Relative Calculation Error Research Articles

RECONSTRUCTION AND PREDICTION OF WATER BALANCE COMPONENTS FROM DENDROCHRONOLOGICAL DATA FOR THE NARYN RIVER BASIN (KYRGYZSTAN)

Suggested new method for reconstruction of runoff includes: 1. Search informative points based weather observations for dependence runoff = f(climate index). Climate index consists of normalized anomalies of annual precipitation and air temperature, together with water vapor pressure and total cloud amount in the June–September. 2. The selection of sites that represent local relationship between the index of climate and tree rings. 3. Getting the multivariate linear regression equation between the runoff V and tree rings D . Basic climatic period 1961–1990 is used as a calibration interval of time. Verification of the equations for 1940–1960 identified the need to use other arguments in addition to the width of tree rings. For this purpose, two climate index: PDSI and SPEI were tested. It is established that the empirical formulae V = f ( D , PDSI ) and V = f ( D , SPEI ) are suitable for assessing the annual flow of the Naryn in 1901–2006. In the report is described a process of reconstruction of flow for the years 1700–2005 based on the data of the width of the tree rings, and taking into account the temporal variability of parameters of regression equations. Chronologies of the width and density of tree rings in the thirty-two tree ring sites were used to reconstruct long-term series of average summer air temperature Ts at meteorological stations of the Pamir and Tien Shan. The calibration interval of time was 1961–1990 to find equations T s = f ( D ) of third-order multiple regression, and independent control of their quality, done in 1932–1960. Combined correlation coefficient in 10 cases out of 15 was more than 0.80, a relative error of calculation T s in 19611990 ranged from 0.13 to 4.73%, and in 1932–1960 from 0.23 to 8.10%. Duration of the reconstructed series T s ranged from 100 to 278 years. Positive results were received for predicting a common and glacial runoff of Naryn river, a long-term range of density of tree rings.

In Silico Multivariate Regressio n Analysis and Validation Studies on Selective MMP-13 Inhibitors

QSAR(Quantitative Structure Activity Relationship) studies were carried out on a set of 72 α-sulfone hydroxamatesas Matrix Metalloproteinase-13 (MMP-13) inhibitors using multiple regression procedure. Outliers were removed based on Relative Error calculation and Extent of Extrapolation. The activity contributions of these compounds were determined from regression equation and the validation procedures such as external set cross-validation r, (R2cv, ext) and the regression of observed activities versus predicted activities and vice versa for validation set was described to analyze the predictive ability of the QSAR model. Parameters concerning predictive ability of QSAR model and Y-randomization tests were found to be within the limits. From a set of 5 models, an accurate and reliable QSAR model involving six descriptors was chosen based on the FIT Kubinyi function, which defines the statistical quality of the model. The generated model could be useful in designing more potent inhibitors of MMP-13.

Electric heating of the silicon rods in Siemens reactor

In the Siemens reactor, all the energy is supplied by the heat generation on silicon rods which are heated up by the passage of current, the center of the rods will become hotter than the surface which is maintained ideally at 1373K. Understanding the thermal and electrical behaviors of silicon rods in electric heating process is crucial for an optimal operation of the Siemens reactor. In the present paper, the electric heating model of silicon rod for the 24-rod Siemens reactor has been developed. In order to verify the present model valid, calculated results by application of the model were compared with industrial data. The results show that comparing to the industrial data obtained using a 24-rod Siemens reactor, the relative error of theoretical calculations are 7.32% and 9.41% for the rods located in the inner ring and outer ring, respectively. Based on the developed model, the influence of the location of silicon rods within Siemens reactor and reactor wall emissivity during electric heating process has been investigated. Interesting results show that the temperature gradient of silicon rods located in the outer ring is larger than the inner ones when the rods are heated up by direct current (DC). The temperature gradient within the rod becomes smaller and the required voltage and current decreases when the emissivity of the reactor wall surface decreases. Two interesting ways to reduce energy consumption can be deduced: increasing radius of the rod at the end of the process and decreasing the wall emissivity by wall surface treatment or/and selecting more appropriate materials.

