Nonlinear Regression Equations Research Articles

Experimental and Numerical Analysis of the Impact of Corrosion on the Failure Pressure of API 5L X65 Pipeline

This paper employs the Finite Element Method (FEM) to simulate and analyze the effects of corrosion defect parameters on the stress and failure pressure of pipelines. It investigates how the boundary conditions of the pipeline model influence stress and examines the sensitivity of failure pressure to corrosion defect parameters. A nonlinear regression equation has been developed from a dataset obtained through simulation experiments to predict the failure pressure of corroded pipelines. To validate the effects of corrosion defect parameters on failure pressure, a hydrostatic test platform for an API 5L X65 pipeline with corrosion defects was established to measure stress levels and failure pressures across varying corrosion defects. This study reveals that failure pressure is negatively correlated with corrosion length and depth, while positively correlated with corrosion width. Among these parameters, corrosion depth exerts a more significant influence on the pipeline’s failure pressure than corrosion length and width. Within the range of corrosion defect parameters examined, the maximum deviation of the prediction equation’s results from the simulation results is 8.71%, with an average deviation of 5.81%. The standard deviation of the fitted residuals is 0.01837. Additionally, the maximum deviation between the predicted results and experimental measurements is 8.39%, with an average deviation of 7.77%. The strong agreement between the predicted results from the equation and the actual measured data underscores the effectiveness of the nonlinear regression equation.

Regression Models for Tree Volume Prediction in Pinus Wallichiana Stands of South Western Himalayan Region of Kashmir

This study focuses on assessing tree species diversity and evaluating the efficacy of both linear and non-linear regression models for predicting tree volume. The research was conducted in the slopes of the Pir Panjal range within the Shopian Forest Division, situated in the South-Western Himalayan Region of Kashmir. Data on Pinus wallichiana stands, including diameter at breast height (D) and tree height (H), were meticulously collected using appropriate measurement instruments. Employing a multi-stage sampling technique, ten plots of uniform size (10m x 10m) were selected across 20 blocks, and subsequently, 25 trees were randomly chosen from each plot. Six different linear and non-linear regression equations were fitted to the data, and the most suitable equation was identified for volume estimation. To evaluate the performance of the fitted regression models, metrics such as R-squared (R²), adjusted R², root-mean-square error (RMSE), and Theil’s U statistic were employed. Additionally, validation procedures involved using the half-split approach and the Chow test. Upon analysis, it was determined that when employing diameter (D) and considering the joint effectof diameter and height (D2H (I)) as independent variables, the linear model (V=-1.41+15.12D) and power model (V=2.301 I0.502), quadratic model (V=1.8726+0.663 I- 0.011 I²) with highest R², lowest RMSE and Theil’s U statistic respectively, emerged as the most suitable for volume estimation, demonstrating superior accuracy compared to alternative models. Consequently, our findings extend beyond academic inquiry, offering practical implications for sustainable forest management and planning in the Western Himalayan Regions of Kashmir. By providing robust volume estimation models tailored to Pinus wallichiana stands, our study equips forest managers and policymakers with essential tools for informed decision-making.

Machine learning-assisted wire arc additive manufacturing and heat input effect on mechanical and corrosion behaviour of 316 L stainless steels

Predicting the track forming factor or height-to-width ratio (H/W) in wire arc additive manufacturing is crucial for optimal path planning, heat distribution, structural integrity, distortion control, process efficiency, and defect prevention, ensuring high-quality and reliable components. Different analytical and numerical modeling methods have been introduced to predict the H/W ratio. However, the accuracy of these predictions is relatively low due to the challenges associated with handling complex and non-linear regression equations. This study addressed the challenges by implementing data-driven predictive modeling to predict the H/W ratio from the input process parameters. A stacking ensemble learning approach is employed, where a meta-model integrates predictions from multiple base learners to enhance overall performance. The model performance was evaluated by Coefficient of determination (R2), mean squared error (MSE), and mean absolute error (MAE). The model was validated by comparing the experimental and predicted values based on which five thin walls are printed with different heat inputs. The study also explores the impact of heat input on microstructure, mechanical, and corrosion properties. The findings indicate that a significantly low heat input (178 J/mm) and higher heat inputs (> 356 J/mm) decrease the wire utilization. With increasing heat input, ferrite content increases, microstructures become coarser, dendritic spacing increases, and ferrite transitions from lathy to skeletal. Further, lower heat input (235 J/mm) reduces δ-ferrite, suppresses atomic segregation, and increases Cr and Mo in the matrix. YS and UTS decrease with higher heat inputs, anisotropy decreases, and Vickers microhardness drops from 228 (178 J/mm) to 194 Hv (586 J/mm). Additionally, the corrosion resistance deteriorates with increasing heat input, as evidenced by higher pitting potential (Epit: 0.389 V vs. 0.368 V vs. −0.023 V) and lower corrosion current density (Icorr: 6.76 ×10−7 A/cm2 vs. 7.946 ×10−7 A/cm2 vs. 8.91 ×10−7 A/cm2) for heat inputs of 235 J/mm, 281 J/mm, and 356 J/mm, respectively.

