Nonlinear Regression Method Research Articles

A Novel Stochastic Model for Hourly Electricity Load Profile Analysis of Rural Districts in Fujian, China

Renewable energy is important for achieving carbon neutralization. However, power generation from renewable energy sources can be uncertain and uncontrollable. Therefore, understanding the features of energy demand is pivotal for integrating renewable energy sources and storage systems within the entire energy network. Traditional load profiles are depicted by fixed typical load curves, which cannot support detailed dynamic simulations of annual hourly electricity consumption. Here, a novel stochastic model for hourly electricity load profile analysis is proposed. A clustering-based model of hourly load was constructed to depict load profiles of typical days, while a non-linear regression method determined the temperature-related factors within annual daily load consumptions, based on which a stochastic simulation model was established for hourly electricity load profiles. The model’s performance was tested with electricity data of rural districts in Fujian Province, China. The proposed model achieved a coefficient of variation of the mean absolute error of 15.7%, which was significantly lower than that of the traditional model. Further, a simplified case was employed to analyze the application of the proposed stochastic model in the design of energy storage systems. The proposed method enables the optimal design of integrated energy networks with renewable energy sources and energy storage systems.

Experimental Study on the Effect of Temperature Up-Step on Human Thermal Perception and Skin Temperature between Activity Intensities at Low Ambient Temperatures

In the north of China, during winter, a large number of activities (such as leisure, work, sightseeing and sports) are engaged in. This paper mainly focuses on human thermal perceptions of outdoor activities in a winter climate, especially the change in thermal perceptions when humans enter a temporary rest space with a shelter effect. A climate chamber was applied in our experiments, and temperature up-steps of 4, 8 and 12 °C were set, respectively. Twenty four college students were invited to engage in activities of different intensities, such as standing, walking (slowly) and biking. Through questionnaire survey and field measurement, the subjects’ thermal sensation, thermal comfort and skin temperature were obtained. Hypothesis testing and non-linear regression methods were introduced to analyze experiment data. Major results were as follows. After temperature up-step changes, thermal sensation and skin temperature reach steady state within 30 min. However, the change in skin temperature caused by a short-term thermal experience does not disappear completely within 40 min. In addition to the influence of ambient temperature changes, activity intensity also influenced the variation in thermal sensation (subjective) and skin temperature (objective). These study results provide a scientific reference for future research and design of a temporary rest space in low ambient temperatures. Experimental studies including broader age groups and outdoor field tests are valuable for future research.

Impact of climate variability on grain yields of spring and summer maize

Crop yield is greatly impacted by climate change, and a systemic assessment of its impacts on crop yields is essential. Aiming to investigate the impact of climate change on spring and summer maize yields in main maize growing areas of China, the observed meteorological and maize yield data over 1988–2017 at the 121 sites (including 85 sitess for spring maize and 36 sites for summer maize) in main maize growing areas of China were collected. The first-order difference, Sen’s slopes and trend test, multi-collinearity detection, Pearson correlation, stepwise linear and nonlinear regression methods were used, and the best statistical regression models between maize yield and climate variables have been established. Of these, the Sen′s slopes quantify the trend magnitude of the related climate variables and spring/summer maize yields during maize growth period. The Pearson correlation coefficients assess the relationship between pairs of climatic variables and maize yields, while the multi-collinearity analysis determines the mutually independent climatic variables with maize yields. The stepwise multi-variate linear and nonlinear regressions were conducted to obtain the best functions of the one-order-differences of spring (summer)maize yields at the 85 (36) sites. The results indicated that: (1) Generally, the precipitation and temperature during growth seasons was rising, while relative air humidity and sunshine hours was declining. Both the yields of spring and summer maize showed increasing trends. (2) Spring maize yields were more related to relative humidity, sunshine hours and precipitation, while summer maize yields were more related to precipitation and temperature. (3) The multivariate nonlinear functions performed better than the linear relationship. Based on the coefficient of determination, climate change has explained 5.8–87.6% variability of spring maize yield and 6.6–78.5% variability of summer maize yield. (4) The contribution importance rank of climate variables to yields of spring and summer maize was precipitation > relative humidity > sunshine hours > minimum temperature > maximum temperature > average temperature. The wet-cold and wet-warm climate, especially the former, had positive effects on maize yield. In conclusion, climate variables affect spring and summer maize yields and their best relationships were site-specific in China. Our research provides new insights for maize planting management under climate change.

