Data-driven Power Flow Method Based on Exact Linear Regression Equations

Power flow(PF)is one of the most important calculations in power systems.The widely-used PF methods are the Newton-Raphson PF(NRPF)method and the fast-decoupled PF(FDPF)method.In smart grids,power generations and loads become intermittent and much more uncertain,and the topology also changes more frequently,which may result in significant state shifts and further make NRPF or FDPF difficult to converge.To address this problem,we propose a data-driven PF(DDPF)method based on historical/simulated data that includes an offline learning stage and an online computing stage.In the offline learning stage,a learning model is constructed based on the proposed exact linear regression equations,and then the proposed learning model is solved by the ridge regression(RR)method to suppress the effect of data collinearity.In online computing stage,the nonlinear iterative calculation is not needed.Simulation results demonstrate that the proposed DDPF method has no convergence problem and has much higher calculation efficiency than NRPF or FDPF while ensuring similar calculation accuracy.

Estimations of Parametric Functions under a System of Linear Regression Equations with Correlated Errors

Estimations of parametric functions under a system of linear regression equations with correlated errors across equations involve many complicated operations of matrices and their generalized inverses. In the past several years, a useful tool -- the matrix rank method was utilized to simplify various complicated operations of matrices and their generalized inverses. In this paper, we use the matrix rank method to derive a variety of new algebraic and statistical properties for the best linear unbiased estimators （BLUEs） of parametric functions under the system. In particular, we give the necessary and sufficient conditions for some equalities, additive and block decompositions of BLUEs of parametric functions under the system to hold.

Constitutive equations of 1060 pure aluminum based on modified double multiple nonlinear regression model

In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperatures of 523?823 K and strain rates of 0.005?10 s?1 on a Gleeble?1500 thermo-simulation machine. The influence rule of processing parameters (strain, strain rate and temperature) on flow stress of pure aluminum was investigated. Nine analysis factors consisting of material parameters and according weights were optimized. Then, the constitutive equations of multilevel series rules, multilevel parallel rules and multilevel series &parallel rules were established. The correlation coefficients (R) are 0.992, 0.988 and 0.990, respectively, and the average absolute relative errors (AAREs) are 6.77%, 8.70% and 7.63%, respectively, which proves that the constitutive equations of multilevel series rules can predict the flow stress of pure aluminum with good correlation and precision.

Performance analysis of empirical models for predicting rock mass deformation modulus using regression and Bayesian methods

Deformation modulus of rock mass is one of the input parameters to most rock engineering designs and constructions.The field tests for determination of deformation modulus are cumbersome,expensive and time-consuming.This has prompted the development of various regression equations to estimate deformation modulus from results of rock mass classifications,with rock mass rating(RMR)being one of the frequently used classifications.The regression equations are of different types ranging from linear to nonlinear functions like power and exponential.Bayesian method has recently been developed to incorporate regression equations into a Bayesian framework to provide better estimates of geotechnical properties.The question of whether Bayesian method improves the estimation of geotechnical properties in all circumstances remains open.Therefore,a comparative study was conducted to assess the performances of regression and Bayesian methods when they are used to characterize deformation modulus from the same set of RMR data obtained from two project sites.The study also investigated the performance of different types of regression equations in estimation of the deformation modulus.Statistics,probability distributions and prediction indicators were used to assess the performances of regression and Bayesian methods and different types of regression equations.It was found that power and exponential types of regression equations provide a better estimate than linear regression equations.In addition,it was discovered that the ability of the Bayesian method to provide better estimates of deformation modulus than regression method depends on the quality and quantity of input data as well as the type of the regression equation.

Prediction on adsorption ratio of carbon dioxide to methane on coals with multiple linear regression

The multiple linear regression equations for adsorption ratio of CO2/CH4 and its coal quality indexes were built with SPSS software on basis of existing coal quality data and its adsorption amount of CO2 and OH4. The regression equations built were tested with data collected from some s, and the influences of coal quality indexes on adsorption ratio of CO2/CH4 were studied with investigation of regression equations. The study results show that the regression equation for adsorption ratio of CO2/CH4 and volatile matter, ash and moisture in coal can be obtained with multiple linear regression analysis, that the influence of same coal quality index with the degree of metamorphosis or influence of coal quality indexes for same coal rank on adsorption ratio is not consistent.

