Empiric Equations Research Articles

Using feature engineering and machine learning in FAO reference evapotranspiration estimation

Abstract The authors of this study investigated the use of machine learning (ML) and feature engineering (FE) techniques to accurately determine FAO reference evapotranspiration (ETo) with a minimal number of climate variables being measured. The recommended techniques for areas with insufficient measurements are based solely on daily temperature readings. Various ML methods were tested to evaluate how sophisticated an ML algorithm is for this task necessary. The main emphasis was on feature engineering, which involves converting raw variables into inputs better suited for ML algorithms, resulting in improved results. FE methods for estimating evapotranspiration include approximations of clear-sky solar radiation based on altitude and Julian day, approximate relative humidity and wind velocity, a categorical month variable, and variables interactions. The authors confirmed that the ability of ML in such tasks is not solely dependent on choosing the suitable algorithm but also on this frequently ignored step. The results of computational experiments are presented, accompanied by a comparison of the proposed method against standard ETo empiric equations. Machine learning methods, mainly due to the transformation of raw variables using FE, provided better results than traditional empirical methods and sophisticated ML algorithms without FE. In addition, the authors tested the applicability of the developed models in the broader area to evaluate the possibility of their generalizability. The potential of this approach to deliver improved predictions, reduced input requirements, and increased efficiency holds interesting promise for optimizing water management strategies, irrigation planning, and decision-making within the agricultural sector.

Експериментално определяне зависимостта на специфичния топлинен капацитет на водни разтвори на LiCl от температурата и концентрацията им

This project is focused on the experimental determination of the specific heat capacity of aqueous solutions of LiCl with different mass concentrations proposed, which is applicable for various liquids and, in contrast to calorimetry, relies on the heat transfer between two media with different temperatures and thus accounts for the heat losses of this thermodynamic system. A theoretical model based on the heat balance equation for Newtonian and Stephan-Boltzmann heat transfer has been constructed. Laboratory experiments have been carried out using aqueous solutions of LiCl with mass concentration ranging from 0 to 15% and at temperatures in the range 20-90 ℃. The data has been analysed using MATLAB and empiric equations for the temperature dependence of the specific heat capacity for fixed mass concentrations of the solute have been obtained. The results are in good agreement with the reference values.

Vibration Analysis of Carbon Fiber-Graphene-Reinforced Hybrid Polymer Composites Using Finite Element Techniques.

In this study, a computational procedure for the investigation of the vibration behavior of laminated composite structures, including graphene inclusions in the matrix, is developed. Concerning the size-dependent behavior of graphene, its mechanical properties are derived using nanoscopic empiric equations. Using the appropriate Halpin-Tsai models, the equivalent elastic constants of the graphene reinforced matrix are obtained. Then, the orthotropic mechanical properties of a composite lamina of carbon fibers and hybrid matrix can be evaluated. Considering a specific stacking sequence and various geometric configurations, carbon fiber-graphene-reinforced hybrid composite plates are modeled using conventional finite element techniques. Applying simply support or clamped boundary conditions, the vibrational behavior of the composite structures are finally extracted. Specifically, the modes of vibration for every configuration are derived, as well as the effect of graphene inclusions in the natural frequencies, is calculated. The higher the volume fraction of graphene in the matrix, the higher the natural frequency for every mode. Comparisons with other methods, where it is possible, are performed for the validation of the proposed method.

Process simulation and economic feasibility assessment of the methanol production via tri-reforming using experimental kinetic equations

The purpose of this paper is to assess via techno-economic metrics the feasibility of a tri-reforming coupled methanol process. The simulation of the tri-reforming reactor considered empiric kinetic equations, developed by our group in previous studies. The flue gas coming from the furnace that provides the energy required by the reforming reactor was also used as feed, in order to reduce the CO2 emissions. A sensitivity analysis was carried out to determine the influence of the feed composition and temperature in the tri-reforming process results, studying H2O/CH4 and O2/CH4 ratios (0.5–1.5 and 0.35–0.40, respectively), and varying the temperature between 850 and 1050 °C. The methanol plant was also simulated, and an economical study was carried out to know if the proposed process would be economically feasible. The most relevant economic parameters (including the Net Present Value, the Internal Rate of Return, the Payback Period and the break-even) were calculated, showing a quite robust process from an economical point of view.

