Functional Relationship Model Research Articles

Constructing artificial cover layers for supercritical carbon dioxide sequestration: A novel approach to old goaf remediation and carbon emission reduction

Over the past centuries, global coal mining activities have resulted in the formation of 242.36 billion cubic meters of underground goaf areas, resulting in the waste of billions of square meters of land resources. Furthermore, this phenomenon has introduced significant safety hazards and environmental risks. In addressing the challenge of the inability to directly sequester supercritical carbon dioxide in coal mine goaf areas due to extensive fracturing of the surrounding rock mass caused by underground mining, an innovative approach is proposed. This involves the construction of artificial cover layers within the overlying rock strata of abandoned coal mine goaf areas, offering a novel strategy for the sequestration of supercritical CO2 in such geological contexts. Considering the development characteristics of fractures in the overlying strata of coal mine goaf areas, a functional relationship model is established to delineate the sealing capacity of artificial cover layers in relation to the burial depth, length, width, and thickness of the cover layers. A design methodology for constructing artificial cover layers tailored for sequestering supercritical CO2 in abandoned coal mine goaf areas is proposed, providing technical support for its widespread application. Building upon this foundation, an assessment model for the sequestration capacity of abandoned coal mine goaf areas for supercritical CO2 is developed. The calculations indicate a global sequestration potential of approximately 72.71–218.12 billion tons of supercritical CO2, with anticipated economic benefits ranging from 657.36 to 1991.47 billion USD. The research outcomes present a promising avenue to assist carbon-neutral initiatives in coal-dependent urban areas globally.

Modelling Wind Speed, Humidity, and Temperature in Butterworth and Melaka during Southwest Monsoon in 2020 with a Simultaneous Linear Functional Relationship

The extension of parameter estimation from a bivariate linear functional relationship model (LFRM) to simultaneous LFRM for linear variables using the maximum likelihood estimation (MLE) method is explored in this paper. The covariance matrix of the parameter estimates is derived through the Fisher information matrix. A simulation study was done to investigate the performance of the parameter estimation. According to the simulation study, the estimated parameters have a small bias. The beauty of simultaneous LFRM lies in developing the model to study the relationship between more than two linear variables while considering error terms for all variables. The applicability of the proposed simultaneous model is demonstrated using wind speed, humidity, and temperature data from Butterworth and Melaka during the southwest monsoon season of 2020.

Nano Zero-Valent Iron (nZVI) Encapsulated with ABS (nZVI/(ABS + EC)) for Sustainable Denitrification Performance and Anti-Aggregation

Aggregation and sharp reactivity decrease are the key problems of using nano zero-valent iron (nZVI) as a potential reaction medium for a permeable reactive barrier (PRB). In this study, nZVI particles encapsulated within an acrylonitrile–butadiene–styrene (ABS) matrix (nZVI/(ABS + EC)) was fabricated, which for the first time successfully simultaneously solved the above problems via accurately regulating the distribution of nZVI particles in the ABS matrix and regulating the contact between nZVI particles and the contaminated aqueous environment. In addition, the size and number of the pores throughout the ABS matrix were first regulated by ethyl cellulose (EC) for the purpose of controlling the contact between nZVI particles and the nitrate contaminant, affording apparent rate constants (kobs) for denitrification performance in the range of 0.0423 to 0.0820 min−1. The remediation of simulated nitrate-contaminated solution by nZVI/(ABS + EC) was suitably described by the first-order kinetics model, with kobs ranging from 0.0423 to 0.2036 min−1, and functional relationship models of kobs with the dosages of EC (dEC) and nZVI (dFe) during encapsulation were developed for the quantitative regulation of a sustainable denitrification performance. Results revealed that encapsulation prevents the aggregation of nZVI, rendering a sustainable denitrification performance of the material; the denitrification performance was demonstrated to be affected and quantitatively regulated by the encapsulation and application conditions. Using nZVI/(ABS + EC) as the reaction medium for PRB, the pore blocking of PRB can be avoided, and the sustainable remediation performance can be quantitatively regulated and predicted.

Cross-column density functional theory-based quantitative structure-retention relationship model development powered by machine learning.

