Low Error Values Research Articles

Advancing Geotechnical Evaluation of Wellbores: A Robust and Precise Model for Predicting Uniaxial Compressive Strength (UCS) of Rocks in Oil and Gas Wells

This study examines the efficacy of various machine learning models for predicting the uniaxial compressive strength (UCS) of rocks in oil and gas wells, which are essential for ensuring wellbore stability and optimizing drilling operations. The investigation encompasses Linear Regression, ensemble methods (including Random Forest, Gradient Boosting, XGBoost, and LightGBM), support vector machine-based regression (SVM-SVR), and multilayer perceptron artificial neural network (MLP-ANN) models. The results demonstrate that XGBoost and Gradient Boosting offer superior predictive accuracy for UCS in drillability, as indicated by low Mean Absolute Percentage Error (MAPE) values of 3.87% and 4.18%, respectively, and high R2 scores (0.8542 for XGBoost). These models emerge as optimal choices for UCS prediction focused on drillability, offering increased accuracy and reliability in practical engineering scenarios. Ensemble methods and MLP-ANN emerge as frontrunners, providing valuable tools for improving wellbore stability assessments, optimizing drilling parameter selection, and facilitating informed decision-making processes in oil and gas drilling operations. Moreover, this study lays a foundation for further research in drillability-centred predictive modelling for geotechnical parameters, advancing our understanding of rock behaviour under drilling conditions.

Structural damage detection using a sensitivity-based model updating approach with autocorrelation function data

ABSTRACT This study presents a novel sensitivity equation for estimating structural parameters using autocorrelation function (ACF) data of dynamic responses. The proposed method reduces the need for extensive excitation frequencies, making structural parameter identification more practical and cost-effective, especially for large-scale structures. Furthermore, due to the quadratic relationship between ACF and the structural dynamic response, this approach exhibited greater sensitivity to damage than time-history-based methods. The method’s effectiveness was evaluated using simulated data from truss and offshore jacket platform models. Incomplete measurements were addressed by using partially measured structural characteristics without model reduction and data expansion processes. Measurement and modelling errors were simulated by adding uniformly distributed random error into the damaged structure data. The low values of the coefficient of variation indicated the method’s robustness against these errors. The accuracy of the method was confirmed through low root mean square error (RMSE) values and high variance accounted for (VAF) values.

Machine learning-based clustering analysis of the banking green credit for the renewable energy industry

Credit policies for clean and renewable energy businesses play a crucial role in supporting carbon neutrality efforts to combat climate change. Clustering the credit capacity of these companies to prioritize lending is essential given the limited capital available. Support Vector Machine (SVM) and Artificial Neural Network (ANN) are two robust machine learning algorithms for addressing complex clustering problems. Additionally, hyperparameter selection within these models is effectively enhanced through the support of a robust heuristic optimization algorithm, Particle Swarm Optimization (PSO). To leverage the strength of these advanced machine learning techniques, this paper aims to develop SVM and ANN models, optimized with the PSO, for the clustering problem of green credit capacity in the renewable energy industry. The results show low Mean Square Error (MSE) values for both models, indicating high clustering accuracy. The credit capabilities of wind energy, clean fuel, and biomass pellet companies are illustrated in quadrant charts, providing stakeholders with a clear view to adjust their credit strategies. This helps ensure the efficient operation of banking green credit policies.

Machine Learning for the Genomic Prediction of Growth Traits in a Composite Beef Cattle Population.

The adoption of genomic selection is prevalent across various plant and livestock species, yet existing models for predicting genomic breeding values often remain suboptimal. Machine learning models present a promising avenue to enhance prediction accuracy due to their ability to accommodate both linear and non-linear relationships. In this study, we evaluated four machine learning models-Random Forest, Support Vector Machine, Convolutional Neural Networks, and Multi-Layer Perceptrons-for predicting genomic values related to birth weight (BW), weaning weight (WW), and yearling weight (YW), and compared them with other conventional models-GBLUP (Genomic Best Linear Unbiased Prediction), Bayes A, and Bayes B. The results demonstrated that the GBLUP model achieved the highest prediction accuracy for both BW and YW, whereas the Random Forest model exhibited a superior prediction accuracy for WW. Furthermore, GBLUP outperformed the other models in terms of model fit, as evidenced by the lower mean square error values and regression coefficients of the corrected phenotypes on predicted values. Overall, the GBLUP model delivered a superior prediction accuracy and model fit compared to the machine learning models tested.