Lattice thermal conduction in cadmium arsenide

Lattice thermal conductivity (LTC) of cadmium arsenide (Cd3As2) is studied over a wide temperature range (1–400 K) by employing the Callaway model. The acoustic phonons are considered to be the major carriers of heat and to be scattered by the sample boundaries, disorder, impurities, and other phonons via both Umklapp and normal phonon processes. Numerical calculations of LTC of Cd3As2 bring out the relative importance of the scattering mechanisms. Our systematic analysis of recent experimental data on thermal conductivity (TC) of Cd3As2 samples of different groups, presented in terms of LTC, κ L, using a nonlinear regression method, reveals good fits to the TC data of the samples considered for T < ∼ 50 K, and suggests a value of 0.2 for the Gruneisen parameter. It is, however, found that for T > 100 K the inclusion of the electronic component of TC, κ e, incorporating contributions from relevant electron scattering mechanisms, is needed to obtain good agreement with the TC data over the wide temperature range. More detailed investigations of TC of Cd3As2 are required to better understand its suitability in thermoelectric and thermal management devices.

Numerical simulation research on two-phase flow boiling heat transfer in helically coiled tube

In this paper, the partial geometric models of helically coiled tube type heat exchanger with different tube diameters (d = 12, 19, 25 mm), tube pitches (P = 50, 100, 150 mm) and helical radius (R = 100, 150, 200 mm), were established. Numerical simulation and performance comparison were carried out using water and water vapor as the working fluid. The gas–liquid phase distribution in the helically coiled tube, the gas volume fraction at different cross-sections, and the changes of heat transfer coefficient and pressure drop along the length of the helically coiled tube were analyzed. The results showed that the gas phase was concentrated in the inner side (near the side of the central axis) and the upper side of the helically coiled tube under boiling condition, and the liquid phase was concentrated in the bottom of the helically coiled tube and is stratified with the gas phase. As the helical radius and tube diameters increased, the heat transfer coefficient and unit pressure drop decreased gradually. Based on the simulated data, the boiling heat transfer correlation was fitted by the method of multiple nonlinear regression, and the mean absolute error was 4.5% compared with the modified Chen's correlation. Therefore, the numerical results were correct and trustable.

Effect of Climate on Carbon Storage Growth Models for Three Major Coniferous Plantations in China Based on National Forest Inventory Data

Forest inventory data (FID) are important resources for understanding the dynamics of forest carbon cycling at regional and global scales. Developing carbon storage growth models and analyzing the difference and climate effect on carbon sequestration capacity have a great importance in practice, which can provide a decision-making basis for promoting high-quality development of forestry and implementing the carbon emission peak and carbon neutralization strategy. Based on the carbon storage dataset of 2680 sample plots from the ninth national forest inventory (NFI) of China, the carbon storage growth models and climate-sensitive variable-parameter carbon storage growth models for three major coniferous plantations (Larix spp., Pinus massoniana, and Pinus tabuliformis) were developed by using weighted nonlinear regression method. The effects of two climate factors (mean annual temperature (MAT) and mean annual precipitation (MAP)) on carbon storage growth and carbon sequestration capacity were analyzed and compared. The mean prediction error (MPE) of carbon storage growth models for three major coniferous plantations was less than 5%, and total relative error (TRE) was approximately less than 2% for self- and cross- validation. The maximum current annual increment of carbon storage for P. massoniana, Larix, and P. tabuliformis was 2.29, 1.89, and 1.19 t/(ha·a), respectively, and their corresponding age of inflection point was 9a, 14a, and 30a, respectively. The maximum average increment of carbon storage for P. massoniana, Larix, and P. tabuliformis was 1.85, 1.50, and 0.94 t/(ha·a), respectively, and their corresponding age of quantitative maturity was 16a, 24a, and 53a, respectively. The maximum average increment of carbon storage for the P. massoniana and Larix plantations was approximately 1.97 and 1.60 times, respectively, that of P. tabuliformis plantation. The average increment of carbon storage for the P. massoniana and Larix plantations reduced approximately by 4.5% and 3.8%, respectively, when the MAT decreases by 1 °C. The average increment of carbon storage for the Larix and P.tabuliformis plantations decreased by approximately 6.5% and 3.6%, respectively, when the MAP decreases by 100 mm. Our findings suggest that: the carbon sequestration capacity is from highest to lowest in the P. massoniana, Larix, and P. tabuliformis forests. MAT and MAP have different effects on the carbon growth process and carbon sequestration capacity of these plantations. The greatest impact on carbon sequestration capacity was detected in the Larix plantation, followed by the P. massoniana and P. tabuliformis plantations. It is essential to coordinate regional development and employ scientific management strategies to fully develop the maximum carbon sequestration capacity in terms of plantations in China. In the present study, we estimate the carbon storage in major coniferous plantations in China and describe a useful methodology for estimating forest carbon storage at regional and global levels.

