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A novel hybrid group method of data handling and Levenberg Marquardt model for estimating total organic carbon in source rocks with explainable artificial intelligence

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2025年 144卷

作者： Mkono, Christopher N. Shen, Chuanbo Mulashani, Alvin K. Carranza, Emmanuel John M. Kalibwami, Daud C. Nyangi, Magori J. China Univ Geosci Key Lab Tecton & Petr Resources Minist Educ Wuhan 430074 Peoples R China China Univ Geosci Sch Earth Resources Dept Petr Engn Wuhan 430074 Peoples R China Mbeya Univ Sci & Technol Coll Engn & Technol Dept Geosci & Min Technol Box 131 Mbeya Tanzania Univ Free State Dept Geol Bloemfontein South Africa Water Inst Dept Water Resources POB 35059 Dar Es Salaam Tanzania

The estimation of Total Organic Carbon (TOC) in source rocks is critical for assessing hydrocarbon potential and source rock quality in petroleum exploration and production. This study presents a novel hybrid model of the group method of data handling and Levenberg Marquardt (GMDH-LM), which integrates mineralogical and well-log data to improve TOC prediction accuracy. The GMDH-LM model employs non-parametric regression, offering superior adaptability and accuracy in solving non-linear problems, even with small datasets. The results show that the GMDH-LM model achieved a higher coefficient of determination (R2) of 0.9784, lower Root Mean Square Error (RMSE) of 0.1162, Mean Absolute Percentage Error (MAPE) of 0.3722 and less computation time of 0.73 s. Furthermore, the integration of mineral constituents into the model significantly improved the accuracy to R2 = 0.9983 as compared to where only well log data is used. Additionally, the application of Shapley Additive Explanation (SHAP) analysis presents a key innovation in this work as a novel method in TOC estimation, offering unprecedented transparency and interpretability of the GMDH-LM model by identifying gamma ray (GR), calcite, K-feldspar and deep lateral resistivity (LLD) as the most impactful input variables, thus contributing to the model's trustworthiness, reliability, and overall performance. This interpretability enhances model reliability and supports informed decision-making. The proposed GMDH-LM model represents a significant advancement in hybrid machine learning applications, offering a robust and efficient tool for TOC estimation. Its scalability and precision make it valuable for petroleum reservoir characterization and exploration, with broader implications for optimizing resource management in the oil and gas industry.

关键词： Total organic carbon group method of data handling Explainable artificial intelligence Transparency in artificial intelligence Levenberg marquardt Shapley additive explanation

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Dynamic Analysis-Based Damage Identification in Laminate Composites via Wavelet Transform and group method of data handling Network

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INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS 2025年第0期

作者： Yan, Pu Zhao, Li-Cai Lanzhou Coll Informat Sci & Technol Sch Elect & Elect Engn Lanzhou 730000 Gansu Peoples R China China Railway 19 Bur Grp Co Ltd Third Engn Co Ltd Shenyang 110136 Liaoning Peoples R China

Understanding the extent of structural damage is critical for effective decision-making in structural health monitoring. While wavelet transforms are powerful tools for detecting damage, they lack the ability to assess damage severity. To address this limitation, this study integrates the group method of data handling (GMDH) to enhance the accuracy of damage identification in laminated composite plates. A finite element model is developed to simulate damaged laminated composite plates and generate 2D signals, which are then processed using wavelet transforms. The GMDH algorithm further quantifies the damage severity at the locations identified by the wavelet transform. To validate the effectiveness of the proposed Wavelet-based GMDH approach (WT-GMDH), multiple damage scenarios are analyzed. The novelty lies in the integration of GMDH with wavelet transforms for damage quantification in laminated composite plates. The results demonstrate that, while wavelet transforms alone struggle to detect low-severity damage in identifying such damage (the WT-GMDH method achieves 98.66% and 98.53% accuracy for train and test stages, respectively). These findings confirm that the integration of the GMDH algorithm significantly enhances the capabilities of wavelet transforms, providing a more robust and efficient solution for structural damage assessment. Also, according to our results, the weakness of wavelet transform in damage detection in boundaries remains controversial.