Predicting equations of main factors affecting regional climate in the"Three-North" Protective Forest Area

The relationship between the change of forest resources and climatic factor in the, “Three-North” region of China were studied in this paper. The predicting equations of climatic factor (dependent variable) with regional independent variable (longitude, latitude and altitude) and stand independent variable (forest coverage rate), were developed by extensively using the linear and nonlinear regression methods. With these models, we can calculate the ecological benefit of Shelter-belt forest.

New empirical model to evaluate groundwater flow into circular tunnel using multiple regression analysis

There are various analytical, empirical and numerical methods to calculate groundwater inflow into tun- nels excavated in rocky media. Analytical methods have been widely applied in prediction of groundwa- ter inflow to tunnels due to their simplicity and practical base theory. Investigations show that the real amount of water infiltrating into jointed tunnels is much less than calculated amount using analytical methods and obtained results are very dependent on tunnel＇s geometry and environmental situations. In this study, using multiple regression analysis, a new empirical model for estimation of groundwater seepage into circular tunnels was introduced. Our data was acquired from field surveys and laboratory analysis of core samples. New regression variables were defined after perusing single and two variables relationship between groundwater seepage and other variables. Finally, an appropriate model for estima- tion of leakage was obtained using the stepwise algorithm. Statistics like R, R2, R2e and the histogram of residual values in the model represent a good reputation and fitness for this model to estimate the groundwater seepage into tunnels. The new experimental model was used for the test data and results were satisfactory. Therefore, multiple regression analysis is an effective and efficient way to estimate the groundwater seeoage into tunnels.

Infrared thermography for prediction of spontaneous combustion of sulfide ores

The method of infrared thermography to predict the temperature of the sulfide ores has a large error. To solve this problem, the temperature of the sulfide ores is measured by thermal infrared imager and recording thermometric instrument contrastively. The main factors, including emissivity, distance, angle and dust concentration that affect the temperature measurement precision, are analyzed. The regression equations about the individual factors and comprehensive factors are obtained by analyzing test data. The application of the regression equations improves the precision of the thermal infrared imager. The geometric information lost in traditional infrared thermometry is determined by visualization grid method and interpolation method, the relationship between the infrared imager and geometry information is established. The geometry location can be measured exactly.

Influence of Tire Slip Angle on Adhesion CoefficientCharacteristic of Road Vehicles

Tire slip angle has a great influence on peak values of both logitudinal and lateral adhesion coefficients as well as optimal slip ratios. Regression equations based on the experi- mental data from several countries are given to describe their dependencies. The peak value of longitudiinal adhesion coefficient has a linear relationship with tire slip angle, but peak value of lateral has a complicated relationship; the optimal slip ratio of longitudinal has an exponent function relationship, the optimal slip ratio of lateral almost has nothinng to do with tire slipangle.

Interpretation of 850 hPa Temperature in Temperature Forecast of Jiamusi Area

Based on the initial field temperature data of ECMWF 850 hPa from Jan- uary 2012 to December 2015, linear interpolation method of ECMWF was employed to calculate the 850 hPa temperature values at 8：00 and 20：00 of 7 stations （Jiamusi, Tangyuan, Huachuan, Huanan, Fujin, Tongjiang, Fuyuan）. Combined with the observed daily minimum and maximum air temperatures at the same time of the 7 stations, the correlations of the 850 hPa temperature values at 8：00 and 20：00 with the daily maximum or minimum air temperature of the ground meteorological obser- vation stations were established, and the ground observation data in accordance with the relevant analysis and correlation test principle of the prediction equation for factor were primarily selected. Regression method was used to establish forecast e- quation dividing into counties, month by month. The results showed that the 850 hPa temperature values at 8：00 and 20：00 were significantly correlated with the daily maximum or minimum air temperature, and the established temperature fore- cast equation was of certain guiding significance for the forecast of daily minimum and maximum temperature, which could help to improve the forecast accuracy.