Nano-silica from kaolinitic clay used as adsorbent for anionic and cationic dyes removal: linear and non-linear regression isotherms and kinetics studies

The increasing occurrence of wastewaters associated with industrial development has begotten a permanent search for new and more efficient techniques for the removal of hazardous substances such as heavy metals and dyes. The use of natural and available resources to develop improved and sustainable commodities for this purpose remains crucial and is among promising emerging green technologies for water treatment. It offers the gradual shifting of hazardous industrial chemicals precursors to the abundant non-metallic mineral resources that receive an added value. This work investigated the uptake capacity by the adsorption process of methylene blue (MB) and azocarmine G (AG) onto nano-silica synthesized from kaolinite clay. The effects of contact time (0-30 min), the adsorbent dosage (5-100 mg), the initial pH of the solution (1-11 for MB and 1-7 for AG), and the initial dye concentration (5-50 mg/L) were studied. The selected conditions to carry out kinetic and isotherm adsorption experiments were: 15 mins, 20 mg, 11 for MB, 1.01 for AG, and 50 mg/L. Four adsorption isotherms and three kinetic models were used to model the adsorption data thanks to linear and non-linear regression methods. From the obtained results, the Freundlich isotherm model fitted well the adsorption phenomenon while the pseudo-second-order kinetic model described well the adsorption mechanism. Furthermore, the free energy of adsorption was similar for the two absorbents, 0.71 kJ, pointing physisorption as the dominant adsorption mechanism. The optimum MB and AG uptake were respectively 13.8 and 36.1 mg/g. Conclusively, the nano-silica represents a potentially viable and powerful adsorbent whose use could lead to a plausible improvement in environmental preservation.

M-CHIPR: A Mathematica program for constructing multi-state coupled adiabatic potential energy functions in triatomic molecule using many body partitioning approach

The permutationally invariant combined hyperbolic inverse power representation (CHIPR) polynomial expansion in terms of hyperbolic secant basis proves to be an efficient model in describing the multi state coupled potential energy surface (MSCPES) and this fact was tested on the O2H+ triatomic ion and its diatomic sub units upon dissociation with an unmatchable accuracy of fitting in comparison with the previous works (below 1cm−1 in the case of diatomic function and below 300cm−1 in the case of triatomic function). In general, this model is capable of modeling A3 (H3, O3 etc.) and ABC (OCS, HCO+ etc.) triatomic system in addition to the A2B (O2H+) system. This paper presents a Mathematica notebook (M-CHIPR.nb file) to perform the fitting of di and triatomic potentials in a user friendly manner with proper explanations written along side wherever required in the .nb file supplied. The advantage of this code is that the computing clusters are not required to use it and can be run in normal pc with good processor and memory, apart from its numerical accuracy and the system independent consistency over the similar programs written in other languages. Program summaryProgram title: M-CHIPRCPC Library link to program files:https://doi.org/10.17632/4mbydkzyts.1Licensing provisions: GPLv3Programming language: Wolfram Mathematica version12 or higherNature of problem: Finding an multi-variable Mathematica combined hyperbolic inverse power representation (M-CHIPR) function to describe a multi state coupled potential energy surface for a typical diatomic and triatomic molecule via extensive nonlinear regression method involving hundreds of optimizable variables with minimal fitting error with respect to the raw data points.Solution method: Default Mathematica implementation of nonlinear least square fitting of ab initio points to obtain a well optimized model function having ability to accurately predicting the data behavior.Additional comments including restrictions and unusual features: The entire work was tested on Apple Mac pc with Intel i7 processor having 4 cores. The version of Mathematica is 12 and therefore, the users are advised to test the supplied notebook with the same version and beyond to avoid incompatibility issues.