关键词： Structural damage detection wavelet transform group method of data handling laminated composite plates finite element model

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Application of group method of data handling and gene expression programming to modeling molecular diffusivity of CO2 in heavy crudes

GEOENERGY SCIENCE AND ENGINEERING

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GEOENERGY SCIENCE AND ENGINEERING 2024年 237卷

作者： Lv, Qichao Zhou, Tongke Zheng, Haimin Rezaei, Farzaneh Chen, Weiyu Mohammadi, Mohammad-Reza Liu, Yang Hemmati-Sarapardeh, Abdolhossein China Univ Petr Coll Carbon Neutral Energy Beijing Peoples R China Univ Manchester Dept Chem Engn Manchester England CNOOC Res Inst Cooperat Engn & Design Dept Beijing Peoples R China Amirkabir Univ Technol Dept Petr Engn Tehran Iran CNOOC Energy Technol & Serv Ltd Engn & Technol Branch Tianjin Peoples R China Shahid Bahonar Univ Kerman Dept Petr Engn Kerman Iran PetroChina Changqing Oilfield Co Xian Shaanxi Peoples R China

Successful enhancement of heavy oil and bitumen production using CO2-based enhanced oil recovery (EOR) techniques requires extensive knowledge about the diffusivity of CO2 in heavy crudes. In this work, two advanced correlative approaches, namely group method of data handling (GMDH) and gene expression programming (GEP), were utilized to establish simple-to-use mathematical correlations by applying a comprehensive dataset including 260 laboratory data of CO2 diffusion coefficient (DC) in heavy crudes and taking into account all the parameters affecting the accuracy of the models. Moreover, the response surface and contour plots were analyzed to obtain the desired response values and operating conditions. The GMDH correlation represented more reliable results with better statistical criteria including average absolute percentage error (AAPRE) values of 7.47%, 7.83%, and 7.54% for training, testing, and the total sets, respectively. Also, the results showed that the increase in pressure and/or temperature caused an increment in the amount of diffusivity of CO2 in heavy crudes;and the maximum amount of CO2 DC was obtained at the upper limit of these operational parameters. At a given temperature and pressure, it appears that the highest CO2 DC in heavy crudes was obtained when the CO2 mass fraction was less than 0.02. Furthermore, the Pearson and Spearman correlation coefficients were used to investigate linear and non-linear relationships between input variables and the responses of GMDH and GEP correlations. The mass fraction of CO2, temperature, pressure, and temperature_PVT had a direct relationship, and on the other hand, the viscosity and density of crudes had a reverse relationship with CO2 DC. Finally, the reliability of the data bank of CO2 DC in heavy crudes along with the high validity of GMDH and GEP correlations was verified by the leverage technique. Notably, no out-of-leverage data were identified, with only seven and five data points considered as suspe

关键词： CO2-Based enhanced oil recovery Heavy crude oil Bitumen CO2 diffusion coefficient group method of data handling Gene expression programming

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Traffic flow modelling of vehicles on a six lane freeway: Comparative analysis of improved group method of data handling and artificial neural network model

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RESULTS IN ENGINEERING 2025年 25卷

作者： Olayode, Isaac Oyeyemi Severino, Alessandro Alex, Frimpong Justice Jamei, Elmira Swinburne Univ Technol Sch Sci Comp & Engn Technol Hawthorn Vic 3122 Australia Univ Kore Enna Dept Civil Engn & Architecture Kore Italy Wuhan Univ Technol Sch Automot Engn Wuhan 430070 Peoples R China Victoria Univ Inst Sustainable Ind & Liveable Cities Coll Sport Hlth & Engn Built Environm Discipline Melbourne Vic 3011 Australia

In recent decades, traffic flow modelling has become increasingly significant for improving road transportation systems and mitigating congestion on freeways. This research presents a comparative analysis of two machine learning methodologies-Improved group method of data handling (GMDH) and Artificial Neural Network (ANN)-for modelling vehicular traffic flow on a six-lane freeway. The primary objective of this study was to evaluate the predictive accuracy and efficacy of both models in replicating complex traffic patterns and to provide insights into their suitability for real-time traffic flow applications. Traffic flow data were obtained from a six-lane freeway during off-peak and on-peak hours using South African road transportation systems as a case study. Traffic flow variables, such as vehicle density, speed, time, and traffic volume, were considered as both inputs and outputs. The models were trained and validated using this dataset, and the GMDH and ANN were assessed according to their regression efficacy R2 and MSE. The results indicate that both models can effectively capture the nonlinear relationships present in the traffic flow of vehicles on a six-lane freeway. However, GMDH outperformed ANN in terms of accuracy and computational efficiency. The optimal regression values for GMDH and ANN were 0.99372 and 0.9167, respectively, demonstrating that GMDH provided a substantially superior fit to the observed data. The exceptional efficacy of the GMDH is attributed to its self-organising architecture and capacity to autonomously identify the most pertinent inputs, thereby reducing model complexity and enhancing generalisation. Artificial Neural Networks, while efficient, require comprehensive tuning and may experience overfitting in high-dimensional datasets. This study suggests that GMDH is a more reliable and effective model for modelling traffic flow on a six-lane freeway, presenting opportunities for real-time traffic prediction and traffic flow manageme