Impacts of Excessive Soaking on N, P, and K in Substrates Plots and Seedling Growth

[Objective] The aim was to study on impacts of excessive soaking N, P, and K insubstrate plots of and seedling growth. [Method] Substrate was designed to add additional 1/2 water after saturation and expansion. Disposable excessive soak- ing and regression relation of nutrition infusion of substrate plots were studied by design of 13 time gradient. Plant nutrition absorption and growth effects after sub- strate plots immersed by water were investigated by growing tomato. [Result] Con- centration and time of the three nutrition immersed in water had the regression equation of each, as follows： N=-2E-05t2＋0.016 lt＋2.0553, P=0.002 2t＋2.248 5 and K=0.004 7t＋0.875 8. With nutrition loss of the three, however, loss amount was al- most same with variance analysis of regression equation, which may result from its volatilization. Regression equations of P and K were： P=0.125 7t-0.117, and K=0.022 5t.1514, which led to adverse impact on plant absorption of N and K above ground, whose equations were N=20.64e-4E-0.4t, and K=E-06t2-0.011 3t＋29.055. Meanwhile, un- der the condition, sound seedling index was not impacted a lot by excessive immer- sion. [Conclusion] This study has provided theoretical reference for guidance of sub- strate plot soaking method, cultivation and regulation, and breeding, as well as agri- cultural production.

Analyses of prognostic indices of chronic liver failure caused by hepatitis virus

AIM: To analyze the related indices about the prognoses of chronic liver failure caused by hepatitis virus. METHODS: Retrospectively reviewed 320 cases of chronic liver failure caused by hepatitis viruses. An improved group and an ineffective group (IG) were made to compare and analyze their clinical manifestations, laboratory examination indices and complications. Logistic regression was also carried out. RESULTS: There were significant differences (P<0.05) between the improved group and the IG upon such indices as age, bilirubin, prothrombin time, albumin, alpha fetoprotein, the size of liver and complications (P<0.05). The regression formula was as follows: P=1/(1+e^(-y)) (y=1.7262-0.0948X_1+2.9846X_2+0.6992X_3+1.6019X_4+2.0398X_5). (Note: X_1-Prothrombin activity; X_2-digestive tract hemorrhage; X_3-hepatic encephalopathy; A_4-hepatorenal syndrome; X_5-pulmonary infection.). CONCLUSION: Laboratory examination such as bilirubin, prothrombin time and alpha fetoprotein can be regarded as indices of the prognoses of chronic liver failure caused by hepatitis. Moreover, the regression equation can evaluate prognoses more comprehensively and direct our treatments.

Estimation of above-ground biomass and carbon stock of an invasive woody shrub in the subtropical deciduous forests of Doon Valley,western Himalaya,India

This study describes the different parameters used to derive the allometric equation for calculating the biomass of an invasive woody shrub Lantana camara L.from the subtropical conditions of western Himalaya.It identifies the most accurate and convenient method for biomass calculation by comparing destructive with nondestructive methodology.Different parameters were measured on a wide range of Lantana from different community levels for the non-destructive calculation of total aboveground biomass.Different explanatory variables were identified and measured such as basal diameter either as a single independent variable or in combination with plant height.The other suitable combinations of available independent variables include crown length,crown width,crown area,crown volume and coverage of the plant.Amongst the wide range of allometric equations used with different variables,the equation with D2 H as a variable was found to be the most suitable estimator of biomass calculation for Lantana.Sahastradhara,being the most disturbed area due to its high tourist activity round the year,showed maximum coverage（58.57 % ha-1）,highest biomass（13,559.60 kg ha-1） and carbon density（6,373.01 kg ha-1）of Lantana.The degree of Lantana’s invasiveness in subtropical conditions was also calculated on the basis of importance value index（IVI）.The maximum IVI（22.77）and mean coverage（26.8 % ha-1） was obtained from the areas near Jolly Grant airport,indicating that physically disturbed areas are more suitable for the growth of Lantana,which may significantly increase shrub biomass.The importance of incorporating allometric equations in calculation of shrub biomass,and its role in atmospheric carbon assimilation has thus been highlighted through the findings of this study.