Quantitative and qualitative 4-point express assessment of soldiers’ body weight according to nonlinear regression equations

The goal of the research is to improve the assessing system of physical fitness of military personnel. Methods: theoretical analysis and generalization; interpolation; method of least squares; regression analysis. Material: the ratings of the 4-point assessment of servicemen and service women readiness of the Armed Forces of Ukraine were obtained according to the requirements of the 100-point ECTS scale. Linear and non-linear regression equations were used to determine the accuracy of scoring for quantitative and qualitative indicators of the body weight of women and men of different height, age and body constitution. Results. It was established that the 4-point assessment of body weight of soldiers according to the rating requirements from ‘excellent, A’ level to ‘unsatisfactory, F’ level determines the quality of the nonlinear regression equation, which is inferior to the maximum possible selection (D = 94.57%) and has accuracy, which is lower than the high one (Ā = 6.88%). Also, the number of calculated points for servicemen and servicewomen body weight was calculated with the most successful selection of the nonlinear regression equation (D = 100%) and its maximum accuracy (Ā = 0%). Conclusions. The proposed method made it possible to obtain the levels of preparedness, to determine their accuracy according to the 4-point assessment of the body weight of women and men, and to achieve the equivalence of its qualitative and quantitative indicators with respect to the requirements of the 100-point rating scale.

Measurement and Calculation of Sediment Transport on an Ephemeral Stream

Sediment transport remains a significant challenge for researchers due to the intricate nature of the physical processes involved and the diverse characteristics of watercourses worldwide. A type of watercourse that is of particular interest for study is the ephemeral streams, found primarily in semiarid and arid regions. Due to their unique nature, a new measurement algorithm was created and a modified bed load sampler was built. Measurement of the bed load transport rate and calculation of the water discharge were conducted in an ephemeral stream in Northeastern Greece, where the mean calculated streamflow rate ranged from 0.019 to 0.314 m3/s, and the measured sediment load transport rates per unit width varied from 0.00001 to 0.00213 kg/m/s. The sediment concentration was determined through various methods, including nonlinear regression equations and formulas developed by Yang, with the coefficients of these formulas calibrated accordingly. The results demonstrated that the equations derived from Yang’s multiple regression analysis offered a superior fit compared to the original equations. As a result, two modified versions of Yang’s stream sediment transport formulas were developed and are presented to the readership. To assess the accuracy of the modified formulas, a comparison was conducted between the calculated total sediment concentrations and the measured total sediment concentrations based on various statistical criteria. The analysis shows that none of Yang’s original formulas fit the available data well, but after optimization, both modified formulas can be applied to the specific ephemeral stream. The results indicate also that the formulas derived from the nonlinear regression can be successfully used for the determination of the total sediment concentration in the ephemeral stream and have a better fit compared to Yang’s formulas. The correlation from the nonlinear regression equations suggests that total sediment transport is primarily influenced by water discharge and rainfall intensity, with the latter showing a high correlation coefficient of 0.998.