Machine learning based prediction of biogas generation from municipal solid waste: A data-driven approach

This study aims to imply different machine learning (ML) (artificial neural network (ANN), linear regression, XGBoost, random forest (RF), support vector machine (SVM)) models to predict and optimize biogas production yield from organic fractions of municipal solid waste (MSW). The data set for six key input variables, including moisture content, C/N ratio, lignocellulose content and MSW age was analyzed and processed using ML models. Further, data exploratory analysis (EDA) analysis was performed using various steps such as data preprocessing, feature selection, train-test-validation splitting, model testing and evaluation. The results revealed that XGBoost and RF regression model exhibited superior performance efficacy. Both the models achieved a higher R2 values of 0.88 and 0.68, and low root mean square error (RMSE) values of 305 and 496, respectively. Furthermore, feature importance analysis was performed to identify the relative significance of input variables in biogas prediction. SVM model revealed significant contributions of moisture content (20.86 %), cellulose (60.21 %), hemicellulose (34.91 %), lignin content (62.84 %), and MSW age (17.23 %) in predicting biogas production. The findings of the study can be a resource for techno-crates/researchers to develop an efficient ML based decision-making tools for accurate predictions and process optimization.

A novel mechanistic model for predicting shrinkage kinetics in plant-based foods by integrating solid matrix mobility and viscoelasticity

Deformation during drying is a major physical change influencing drying kinetics and final product quality. Therefore, accurate prediction of shrinkage kinetics is essential for determining the optimal drying conditions for these foods. Shrinkage kinetics is greatly influenced by their structural mobility (rubbery-glassy transition) and viscoelastic properties. The current deformation models lack a comprehensive integration of structural mobility and viscoelasticity concepts, resulting in limitation in attaining insights on physiochemical state variations and viscoelastic stresses developed during drying. In order to overcome this limitation, this study proposes a novel mechanistic shrinkage model that combines solid matrix mobility-based shrinkage velocity and viscoelasticity consideration, incorporating variable mechanical properties to simulate deformation arising from moisture loss and pressure gradient respectively. Comparison between predicted drying kinetics and shrinkage evolution with experimental observation yielded close agreement, achieving low mean absolute error values. As the drying process progressed, a distinct anisotropic shrinkage pattern emerged, which is attributed to varied structural mobility based on temperature and moisture distribution across the food sample. Notably, shrinkage driven by moisture loss significantly outweighed that induced by pressure, exerting a predominant influence on overall volume change. Furthermore, the model demonstrated heightened sensitivity to water transport parameters compared to mechanical factors, which indicates the significance of moisture dynamics in shaping the drying process. Combined consideration of physiochemical changes and viscoelastic concept in the developed deformation model extends new possibility towards optimizing the drying process as well as quality aspect evaluation.

Geoinformatics and Modeling Approaches for Estimating Above-Ground Biomass in the Moist Deciduous Forests of Uttara Kannada, Karnataka, India