Quantitative structure-retention relationship (QSRR) modeling has emerged as an efficient alternative to predict analyte retention times using molecular descriptors. However, most reported QSRR models are column-specific, requiring separate models for each high-performance liquid chromatography (HPLC) system. This study evaluates the potential of machine learning (ML) algorithms and quantum mechanical (QM) descriptors to develop QSRR models that can predict retention times across three different reversed-phase HPLC columns under varying conditions. Four machine learning methods-partial least squares (PLS) regression, ridge regression (RR), random forest (RF), and gradient boosting (GB)-were compared on a dataset of 360 retention times for 15 aromatic analytes. Molecular descriptors were calculated using density functional theory (DFT). Column characteristics like particle size and pore size and experimental conditions like temperature and gradient time were additionally used as descriptors. Results showed that the GB-QSRR model demonstrated the best predictive performance, with Q2 of 0.989 and root mean square error of prediction (RMSEP) of 0.749min on the test set. Feature analysis revealed that solvation energy (SE), HOMO-LUMO energy gap (∆E HOMO-LUMO), total dipole moment (Mtot), and global hardness (η) are among the most influential predictors for retention time prediction, indicating the significance of electrostatic interactions and hydrophobicity. Our findings underscore the efficiency of ensemble methods, GB and RF models employing non-linear learners, in capturing local variations in retention times across diverse experimental setups. This study emphasizes the potential of cross-column QSRR modeling and highlights the utility of ML models in optimizing chromatographic analysis.

A Fault Identification Method for Metal Oxide Arresters Combining Suppression of Environmental Temperature and Humidity Interference with a Stacked Autoencoder

Most existing methods aiming to solve the fault identification problem of metal oxide arresters (MOAs) are limited by strong subjectivity in judgment, the significant impact of environmental temperature and humidity on the online monitoring of the resistance current, and poor generalization ability. Therefore, in this article, we propose an MOA fault identification method that combines suppressing environmental temperature and humidity interference with a stacked autoencoder (SAE). Firstly, a functional relationship model between resistance current and environmental temperature and humidity is established. Then, a temperature and humidity interference suppression method based on weighted nonlinear surface modeling is proposed to normalize the resistance current to the same reference temperature and humidity conditions. Finally, an MOA fault identification method combining the suppression of environmental temperature and humidity interference with an SAE is proposed. Furthermore, a comprehensive comparison is conducted on the recall, accuracy, F1-score, and average accuracy of support vector machine, random forest, logistic regression, and SAE classification algorithms in three different scenarios to demonstrate the effectiveness of the proposed method. The results indicate that environmental temperature and humidity interference suppression for resistive current prior to MOA fault classification significantly reduce the number of false alarms. Compared with other methods, the MOA fault identification method, which combines environmental temperature and humidity interference suppression with an SAE, has the highest average accuracy of 99.7%.

Parameter Estimation for Circular Simultaneous Functional Relationship Model (CSFRM) for Unequal Variances

In this study, we propose an extended model of the Circular Simultaneous Functional Relationship Model from the Circular Functional Relationship Model. In this case, the circular model and the circular variable will be applied where assuming the error variances are not equal. All estimations of the parameter followed von Mises distribution. The angular and slope parameters are obtained using the ms function, while concentration parameter estimation is obtained from the polyroot function provided in the SPLUS statistical package. The simulation study has been conducted to assess the efficiency of the proposed model. The simulation results showed that as sample size and concentration parameters increase, all parameters’ estimates are close to the true value and have a smaller bias. The illustration of real wind and wave direction data from two different bases of data is given to show its practical applicability. We note that the proposed method for parameter estimation works well with the proposed model.

Autocorrelated unreplicated linear functional relationship model for multivariate time series data

The conventional practices in handling cross-sectional data treated the explanatory variables as fixed variables without measurement errors. This article proposed a novel autocorrelated unreplicated linear functional relationship model (AULFR) model to accommodate the autocorrelated errors in the measurement errors model. Some basic properties of the model have been derived. A modified backshift operator is used in transforming the autocorrelated error into uncorrelated error. Simulation studies show that AULFR outperforms other benchmarking models even with a relatively small training data percentage or a sample size of 100 training observations. The application of the AULFR model on an actual economic case shows consistent results with simulation studies. The advantages of the proposed model are (i) it models the relationship between a time-based dependent variable and a set of time-based explanatory variables which subjected to measurement errors, and (ii) it can predict the current or future values of both dependent and explanatory variables using historical data.