Proposed Equation to Estimate the Length of a Hydraulic Jump in a Rectangular Open Channel Hydraulic with Variable Slope, and Its Comparison with Seven Theoretical Equations of Specialized Literature

A hydraulic jump is a localized phenomenon that generates on an open hydraulic channel; however, its mathematical demonstration is not possible in the turbulent area of the phenomenon, especially in the area where the jump occurs and where its length is measured, so the data must be obtained with direct measurements in a laboratory and through empiric equations. This work presents the results of the generated hydraulic jumps and the measure of its length in a series of tests, where we input different flow rates in a transportable open channel hydraulic with a constant gate opening “a” and a slope of S = 0.0035, in the Engineering Faculty Research Centre of the Autonomous University of Chiapas. We also present the experimental method to generate a hydraulic jump, the measure of its length and a comparison with seven empirical equations, including the Sieñchi equation used in H-Canales, the most used software for hydraulic channels design in Latin America. The results show that the calculus of L with the proposed equation has a mean squared error (MSE) of 0.1337, a Bias of -0.0049, a model efficiency (ME) of 0.9991 and a determination coefficient (R2) of 0.9993 when compared with the experimental model. Meanwhile, the comparison of L calculated with the Sieñchi equation versus the experimental model resulted in a MSE of 0.1741, a bias of -0.0437, a ME of 0.9984 and a R2 of 0.9997. Both equations are highly recommended to estimate L in rectangular channels under the conditions presented in this paper, thus, the proposed equation can be applied if y . Finally, it must be stated that we also proved that the Pavlosky equation is comparable in precision and accuracy concerning to proposed equation and Sieñchi equation.

Optimal Energy Production In The Yeşilirmak River Basin

Optimal planning and operation of water resources are depend on a complex structure and process that include country economics and life standards. Currently, sustainable use and development of water resources to maximize possible benefits are the two big challenges to be overcome and efficient use of hydro power forms a significant component of this. In this study, a water resources system with multi-objectives and multiple reservoirs is described. It is considered to three scenarios in this system. The system is set up on the optimal operation model for the long term planning. The technique of the dynamic programming with successive approximations is used for the model. Objective function in the optimization model has two stage, maximization of firm and total energies. The model is applied to a water resources system with multi-objective and multiple reservoirs presented successively on the main and secondary line of the Yeşilırmak River in the Yeşilırmak River Basin. Results obtained are evaluated to the maximization of the energy production. Accordingly, the firm energy obtained from the optimal operational model for long term planning is presented approximate the value determined by empiric equations, and also the average energy in the model is % 32 better than the value determined by empiric equations. It is observed that the optimization process of the reservoirs with the highest operational storage was controlled and managed.

Testing and predicting of yarn pull-out in aroma-textile

PurposeThe purpose of this paper is to predict the pull-out force of loop pile of ramie/cotton terry woven fabrics treated with aroma-microcapsules as well as to understand and to interpret the pull-out behaviour developing the mathematical model.Design/methodology/approachThe displacements and forces associated with pulling a yarn from different structures of fabrics were determined. Regression analysis and factorial designs were performed.FindingsThe yarn pull-out behaviour of terry fabric is highly dependent on the applied treating and demonstrated various extents of variability under the different pulling distances. The character of yarn pull-out is periodic and depends on fabric construction. The difference between the resistance to pile loop extraction for the grey and modified terry fabrics depends on the changed fabric’s structure. The existence of good relation between binder’s concentration and resistance to pile loop extraction of terry fabric was proved.Practical implicationsThe study enables to forecast important loop feature for terry aroma-textiles: to be securely held in the place preventing loop pulling.Originality/valueThe assessment of the influence of fabric’s weft density and binder’s concentration for the yarn pull-out of terry aroma-textile was proposed. The research developed analysis and empiric mathematical equations suitable for predicting of displacements and forces related to pulling phenomenon as well as designing new multifunctional terry fabrics with resistance to pile loop extraction required. The received knowledge could enlarge the base of information needful for design of new products for clothing, home textile and healthcare/well-being applications as well.

Validity of bioelectrical impedance analysis in estimation of fat-free mass in colorectal cancer patients