Mass flow stability method in the extraction process calculations

Mass flow stability method, allowing to clarify the existing analytical dependences for calculating the target component withdrawal from the classical-shape bodies (unlimited plate, cylinder, sphere) was proposed. On the example of the III class bodies, application of the method is shown. A mathematical model of the target component extraction from the round particle was developed and the dependence to calculate the concentration was obtained. Consideration of the real body shape deviations from perfect in the form of the shape factor allows to refine the design value for the bodies, corresponding to the III class. It was found that the deviation of the concentration values for the perfect body from real would be the greater, the smaller the particle radius. The maximum relative error of calculations is 11.3 %. It is shown that the target component extraction process is rather complicated and depends strongly on a large number of defining physical characteristics: particle size, diffusion coefficient, mass transfer coefficient, temperature, duration.

Mathematical model of heat transfer during the extraction of particles of ideal (spherical) and real forms

Mass flow stability method, allowing to clarify the existing analytical dependences for calculating the target component withdrawal from the classical-shape bodies (unlimited plate, cylinder, sphere) was proposed. On the example of the III class bodies, application of the method is shown. A mathematical model of the target component extraction from the round particle was developed and the dependence to calculate the concentration was obtained. Consideration of the real body shape deviations from perfect in the form of the shape factor allows to refine the design value for the bodies, corresponding to the III class. It was found that the deviation of the concentration values for the perfect body from real would be the greater, the smaller the particle radius. The maximum relative error of calculations is 11.3%. It is shown that the target component extraction process is rather complicated and depends strongly on a large number of defining physical characteristics: particle size, diffusion coefficient, mass transfer coefficient, temperature, duration.

Comparative study of the stress flow models for high-boron corrosion-resistant steel based on an Arrhenius-type equation and artificial neural networks

A comparative analysis is performed for the stress flow models of a steel containing 2.3 wt % B during its compressive hot deformation based on an Arrhenius-type equation and artificial neural networks. It is shown that the accuracy of the obtained data using the model based on artificial neural networks is much higher (relative calculation error is 0.2%) as compared to that of the regression model (relative error is 11%).

Which data for quantitative landslide susceptibility mapping at operational scale? Case study of the Pays d'Auge plateau hillslopes (Normandy, France)

Abstract. This paper aims at assessing the impact of the data set quality for landslide susceptibility mapping using multivariate statistical modelling methods at detailed scale. This research is conducted on the Pays d'Auge plateau (Normandy, France) with a scale objective of 1 / 10 000, in order to fit the French guidelines on risk assessment. Five sets of data of increasing quality (considering accuracy, scale fitting, and geomorphological significance) and cost of acquisition are used to map the landslide susceptibility using logistic regression. The best maps obtained with each set of data are compared on the basis of different statistical accuracy indicators (ROC curves and relative error calculation), linear cross correlation and expert opinion. The results highlight that only high-quality sets of data supplied with detailed geomorphological variables (i.e. field inventory and surficial formation maps) can predict a satisfying proportion of landslides in the study area.

大口径宽波段高能激光发射窗口的设计与测试

An automatic shutter-type mechanical window was designed for the multi-band, high-power and large-caliber laser launch system to meet the requirements of complex service environment for long interval emission and crystal window. The window is composed of two parts of the dust cover: pressing mechanism and driving mechanism. By using transmission links, such as screw, wire rope, and time synchronous belt, the pressing mechanism realizes multi-task driving of a single motor synchronously and the flexible hinges compensate installation errors. Then the relationship between wind pressure forced on dust cover and pressing force of the pressing mechanism was analyzed by nonlinear analysis methods and integral principles. The expression of wind pressure and motor torque was established by inverse method. According to the relationship of motor torque and frequency, the rotating speed range of the mechanism and the largest wind pressure of the dust cover were calculated. Experimental results show when the motor output torque is 0.341 Nm, the mechanism can resist the impact of wind of 10 m/s. The least intervals of the window are stably within 3 s no matter it is opened or closed. The relative calculation error of the expression between wind pressure and motor output torque is less than 15%, which satisfies working requirements of systems.

Study of a Method for Identification of Parameters of the Nonlinear Equivalent Circuit of Electric Admittance of Skin

Biophysical mechanisms of formation of nonlinear electric properties of skin are discussed. The possibility of corneal layer monitoring during transdermal delivery of medication, examination of skin moisture, and evaluation of functional and psychoemotional state is demonstrated. The suggested monitoring technique is based on measurements of linear and nonlinear components of electric admittance of skin. As a result of research on the nonlinear equivalent circuit of electric admittance of skin, errors in measurement of its parameters for third-order power series approximation of skin conductance are determined. The interconnections between the relative error of calculation of polynomial coefficients, the electric capacity, the corneal layer hydration rate, and the normalized magnitude of interference caused by near-electrode electrochemical processes, as well as industrial power-line noise, are established.