Modelling Wind Speed Data in Langkawi Island with Functional Relationship

Wind speed influenced weather predictions, aerospace operations, and maritime operations, construction projects. This research aims to examine the relationship between Pulau Langkawi wind speed data during the southwest monsoons in 2019 and 2020. To model wind speed data that follows a normal distribution. An error-in-variables model (EIVM) is utilised, which is a linear functional relationship model (LFRM). The QQ-plots will be utilised to investigate the adequacy of the model’s fit. The maximum likelihood estimation (MLE) approach is employed to estimate the parameters of the model, while the covariance is calculated using the Fisher Information matrix. As a result, it is found that the estimated values demonstrate consistency and reduced dispersion. Thus, the findings could lead to a better knowledge of wind energy prediction.

Study of the Macro and Micro Characteristics of and Their Relationships in Cemented Backfill Based on SEM

Nuclear magnetic resonance can only quantitatively obtain porosity and pore size distribution, but as a conventional microstructure observation technology, scanning electron microscope (SEM) can select different magnifications to observe the microstructure of backfill materials. However, the processing of SEM images is not deep enough. In this paper, Image-Pro Plus 6.0 software was used to extract the data from SEM images, and the parameters of the area, and the perimeter, aspect ratio and roundness of the pores in the SEM images were obtained. The fractal characteristics of the pores in the SEM image were obtained by using the slit island method fractal theory. The concretization and quantification analysis of the pores’ complexity were achieved. A functional relationship model for the strength and pore parameters was constructed; thus, the influence law of pore characteristics on strength was quantitatively analyzed. The conclusions included: (1) Pore parameters indicate that most pores in backfill are irregular, and only a few pores are regular—however, the whole structure has good fractal characteristics (R2 > 0.96). (2) The fractal dimension of pores is directly proportional to the roundness, the aspect ratio, and the pore content of pores—which indicates that the complexity of pores is related to both pore shape and pore content. (3) The strength had a linear inverse relationship with the roundness, aspect ratio, pore content, and fractal dimension—which indicates that all characteristics of pores have a certain influence on the strength.

Identifying Multiple Outliers in Linear Functional Relationship Model using a Robust Clustering Method

Outliers are some observation points outside the usual pattern of the other observations. It is essential to detect outliers as anomalous observations can affect the inference made in the analysis. In this study, we propose an efficient clustering procedure to identify multiple outliers in the linear functional relationship model using the single linkage algorithm with the Euclidean distance as the similarity measure. A new robust cut-off point using the median and median absolute deviation for the tree heights to classify the potential outliers are proposed in this study. Experimental results from the simulation study suggest our proposed method is able to identify the presence of multiple outliers with very small probability of swamping and masking. Application in real data also shows that the proposed clustering method for this linear functional relationship model successfully detects the outliers, thus suggesting the method's practicality in real-world problems.

Convolution Neural Network with Coordinate Attention for Real-Time Wound Segmentation and Automatic Wound Assessment.

Wound treatment in emergency care requires the rapid assessment of wound size by medical staff. Limited medical resources and the empirical assessment of wounds can delay the treatment of patients, and manual contact measurement methods are often inaccurate and susceptible to wound infection. This study aimed to prepare an Automatic Wound Segmentation Assessment (AWSA) framework for real-time wound segmentation and automatic wound region estimation. This method comprised a short-term dense concatenate classification network (STDC-Net) as the backbone, realizing a segmentation accuracy-prediction speed trade-off. A coordinated attention mechanism was introduced to further improve the network segmentation performance. A functional relationship model between prior graphics pixels and shooting heights was constructed to achieve wound area measurement. Finally, extensive experiments on two types of wound datasets were conducted. The experimental results showed that real-time AWSA outperformed state-of-the-art methods such as mAP, mIoU, recall, and dice score. The AUC value, which reflected the comprehensive segmentation ability, also reached the highest level of about 99.5%. The FPS values of our proposed segmentation method in the two datasets were 100.08 and 102.11, respectively, which were about 42% higher than those of the second-ranked method, reflecting better real-time performance. Moreover, real-time AWSA could automatically estimate the wound area in square centimeters with a relative error of only about 3.1%. The real-time AWSA method used the STDC-Net classification network as its backbone and improved the network processing speed while accurately segmenting the wound, realizing a segmentation accuracy-prediction speed trade-off.