Carbon storage and sequestration rate assessment and allometric model development in young teak plantations of tropical moist deciduous forest, India

Carbon （C） sequestration through plantations is one of the important mitigation measures for rising levels of carbon dioxide and other greenhouse gases in the atmosphere. This study aimed to assess C stocks and their sequestration rate, and to develop allometric models for estimation of C stocking in age-series young teak （Tectona grandis） planta- tions （1, 5, 11, 18, 24 and 30 years） by using biomass and productivity estimation and regression, respectively. These plantations were raised in tropical moist deciduous forests of Kumaun Himalayan tarai. Total C stocks estimated for these plantations were 1.6, 15.8, 35.4, 39.0, 61.5 and 73.2 Mg ha-1, respectively. Aboveground and belowground C storage in- creased with increasing plantation age; however, the range of their percentage contribution showed little variation （87.8-88.2 and 11.7-12.7 %, respectively）, The rate of C sequestration for these respective plantations was 1.06, 6.95, 5.46, 5.42, 3.39 and 5.37 Mg ha-1 a-1. Forty percent of the aboveground annual storage was retained in the tree while 60 % was released in the form of foliage, twigs, and fruit litter. In the case of total （tree） annual production, 43 % was retained while 57 % was released as litter including root. C stock, C sequestration rate, accumulation ratio （1.4-18.1）, root：shoot C ratio （0.61--0.13） and production efficiency （0.01-0.18） were comparable to some previous reports for other species and forests. These data could be useful in deciding the harvesting age for young teak with respect to C storage and sequestrationrate. Four allometric models using linear regression equations were developed between biomass （twice the C stock） and diameter, girth, and height of the tree at different ages. The diameter model was found more suitable for C stock predic- tion in similar areas.

Characterization of larval instars of artemisia weevil,Adosomus sp.

The artemisia weevil, Adosomus sp., has become an important wormwood （Artemisa ordosoca and A. sphaerocephala） pest in recent years in Ningxia Province, China. The number of larval instars should be determined before further studies on its life history, biology and integrate management of pest （IMP）. In this study, we measured the length and width of head capsule, based on frequency histograms and Dyar＇s law, from which we concluded that the larvae ofAdosomus sp. have four instars. Of the two variables measured, the width of head capsule provided the best division of instars. The average width of head capsule of the 1st instar larvae was 1.348±0.152 mm, the 2nd 2.109±0.199 mm, the 3rd 3.563±0.492 mm and the 4th 5.974±0.581 mm.

Comprehensive modeling approach of axial ultrasonic vibration grinding force

The theoretical model of axial ultrasonic vibration grinding force is built on the basis of a mathematical model of cutting deforming force deduced from the assumptions of thickness of the undeformed debris under Rayleigh distribution and a mathematical model of friction based on the theoretical analysis of relative sliding velocity of abrasive and workpiece. Then, the coefficients of the ultrasonic vibration grinding force model are calculated through analysis of nonlinear regression of the theoretical model by using MATLAB, and the law of influence of grinding depth, workpiece speed, frequency and amplitude of the mill on the grinding force is summarized after applying the model to analyze the ultrasonic grinding force. The result of the above-mentioned law shows that the grinding force decreases as frequency and amplitude increase, while increases as grinding depth and workpiece speed increase; the maximum relative error of prediction and experimental values of the normal grinding force is 11.47% and its average relative error is 5.41%; the maximum relative error of the tangential grinding force is 10.14% and its average relative error is 4.29%. The result of employing regression equation to predict ultrasonic grinding force approximates to the experimental data, therefore the accuracy and reliability of the model is verified.

