High-order Polynomial Fitting Research Articles

DYNAMIC RECRYSTALLIZATION AND PRECIPITATION BEHAVIORS OF A KIND OF LOW CARBON V–MICROALLYED STEEL

By using thermo-mechanical simulator,OM and TEM,the dynamic recrystallization (DRX) and precipitation behaviors of a kind of low carbon V-microalloyed steel have been investigated at temperatures ranging from 900 to 1050℃and strain rates from 0.01 to 10 s~(-1).The activation energy (Qdef) for hot deformation of this kind of V-microalloyed steel was calculated to be 341.97 kJ/mol by regression analysis,while the apparent stress exponent(n) was calculated to be 4.24.The equation describing the hot working process was also obtained.The critical strain for DRX was accurately determined based on the P-J method and high order polynomial fitting between strain hardening rate and true stress,and mathematical models of critical strain and peak strain versus Z parameter were deduced.The dynamic precipitation behavior of V(C,N) particles at low strain rate was further investigated.The results show that with increasing the strain,the average size of V(C,N) particles increases and the size distribution of the precipitates become wide.The calculations of the driving force for recrystallization and pinning force show that once the dynamic recrystallization take place, the dynamic precipitation could not prevent dynamic recrystallization from occurring.

An empirical method to estimate the viscosity of mineral oil by means of ultrasonic attenuation

This paper presents an empirical method for measuring the viscosity of mineral oil. In a built-in pipeline application, conventional ultrasonic methods using shear reflectance or rheological and acoustical phenomena may fail because of attenuated shear wave propagation and an unpredictable spreading loss caused by protective housings and comparable main flows. The empirical method utilizing longitudinal waves eliminates the unknown spreading loss from attenuation measurements on the object fluid by removing the normalized spreading loss per focal length with the measurement of a reference fluid of a known acoustic absorption coefficient. The ultrasonic attenuation of fresh water as the reference fluid and mineral oil as the object fluid were measured along with the sound speed and effective frequency. The empirical equation for the spreading loss in the reference fluid is determined by high-order polynomial fitting. To estimate the shear viscosity of the mineral oil, a linear fit is applied to the total loss difference between the two fluids, whose slope (the absorption coefficient) is combined with an assumed shear-to-volume viscosity relation. The empirical method predicted the viscosities of two types of the mineral oil with a maximum statistical uncertainty of 8.8% and a maximum systematic error of 12.5% compared with directly measured viscosity using a glass-type viscometer. The validity of this method was examined by comparison with the results from theoretical far-field spreading.

Study on Static Deformation Characteristics of Mental Rubber Material

Mental rubber material is a new kind of high elastic and large damping material. In this paper the static deformation of mental rubber components had been studied from stretch, compression and shearing experiment. By the method of high-order polynomial fitting, the empirical formula of static deformation characters of mental rubber component had been established, and some deformation rules of mental rubber had been obtained.

A windowing-recursive approach for GPS real-time kinematic positioning

All conventional Kalman filtering methods depend to a great extent on dynamic models for describing the motion state of vehicle. However, low-cost GPS navigation systems do not provide velocity and acceleration measurements to construct dynamic models. Therefore, it is rather difficult to establish reasonable dynamic models. A windowing-recursive approach (WRA) which employs previous positions to predict the current position is proposed, and the transition matrix is modeled for transforming the previous positions to the current one. Two typical transition matrices are constructed by numerical polynomial fitting and extrapolation. A real vehicular GPS experiment is carried out to demonstrate the WRA performances in two relative positioning scenarios. The data are processed by the least squares approach and by WRA using the two developed transition matrices. The results show that the WRA performed excellently in a high sampling rate data. In case of a lower sampling rate, higher-order polynomial fitting and extrapolation models work better than lower-order models for a given window. In addition, the extrapolation models can alleviate the computation burdens significantly relative to the polynomial fitting models.