Applications of three distinct regression models in GDP predication

This paper introduces the basic theory and formula of linear regression, multiple linear regression, and nonlinear regression. Linear regression is one of the commonly used analysis methods in statistical analysis, which can predict the trend of model data change to a certain extent. Multiple linear regression involves more variables to predict and analyze the change trend of data, and can predict the change of data more accurately. Nonlinear regression can predict the model of arbitrary relationship between variables, thus obtaining more accurate prediction data. In the selection of regression analysis method, data characteristics and problem background should be considered, and model assumptions and validation should be paid attention to ensure accuracy and reliability. In the applications, the paper discusses the application of simple linear regression to Okuns law and delves into the complex relationship between multiple variables and gross domestic product (GDP). Finally, it uses nonlinear regression equations to analyze the global inflation rate and the annual data, and proves that there is a nonlinear relationship between the two and a downward trend, which is supported by analyzing the data of Australia and Canada.

Combined effect of zinc and cadmium ions on nitrification performance during the biological nitrogen removal of simulated livestock breeding wastewater.

Zinc and cadmium ions are usually found in livestock breeding wastewater, and the mixed ions will have an impact on the biological nitrogen removal. Nitrification performance plays an important role in biological nitrogen removal. In order to investigate the combined effect of zinc and cadmium ions on nitrification performance and to reveal the interactions between zinc and cadmium ions, three concentration ratios of zinc and cadmium ions, as well as 18 different concentration gradients were designed with the direct equipartition ray and the dilution factor method. The effect of pollutants on the nitrification performance of biological nitrogen removal was analyzed by the nonlinear regression equation, and the concentration-addition model was conducted to probe into the relationship between the mixed pollutants and the nitrification performance. The results showed that the effect on nitrification performance increased significantly with the increase of reaction duration and pollutant concentration, which indicated that the effects are concentration-dependent and time-dependent. The concentration-addition model suggested that the interactions between zinc and cadmium ions with different concentration ratios were mainly antagonistic, and as the percentage of cadmium ions in the mixtures increased, the antagonism between the mixtures became stronger. This study will provide a relevant theoretical basis for the regulation of the ratios and concentrations of heavy metal ions during the biological treatment of livestock breeding wastewater.

Optimizing the Utilization of Steel Slag in Cement-Stabilized Base Layers: Insights from Freeze-Thaw and Fatigue Testing.

This paper presents a study on the mechanical properties of cement-stabilized steel-slag-based materials under freeze-thaw cycles for a highway project in Xinjiang. Using 3D scanning technology the specimen model conforming to the real steel slag shape was established. The objectives of the study are as follows: to explore the sensitivity between the macro- and micro-parameters of the specimen and to establish a non-linear regression equation; and to study the changes in mechanical properties of materials under freeze-thaw cycles, fatigue loading, and coupled freeze-thaw cycle-fatigue loading. The results show that there are three stages of compression damage of the specimen, namely, linear elasticity, peak plasticity, and post-peak decline. Maximum contact forces between cracks and particles occur mainly in the shear zone region within the specimen. The compression damage of the specimen is a mixed tensile-shear damage dominated by shear damage. When freeze-thaw cycles or fatigue loads are applied alone, the flexural strength and fatigue life of the specimens show a linear relationship of decline. The decrease in flexural modulus at low stress is divided into the following: a period of rapid decline, a relatively smooth period, and a period of fracture, with a tendency to change towards linear decay with increasing stress. In the case of freeze-thaw-fatigue coupling, the flexural modulus of the specimen decreases drastically by about 50% in the first 2 years, and then enters a period of steady decrease in flexural modulus in the 3rd-5th years.

Study on the profitability of agricultural enterprises in Ukraine during the russian military invasion of Ukraine

This paper examines the effectiveness of grouping agricultural enterprises according to the wheat harvested area and assesses their profitability. We have developed linear and non-linear regression equations to predict the income for said groups of enterprises. The methodology is designed for cases when future market prices are probabilistic in nature. With the help of the developed methodology, it is possible to calculate the necessary production volumes in the conditions of price fluctuations. We have used the Goldfeld–Quandt parametric test to test the model for heteroscedasticity. Calculations show that agricultural holdings are indeed inefficient, and preference should be given to enterprises with medium crop areas. Application of the Lagrange multipliers method when solving the problem of agricultural enterprise optimization makes it possible to increase profitability. The case of price risk, when future market prices are not deterministic, is considered. Therefore, it is necessary to be guided by two criteria when making managerial decisions: to maximize the expected total net income and to minimize the variance of the total net income.