Bioelectrical impedance analysis (BIA) is an accessible and cheap method to measure fat-free mass (FFM). However, BIA estimates are subject to uncertainty in patient populations with altered body composition and hydration. The aim of the current study was to validate a whole-body and a segmental BIA device against dual-energy X-ray absorptiometry (DXA) in colorectal cancer (CRC) patients, and to investigate the ability of different empiric equations for BIA to predict DXA FFM (FFMDXA). Forty-three non-metastatic CRC patients (aged 50-80 years) were enrolled in this study. Whole-body and segmental BIA FFM estimates (FFMwhole-bodyBIA, FFMsegmentalBIA) were calculated using 14 empiric equations, including the equations from the manufacturers, before comparison to FFMDXA estimates. Strong linear relationships were observed between FFMBIA and FFMDXA estimates for all equations (R2=0.94-0.98 for both devices). However, there were large discrepancies in FFM estimates depending on the equations used with mean differences in the ranges-6.5-6.8kg and-11.0-3.4kg for whole-body and segmental BIA, respectively. For whole-body BIA, 77% of BIA derived FFM estimates were significantly different from FFMDXA, whereas for segmental BIA, 85% were significantly different. For whole-body BIA, the Schols* equation gave the highest agreement with FFMDXA with mean difference ±SD of-0.16±1.94kg (p=0.582). The manufacturer's equation gave a small overestimation of FFM with 1.46±2.16kg (p<0.001) with a tendency towards proportional bias (r=0.28, p=0.066). For segmental BIA, the Heitmann* equation gave the highest agreement with FFMDXA (0.17±1.83kg (p=0.546)). Using the manufacturer's equation, no difference in FFM estimates was observed (-0.34±2.06kg (p=0.292)), however, a clear proportional bias was detected (r=0.69, p<0.001). Both devices demonstrated acceptable ability to detect low FFM compared to DXA using the optimal equation. In a population of non-metastatic CRC patients, mostly consisting of Caucasian adults and with a wide range of body composition measures, both the whole-body BIA and segmental BIA device provide FFM estimates that are comparable to FFMDXA on a group level when the appropriate equations are applied. At the individual level (i.e. in clinical practice) BIA may be a valuable tool to identify patients with low FFM as part of a malnutrition diagnosis.

Estimations of grain-boundary surface tension in elemental solids

The empiric equations estimating the temperature dependences of average surface tension of high-angle grain boundaries in elemental solids are presented. The grain boundaries are considered as a homogeneous liquid-like layer in a solid matrix. The expressions present the grain-boundary surface tension as functions of the melting temperature, melting enthalpy, and molar volume of the elemental solid at the melting temperature. The empiric expressions relating grain-boundary surface tension with the surface tensions of elements in the solid and liquid states at melting temperature are obtained on this basis. The relations proposed can be useful to estimate the averaged surface tension of high-angle grain boundaries in elemental solids at high enough homologous temperature.

Empirical correlation of shear wave velocity (vs) with spt of soils in Madrid

Empirical correlations are usually used as a predictive tool in geotechnical engineering. However, equations calculated for soils very different to the ones to be characterized are frequently used, and so they are not representative of their mechanical properties. This fact, added to the increasing interest of civil engineering in knowing the shear wave velocity (Vs) of the ground, has led to the calculation of different empirical equations to predict the Vs value of the soils of Madrid. In this study this has been achieved by calculating the empirical correlations between the Vs value obtained through the ReMi (Refraction Microtremor) technique and the Standard Penetration Test (500 NSPT values). The empirical correlations proposed are applicable to the whole metropolitan area of Madrid, and have an excellent predictive capability owing to the incorporation of the measurement depth to the equations, which has an important influence in the resistance properties of soils. It is always better to have data collected in the studied site. But often there are too many difficulties to carry out some of these surveys. It may also happen that the surveys take too long or are too expensive to carry out. In these situations, empiric equations can be used to estimate this data. In geotechnical engineering, these empiric correlations are used frequently as a predictive tool, especially in the project’s design primary phases, when vast extensions of terrain are to be characterized in a short period of time, and to define if the soil fits a specific purpose. Because of this factor, there are plenty of estimations published that link between them different types of mechanical properties and geotechnical parameters.

Characterization of structure and air permeability of aromatherapic terry textile

Purpose – The purpose of this paper is to investigate the physical properties of smart aromatherapic ramie/cotton terry fabrics containing microcapsules (MC) with essential Eucalyptus oil. Design/methodology/approach – Terry fabrics are manufactured by changing the weft density. The air permeability is determined for grey and microencapsulated textile. The factorial designs are made. For informative experiment the linear type of regression is analysed. Development of physical properties of microencapsulated terry fabrics is discussed. Findings – The air permeability of aromatherapic terry fabrics is determined. All statistical analysis is performed. Appropriate conclusions about the influence of fabric’s structure and microencapsulating process on terry fabric quality are made. Originality/value – To date there are no investigations concerning terry textiles with fragrance MC. This study developed analysis and empiric mathematical equations suitable for evaluating and designing terry fabrics with the air permeability required. Assessment of the influence of fabric’s weft density and binder concentration for the air permeability of terry textile is proposed.