The present study aims to estimate Above-Ground Biomass (AGB) in the moist deciduous forests of Mundgod Taluk, Uttara Kannada district, Karnataka, India using a combination of field sampling and remote sensing techniques. AGB was assessed using Sentinel-2A satellite imagery with a spatial resolution of 10 meters. Field data were collected using the Point-Centered Quarter (PCQ) method, it includes measuring tree girth at breast height (GBH), tree height, and canopy density. AGB was calculated using artificial form factor and specific gravity of tree species and further modelled using the Normalized Difference Vegetation Index (NDVI) derived from satellite data. The results showed a significant correlation between canopy density and biomass, with very dense forests exhibiting the highest AGB values. The field-measured AGB was 436.96 t/ha for very dense forests, 259.89 t/ha for moderately dense forests, and 161.67 t/ha for open forests. A linear regression model developed between AGB and NDVI showed a high R² value of 0.91 for open forests, 0.87 for moderately dense forests, and 0.85 for very dense forests. The total area-weighted biomass for the study area was estimated at 8.87 million tons, with 4.79 million tons in very dense forests, 3.44 million tons in moderately dense forests, and 0.76 million tons in open forests. The regression model validation indicated low Root Mean Square Error (RMSE) values, with the moderately dense forests 8.81 t/ha and the in very dense forests 7.54 t/ha. This study highlights the effectiveness of integrating field measurements with remote sensing for rapid, reliable AGB estimation. The approach offers valuable insights into biomass distribution and carbon sequestration potential, providing a scalable method for carbon inventories at state and national levels, contributing to forest management and climate change mitigation efforts.

Quantifying Solar Radiation Over Northern India and Validating with Cropwat for Agricultural and Renewable Energy Applications

Precise computation of global solar energy is crucial for many fields of investigation such as renewable energy, meteorology, and agriculture especially crop water requirement and irrigation requirement. This paper presents the quantification of solar radiation using weather data during the years from 2020-21. The results obtained were validated with the solar radiation estimated with the help of CROPWAT during the year. Statistical and visual approaches were adopted to validate the quantified results. Analysis revealed the high degree of similarity between simulated and CROPWAT determined daily solar radiation during the year 2020-21 over the study area. Very high values of Willmot index of agreement (1.0), Nash-Sutcliffe efficiency (0.999), and Pearson correlation coefficient (0.998), and low values of mean absolute error (0.138), mean bias error (-0.024), and root mean square error (0.182) between them was observed during the year 2020-21 in the area. The minimum solar radiation reaching over the region were observed to be around 5.71 MJ/m2/day during winter season (January) with a normal value of 13.50 MJ/m2/day, while the maximum value of 24.5 MJ/m2/day was observed during the summer season (June) with a normal value of 24.13 MJ/m2/day over the region. The use of these data for further study is recommended as it is worthful quantification over the region.

NIR Spectroscopy for the Online Monitoring of Water and Olive Oil Content in Pomace during the Extraction Process

The main challenge of this scientific work was the implementation on an industrial olive oil extraction plant of an NIR device for the multispectral analysis of pomace to predict the percentage of humidity and oil contained in it. Subsequent to the implementation of the NIR device on the oil extraction line on the solid’s outlet from the decanter, NIRS interaction measurements in the 761–1081 nm region were used to probe the pomace. NIRS calibration models for the prediction of water and oil content in the pomace were obtained and successfully tested and validated. The correlations of calibration results for oil and water content were 0.700 and 0.829, while the correlations of validation were 0.773 and 0.676, respectively. Low values of root mean square error were found for both the prediction and validation set. The results highlight the good robustness of an NIR approach based on a PLS calibration model to monitor the industrial olive oil process. The results obtained are a first step toward the large-scale implementation of NIR devices for monitoring pomace in oil mills. The possibility of knowing the oil lost in the pomace, moment by moment, would open a new frontier towards system control and the sustainability of the olive oil extraction process.

Cross-Cultural Adaptation, Reliability, and Validity of the Greek Version of the Fremantle Neck Awareness Questionnaire (FreNAQ-GR) in Patients with Chronic Neck Pain