Effects of Morphological Traits on Total Weight of Clam Meretrix lamarchii

Clam Meretrix lamarchii is delicious seafood with high economic value. The M. lamarchii in present market is mainly collected from wild population due to the lack of large-scale artificial seed production. In 2013,we carried out the artificial seedling exploration of M. Lamarchii. The current study utilized several statistical methods to analyze the effects of morphological traits on M. Lamarchii,which may provide knowledge for clam quality seedlings breeding work. The samples of M. Lamarchii were randomly sampled from Donghai Island,Zhanjiang. Shell length（ SL）,shell width（ SW）,shell height（ SH）,ligament length（ Li L）,lunule length（ Lu L） and total weight（ TW） of two-year-old M. Lamarchii were measured. A correlation coefficient matrix was constructed based on the results,where the total weight was set as the dependent variable and others as independent variables. Path coefficient and correlation index were calculated,and the major phenotypic characters were determined. The results showed that all the correlation coefficients between independent variables and dependent variable were significant（ P < 0. 01）,with an exception of the lunule length（ P > 0. 05）. The effects of the shell length,shell width,and shell height on the total weight were significant（ P < 0. 01）,and the shell length had dominant effect on the weight as a key effective factor. The multiple regression equation between the weight and the other traits was established as Y;=- 126. 784 + 1. 249X;+ 2. 036X;+ 0. 911 X;,where YWis total weight,X;,X;and X;are the shell length,shell width and shell height,respectively. The current study may contribute to the artificial breeding of the species.

Resistance characteristics of the ball packed-bed regenerator of the new-type swirl flow hot blast stove

A renovation project of miniaturization and high efficiency is provided for the hot blast stove .The experimental data tested feasibility of the new-type swirl flow hot blast stove. The normal and hot state experiments have been done through changing the angle of gas entering into the regenerator. Factors influencing pressure drop have been studied and analyzed. The experimental results can be formulated in the form of the Ergun equation. The regression equation is obtained. And two modified coefficients are offered to the regenerator pressure drop of the new-type swirl flow hot blast stove.

Soil CO_2 evolution from Korean pine virgin forest at Changbai Mountain

The soil CO2 evolution rate was measured in a virpin Korean pine forest. The results in June showed that the lowest value of evolution rate was 220 mg /(m2·h) and appeared at 6:00 a.m. The highest value was 460 mg /(m2·h) at 18:00. The rates of CO2 evolution were related with soil temperature. On the basis of the constructed regression equation and the monthly average values of temperature, the magnitude of CO2 evolution from Korean pine forest soil was 10.4 t /hm2 during a growing season.

Correlation between coal characteristics and methane adsorption on China＇s coals

It is highly important to investigate relationship between coal characteristics and methane adsorption on coal in the fields of coalbed methane recovery. Based on data examination of coal quality indexes collected from the literatures, regression equations for Langmuir adsorption constants, VL or VLIPL, and coal quality indexes for selected coal samples were developed with multiple linear regression of SPSS software according to the degree of coal metamorphosis. The regression equations built were tested with data collected from some literatures, and the influences of coal quality indexes on CH4 adsorption on coals were studied with investigation of regression equations, and the reasons of low accuracy to Langmuir constants calculated with regression equation for a few coal samples were investigated. The results show that the regression equations can be employed to predict Langmuir constants for methane adsorption isotherms on coals obtained using volumetric gas adsorption experiments, which are conducted at 30 ℃ on a wet or dried coal samples with less than 30% ash content in coal. The influence of same coal quality index with various coal rank or influence of various coal quality indexes for same coal rank on CH4 adsorption is not consistent. The regression equations have different accuracy to different coal rank, in which the VL equations supply better prediction accuracy for anthracite and higher prediction error for lower metamorphosis coal, and the PL prediction error with VL and VL/PL equations is lower to bituminous coal and higher to anthracite.