Theoretical derivation and analysis of strength calculation formulas of internal gear pair with double contact points

To describing the strength conditions of tooth surfaces of internal gear pair with double contact points (IGPDCP) accurately, theoretical calculation method of the strength of tooth surfaces is proposed in this paper. Theoretical derivation and analysis of strength calculation formulas of the IGPDCP drive are carried out. For contact strength analysis, based on Hertz point contact theory, general calculation idea of contact strength is provided. The main curvature of the active contact line on tooth surfaces of the pinion and internal gear are derived, respectively. Furtherly, according to theoretical calculation and derivation, the formula for calculating the contact strength of the IGPDCP drive is obtained. Orthogonal test method is used to derive the calculation formula of bending strength of the IGPDCP drive, considering test factors include the modulus, tooth number of gear, transmission ratio, helix angle, contact angle, pressure angle, and torque. Nonlinear regression equations of bending stress of the pinion and internal gear are derived, respectively. The discussion of results of contact and bending strength between formula calculation and finite element analysis are present. The conclusions show that the proposed formulas can satisfy theoretical analysis and engineering application.

New 2D roughness parameters with geometric and physical meanings for rock joints and their correlation with joint roughness coefficient

Determining the joint roughness accurately will better serve the peak shear strength estimation models of rock joints used for stability assessment of rock masses. Considering the defects of the existing quantitative characterization parameters for two-dimensional (2D) joint roughness, especially the lack of explicit geometric and physical meaning, we proposed two new 2D roughness parameters, θ2D and h2D. The former, θ2D, represents the average inclination angle of all potential contact asperities over the entire joint profile, while the latter, h2D, characterizes their average undulation height. Both parameters are closely related to the shear strength of rock joints. Then, the roughness parameters θ2D and h2D of 102 rock joint profiles digitized at 0.5 mm sampling interval were calculated, and a new nonlinear regression equation for the determination of the 2D joint roughness coefficient (JRC) was established by combining the calculated results of the two roughness parameters. It was verified that the proposed equation could give accurate JRC estimation values of the 10 standard profiles of rock joints. Through the comparative analysis of the experimental data collected from earlier studies for the peak shear strength of 73 rock joint samples and corresponding estimated values, the equation was further verified to be applicable and accurate for estimating the JRC values of rock joints. Furthermore, we discussed the effects of shear direction and sampling interval on roughness and further provided another equation that could be applied to estimate the JRC values of joint profiles at the sampling interval of 1.0 mm.

Influence of Weather Factors on the Incidence of Major Insect Pests of Sesame (Sesamum indicum L.)

Population dynamics of major pests viz., web worm, Antigastra catalaunalis (Duponchel), leaf hoppers Orosius albicinctus (Distant) and gallfly Asphondilia sesami (Felt) infesting sesame was studied in Coimbatore, Tamil Nadu, India during Rabi and Kharif seasons of the year 2020. Correlation between the pest population, percent damage and weather parameters was analyzed and regression equations were developed. The incidence of leaf hoppers, web worm and gallfly on sesame crop during Rabi season started on 4th, 3rd and 7th Standard meteorological week (SMW) respectively. The peak attained on 8th,11th, and 11th SMW with population of leafhoppers and damage by web worm and gallfly (2.01/plant,60.04 percent and 49.68 percent) respectively during Rabi season. In case of leafhopper and web worm, minimum temperature (r=0.031r=0.373) had non-significant positive correlation whereas mean relative humidity (r=-0.02) registered non-significant negative correlation with leaf hopper and web worm significant negative correlation Gall fly incidence showed significant positive correlation with maximum and minimum temperature. Whereas in Kharif season, incidence of leafhoppers, web worm and gallfly on sesame crop started on 33rd, 32nd and 37th SMW respectively. The peak activity and incidence was noticed during 37th, 39th and 40th SMW for leafhoppers, web worm and gallfly respectively. The correlation between weather parameters and incidence of major pests followed a similar pattern to kharif season. Regression analysis data revealed that the multiple non-linear regression equations are sufficient to predict the pest population with prevailing weather parameters.