关键词： Traffic flow group method of data handling Machine learning Freeway Artificial neural network

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Enhancing Mine Blasting Safety: Developing Intelligent Systems for Accurate Flyrock Prediction through Optimized group method of data handling methods

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NATURAL RESOURCES RESEARCH 2025年第2期34卷 1199-1218页

作者： Ding, Xiaohua Hasanipanah, Mahdi Monjezi, Masoud Abdullah, Rini Asnida Nguyen, Tung Ulrikh, Dmitrii Vladimirovich China Univ Min & Technol Sch Mines Xuzhou 221116 Peoples R China China Univ Min & Technol State Key Lab Coal Resources & Safe Min Xuzhou 221116 Peoples R China Duy Tan Univ Inst Res & Dev Da Nang Vietnam Duy Tan Univ Sch Engn & Technol Da Nang Vietnam Tarbiat Modares Univ Fac Engn Tehran Iran Univ Teknol Malaysia Fac Civil Engn Johor Baharu Malaysia St Petersburg State Univ Architecture & Civil Engn Dept Water Use & Environm 4 2nd Krasnoarmeiskaya Str St Petersburg 190005 Russia

Flyrock, the unintended projection of rocks during mining blasts, poses significant safety risks and potential damage. Predicting flyrock is essential for implementing safety measures, minimizing injuries, preventing equipment and structural damage, optimizing blast plans, reducing downtime, and saving costs. Accurate predictions mitigate hazards, improve operational efficiency, and ensure the safety of workers and surrounding infrastructure. This study explored and developed hybrid methods for predicting flyrock using the group method of data handling (GMDH). Four swarm-based algorithms-particle swarm optimization (PSO), artificial bee colony (ABC), ant colony optimization (ACO), and whale optimization algorithm (WOA)-were combined with GMDH to enhance prediction accuracy. Additionally, a k-fold cross-validation method was applied to the datasets to improve reliability. The accuracy of these methods was evaluated using various statistical functions, such as Nash-Sutcliffe coefficient and Willmott's index, along with R-squared correlation (R2) graphs, half-violin plots, and quantile-quantile plots. The R2 values for the WOA-GMDH, ACO-GMDH, ABC-GMDH, and PSO-GMDH models were 0.99, 0.97, 0.96, and 0.96, respectively. The WOA-GMDH method yielded the most accurate results, demonstrating superior performance when combined with GMDH. Furthermore, the performance of the WOA-GMDH model was compared with models developed in the literature using the same database, confirming its effectiveness. Sensitivity analysis identified that, in WOA-GMDH modeling, the powder factor as the most significant parameter while the spacing parameter was the least significant. The ACO-GMDH method exhibited the narrowest uncertainty band;whereas, the PSO-GMDH method had the widest, indicating the highest level of uncertainty.

关键词： Surface mines Flyrock group method of data handling Whale optimization algorithm

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Application of the group method of data handling (GMDH) approach for travel distance prediction of landslides

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LANDSLIDES 2023年第3期20卷 645-661页

作者： Wan, Jiancheng Xue, Xinhua Sichuan Univ Coll Water Resource & Hydropower State Key Lab Hydraul & Mt River Engn Chengdu 610065 Peoples R China

Landslides have claimed many lives and caused significant economic losses in recent years. Therefore, assessing the potential risk for landslide hazard prevention and mitigation is vital and the landslide travel distance is a key aspect in this process. In this study, the group method of data handling (GMDH) was used to predict the landslide travel distance. A total of 111 landslide datasets collected from the literature were used to construct and validate the proposed GMDH model. Five parameters were selected as the input parameters, including initial slope angle, body height, average body thickness, the logarithm of source volume, and body aspect ratio. The GMDH model was compared with the gene expression programming (GEP) model as well as four empirical models proposed by other researchers. The comparison results demonstrated that the predicted results of the GMDH model agreed well with the measured values, with a correlation coefficient of 0.9123, which was higher than the GEP model and the four empirical models. It was concluded that the proposed GMDH model had great potential in estimating the landslide travel distance.