Physics-aware nonparametric regression models for Earth data analysis

Process understanding and modeling is at the core of scientific reasoning. Principled parametric and mechanistic modeling dominated science and engineering until the recent emergence of machine learning (ML). Despite great success in many areas, ML algorithms in the Earth and climate sciences, and more broadly in physical sciences, are not explicitly designed to be physically-consistent and may, therefore, violate the most basic laws of physics. In this work, motivated by the field of algorithmic fairness, we reconcile data-driven ML with physics modeling by illustrating a nonparametric and nonlinear physics-aware regression method. By incorporating a dependence-based regularizer, the method leads to models that are consistent with domain knowledge, as reflected by either simulations from physical models or ancillary data. The idea can conversely encourage independence of model predictions with other variables that are known to be uncertain either in their representation or magnitude. The method is computationally efficient and comes with a closed-form analytic solution. Through a consistency-vs-accuracy path diagram, one can assess the consistency between data-driven models and physical models. We demonstrate in three examples on simulations and measurement data in Earth and climate studies that the proposed ML framework allows us to trade-off physical consistency and accuracy.

Analysis and Control of Cracks in Ni60 Coating of 7050 Aluminum Alloy by Electron Beam Cladding

Ni60 electron beam cladding can play an important role in improving the properties of 7050 aluminum alloy. The cracking of the cladding layer, however, greatly affects the cladding quality. To solve this problem, the optimum range of cladding process parameters is determined by an experimental method: electron beam current [25–30 × 10−3 A], scanning speed [10–12 mm/s] and focusing current [700–720 × 10−3 A]. Through range analysis of the experiment results, the primary and secondary order of the influence of the cladding process parameters on the crack areal density is determined as follows: electron beam current &gt; scanning speed &gt; focusing current. A mathematical model of the crack areal density of the cladding layer is established based on the method of nonlinear regression, which is y = 4.1553 × 104 I2.2887V−0.8379I210.2675. It is shown that the model has obvious significance in the results of variance analysis, which can provide a basis for the selection of electron beam cladding process parameters.

Phase field fracture modeling of transversely isotropic piezoelectric material with anisotropic fracture toughness

Fracture analysis of piezoelectric devices and structures is of great importance in science and engineering. In the present work, a new phase field fracture model in the context of transversely isotropic electro-elasticity is developed by means of the variational method. A structural tensor is introduced in the crack surface density function to quantify the anisotropy in fracture toughness. To characterize the asymmetric fracture behavior of piezoelectric solid, the contribution of the mechanical energy is employed to drive the crack propagation. An efficient and robust staggered scheme is adopted to deal with the corresponding fracture problems, which is implemented in the commercial finite element software Abaqus. Numerical simulations are carried out to investigate the effect of the anisotropic fracture toughness, poling direction and external electrical field on the fracture behavior of the piezoelectric materials. The anisotropic fracture toughness would significantly affect the crack path and fracture load. With the help of the nonlinear regression method, a phenomenological model is proposed to predict the fracture load. The present researches may benefit the safety assessment of piezoelectric materials in practical applications.

Statistical Modelling of Carbonation Process in Reinforced Concrete Structure.

In order to quantitatively analyze the factors affecting the carbonation of reinforced concrete structures, the carbonation coefficient model is established based on 1834 groups of test data from natural carbonation and indoor accelerated tests in this paper. The main factors considered in the statistical model are the environmental temperature, the concentration of carbon dioxide, relative humidity, water–cement ratio, fly ash replacement, compressive strength of 28 days, curing time, compaction type, exposure to a salt environment, and environmental exposure classes. Based on the multiple nonlinear regression method, the carbonation coefficient model is fitted in two sections according to the different environmental exposures of the concrete structure. To analyze the applicability of the formula, the statistical formulas of relative humidity less than 70% and relative humidity higher than 70% are verified by the test data, and satisfactory results are obtained. Based on the quantitative analysis of the statistical model, the specific effects of relative humidity, strength, carbon dioxide content, fly ash, and curing time on concrete carbonation are clarified. The results show that the factors affecting carbonation are also different with different humidity values in the exposed environment of the concrete structure. When the relative humidity of the exposed environment is less than 70%, the parameters that have a great impact on concrete carbonation are fly ash replacement, compressive strength of 28 days, relative humidity, and the concentration of carbon dioxide. Among them, fly ash replacement, relative humidity, and the concentration of carbon dioxide can promote the carbonation of concrete. When the relative humidity of the exposed environment is higher than 70%, the parameters that have a great impact on concrete carbonation are the concentration of carbon dioxide, relative humidity, compressive strength of 28 days, curing time, and exposure classes. Only the concentration of carbon dioxide is conducive to the carbonation of concrete, and relative humidity has a very significant effect on concrete carbonation.