Study on the Consumption Mechanism and Lubrication of Mold Powder Based on Non-Sinusoidal Oscillation Mode

A two-dimensional mold model coupled multiphase flow, heat transfer, solidification and mold oscillation was established based on the casting parameters of the mold of plant. The accuracy of the model was verified by comparing the measured by plant and calculated mold powder consumption under the same casting conditions. The mechanism of mold powder consumption and lubrication was analyzed based on the non-sinusoidal oscillation mode, and the effect of non-sinusoidal oscillation parameters on mold powder consumption was discussed. Mold powder consumption was determined by the downward flow velocity of liquid mold powder and the thickness of liquid mold powder film, the liquid mold powder consumption decreased with the decrease of those. When the mold moved downward, the mold powder thickness and downward flow velocity decreased, the minimum mold powder consumption reached at the middle of the negative strip time, and the variation was to opposite when the mold moved upward, the maximum mold powder consumption appeared during the positive strip time. With the decrease of casting speed and modification ratio, and increase of oscillation frequency and oscillation amplitude, the mold powder consumption had the tendency to increase. The nonlinear regression equation was fitted by the Levenberg–Marquardt method combined with the universal global optimization method to evaluate mold powder consumption.

Structure-Function Relationship in Keratoconus: Spatial and Depth Vision.

The purpose of this study was to determine changes in spatial and depth vision with increasing severity of keratoconus and to model the structure-function relationship to identify distinct phases of loss in visual function with disease severity. Best-spectacle corrected, monocular high-contrast visual acuity, contrast sensitivity function (CSF) and stereoacuity of 155 cases (16-31years) with mild to advanced bilateral keratoconus was determined using standard psychophysical tests. Disease severity was quantified using the multimetric D-index. The structure-function relationship was modeled using linear, positive exponential, negative exponential, and logistic nonlinear regression equations. The logistic regression model explained the highest proportion of variance for spatial vision, without bias in the residual plots (R2 ≥ 66%, P < 0.001). Visual acuity showed a distinct ceiling phase and a steeper loss rate with increasing D-index (1.8units/D-index) in this model. The area under the CSF lacked this ceiling phase and had a shallower loss rate (0.28units/D-index). Stereoacuity loss with D-index was poorly explained by all models tested (P ≤ 0.2). Cases with lower and bilaterally symmetric D-index had better stereoacuity (181.6-376 arc seconds) than those with higher D-index (>400 arc second); both were significantly poorer than controls (approximately 30 arc second). Vision loss in keratoconus varies with the visual function parameter tested. Contrast sensitivity may be an earlier indicator of spatial vision loss than visual acuity. Depth perception is significantly deteriorated from very early stages of the disease. The study outcomes may be used to forecast longitudinal vision loss in keratoconus and to apply appropriate interventions for timely preservation/enhancement of vulnerable visual functions.

Achieving Real-World Saturated Hydraulic Conductivity: Practical and Theoretical Findings from Using an Exponential One-Phase Decay Model

Obtaining accurate values of saturated hydraulic conductivity (Ksat) is very important for managing all natural or artificial processes involving water flow into soils. Double-ring infiltration (DRI) is one of the easiest-to-work-with techniques commonly used for Ksat determination. Unfortunately, when improperly used, it leads to important variations and inaccurate results. This study was designed to investigate the necessary conditions to reach the true-value or real-world saturated hydraulic conductivity (Ksat-real-world) in the field. For this purpose, the effects of two factors—namely, the measured infiltration data type (cumulative, instant rate, and average rate) and the related non-linear regression equation type—were analyzed. Measurements with DRI were performed with samples from 106 locations in three West African countries, namely, Burkina Faso, Mali, and Cote d’Ivoire. The soils were composed of loam, sandy loam, and sandy clay loam. The results show that when infiltration rates are used rather than cumulative infiltration non-linear regression curves, the variability between the measured Ksat and the real-world saturated hydraulic conductivity (Ksat-real-world) could reach from 2.2% to 58.8%. This variability was caused by the approximate amplification—according to the procedure used—of time-increment measurement errors. Extending the test duration to more than 4 h, especially when clay soils were involved, and using the exponential one-phase decay non-linear regression of the cumulative infiltration data based on a clear measurement protocol provided the Ksat values that were closest to Ksat-real-world.