Background: Neck self-awareness, related to sensorimotor dysfunction, can be monitored with the Fremantle Neck Awareness Questionnaire (FreNAQ). The cross-cultural adaptation of the FreNAQ in Greek (FreNAQ-GR) and an assessment of its psychometric properties were conducted. Methods: This study included 104 participants (65 female) with non-specific chronic neck pain (NSCNP). Once the cross-cultural adaptation process of the FreNAQ-GR was complete, the testing of its construct validity was conducted via an exploratory factor analysis (EFA). The construct validity examination also included a correlational analysis with a Pain Intensity Visual Analogue Scale (PI-VAS), the Neck Disability Index (NDI), the Tampa Scale of Kinesiophobia (TSK), the Pain Catastrophizing Scale (PCS), and demographics. The internal consistency of the FreNAQ-GR was also examined. A sub-sample of participants (n = 30) completed the FreNAQ-GR again after 5–7 days. Results: The dataset was appropriate for EFA (measure of sampling adequacy KMO = 0.763 and Bartlett’s test of sphericity p < 0.001). The FreNAQ-GR demonstrated a single-factor 6-item structure (items 7–9 removed), explaining 53.69% of the common variance. Statistically significant correlations (Spearman’s) were registered between the FreNAQ-GR (both versions) and the NDI (r = 0.33/0.29, p < 0.001), the TSK (r = 0.46/0.41, p < 0.001), and the PCS (r = 0.37/0.33, p < 0.001). For the 9-item and the 6-item FreNAQ-GR, the internal consistency (Chronbach’s a/McDonald’s ω) was 0.80/0.79 and 0.826/0.816, respectively. The test–retest reliability was excellent for both versions ICC2,1 (95% CI) = 0.98/0.98 (0.97–0.99/0.95–0.99), with low error values SEM = 0.90/0.74 and MDC95% = 2.49/2.05 points. Conclusions: The FreNAQ-GR is suitable for assessing neck self-awareness in Greek-speaking patients with NSCNP.

An Experimental and ANN Analysis of Ammonia Energy Integration in Biofuel Powered Low-Temperature Combustion Engine to Enhance Cleaner Combustion

In the pursuit of global net-zero emissions targets and cleaner combustion technologies, researchers are increasingly turning to innovative solutions. Ammonia, as a carbon-free fuel, holds promise for achieving low emissions and efficient combustion. This study explores the potential synergies of various ammonia shares (20%, 40%, and 60%) combined with Citronella biofuel in a Low-Temperature Combustion (LTC) Reactivity Controlled Compression Ignition (RCCI) engine. Comparative analysis between a 40% ammonia blend Citronella biofuel (A40) and a Standard Diesel (SDL) in an RCCI engine demonstrates significant reductions in oxides of nitrogen (by 17%), carbon dioxide (by 6.6%), and smoke (by 9.8%), along with a notable enhancement in Brake Thermal Efficiency (BTE) by 5.4% for A40. The validation of results using an Artificial Neural Network (ANN) model shows robust coefficients of determination (97%), high R values (0.9945 to 0.9995), and low Root Mean Square Error values (ranging from 0.0219 to 0.0483). These findings strongly support the efficacy of the A40 blend, positioning it as a promising and viable alternative fuel for achieving cleaner combustion in LTC-RCCI engines.

Gap filling of missing satellite data from MODIS and CMEMS for chlorophyll-a in the waters of Aceh, Indonesia

The motivation behind our study is to identify a robust method to enhance the accuracy of missing data, particularly chlorophyll-a data, which often goes undetected due to various factors. This study analyzes chlorophyll-a concentrations and sea level changes due to tides using three methods: Linear Interpolation, Fillgaps, and Modified Fillgaps. Two experiments were conducted: Experiment I involved random data removal (60% and 70%), and Experiment II combined sequential and random data removal (25% sequentially on the right, 35% and 45% randomly on the left). In Experiment I, the Modified Fillgaps method showed high correlation coefficients (up to 0.96) between original and reconstructed data, demonstrating its effectiveness in accurately filling significant data gaps. This method also exhibited low Root Mean Square Error and Mean Absolute Error values, confirming its predictive precision. In Experiment II, despite structured and realistic data loss patterns, the method maintained high correlation and low prediction errors, with low Normalized Root Mean Squared Error and Mean Absolute Percentage Error values, further validating its reliability. Additionally, the method excelled in two-dimensional chlorophyll-a maps, outperforming Linear Interpolation and Fillgaps methods in scenarios with 50% and 60% data loss, achieving higher correlation and lower prediction errors. These findings are crucial for environmental and climatological studies relying on satellite-derived data, confirming the Modified Fillgaps method as the most reliable and effective for handling significant data loss in chlorophyll-a map analyses. Future research should explore its application to other environmental data types and more complex data loss patterns.