关键词： Landslide Travel distance group method of data handling Gene expression programming

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group method of data handling Using Christiano-Fitzgerald Random Walk Filter for Insulator Fault Prediction

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SENSORS 2023年第13期23卷 6118页

作者： Stefenon, Stefano Frizzo Seman, Laio Oriel Sopelsa Neto, Nemesio Fava Meyer, Luiz Henrique Mariani, Viviana Cocco Coelho, Leandro dos Santos Fdn Bruno Kessler Digital Ind Ctr I-38123 Trento Italy Univ Udine Dept Math Comp Sci & Phys I-33100 Udine Italy Univ Vale Itajai Grad Program Appl Comp Sci BR-88302901 Itajai SC Brazil Univ Reg Blumenau Elect Engn Grad Program BR-89030000 Blumenau SC Brazil Pontificia Univ Catolica Parana Mech Engn Grad Program BR-80215901 Curitiba PR Brazil Univ Fed Parana Dept Elect Engn BR-81530000 Curitiba PR Brazil Pontificia Univ Catolica Parana Ind & Syst Engn Grad Program BR-80215901 Curitiba PR Brazil

Disruptive failures threaten the reliability of electric supply in power branches, often indicated by the rise of leakage current in distribution insulators. This paper presents a novel, hybrid method for fault prediction based on the time series of the leakage current of contaminated insulators. In a controlled high-voltage laboratory simulation, 15 kV-class insulators from an electrical power distribution network were exposed to increasing contamination in a salt chamber. The leakage current was recorded over 28 h of effective exposure, culminating in a flashover in all considered insulators. This flashover event served as the prediction mark that this paper proposes to evaluate. The proposed method applies the Christiano-Fitzgerald random walk (CFRW) filter for trend decomposition and the group data-handling (GMDH) method for time series prediction. The CFRW filter, with its versatility, proved to be more effective than the seasonal decomposition using moving averages in reducing non-linearities. The CFRW-GMDH method, with a root-mean-squared error of 3.44x10(-12), outperformed both the standard GMDH and long short-term memory models in fault prediction. This superior performance suggested that the CFRW-GMDH method is a promising tool for predicting faults in power grid insulators based on leakage current data. This approach can provide power utilities with a reliable tool for monitoring insulator health and predicting failures, thereby enhancing the reliability of the power supply.

关键词： Christiano-Fitzgerald random walk filter electrical power grids group method of data handling leakage current time series forecasting

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group method of data handling (GMDH) Neural Network for Estimating Total Organic Carbon (TOC) and Hydrocarbon Potential Distribution (S1, S2) Using Well Logs

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NATURAL RESOURCES RESEARCH 2021年第5期30卷 3605-3622页

作者： Mulashani, Alvin K. Shen, Chuanbo Asante-Okyere, Solomon Kerttu, Paulus N. Abelly, Elieneza N. China Univ Geosci Key Lab Tecton & Petr Resources Minist Educ Wuhan 430074 Peoples R China Mbeya Univ Sci & Technol Dept Geosci & Min Technol Coll Engn & Technol Box 131 Mbeya Tanzania Univ Mines & Technol Sch Petr Studies Dept Petr & Nat Gas Engn Tarkwa Ghana China Univ Geosci Fac Geophys & Geomat Wuhan 430074 Peoples R China

Recent advancement in computing capabilities has brought to light the application of machine learning methods in estimating geochemical data from well logs. The widely employed artificial neural network (ANN) has intrinsic problems in its application. Therefore, the objective of this study was to present a group method of data handling (GMDH) neural network as an improved alternative in predicting total organic carbon (TOC), S-1,S- and S-2 from well logs. The study used bulk density, sonic travel time, deep lateral resistivity log, gamma-ray, spontaneous potential, neutron porosity well logs as input variables to predict TOC, S-1, and S-2 of the Nondwa, Mbuo, and Mihambia Formations in the Triassic to mid-Jurassic of the Mandawa Basin in southeast Tanzania. The TOC prediction results indicated that the GMDH model trained well while generalizing better across the testing data than both ANN and Delta logR. Specifically, the GMDH provided TOC testing predictions having the least errors of 0.40 and 0.45 for mean square error (MSE) and mean absolute error (MAE), respectively, as compared to 1.27 and 0.81, 0.68 and 0.7, 1.4 and 0.89 obtained by backpropagation neural network (BPNN), radial basis function neural network (RBFNN), and Delta logR, respectively. For S-1 and S-2, the ANN models performed excellently during training but were unable to produce similar results when tested on the completely unseen well data. This represents a clear case of over-fitting by ANN. During testing, the GMDH avoided over-fitting and outperformed ANN by obtaining the least MSE of 0.04 and 1.16 and MAE of 0.07 for S-1 and S-2, respectively, while BPNN achieved MSE and MAE of 0.08 and 0.17 for S-1, 1.96, and 0.9 for S-2, and RBFNN obtained MSE and MAE of 0.15 and 0.25 for S-1 and 1.4 and 0.87 for S-2. Hence, the improved generalization performance of the GMDH makes it an improved form of a neural network for TOC, S-1,S- and S-2 prediction. The proposed model was further adopted to predict th