Research on the Development of Wordle Based on Multi-Model Analysis

Wordle is becoming more and more popular around the world, so it is of great significance to study its healthy development. This paper predicts the number of Wordle 's report results and predicts the percentage of attempts for different words. Firstly, this paper establishes a prediction model of the number of ARIMA report results, and analyzes the relationship between word attributes and the percentage of players in difficult mode. This article collects data on the number of Wordle 's daily reporting results from January 7 to December 31, 2022, and predicts that the number of reporting results in 2023 will be: 10220-10637. This paper constructs three indicators to measure word attributes: the number of vowel letters, the number of affixes and the number of repeated letters. Using Pearson correlation coefficient method and AIC information criterion, according to the correlation coefficient of the three indicators, it is analyzed that there is no relationship between word attributes and the percentage of players in difficult mode. Then, this paper establishes a prediction model of the distribution of the number of attempts, and accurately predicts the percentage of attempts of EERTE words. This paper constructs the data into a lexicon and quantifies the letters. Multiple linear regression equation and multiple nonlinear regression equation were established by using the number of vowel letters, the number of affixes and the number of repeated letters corresponding to each letter in the word. The average number of guessing words and variance were fitted. It was found that the fitting effect of multiple nonlinear regression was better, was 0.805 and 0.821. Finally, the related attributes of “EERIE” were counted, and its distribution percentage was obtained. The results were 0, 1 %, 16 %, 49 %, 29 % and 3 %. The model constructed in this paper can provide some theoretical support for the good development of Wordle.

Multivariate nonlinear regression analysis of hydraulic fracturing parameters based on hybrid FEM–DEM

PurposeThis paper aims to employ a multivariate nonlinear regression analysis to establish a predictive model for the final fracture area, while accounting for the impact of individual parameters.Design/methodology/approachThis analysis is based on the numerical simulation data obtained, using the hybrid finite element–discrete element (FE–DE) method. The forecasting model was compared with the numerical results and the accuracy of the model was evaluated by the root mean square (RMS) and the RMS error, the mean absolute error and the mean absolute percentage error.FindingsThe multivariate nonlinear regression model can accurately predict the nonlinear relationships between injection rate, leakoff coefficient, elastic modulus, permeability, Poisson’s ratio, pore pressure and final fracture area. The regression equations obtained from the Newton iteration of the least squares method are strong in terms of the fit to the six sensitive parameters, and the model follow essentially the same trend with the numerical simulation data, with no systematic divergence detected. Least absolutely deviation has a significantly weaker performance than the least squares method. The percentage contribution of sensitive parameters to the final fracture area is available from the simulation results and forecast model. Injection rate, leakoff coefficient, permeability, elastic modulus, pore pressure and Poisson’s ratio contribute 43.4%, −19.4%, 24.8%, −19.2%, −21.3% and 10.1% to the final fracture area, respectively, as they increased gradually. In summary, (1) the fluid injection rate has the greatest influence on the final fracture area. (2)The multivariate nonlinear regression equation was optimally obtained after 59 iterations of the least squares-based Newton method and 27 derivative evaluations, with a decidability coefficient R2 = 0.711 representing the model reliability and the regression equations fit the four parameters of leakoff coefficient, permeability, elastic modulus and pore pressure very satisfactorily. The models follow essentially the identical trend with the numerical simulation data and there is no systematic divergence. The least absolute deviation has a significantly weaker fit than the least squares method. (3)The nonlinear forecasting model of physical parameters of hydraulic fracturing established in this paper can be applied as a standard for optimizing the fracturing strategy and predicting the fracturing efficiency in situ field and numerical simulation. Its effectiveness can be trained and optimized by experimental and simulation data, and taking into account more basic data and establishing regression equations, containing more fracturing parameters will be the further research interests.Originality/valueThe nonlinear forecasting model of physical parameters of hydraulic fracturing established in this paper can be applied as a standard for optimizing the fracturing strategy and predicting the fracturing efficiency in situ field and numerical simulation. Its effectiveness can be trained and optimized by experimental and simulation data, and taking into account more basic data and establishing regression equations, containing more fracturing parameters will be the further research interests.

Analysis of left-turn behaviors of non-motorized vehicles and vehicle-bicycle conflicts.