PSX-5 Repeatability of overreach, term and acuteness in Peruvian Paso horse

Abstract The Peruvian Paso Horse is considered one of the best saddle horses worldwide due to the gait that makes this horse perform one of the smoothest walks. The overreach, term, and acuteness are the most characteristic movements in the gait, making them the most desirable attributes in its breeding and reproduction. Repeatability of overreach, term, and acuteness in Peruvian Paso horses (PPH) have not been determined to date. It is important to estimate this parameter for application in PPH breeding, therefore, the aim of this study was to estimate the repeatability of overreach, term, and acuteness of PPHs. The study included records of 137 stallions and mares. All measurements were recorded in MP4 video format with a resolution of 1920 x 1080 megapixels and at 60 frames per second. All traits were measured three times (once per stride), and each trait was analyzed. KINOVEA software version 0.9.5 was used to analyze the measurements. A multivariate repeated measures animal model with sex effect was used to estimate the variance components for each trait using WOMBAT software. Repeatability was high in all traits (> 0.78; Table 1). The low standard error values close to 0.02 indicate high precision in all traits (0.904, 0.855, and 0.903 for overreach, term, and acuteness, respectively), being defined as the variance of the mean of “n” measurements as a percentage of the variance of one measurement, indicating that this parameter has little effect on the temporal environment of the three traits. These results demonstrate that previous training can influence the regularity of the gait, in agreement with the present study, in which only adult animals that have already had previous training were evaluated. Furthermore, our results corroborate that traits with high repeatability require few measurements (3 in this study) to obtain greater precision, and an increase in the number of measurements may be irrelevant for parameter estimation. In a breeding plan, this high precision may be due to an increase in the additive genetic variance, indicating that two or more measurements have greater heritability than a single measurement, allowing a better breeding value estimate to be obtained. Considering the high repeatability values found, this parameter can be used as an indicator of how effective the selection process can be, considering its relationship with heritability, as repeatability values are higher than heritability, due to the inclusion of permanent environmental variance (within-individual variance) in its estimation. High values also indicate that individuals tend to have consistent performance, and therefore, obtaining several measures for evaluation may be impractical. It can be concluded that overreach, term, and acuteness have high repeatability values, which allows these traits to respond better in a selection process and performance evaluation for subsequent competitions.

Optimization and prediction of biogas yield from pretreated Ulva Intestinalis Linnaeus applying statistical-based regression approach and machine learning algorithms

A statistical-based regression approach and machine learning (ML) algorithms (response surface methodology (RSM), feed-forward backpropagation artificial neural network (ANN) and multi-layer adaptive neuro-fuzzy inference system (ANFIS)) were explored for the optimization and prediction of biogas resulting from the anaerobic digestion (AD) of pretreated Ulva Intestinalis Linnaeus (UIL). ANFIS model was found to better predict and model the process of biogas production from the AD of pretreated UIL owing to low mean square error (MSE) and RMSE values (0.8841 and 0.9402-US, 0.9628 and 0.9812-O3, 0.1387 and 0.3724-MW and 0.3018 and 1.1410-Fe3O4) and highest values of R2 (0.9998-US, 0.9996-O3, 0.9996-MW and 0.9995-Fe3O4). Optimum conditions for biogas yield as a result of the various pretreatment processes based on the ANFIS model were US-15 power/time, time-40 min and the biogas yield-181.0 mL.gVS−1, O3-15.0 mg/min, time-40.0 min and biogas yield of 164.0 mL.gVS−1, MW-2.3 power/time, time-40.0 min and biogas yield-81.7 mL.gVS−1 and Fe3O4-20.0 mg L−1, time-40.0 min and biogas yield-154 mL.gVS−1. The results obtained show that the ML and statistical-based models were effective in approximating the biogas yield with high precision and low error and could be beneficial for the biogas production scale-up process.

Reservoir computing with logistic map.