Analysis and prediction of uniaxial compressive strength of icy lunar regolith under extreme temperature

Water ice exists in the permanently shadowed region (PSR) of the moon. It can become a vital survival material for the lunar base and provide fuel for the moon to make the moon a relay station for deep space exploration. For in-situ sampling and detection of lunar water ice, the design of sampling equipment has to consider the mechanical properties of the icy lunar regolith (ILR) to be broken during the drilling process. According to the mineral and chemical composition of the soil in the PSR, basalt rocks and anorthosite rocks are selected as two basic raw materials to simulate lunar soil. Multiple sets of ILR simulated samples are prepared with different raw material ratios (five kinds), water content (5–25 wt%), dry density (bulk density, excluding water, 1.45–1.97 g/cm3), and temperature (−240 to −10 °C). Uniaxial compressive strength (UCS) tests are carried out on these samples. A comprehensive mapping model between the UCS and the above four factors is constructed using multiple nonlinear regression methods. Based on the existing remote sensing data, the relationships or hypotheses of the subsurface dry density, temperature, and water content with depth are given. Furthermore, the UCS and drillability grade of ILR are predicted to change with depth. The results show that the ratio of raw materials has far less influence on the UCS than the other three factors. When the sample temperature is lower than −180 °C, the degree of influence of temperature changes on the UCS is significantly reduced. The UCS of the sample increases nonlinearly with the increase of dry density. The samples have an extreme strength value in the saturated water content state. This study provides a standard for the design of the equipment for drilling detection of water ice and lays a foundation for presetting operating procedures of the drilling tool.

Numerical modelling for geotechnical assessment of rock mass behaviour and performance of support system for diversion tunnels using optimized Hoek-Brown parameters

Purpose. Empirical and numerical methods play a vital role in assessing rock mass behaviour quantitatively and qualitatively to design underground structures/caverns and support systems. This research aims to assess and evaluate the rock mass be-haviour for safe, stable, efficient, and economical design of support system for underground structures especially tunnels in diverse rock mass conditions. Methods. In this research, such empirical design methods as Rock Mass Rating (RMR), Q-system and GSI were used to characterize and classify the rock mass environment along the tunnel for the preliminary design of twin tunnels and support systems. The geomechanical parameters, Hoek-Brown failure criterion, and its variants for assessing rock mass behaviour were optimized using multiple regression of Stewart, generalized and globalized variant of nonlinear regression method. The rock mass was classified for the selected section A-A. The excavation method and support system for the said section were designed based on the results obtained from empirical modelling. 2D elasto-plastic finite element method (FEM) was used for numerical analysis of rock mass behaviour and performance of the designed supports in section A-A. Findings. The major rock type encountered in the diversion scheme comprises gabbronorite (GN) and Ultramafic Association (UMA). Based on the quantification of RMR, Q-system, and GSI, section A-A’s rock mass ranges from very poor to poor. From the numerical analysis for the said rock mass environment both RMR and Q system support recommendations are equally efficient to support the rock mass surrounding the tunnel. However, keeping in view the yield zone, especially in the crown, the rock bolt’s length should not be less than 5 meters. Based on the analysis of results, both the tunnels are at a safe distance from each other. Originality. In this research, the design input parameters for numerical modeling were optimized by using different techniques to eliminate the chances of error in evaluating rock mass behaviour and designing an optimum support system in the said rock mass environment. Practical implications. The assessment of rock mass behaviour and the design of optimum support systems in heterogenous conditions is quite challenging and requires thorough investigation through different design techniques. This research provides a refined meth-od to be used for the safe, stable, and economical design of tunnels.