In order to further study the expansion characteristics of left-turning non-motorized vehicles at intersections and the relationship between expansion characteristics and vehicle-bicycle conflicts, the trajectory point data of left-turning non-motorized vehicles are extracted using video trajectory tracking technology, and construct the cubic curve expansion envelope equation with the highest fitting degree. For the purpose of quantifying the expansion degree of non-motor vehicles after starting, two intersections in Guangxi Zhuang Autonomous Region were selected for case analysis, and the numerical range of expansion degree of the intersection with a left-turn waiting area and the intersection without a left-turn waiting area was obtained. Study the mathematical relationship between the expansion degree and its influencing factors, and establish the multivariate nonlinear regression equation between the expansion degree and the left-turn non-motorized vehicle flow, the number of parallel non-motorized vehicles, and the left-turn green light time. Analyze the vehicle-bicycle conflicts caused by the expansion of left-turning non-motorized vehicles, determine the essential factors affecting the number of non-motorized vehicles, and establish the multiple linear regression equation between the number of non-motorized vehicles and the number of left-turning non-motorized vehicles, the expansion degree, and the number of parallel non-motorized vehicles, the results show that the model has high accuracy. By analyzing the expansion characteristics of left-turning non-motorized vehicles at intersections, the relationship between different influencing factors and the expansion degree is obtained. Then the vehicle-bicycle conflicts under the influence of expansion characteristics is analyzed, providing theoretical ideas for improving traffic efficiency and optimizing traffic organization at intersections.

Influence of initiation conditions of methane-air mixture on the explosion parameters in the degasation pipeline

Purpose. Increasing the safety of personnel at underground works in case of the threat of gas explosions, including explosion of degassing pipelines by taking into account the influence of the place of initiation of the explosion and the mode of combustion when calculating the parameters of the explosion. Mathematical modeling of the process of ignition and combustion of the methane-air mixture in the degassing pipeline. Research methods. nalysis and generalization of theoretical studies, numerical simulation of gas-dynamic detonation combustion of a gas-air mixture, including a model of chemical combustion kinetics, which, on the whole, allows one to trace the dynamics of formation of shock air waves in conditions of mine workings. Mathematic processing of the results of the experiment by the method of least squares. When solving the nonlinear regression equations, linearization was used by the method of logarithm. Results. It is established that the combustion dynamics of the gas-air mixture has a decisive influence on the formation of UVB: in the deflagration combustion mode of the gas-air mixture, with the initiation at the edge of the cloud, the length of the blast wave is increased 3.6 times in the direction opposite to combustion, and the wave amplitude by 10% spread of flame. In the detonation mode, the effect of a directed explosion is observed, in which the amplitude of the shock air wave is opposite to the motion of the detonation wave 5 times less than in the direct shock air wave. The model of an instantaneous volumetric explosion, in comparison with combustion models, yields an underestimated amplitude value. Scientific novelty. As a result of numerical modeling of the ignition and combustion of the sealed section of the mine atmosphere, regularities in the formation and propagation of shock air waves, the dependence of their parameters on the combustion regime and the location of the initiation of the gas-air mixture were obtained. Practical value. The conducted research allows to improve the method of calculating the resistance of degassing pipelines and their elements to explosive load.

Improvement of the metod of protein content prediction in wheat kernels

The study was conducted in order to expand the possibilities of using the developed multiple nonlinear regression equation, re ecting the dependence of the protein content in wheat grain (Y, %) on the content of raw gluten (X1, %) and the mass of 1000 grains (X2, g). The possibility of practical use of the developed and three improved equations for predicting the protein content of wheat grain is shown. An algorithm and results of checking the prognostic capabilities and accuracy of predict equations from independent data are presented. Generalization of experimental data from 288 literature sources of domestic and foreign authors with a total number of observations n = 4604 on more than three hundred varieties of winter and spring soft and durum wheat grown in the period from 1959 to 2020 in Russia and abroad (Albania, Belarus, Bulgaria, Egypt, Kazakhstan, Lithuania, Poland, Slovakia and Ukraine) showed that the number of values that go beyond to limits regulated by GOST 10846-91 «Protein determination method» was 755 or 16.4 %. At the same time, the accuracy of prediction the protein content reached 83.6 %. The developed equations can be used to predict of protein content in almost all cases: when the results of the analysis of protein content and raw gluten in wheat kernel, as well the 1000-kernels weight are given at actual or fxed moisture content, or in terms of dry matter