Flexural model for a notched beam: Direct and inverse problems

Matching conditions simulating a transverse notch in a beam are proposed. These conditions are used to determine the location and size of the notch. The notch is identified from beam deflections at several points in the static case and from the first eigenfrequencies of the beam in the dynamic case. Dependences of the first eigenfrequencies on the characteristic parameters of the problem are obtained. The effect of the relative error of frequency measurements on the relative error of calculation of the notch parameters is studied. It is shown that the use of the first eigenfrequencies of flexural vibrations of the beam with respect to different axis provides a more accurate identification than the use of eigenfrequencies of flexural vibrations relative to one axis. Since local defects such as hollows, local corrosion, and an open crack can be simulated by a notch, the results can also be used to identify these defects.

Calculation model of AC loss for CICC (cable-in-conduit conductor) based on strain

The CICC (cable-in-conduit conductor) in ITER (International Thermal-nuclear Experimental Reactor) will run in high-current, fast transient magnet field and complex environment. In response to the impact of magnet fields above 10 T, the Nb3Sn conductor has been introduced. However, the AC (alternating current) loss mechanism of Nb3Sn conductor on strain has not been explored. So, it is necessary to study the AC loss calculation method with transient electromagnetic field and wide range of strain, the coupling current in complex field and current signal of field is simplified to the spectrum effects of coil excitation, and calculation technology of AC loss, which contains the frequency, magnet field, coil characteristics and other parameters, is constructed to meet the discrete Fourier transform (DFT). By comparative analysis of simulation, it is found that the AC loss calculation of the conductor with spectrum algorithm is closer to the actual project value than the traditional algorithm. For the rapid excitation, in particular plasma discharge and burst, spectrum algorithm and the traditional algorithm are consistent. For the relative error calculation of hysteresis loss and coupling loss, it is found that the coupling loss is cumulative linearly, where the hysteresis loss is not so. As a function of the amplitude, frequency and phase angle, the relative error is less than 40%. The results showed that the method of Fourier restructuring is satisfactory.

Errors in the use of the Koutecky–Levich plots

A frequently employed method for the diagnosis of electrochemical mechanisms is the Koutecky–Levich (KL) method. This method is based on the extrapolation of the reciprocal of the current intensity (or density) versus the reciprocal of the square root of the rotational rate of a rotating disc electrode (plot 1 /j vs . ω − 1/2 ). From the intercept and slope of this plot, several diffusional and kinetic parameters of the mechanism can be obtained. In this article, the relative error of j k (kinetic current density term) and of k 0 (standard rate constant) is estimated and discussed. Moreover, the relative error calculation is also estimated for the case when none of the kinetic terms in the KL expression (forward and backward reactions) can be disregarded.

Estimation of residual magnetization of steel items with a low demagnetizing factor by coercive force

An equation is developed for calculation of residual magnetization of steel items using the coercive force of their material and demagnetizing factor N. The relative calculation error for items with low N (for which the known equation provides physically invalid results) is not higher than 30%.

Precision of Earthwork Computation by Grid

Based on theoretical models,the accuracy is analyzed to earthwork calculation in grid method under different terrain rolling rates, different grid widths.And the basic relationship between relative error of theoretical calculation and grid and terrain parameters is obtained, which can be used for evaluation of practical earthwork calculation.

A neural network approach for predicting steel properties characterizing cyclic Ramberg-Osgood equation

This paper attempts to demonstrate the applicability of artificial neural networks to the estimation of steel properties, cyclic strain-hardening exponent and cyclic strength coefficient, characterizing cyclic Ramberg-Osgood equation on the basis of monotonic tensile test properties. For this purpose, steel tensile data were extracted from the literature and two separate neural networks were constructed. One set of data was used for training the two networks and the remaining for testing purposes. Regression analysis and mean relative error calculation were used to check the accuracy of the system in the training and testing phases. Comparison of the results obtained from the neural networks and the values obtained from direct fitting of experimental data, indicated the reasonable prediction of cyclic strain-hardening exponent and cyclic strength coefficient, which are often used to characterize the cyclic deformation curve by a Ramberg-Osgood type equation.