Accuracy improvement of electrical load forecasting against new cyber-attack architectures

• Developing contributions to consider data integrity aspects in load forecasting problem. • Proposing robust schemes to perform accurate load forecasting under new cyber-attacks. • A novel cyber-attack named Civil Attack (CA) is employed to strength the forecasting. • Using accurate non-linear techniques in zones with high load covariance. • Gaussian Process Regression and Random Forest Regression is used to increase accuracy. The cyber challenges faced by cybercriminals are growing dramatically as the power system strives to become more intelligent and more stable. Load forecasting is a well-known problem in the energy management field, but the state-of-the-art lacks contributions that consider data integrity aspects. Despite the existing effective methods on load forecasting, power system requires robust schemes that are also successful in performing accurate load forecasting under cyber-attacks. A novel cyber-attack named Civil Attack (CA) is employed and faced by the two non-linear regression methods. In recent years, numerous regression techniques such as methods called Multiple Linear Regression (MLR), Artificial Neural Network (ANN), Support Vector Regressor (SVR) and etc., were employed to perform electricity load forecasting under false data injection (FDI) attacks. While all of the techniques listed are inaccurate in zones with high load covariance, mostly industrial zones, we propose two non-linear methods called Gaussian Process Regression (GPR) with optimized kernel functions and Random Forest Regression (RFR) to address the problem, while the data integrity attack is used for comparing our methods with other proposed methods.

Thin-layer modelling of sweet potato slices drying under naturally-ventilated warm air by solar-venturi dryer

The drying of agricultural produce is an important food preservation measure. However, high energy requirements for drying, limited access to energy sources, small-medium scale farmers experience high post-harvest losses of their produce. Therefore, there is a need to develop and optimize low-cost food preservation technologies. In this study, eleven mathematical models were used to estimate the drying coefficients following non-linear regression method, in hot-air oven and naturally-ventilated solar-venturi drying to find the best fit of the moisture ration models. Sweet potato tubers were sliced at 3, 5 and 7 mm thickness sizes with and without pre-drying treatments. The prepared sweet potato slices were dried in a hot-air oven dryer at a constant temperature of 70 °C in comparison to the naturally-ventilated solar-venturi dryer with a heated ambient air that varied according to the outside environmental conditions. The drying rate of the samples in a hot-air oven dryer was higher than for those in the naturally-ventilated solar-venturi dryer. The results showed that the drying time was significantly (P < 0.05) affected by the thickness size of sweet potato slices (SPS) and that the drying took place at the falling rate period and a constant drying time. The Midilli et al. model was the best fit for predicting the moisture ratio of SPS dried in hot-air oven dryer and naturally-ventilated solar-venturi dryer based on statistical analysis (R2 = 0.982–0.999, χ2 = 4.60 × 10−6-5.56 × 10−5 and RMSE = 0.011–0.067). The Deff was 3.32 × 10−9- 6.31 × 10−9 m s−1 for the naturally-ventilated solar-venturi dryer and 1.02 × 10−8 - 2.19 × 10−8 m s−1 for the hot-air oven dryer. According to the results obtained, naturally-ventilated, solar-venturi dryer and lemon juice pre-drying treatment are the suitable application for small-medium scale drying of SPS under Pietermaritzburg conditions.

Ranking the importance of demographic, socioeconomic, and underlying health factors on US COVID-19 deaths: A geographical random forest approach.

A growing number of studies show that the uneven spatial distribution of COVID-19 deaths is related to demographic and socioeconomic disparities across space. However, most studies fail to assess the relative importance of each factor to COVID-19 death rate and, more importantly, how this importance varies spatially. Here, we assess the variables that are more important locally using Geographical Random Forest (GRF), a local non-linear regression method. Through GRF, we estimated the non-linear relationships between the COVID-19 death rate and 29 socioeconomic and health-related factors during the first year of the pandemic in the USA (county level). GRF outputs are compared to global (Random Forest and OLS) and local (Geographically Weighted Regression) models. Results show that GRF outperforms all models and that the importance of variables highly varies by location. For example, lack of health insurance is the most important factor in one-third (34.86%) of the US counties. Most of these counties are (concentrated mainly in the Midwest region and South region). On the other hand, no leisure-time physical activity is the most important primary factor for 19.86% of the US counties. These counties are found in California, Oregon, Washington, and parts of the South region. Understanding the location-based characteristics and spatial patterns of socioeconomic and health factors linked to COVID-19 deaths is paramount for policy designing and decision making. In this way, interventions can be designed and implemented based on the most important factors locally, avoiding thus general guidelines addressed for the entire nation.