Sensitivity analysis of an inverse procedure for determination of elastic coefficients for strong anisotropy

The elastic coefficients of anisotropic solids are often evaluated from measurements of phase or group velocities of ultrasonic bulk waves by the usage of inverse optimizing procedures. This paper discusses the effects of various factors on such procedures results for transversely isotropic solids with considerably strong anisotropy. First, the inverse determination of all elastic coefficients of unidirectional CFRP composite is briefly outlined. Then the results of the optimization are treated as exact values and the sensitivity of the optimizing process versus main considered sources of inaccuracies is analyzed. Results of extensive simulations are presented to illustrate the effect of input data distortion, input data incompleteness, and geometrical conversion from experimentally obtained group velocities into corresponding phase velocities used as input data for the optimizing procedure. The paper takes note of how information about the elastic coefficients can be extracted from the different segments of the phase velocity surface. The stability versus input data distortion for inversion from group velocities and phase velocities is compared and the importance of reliable geometrical converting from group into phase velocities is illustrated. An novel method for geometrical conversion of distorted group velocity data into corresponding phase velocities based on affine combinations of low-order polynomials is presented and compared with piecewise or high-order polynomial fitting.

Local polynomial fitting under association

We consider the estimation of multivariate regression functions r( x 1,…, x d ) and their partial derivatives up to a total order p⩾1 using high-order local polynomial fitting. The processes { Y i , X i } are assumed to be (jointly) associated. Joint asymptotic normality is established for the estimates of the regression function r and all its partial derivatives up to the total order p. Expressions for the bias and variance/covariance matrix (of the asymptotic distribution) are given.

Multivariate regression estimation of continuous-time processes from sampled data: local polynomial fitting approach

Let (Y,X)={Y(t),X(t),-/spl infin/<t</spl infin/} be real-valued continuous-time jointly stationary processes and let (t/sub j/) be a renewal point processes on (0,/spl infin/), with a finite mean rate, independent of (Y,X). We consider the estimation of regression function r(x/sub 0/, x/sub 1/,...,x/sub m-1/; /spl tau//sub 1/,...,/spl tau//sub m/) of /spl psi/(Y(/spl tau//sub m/)) given (X(0)=x/sub 0/, X(/spl tau//sub 1/)=x/sub 1/,...,X(/spl tau//sub m-1/)=/sub x-1/) for arbitrary lags 0</spl tau//sub 1/<...< /spl tau//sub m/ on the basis of the discrete-time observations {Y(t/sub j/),X(t/sub j/),t/sub j/)/sub j=1//sup n/. We estimate the regression function and all its partial derivatives up to a total order p/spl ges/1 using high-order local polynomial fitting. We establish the weak consistency of such estimates along with rates of convergence. We also establish the joint asymptotic normality of the estimates for the regression function and all its partial derivatives up to a total order p/spl ges/1 and provide explicit expressions for the bias and covariance matrix (of the asymptotically normal distribution).

Multivariate regression estimation: Local polynomial fitting for time series

Abstract We consider the estimation of the multivariate regression function m(x1, …, xd) = E[ψ(Yd)|X1 = x1, …, Xd = xd], and its partial derivatives, for stationary random processes Yi, Xi using local higher-order polynomial fitting. Particular cases of ψ yield estimation of the conditional mean, conditional moments and conditional distributions. Joint asymptotic normality is established for estimates of the regression function and its partial derivatives for strongly mixing and ϱ-mixing processes. Expressions for the bias and variance/covariance matrix (of the asymptotically normal distribution) for these estimators are given.

Multivariate regression estimation local polynomial fitting for time series

We consider the estimation of the multivariate regression function m( x 1, …, x d ) = E[ ψ( Y d )| X 1 = x 1, …, X d = x d ], and its partial derivatives, for stationary random processes Y i , X i using local higher-order polynomial fitting. Particular cases of ψ yield estimation of the conditional mean, conditional moments and conditional distributions. Joint asymptotic normality is established for estimates of the regression function and its partial derivatives for strongly mixing and ϱ-mixing processes. Expressions for the bias and variance/covariance matrix (of the asymptotically normal distribution) for these estimators are given.