Recent studies on reservoir computing essentially involve a high-dimensional dynamical system as the reservoir, which transforms and stores the input as a higher-dimensional state for temporal and nontemporal data processing. We demonstrate here a method to predict temporal and nontemporal tasks by constructing virtual nodes as constituting a reservoir in reservoir computing using a nonlinear map, namely, the logistic map, and a simple finite trigonometric series. We predict three nonlinear systems, namely, Lorenz, Rössler, and Hindmarsh-Rose, for temporal tasks and a seventh-order polynomial for nontemporal tasks with great accuracy. Also, the prediction is made in the presence of noise and found to closely agree with the target. Remarkably, the logistic map performs well and predicts close to the actual or target values. The low values of the root mean square error confirm the accuracy of this method in terms of efficiency. Our approach removes the necessity of continuous dynamical systems for constructing the reservoir in reservoir computing. Moreover, the accurate prediction for the three different nonlinear systems suggests that this method can be considered a general one and can be applied to predict many systems. Finally, we show that the method also accurately anticipates the time series of the all the three variable of Rössler system for the future (self-prediction).

A hybrid data-driven approach for state of health estimation in lithium-ion batteries

ABSTRACT The assessment of the state of health (SOH) in lithium-ion batteries is essential for ensuring safe operation and implementing scientific management practices. This paper proposes a novel hybrid data-driven approach for accurately estimating the SOH of lithium-ion cells. Initially, the sparrow search algorithm (SSA) was implemented to optimize the structural configuration of a hybrid long-short-term memory neural network and convolutional neural network model. Second, four health indicators, namely, constant current charging time (CCCT), constant current charging capacity (CCCC), discharging time (DT), and discharging capacity (DC), were identified as inputs to the estimation model by Pearson correlation analysis. The CALCE battery dataset is utilized for conducting experiments, yielding remarkably low average values of root mean square error (RMSE) and mean absolute error (MAE), standing at merely 0.6737% and 0.5286%, respectively. And comparing with GRU, TCN, CNN, LSTM, and PSO optimization models, the proposed method has higher SOH estimation accuracy, which is more than 11% better than that. The robustness of three additional kinds of batteries is tested to validate their performance under varying current rates and temperatures. The results demonstrate that the accurate estimation of SOH, and the estimated values’ relative errors for each cycle of the three different types of batteries are all basically within 1%, with their maximum average RMSE are only 0.4840%, 0.3609%, and 0.5681%, respectively, and their maximum average MAE are only 0.3900%, 0.2828%, and 0.4149%, respectively.

A novel low-cost sensors system for real-time multipollutant indoor air quality monitoring – Development and performance

Indoor air pollution poses a significant health risk, thus demanding effective indoor air quality (IAQ) monitoring strategies. Low-cost sensors (LCS) have gained attraction for IAQ monitoring, but their data accuracy and robustness remain key challenges. This study addresses gaps in the literature by developing and evaluating a novel low-cost monitor prototype for IAQ monitoring. A detailed design methodology based on requirements analysis was used to create two identical low-cost monitors (LCM) prototypes for multipollutant monitoring, including PM2.5, CO2, CO, O3, NO2, temperature and relative humidity. The LCM were deployed in an in-field monitoring campaign alongside research-grade instruments. The uncorrected sensor signals showed linear response compared to research-grade instruments with high Pearson Correlation Coefficients for 1-min mean: PM2.5 (0.97), CO2 (0.81–0.89), CO (0.95–0.98), and O3 (0.80–0.85). The concentration range of pollutants was observed to play a crucial role in the response and accuracy of the LCS. Kalman filter was implemented with optimised parameters to reduce noise from the signal of ozone sensors. Univariate and multivariate linear models were used to field calibrate the sensors. Linear regression models, with high coefficients of determination (>0.8) and low error values, imply that the developed LCM prototypes can be reliably used for indicative monitoring. In most of the cases, univariate linear models using only the sensor response of LCS as explanatory variables showed significant improvement. Future work will involve longer monitoring campaigns in different microenvironments, evaluation of calibration drift and to assess failure episodes in long-term use.