Parameter Estimation for Balance-Equal Replicated Linear Functional Relationship Model: An Application to the Wind Directional Data

A linear functional relationship model can be used to model the relationship between two circular variables when both variables are observed with errors. When the ratio of error concentration parameter is unknown, it is suggested that the replicated linear functional relationship model be used. The purpose of this paper is to present all the parameter estimates of the replicated linear functional relationship model for balance replicates and equal circular variables. Simulations studies are performed to study understand the behavior of the parameter estimators for the balance-equal replicated linear functional relationship model. The empirical results obtained suggest that the proposed parameter estimation method performs well with small bias. A simple application of the model is demonstrated by analyzing a real dataset of a wind directional data.

Density Functional Theory and Machine Learning-Based Quantitative Structure-Activity Relationship Models Enabling Prediction of Contaminant Degradation Performance with Heterogeneous Peroxymonosulfate Treatments.

Heterogeneous peroxymonosulfate (PMS) treatment is recognized as an effective advanced oxidation process (AOP) for the treatment of organic contaminants. Quantitative structure-activity relationship (QSAR) models have been applied to predict the oxidation reaction rates of contaminants in homogeneous PMS treatment systems but are seldom applied in heterogeneous treatment systems. Herein, we established QSAR models updated with density functional theory (DFT) and machine learning approaches to predict the degradation performance for a series of contaminants in heterogeneous PMS systems. We imported the characteristics of organic molecules calculated using constrained DFT as input descriptors and predicted the apparent degradation rate constants of contaminants as the output. The genetic algorithm and deep neural networks were used to improve the predictive accuracy. The qualitative and quantitative results from the QSAR model for the degradation of contaminants can be used to select the most appropriate treatment system. A strategy for selection of the optimum catalyst for PMS treatment of specific contaminants was also established according to the QSAR models. This work not only increases our understanding of contaminant degradation in PMS treatment systems but also highlights a novel QSAR model to predict the degradation performance in complicated heterogeneous AOPs.

Optimization of Preparation Conditions of Modified Oyster Shell Powder/Ce-N-TiO<sub>2</sub> by Response Surface Methodology (RSM)

A new composite photocatalyst of modified oyster shell powder/Ce-N-TiO2 was prepared by sol-gel method. Based on single factor experiment, Ce doping rate, N doping rate and calcination temperature were taken as input variables. Based on the central composite design (BBD) response surface model, two functional relationship models between three independent variables and glyphosate removal rate were established to evaluate the influence degree of independent variables and interaction on catalyst. The significance of the model and regression coefficient was tested by variance analysis. The analysis of the obtained data showed that the degradation performance of the composite photocatalyst was significantly affected by the calcination temperature and the rate of N doping, while the rate of Ce doping had little effect; at the calcination temperature of 505.440°C, the degradation rate of glyphosate reached the maximum of 82.15% under the preparation conditions of 17.057 mol% N doping and 0.165 mol% Ce doping, respectively.