Unsteady Flow of Shear-Thinning Fluids in Porous Media with Pressure-Dependent Properties

Inthispaper,amodelforinjectionofapower-lawshear-thinningfluidinamedium withpressure-dependentpropertiesisdevelopedinageneralizedgeometry(plane,radial,and spherical). Permeability and porosity are taken to be power functions of the pressure incre- ment with respect to the ambient value. The model mimics the injection of non-Newtonian fluids in fractured systems, in which fractures are already present and are enlarged and even- tually extended and opened by the fluid pressure, as typical of fracing technology. Empiric equations are combined with the fundamental mass balance equation. A reduced model is adopted, where the medium permeability resides mainly in the fractures; thefluid and porous medium compressibility coefficients are neglected with respect to the effects induced by pressure variations. At early and intermediate time, the flow interests only the fractures. In these conditions, the problem admits a self-similar solution, derived in closed form for an instantaneous injection (or drop-off) of the fluid, and obtained numerically for a generic monomial law of injection. At late times, the leak-off of the fluid towards the porous matrix is taken into accountvia a sink term in the mass balance equation. In this case, the original set of governing equations needs to be solved numerically; an approximate self-similar solution valid for a special combination of parameters is developed by rescaling time. An example of application in a radial geometry is provided without and with leak-off. The system behaviour isanalysedconsideringthespeedofthepressurefrontandthevariationofthepressurewithin

Experiment of air flow behavior and heat transfer characteristics in microchannels with different aspect ratios

Experiments were conducted to investigate the flow behavior and heat transfer characteristics in minichannels with different aspect ratios. The widths of microchannels are constant of 0. 4 mm. The aspect ratios of the microchannels are 2 /5,1 /2,2 /3 and 1,respectively. All tests were performed with air. The experiments were completed with the Reynolds number in the range of 200 to 1 600. Results of experiments show that the aspect ratios of microchannels have a remarkable effect on the performance of flow behavior and heat transfer characteristics. The friction factors decrease with the increase of the Reynolds numbers. The Poiseuille numbers increase when the Reynolds numbers keep rising. Both of the friction factors and Poiseuille numbers drop as the aspect ratios increase. Nusselt numbers increase as Reynolds numbers increase,but decrease with the increase of aspect ratios. The corresponding empiric equations for the flow resistance and heat transfer characteristics in microchannels with different aspect ratios are fitted.

The Development of Ejection Reagent Input in Water Treatment Systems

The universal ejection scheme of the reagent's preparation and input is offered in this work, wherein hydrodynamic jet-mixing devices are used. Ejectors in the system act as mixing devices, batchers and cavitators at the same time. It is possible to obtain cavitation (two-phase) liquid flow mode, basing on the assessment of cavitation number. Principle scheme of the reseach unit is offered for modelling and water treatment. In this scheme the module for reagents and air ejection is used. Furthermore, the calculation of water-moderated and water-air ejectors, working in the cavitation mode, was performed on the base of empiric equations.

Investigation of the roughness effect on flow behavior and heat transfer characteristics in microchannels

Experiments were conducted to investigate the flow behavior and heat transfer characteristics in microchannels with various surface roughnesses. In the experiments, six test pieces with various roughnesses were fabricated in the stainless steel panel and divided into three groups. Each panel includes 30 microchannels in parallel with uniform geometrical parameters. Both width and depth of microchannels are 0.4mm. The relative roughness of surface in the microchannel is from 0.58% to 1.26%. All tests were performed with air. The experiments were completed with the Reynolds number in the ranges of 200–2100. The friction factor, heat transfer coefficient, Nusselt number and thermal performance were analyzed based on the experimental results. Results of experiments showed that the surface roughness in microchannel has a remarkable effect on the performance of flow behavior and heat transfer. Based on the experimental data, the friction factor and the Nusselt number increase with the increasing of the surface relative roughness. At the same time, the effect of roughness in the thermal performances is small within the range of experimental parameters. The results also indicate that the heat flux rarely affects the Nusselt number. In this paper, the corresponding empiric equations for flow resistance and heat transfer characteristics in microchannels were developed.

Influence of terry fabrics structure and finishing on yarn pull-out behaviour

Purpose – The purpose of this paper is to investigate the resistance to pile loop extraction of terry fabrics regarding the pile height and impact/finishing. Design/methodology/approach – Fabrics are manufactured by changing the pile height and applying impact/finishing procedures. The resistance to pile loop extraction are determined. The factorial designs are made. For informative experiment the linear type of regression are analysed. Yarn pull-out behaviour in terry fabrics is discussed. Findings – The dynamics of yarn pull-out process in terry fabrics is estimated through the force-pulling distance curves presented. The resistance to pile loop extraction is determined. All statistical analysis is performed. Appropriate conclusions about the influence of fabrics structure and impact/finishing on yarn pull-out process are made. Originality/value – The study developed analysis and empiric mathematical equations suitable for evaluating and designing fabrics with the resistance to pile loop extraction ability required. Assessment of the influence of fabric's pile height and impact/finishing on the yarn pull-out is proposed.