Additively manufactured carbon fiber reinforced-polyamide component: a study based on statistical modeling and regression analysis

This paper presents the experimental assessment of the hardness characteristic of additively manufactured polyamide (PA 6) composite reinforced with carbon micro-fibers. The carbon fiber-reinforced polyamide (CFPA) components were manufactured using the additive manufacturing technique—fused deposition modeling (FDM). The experiments were conducted for testing the hardness of the samples using a Shore-D hardness tester. The novel contributions of the work towards the manufacturing fraternity include selecting a scantly researched material like CFPA, and the elaborative investigation of hardness variation with the alteration of the prime parameters pertaining to FDM. The effect of the print-related parameters, namely, layer height (LH), infill density (ID), and raster orientation (RO) on the hardness of the CFPA component was studied, and the results were analyzed using statistical analysis tool ‘analysis of variance (ANOVA)’. Moreover, a regression model was developed to predict the output response, i.e. hardness for different combinations of the input parameters. Considering an ID of 100% and an RO of 0°, the hardness value of 93.89 at 0.1 mm LH reduced to 88.44 at 0.3 mm LH, depicting a reduction of 5.81%. An increasing trend was observed for hardness with the increase in ID for all the levels of LH and RO. The highest value of hardness (93.89) was achieved at an ID of 100%, with the LH and RO values kept at 0.1 mm and 0°, respectively. The ANOVA suggested that the effect of all three parameters is significant in the study, ID being the most affecting parameter with an effect contribution of 37.88%. The fitness of the adopted model was well justified by the high R-sq value of 0.9618 and significantly low error values in the range of 0.002–0.08.

Prediction of Geometrical Characteristics of an Inclined Negatively Buoyant Jet Using Group Method of Data Handling (GMDH) Neural Network

A new approach to predicting the geometrical characteristics of the mixing behavior of an inclined dense jet for angles ranging from 15° to 85° is proposed in this study. This approach is called the group method of data handling (GMDH) and is based on the artificial neural network (ANN) technique. The proposed model was trained and tested using existing experimental data reported in the literature. The model was then evaluated using statistical indices, as well as being compared with analytical models from previous studies. The results of the coefficient of determination (R2) indicate the high accuracy of the proposed model, with values of 0.9719 and 0.9513 for training and testing for the dimensionless distance from the nozzle to the return point xr/D and 0.9454 and 0.9565 for training and testing for the dimensionless terminal rise height yt/D. Moreover, four previous analytical models were used to evaluate the GMDH model. The results showed the superiority of the proposed model in predicting the geometrical characteristics of the inclined dense jet for all tested angles. Finally, the standard error of the estimate (SEE) was applied to demonstrate which model performed the best in terms of approaching the actual data. The results illustrate that all fitting lines of the GMDH model performed very well for all geometrical parameter predictions and it was the best model, with an approximately 10% error, which was the lowest error value among the models. Therefore, this study confirms that the GMDH model can be used to predict the geometrical properties of the inclined negatively buoyant jet with high performance and accuracy.

Grey-box solution for predicting thermo-mechanical response of rocks

Evaluating the thermo-mechanical response of rocks under high temperature treatments is crucial for various engineering geology projects. Current predictions of rock thermo-mechanical response rely on simplistic mathematical fittings treating temperature as a reduction factor, while existing machine learning algorithms often present practical challenges due to their black-box solutions. In this study, highly practical grey-box solutions, utilizing gene expression programming (GEP) are proposed for forecasting rock strength following high-temperature treatments. The dataset, comprising temperature, rock type, rock density, sample size, crack damage stress, confining pressure, and elastic modulus, serves as input parameters, with rock strength from triaxial compression tests as the output. Three grey-box solutions (mathematical formulations) based on distinct input parameter sets are proposed, all demonstrating excellent accuracy with high R2-values (R2 > 0.95) and low error values across both the training and testing phases. Feature importance analysis highlights crack damage stress, confining pressure, and elastic modulus as statistically significant parameters influencing the strength of rocks subjected to high temperatures. External validation of the proposed models indicates strong generalization capabilities, underscoring their ability to perform well beyond the training data. Furthermore, a monotonicity study demonstrates that the proposed models align with the expected physical processes. The proposed formulations offer valuable field implications, effectively addressing the limitations of labor-intensive and costly laboratory processes for evaluating rock thermo-mechanical responses.