An Efficient and Fully Refined Deformation Extraction Method for Deriving Mining-Induced Subsidence by the Joint of Probability Integral Method and SBAS-InSAR

This study proposes a novel approach to derive the mining-induced goaf deformation, named the fully refined deformation extraction method (FRDEM). In this method, the Probability Integral Method (PIM) and the Small Baseline Subset Interferometric Synthetic Aperture Radar (SBAS-InSAR) technique are geographically integrated in a low-cost way to derive the fully refined goaf deformation and therefore to improve the detection ability for mining subsidence with fast deformation rate and large-gradient. To achieve this, we first established a functional relationship model to connect the 3-D parameters of PIM with SBAS-InSAR. Then, an improved genetic algorithm (IGA) was presented for parameter inversion, thus the optimal parameter set for PIM and the predicted displacements of the mining goaf was achieved economically. Afterward, we developed a geographically weighted data fusion model by presenting a data fusion strategy to eliminate the spatial heterogeneity in goaf boundary areas, and the fully refined goaf deformation field for the working face 2302 in the Guotun coal mining area was finally derived. Results demonstrate that FRDEM-derived displacements are highly consistent with field measurements, with RMSE decreasing to 0.053, 0.057, and 0.044 m respectively for the entire goaf, goaf center, and goaf boundary field, compared with those of ~0.092, ~0.095, and ~0.084 m for PIM and ~0.578, ~0.696, and ~0.046 m for SBAS-InSAR, respectively. This implies that the proposed FRDEM has significantly improved detection ability in deriving the mining-induced deformation, and thus can be a very promising tool to forecast and evaluate potential geohazards in the coal mining area.

Determining an effective short term COVID-19 prediction model in ASEAN countries

The challenge of accurately short-term forecasting demand is due to model selection and the nature of data trends. In this study, the prediction model was determined based on data patterns (trend data without seasonality) and the accuracy of prediction measurement. The cumulative number of COVID-19 affected people in some ASEAN countries had been collected from the Worldometers database. Three models [Holt’s method, Wright’s modified Holt’s method, and unreplicated linear functional relationship model (ULFR)] had been utilized to identify an efficient model for short-time prediction. Moreover, different smoothing parameters had been tested to find the best combination of the smoothing parameter. Nevertheless, using the day-to-day reported cumulative case data and 3-days and 7-days in advance forecasts of cumulative data. As there was no missing data, Holt’s method and Wright’s modified Holt’s method showed the same result. The text-only result corresponds to the consequences of the models discussed here, where the smoothing parameters (SP) were roughly estimated as a function of forecasting the number of affected people due to COVID-19. Additionally, the different combinations of SP showed diverse, accurate prediction results depending on data volume. Only 1-day forecasting illustrated the most efficient prediction days (1 day, 3 days, 7 days), which was validated by the Nash–Sutcliffe efficiency (NSE) model. The study also validated that ULFR was an efficient forecasting model for the efficient model identifying. Moreover, as a substitute for the traditional R-squared, the study applied NSE and R-squared (ULFR) for model selection. Finally, the result depicted that the prediction ability of ULFR was superior to Holt’s when it is compared to the actual data.

A Nonlinear Gauss-Helmert Model and Its Robust Solution for Seafloor Control Point Positioning

Using GNSS-Acoustic (GNSS-A) technology to establish the seafloor geodetic datum is both feasible and flexible and thus has become an important way to obtain the absolute positions of seafloor control points. However, numerous errors are inevitable in marine surveying, including systematic errors and gross errors caused by GNSS dynamic positioning, inaccurate sound velocity profile measurements, and ocean ambient noise, and their interference will be directly reflected in the positioning results. To accurately calculate the seafloor control point coordinates, this paper first notes that the general error propagation law (EPL) method is defective in dealing with various error factors in GNSS-A positioning. A more rigorous method incorporates the time-varying term of the sound velocity ranging error into the coefficient matrix of the underwater observation equation, and the transducer position error should be considered. Therefore, a Gauss-Helmert (GH) model is used for seafloor control point positioning. Then, considering the dual nonlinearity of the model, a Lagrange objective function is constructed to derive its solution algorithm. On this basis, considering the gross errors polluting of the observations, the robust estimation principle is introduced, and the robust solution steps are given. Finally, simulation experiments and a testing experiment in the sea area near Jiaozhou Bay are used to verify the performance of the new method. The results show that the functional relationship and stochastic model of the nonlinear GH model for seafloor point positioning are reasonably described. Under ideal conditions with no gross errors and either different water depths or different transducer position errors, the accuracy and stability of the new method are both higher than those of the EPL method. When the observations are polluted by gross errors, the robust algorithm of the new method can accurately identify the abnormal information. By improving the robustness of the observation and structure spaces, the positioning precision of the 3D point deviation results can be optimized, and the solution performance of the new method is superior to that of the general method.

