features is mapped to the expected response by creating a multistage nonlinear pattern. Usually, each neuron of the GMDH is considered a quadratic partial function. In this paper, the basic structure of the GMDH technique is adapted by changing the partial functions to enhance the complexity modeling ability. To accomplish this, popular ML models that have shown reasonable function approximation performance, such as support vector regression and random forest, are used, and the basic polynomial functions in the GMDH are replaced by these ML models. The regression feasibility and validity of the ML-based GMDH models are confirmed by computer simulation.

Ionic liquids (ILs) are more widely used within the industry than ever before, and accurate models of their physicochemical characteristics are becoming increasingly important during the process optimization. It is especially challenging to simulate the viscosity of ILs since there is no widely agreed explanation of how viscosity is determined in liquids. In this research, genetic programming (GP) and group method of data handling (GMDH) models were used as white-box machine learning approaches to predict the viscosity of pure ILs. These methods were developed based on a large open literature database of 2813 experimental viscosity values from 45 various ILs at different pressures (0.06–298.9 MPa) and temperatures (253.15–573 K). The models were developed based on five, six, and seven inputs, and it was found that all the models with seven inputs provided more accurate results, while the models with five and six inputs had acceptable accuracy and simpler formulas. Based on GMDH and GP proposed approaches, the suggested GMDH model with seven inputs gave the most exact results with an average absolute relative deviation (AARD) of 8.14% and a coefficient of determination (R2) of 0.98. The proposed techniques were compared with theoretical and empirical models available in the literature, and it was displayed that the GMDH model with seven inputs strongly outperforms the existing approaches. The leverage statistical analysis revealed that most of the experimental data were located within the applicability domains of both GMDH and GP models and were of high quality. Trend analysis also illustrated that the GMDH and GP models could follow the expected trends of viscosity with variations in pressure and temperature. In addition, the relevancy factor portrayed that the temperature had the greatest impact on the ILs viscosity. The findings of this study illustrated that the proposed models represented strong alternatives to time-consuming and costly experimental methods of ILs viscosity measurement.

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

The Group Method of Data Handling (GMDH) is a typical inductive modeling method that is built on principles of self-organization for modeling complex systems. However, it is known to often under-perform on non-parametric regression tasks, while time series modeling GMDH exhibits a tendency to find very complex polynomials that cannot model well future, unseen oscillations of the series. In order to alleviate these problems, GMDH has been recently hybridized with some computational intelligence (CI) techniques resulting in more robust and flexible hybrid intelligent systems for solving complex, real-world problems. The central theme of this book is to present in a very clear manner hybrids of some computational intelligence techniques and GMDH approach. The hybrids discussed in the book include GP-GMDH (Genetic Programming-GMDH) algorithm, GA-GMDH (Genetic Algorithm-GMDH) algorithm, DE-GMDH (Differential Evolution-GMDH) algorithm, and PSO-GMDH (Particle Swarm Optimization) algorithm. Also included is the description of the recently introduced GAME (Group Adaptive Models Evolution algorithm. The hybrid character of models and their self-organizing ability give these hybrid self-organizing modeling systems an advantage over standard data mining models. The modeling and data mining solutions of several real-life problems in the areas of engineering, bioinformatics, finance, and economics are presented in the chapters. The book will benefit amongst others, people who are working in the areas of neural networks, machine learning, artificial intelligence, complex system modeling and analysis, and optimization.

A simultaneous survey of several types of droughts, such as meteorological, hydrological, agricultural, economic, and social droughts, is possible by using the multivariate standardized precipitation index (MSPI). In this study, the accuracy of four artificial intelligence (AI) methods, including the generalized regression neural network (GRNN), least-square support vector machine (LSSVM), group method of data handling (GMDH), and adaptive neuro-fuzzy inference systems with fuzzy C-means clustering (ANFIS-FCM), were investigated in forecasting the MSPI of three synoptic stations (Jolfa, Kerman, and Tehran) located in the arid-cold climate of Iran. The data used was monthly precipitation and belongs to a 30-year period (1988–2017). MSPI values were calculated in five time windows, including the following: 3–6 (MSPI3–6), 6–12 (MSPI6–12), 3–12 (MSPI3–12), 12–24 (MSPI12–24), and 24–48 (MSPI24–48). The period of 1988–2016 was considered for training (75%) and testing (25%), and 2017 (12 months) was used for long-term forecasting. The methods were evaluated by the root mean square error (RMSE), mean absolute error (MAE), Willmott index (WI), and Taylor diagram. In the short-term forecasting phase, results showed that the methods had their best performances in forecasting multivariate drought types of groundwater hydrology-economic-social (MSPI24–48), agricultural-groundwater hydrology (MSPI12–24), surface hydrology-agricultural (MSPI6–12), soil moisture-surface hydrology-agricultural (MSPI3–12), and soil moisture-surface hydrology (MSPI3–6), respectively. Also, among the mentioned methods, the weakest accuracy was reported for GRNN with an RMSE=0.673, MAE=0.499, and WI=0.750 (related to MSPI3–6 of the Kerman station); the most accurate performance resulted from the GMDH with RMSE=0.097, MAE=0.074, and WI=0.989 (related to MSPI24–48 of the Jolfa station). In spite of the acceptable performance of the models in short-term forecasting, by increasing the forecasting horizons, the models’ errors were increased in the long-term forecasting phase. The models could have acceptable long-term forecasts for just two months (or in some exceptional cases, three months) ahead. Further, according to the investigations, it can be shown that the methods show better performances in mountainous arid-cold regions, compared to desert arid-cold regions. As a theoretical study of multivariate drought forecasting, the AIs have promising results, and this research can be extended for the other regions.