关键词： group method of data handling Total organic carbon Hydrocarbon potential distribution Artificial neural network

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Intelligent step-length adjustment for adaptive path-following in nonlinear structural mechanics based on group method of data handling neural network

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MECHANICS OF ADVANCED MATERIALS AND STRUCTURES 2022年第20期29卷 2895-2912页

作者： Maghami, Ali Hosseini, Seyed Mahmoud Ferdowsi Univ Mashhad Dept Ind Engn Fac Engn POB 91775-1111 Mashhad Razavi Khorasan Iran

A novel step-length adjustment method for adaptive path-following in geometrically nonlinear problems of solid mechanics is proposed in this paper. The core idea is how to predict the critical points on the equilibrium path properly, and then distribute the points on the path accordingly. We characterize the equilibrium path employing a scalar stiffness parameter. Here, we show how the stiffness parameter could be used to detect the critical points on the path. Then, we employ time-series forecasting based on group method of data handling (GMDH) to predict the stiffness parameter which in fact leads to the prediction of critical points. To adaptively adjust the step-length to the predicted critical point, we present a simple formulation to distribute the points on the equilibrium path. In this paper, a novel adaptive path-following algorithm is presented to trace and predict the path efficiently. The proposed algorithm, minimum residual displacement method (MRDM), arc length method (ALM) and generalized displacement method (GDM) are comparatively investigated for the geometrically nonlinear analysis of structures in both continuum and discrete problems (truss and cylindrical shell). Selected examples present large fluctuations in stiffness. We demonstrate with the numerical examples that the trained neural network can properly predict the critical points on the path. The results also illustrate that our adaptive path-following method is able to distribute converged points properly and trace the equilibrium path with a significantly reduced number of points compared to the analyses with the uniform step-length.

关键词： Nonlinear solution scheme adaptive path-following step-length adjustment stiffness parameter critical points group method of data handling time-series forecasting

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A parametric study of ground vibration induced by quarry blasting: an application of group method of data handling

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ENVIRONMENTAL EARTH SCIENCES 2022年第4期81卷 1-15页

作者： Zeng, Jie Mohammed, Ahmed Salih Mirzaei, Fatemeh Moosavi, Seyed Mohammad Hossein Armaghani, Danial Jahed Samui, Pijush Chongqing Jianzhu Coll Dept Transportat & Municipal Engn Chongqing 400072 Peoples R China Univ Sulaimani Coll Engn Civil Engn Dept Sulaymaniyah Kurdistan Regio Iraq Laval Univ Dept Civil & Water Engn Quebec City PQ Canada Univ Malaya Fac Engn Dept Civil Engn Kuala Lumpur 50603 Malaysia South Ural State Univ Dept Urban Planning Engn Networks & Syst Inst Architecture & Construct 76 Lenin Prospect Chelyabinsk 454080 Russia Natl Inst Technol Patna Dept Civil Engn Patna 800005 Bihar India

Blasting is a common technique for rock breakage in the numerous civil and mining engineering activities such as excavation, leveling, and tunneling. However, this technique has several environmental issues, such as ground vibration. More importantly, the peak particle velocity (PPV), as the main indicator of ground vibration, should be considered by engineers/designers due to its potential risk of damaging structures in the nearby area. This research introduces a different modeling procedure to predict PPV resulting from blasting by developing a group method of data handling (GMDH) technique. data collection and preparation were conducted based on 117 blasting operations at a quarry site, and the effective parameters were considered for prediction purposes. Then, various strategies were defined based on the most important PPV factors, and these strategies were modeled using a variety of parametric studies. After an evaluation process, the best GMDH model was selected for each strategy. As a result, the best GMDH model was related to strategy 3 where four input parameters, i.e., powder factor, charge per delay, sub-drilling, and distance were selected and used. Coefficient correlation results of 0.933 and 0.942 were obtained, respectively, for the training and testing stages of the best GMDH model. To indicate the capability and power of the GMDH model in predicting PPV values, a neuro-fuzzy technique was also proposed for PPV prediction. The obtained results confirmed the power of the developed GMDH model as well as the practical application of this technique in predicting PPV values resulting from blasting.

关键词： Peak particle velocity Blasting Environmental issues group method of data handling Neuro-fuzzy

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