Mass estimation method of loose parts based on function model

Abstract The nuclear main pump has a complex structure and contains a large number of components. With the continuous flow of the primary circuit coolant, there is a risk of loosening and falling off of the components in the reactor. The existence of loose parts in the reactor makes the reactor operation a safety hazard. Accurate mass estimation of the loose parts is conductive to quickly judge the degree of the failure of loose parts, provide effective suggestions for the subsequent maintenance of the reactor and ensure the safety of reactor operation. The existing mass estimation methods have problems of large errors and poor consistency. This article proposes a method for estimating the mass of loose parts by establishing a functional relationship model based on signal characteristic value. The characteristic value of the signal is constructed by extracting the Root Mean Square value and the main frequency of the shock signal, and then the functional relationship between the quality of the loose part and the characteristic value of the signal is established, which is used to estimate the mass of the loose part. The experimental results show that the method proposed in this paper has the characteristics of small estimation error and good consistency, which can meet the needs of practical engineering applications.

Outlier Detection in Balanced Replicated Linear Functional Relationship Model

Identification of outlier in a dataset plays an important role because their existence will affect the parameter estimation. Based on the idea of COVRATIO statistic, we modified the procedure to accommodate for replicated linear functional relationship model (LFRM) in detecting the outlier. In this replicated model, we assumed the observations are equal and balanced in each group. The derivation of covariance matrices using Fisher Information Matrices is also given for balanced replicated LFRM. Subsequently, the cut-off points and the power of performance are obtained via a simulation study. Results from the simulation studies suggested that the proposed procedure works well in detecting outliers for balanced replicated LFRM and we illustrate this with a practical application to a real data set. The implication of the study suggests that with some modification to the procedures in COVRATIO, one could apply such a method to identify outliers when modelling balanced replicated LFRM which has not been explored before.

Can slope spectrum information entropy replace slope length and steepness factor: A case study of the rocky mountain area in northern China

Slope spectrum information entropy (SSIE) can reflect the overall fluctuation characteristics of the topography with convenient calculation. In order to explore whether the complex slope length and steepness factor (LS factor) can be replaced by SSIE in the evaluation of soil erosion in the rocky mountain area, this study took the rocky mountain area in northern China (the first zone of soil and water conservation) as the research object. The soil texture of study area is the most typical “soil-rock dual structure”. The SSIE, soil erosion intensity (SEI), and LS factor were calculated using ASTER GDEM and Landsat8 image data (30 m × 30 m). The correlation between the SSIE and SEI was revealed, and a functional relationship model of SSIE and LS factor was built. This study clarified whether SSIE could replace the LS factor to evaluate soil erosion in the “soil-rock dual structure” area. The results showed that: (1) The slope spectrum curves of the six secondary zones of soil and water conservation in the study area presented “L” shape, and the SSIE was between 0.59 and 2.79 nat. SEI grades were mainly micro-erosion, with strong erosion and above accounting for 1.7%. The spatial distribution difference was significant and strong erosion and above was mostly distributed in mountainous and hilly areas. The LS factor of the whole region was between 0 and 55.03, with an average value of 1.37. The regions with an average LS factor < 5 accounted for more than 82% in each secondary zone. (2) The significant logarithmic function relationship of SSIE and SEI was displayed on the secondary zone (R2 = 0.9372, P < 0.01), tertiary zone (R2 = 0.7908, P < 0.01), and basin scales (R2 = 0.3534, P < 0.01). (3) The relationship of SSIE and LS factor also was significant logarithmic function on the secondary zone (R2 = 0.7866, P < 0.05), tertiary zone (R2 = 0.8269, P < 0.01), and basin scales (R2 = 0.8958, P < 0.01). It was indicated that in the typical hydraulic erosion areas of “soil-rock dual structure”, SSIE can replace the LS factor to evaluate SEI and soil erosion modulus.