Application of Soft Computing Techniques to Estimate Cutter Life Index Using Mechanical Properties of Rocks

The wear of cutting tools is critical for any engineering applications dealing with mechanical rock excavations, as it directly affects the cost and time of project completion as well as the utilization rate of excavators in various rock masses. The cutting tool wear could be expressed in terms of the life of the tool used to excavate rocks in hours or cutter per unit volume of excavated materials. The aim of this study is to estimate disc cutter wear as a function of common mechanical rock properties including uniaxial compressive strength, Brazilian tensile strength, brittleness, and density. To achieve this goal, a database of cutter life was established by analyzing data from 80 tunneling projects. The data were then utilized for evaluating the relationship between rock properties and cutter consumption by means of cutter life index. The analysis was based on artificial intelligence techniques, namely artificial neural networks (ANN) and fuzzy logic (FL). Furthermore, linear and non-linear regression methods were also used to investigate the relationship between these parameters using a statistical software package. Several alternative models are introduced with different input variables for each model, to identify the best model with the highest accuracy. To develop these models, 70% of the dataset was used for training and the rest, for testing. The estimated cutter life by various models was compared with each other to identify the most reliable model. It appears that the ANN and FL techniques are superior to standard linear and non-linear multiple regression analysis, based on the higher correlation coefficient (R2) and lower Mean square error (MSE).

Linear and Non-Linear Regression Analysis for the Adsorption Kinetics of SO2 in a Fixed Carbon Bed Reactor—A Case Study

Here, we determined the kinetic parameters of SO2 adsorption on unburned carbons from lignite fly ash and activated carbons based on hard coal dust. The model studies were performed using the linear and non-linear regression method for the following models: pseudo first and second order, intraparticle diffusion, and chemisorption on a heterogeneous surface. The quality of the fitting of a given model to empirical data was assessed based on: R2, R, Δq, SSE, ARE, χ2, HYBRID, MPSD, EABS, and SNE. It was clearly shown that the linear regression more accurately reflects the behaviour of the adsorption system, which is consistent with the first-order kinetic reaction—for activated carbons (SO2 + Ar) or chemisorption on a heterogeneous surface—for unburned carbons (SO2 + Ar and SO2 + Ar + H2O(g) + O2) and activated carbons (SO2 + Ar + H2O(g) + O2). Importantly, usually, each of the approaches (linear/non-linear) indicated a different mechanism of the studied phenomenon. A certain universality of the χ2 and HYBRID functions has been proved, the minimization of which repeatedly led to the lowest SNE values for the indicated models. Fitting data by any of the non-linear equations based on the R or R2 functions only cannot be treated as evidence/prerequisite of the existence of a given adsorption mechanism.

Accurate parameterization of the kinetic energy functional for calculations using exact-exchange.

Electronic structure calculations based on Kohn-Sham density functional theory (KSDFT) that incorporate exact-exchange or hybrid functionals are associated with a large computational expense, a consequence of the inherent cubic scaling bottleneck and large associated prefactor, which limits the length and time scales that can be accessed. Although orbital-free density functional theory (OFDFT) calculations scale linearly with system size and are associated with a significantly smaller prefactor, they are limited by the absence of accurate density-dependent kinetic energy functionals. Therefore, the development of accurate density-dependent kinetic energy functionals is important for OFDFT calculations of large realistic systems. To this end, we propose a method to train kinetic energy functional models at the exact-exchange level of theory by using a dictionary of physically relevant terms that have been proposed in the literature in conjunction with linear or nonlinear regression methods to obtain the fitting coefficients. For our dictionary, we use a gradient expansion of the kinetic energy nonlocal models proposed in the literature and their nonlinear combinations, such as a model that incorporates spatial correlations between higher order derivatives of electron density at two points. The predictive capabilities of these models are assessed by using a variety of model one-dimensional (1D) systems that exhibit diverse bonding characteristics, such as a chain of eight hydrogens, LiF, LiH, C4H2, C4N2, and C3O2. We show that by using the data from model 1D KSDFT calculations performed using the exact-exchange functional for only a few neutral structures, it is possible to generate models with high accuracy for charged systems and electron and kinetic energy densities during self-consistent field iterations. In addition, we show that it is possible to learn both the orbital dependent terms, i.e., the kinetic energy and the exact-exchange energy, and models that incorporate additional nonlinearities in spatial correlations, such as a quadratic model, are needed to capture subtle features of the kinetic energy density that are present in exact-exchange-based KSDFT calculations.