One-flow feed divided electrochemical reactor for indirect electrolytic production of hypochlorite from brine for swimming pool treatment-experimental and theoretical optimization

• Optimization of an electrochemical chlorinator for swimming pool. • Divided asymmetric electrochemical continuously stirred reactor. • Convective transfer of the anolyte across the separator to the cathodic compartment. • The brine (5 M NaCl) conversion reaches 50% under 3 kA m −2 with a faradic yield of 80%. • Correlation of current density versus chloride concentration for concentrated brine. A ‘two-compartment’ asymmetric electrochemical reactor, operating without electrodes polarity inversion, was designed and optimized for the chlorination of swimming pools. Gaseous chlorine, produced at the anode and absorbed in the alkalinized catholyte, provides the hypochlorite solution. Empiric equations providing the chloride concentration dependence on the initial current density magnitude were established. Experimental optimization of the effect of the various operating parameters allows a chloride conversion close to 50% with faradic yields higher than 80%, and a chlorine production of 1 kmol/day/m 2 to be achieved. Macroscopic mass balance, was performed and the obtained theoretical results correlate with the experimental ones ( X theor . Cl - - X exper . Cl - < 10%).

Modeling the Solubility of Dihydroxybenzoic Acid and Methylbenzoic Acid Isomers in Supercritical Carbon Dioxide

In this work, we propose to correlate and predict the solubility in supercritical CO2 of disubstituted aromatic isomers of hydroxybenzoic acid and methylbenzoic acid with a new methodology based on the expanded liquid theory, in which the solid–fluid equilibrium is modeled using the local composition model of UNIQUAC in which the interaction parameters are related to the solvent reduced density with an empiric exponential form equations. The experimental solubility of hydroxybenzoic acid isomers, methylbenzoic acid isomers and mixed isomers (m-hydroxybenzoic acid+p-hydroxybenzoic acid) are used for evaluating the correlation and prediction capabilities of this new methodology. The results obtained using the proposed model show good agreement with the experimental data used.

Correlation and Prediction of the Solubility of Solid Solutes in Chemically Diverse Supercritical Fluids Based on the Expanded Liquid Theory

For the proper design of any extraction procedure based on supercritical solvents, it is essential to have a sound knowledge of the solubility data of different compounds and the accurate way to represent it. The solute’s solubility in a supercritical solvent is dependent on the solute, the solvent, and the operating conditions (temperature and pressure). Developing a comprehensive experimental data set is an onerous task and time consuming and, thus, the incentive to develop predictive tools is substantial. In this paper, a technique is presented and tested to correlate and predict solute’s solubility in different supercritical fluids with a methodology based on the expanded liquid theory, in which the solid-fluid equilibrium is modeled using the local composition model of UNIQUAC in which the interaction parameters are related to the solvent reduced density with empiric equations. The most advantages of this model include: it does not require the knowledge of critical properties and sublimation pressure of solid solutes and does take into account the binary interaction between solid solute and solvent. The evaluation of the proposed model capabilities is done by testing it on a large data base consisting of experimental solubility data taken from literature of 33 binary systems solid-SC fluid. The results obtained for both correlation and prediction show good agreement with the experimental data used. For the comparison we have considered some literature models that account for effect of the system conditions (temperature and pressure) in addition to the sublimation pressure of the solute through their introduction of the enhancement factor and a model based on a modified Peng-Robinson equation of state.

RESEARCH OF NATURAL WOOD COMBUSTION AND CHARRING PROCESSES

Wood is a material widely used for construction purposes and – in some cases – it is the main element of building structures. In comparison with other materials, wood has a number of advantages, such as lightness, strength, resistance to impacts and vibration, simplicity in terms of processing and etc. However, one of the largest drawbacks of wood is flammability. Charring of wooden structures is the most apparent feature of combustion in case of fire in wooden buildings or buildings made of wooden structures. This property is important in identifying causes of fire; therefore it is necessary to relate charring of wooden structures with certain significant effects of fire, such as its duration or temperature. The article addresses the wood characteristics that impact on combustion and charring. It describes test methods and properties of wood samples under research. Research of charring rate of natural softwood and hardwood as a function of heating time, and regressive analysis of data were carried out. Empiric equations were derived. The calorific value of carbon residue resulting in different temperatures was determined in accordance with LST EN ISO 1716. Thermographic research of oak and pine wood was carried out in different gaseous environments. The research results were summarised in the form of conclusions.