Estimation of the field strength of a low-frequency ionospheric source in the vicinity of the main maximum of distribution on the Earth surface

Simple analytical formulas are derived to estimate the parameters of the main maximum in the surface distribution of the field strength for the low-frequency source located in the Earth ionosphere. The dependences of the relative calculation errors on the source frequency and position are presented. The resulting formulas are applied for loop antennas and for the wave propagation in geomagnetic waveguides (ducts).

Numerical Study on Convection Diffusion for Gasification Agent in Underground Coal Gasification (UCG). Part II: Determination of Model Parameters and Results Analysis

The determination methods of the major model parameters are explained in this article, and the upstream weighted multi-cell balance method is adopted to solve the numerical models established. The author also analyzes and discusses the simulated calculation results, which show that, except for very few points in the loosening zone, where the relative calculation error is comparatively high resulting from the low oxygen concentration, the relative calculation error of other points falls between 8% and 19%. Therefore, the calculation value and the experiment value take on a good conformity. The simulated results indicate that the calculation value of the oxygen concentration is a little bit lower than the experiment one. On top of that, with the prolonging of gasification time, in a high temperature zone the change gradient of oxygen concentration for experimental value is bigger than that of the calculation value. The oxygen concentration is in direct proportion to its distance from the flame working face, i.e., the longer its distance is, the higher the oxygen concentration is; otherwise, the lower the oxygen concentration is.

A “Hydrokinematic” Method of Measuring the Glide Efficiency of a Human Swimmer

The aim of this study was to develop and test a method of quantifying the glide efficiency, defined as the ability of the body to maintain its velocity over time and to minimize deceleration through a rectilinear glide. The glide efficiency should be determined in a way that accounts for both the inertial and resistive characteristics of the gliding body as well as the instantaneous velocity. A displacement function (parametric curve) was obtained from the equation of motion of the body during a horizontal rectilinear glide. The values of the parameters in the displacement curve that provide the best fit to the displacement-time data of a body during a rectilinear horizontal glide represent the glide factor and the initial velocity of the particular glide interval. The glide factor is a measure of glide efficiency and indicates the ability of the body to minimize deceleration at each corresponding velocity. The glide efficiency depends on the hydrodynamic characteristic of the body, which is influenced by the body's shape as well as by the body's size. To distinguish the effects of size and shape on the glide efficiency, a size-related glide constant and a shape-related glide coefficient were determined as separate entities. The glide factor is the product of these two parameters. The goodness of fit statistics indicated that the representative displacement function found for each glide interval closely represents the real displacement data of a body in a rectilinear horizontal glide. The accuracy of the method was indicated by a relative standard error of calculation of less than 2.5%. Also the method was able to distinguish between subjects in their glide efficiency. It was found that the glide factor increased with decreasing velocity. The glide coefficient also increased with decreasing Reynolds number. The method is sufficiently accurate to distinguish between individual swimmers in terms of their glide efficiency. The separation of glide factor to a size-related glide constant and a shape-related glide coefficient enabled the effect of size and shape to be quantified.

Increase in the accuracy of evaluating spectra of discrete signal realization

An improved algorithm for calculating spectra with the use of a rapid Fourier transform and quadrature equations of the trapezium and Simpson’s methods is considered. The relative error of calculation by comparing the relative deviation of a continuous spectrum of final realization of the signal from spectra, found by means of improved algorithms at a discrete set of frequencies, is analyzed. A more precise initial estimation of a spectrum is obtained using the improved calculation algorithms.

Three-Dimensional Unstable Non-linear Numerical Analysis of the Underground Coal Gasification with Free Channel

The three-dimensional unstable non-linear coupled mathematical model on the underground coal gasification with free channel is established in this article. The determination methods for the major model parameters are explained. Adopting the SIMPLE method, the numerical solution of the mathematical model is found. Additionally, the patterns of variation and development for the temperature field, concentration field and pressure field in the gasification panel are studied. On the basis of the model test, the calculation results are analyzed. Research shows that calculated values of the temperature field are a little higher than the experimental ones, and the relative error for every measuring point is virtually within 16%. Also, a good conformity takes on between the experimental values for the concentration field of the gas compositions and the calculated ones. The simulated results indicate that the relative calculation error of the pressure field is 10.20%–19.44%. Through the analysis of measured data, the change mechanisms of the gas compositions, heating value and pressure field in the underground gasification with free channel are pointed out.