Scaling parameters selection principle for the scaled unscented Kalman filter

The paper deals with the state estimation of the widely used scaled unscented Kalman filter（UKF）. In particular, the stress is laid on the scaling parameters selection principle for the scaled UKF. Several problems caused by recommended constant scaling parameters are highlighted. On the basis of the analyses, an effective scaled UKF is proposed with self-adaptive scaling parameters,which is easy to understand and implement in engineering. Two typical strong nonlinear examples are given and their simulation results show the effectiveness of the proposed principle and algorithm.

Lacunary Interpolation by Fractal Splines with Variable Scaling Parameters

For a prescribed set of lacunary data{(x_(ν),f_(ν),f^(″)_(ν)):ν=0,1,...,N}with equally spaced knot sequence in the unit interval,we show the existence of a fam-ily of fractal splines S^(α)_(b)∈C 3[0,1]satisfying S^(α)_(b)(x_(ν))=f_(ν),(S^(α)_(b))^(2)(x_(ν))=f^(″)_(ν)forν=0,1,...,N and suitable boundary conditions.To this end,the unique quintic spline introduced by A.Meir and A.Sharma[SIAM J.Numer.Anal.10(3)1973,pp.433-442]is generalized by using fractal functions with variable scaling pa-rameters.The presence of scaling parameters that add extra“degrees of freedom”,self-referentiality of the interpolant,and“fractality”of the third derivative of the in-terpolant are additional features in the fractal version,which may be advantageous in applications.If the lacunary data is generated from a functionΦsatisfying certain smoothness condition,then for suitable choices of scaling factors,the corresponding fractal spline S^(α)_(b)satisfies||Φ^(r)−(S^(α)_(b))(r)||∞→0 for 0≤r≤3,as the number of partition points increases.

A Method Determining Vertical Scaling Parameters of Fractal Interpolation

A method determining vertical scaling parameters of fractal interpolation is given in this paper. By computer experiments, it is clear that this method is very effective.

Iterative regularization method for image denoising with adaptive scale parameter

In order to decrease the sensitivity of the constant scale parameter, adaptively optimize the scale parameter in the iteration regularization model （IRM） and attain a desirable level of applicability for image denoising, a novel IRM with the adaptive scale parameter is proposed. First, the classic regularization item is modified and the equation of the adaptive scale parameter is deduced. Then, the initial value of the varying scale parameter is obtained by the trend of the number of iterations and the scale parameter sequence vectors. Finally, the novel iterative regularization method is used for image denoising. Numerical experiments show that compared with the IRM with the constant scale parameter, the proposed method with the varying scale parameter can not only reduce the number of iterations when the scale parameter becomes smaller, but also efficiently remove noise when the scale parameter becomes bigger and well preserve the details of images.

Vertical Scale Parameter Estimates for 48 Non-edge-on Spiral Galaxies

In the first paper of this series, we directly studied the mathematicalforms, symmetry of spiral structure, and the projection of galactic discs on the images, andmeasured the pitch angles of the spiral arms and inclination angles of the galactic discs for 60spiral galaxies. In this second paper, we estimate the vertical scale parameters of 48 non-edge-onspiral galaxies based on the method proposed by Peng et al. and on the results given in Paper I. Aswe know, for edge-on disc galaxies we can obtain the vertical scale parameter from the photometry,once a mathematical form is specified for the vertical light distribution. For non-edge-on galaxies,some other methods have to be used. The statistical result was that the vertical scale parameter iscomparable for edge-on and non-edge-on galaxies, although it is obtained from two very differentmethods.

Establishment of size-dependant constitutive model of micro-sheet metal materials

The inherent mechanism of size effect in micro-sheet material behavior of plastic forming was explained by the surface layer model and theory of metal crystal plasticity. A size-dependant constitutive model based on the surface layer model was established by introducing the scale parameters and modifying the classical Hall-Petch equation. The influence of the geometric dimensions and the grain size on the flow behavior of the material was discussed using the new material constitutive model. The results show that, the flow stress decreases while the sheet metal thickness decreases when the grain size keeps constant, and the micro-sheet metal with a larger grain size is more easily to be influenced by the size effects. The material constitutive model established is validated by the stress-strain curve of the micro-sheet metal with different thicknesses derived from the tensile experiments. The rationality of the material model is verified by the fact that the calculation results are consistent with the experimental results.

Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect

Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising.Size dependency is included in governing equations based on the modified couple stress theory.Hamilton’s principle is used to derive governing equations of the cylindrical micro/nano shell.Solution procedure is developed using Navier technique for simply-supported boundary conditions.The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters,material properties,applied voltages and temperature rising on the free vibration responses.

Impacts of the Thermal Effects of Sub-grid Orography on the Heavy Rainfall Events Along the Yangtze River Valley in 1991

A P - σ regional climate model using a parameterization scheme to account for the thermal effects of the sub-grid scale orography was used to simulate the three heavy rainfall events that occurred within the Yangtze River Valley during the mei-yu period of 1991. The simulation results showed that by considering the sub-grid scale topography scheme, one can significantly improve the performance of the model for simulating the rainfall distribution and intensity during these three heavy rainfall events, most especially the second and third. It was also discovered that the rainfall was mainly due to convective precipitation. The comparison between experiments, either with and without the sub-grid scale topography scheme, showed that the model using the scheme reproduced the convergence intensity and distribution at the 850 hPa level and the ascending motion and moisture convergence center located at 500 hPa over the Yangtze River valley. However, some deviations still exist in the simulation of the atmospheric moisture content, the convergence distribution and the moisture transportation route, which mainly result in lower simulated precipitation levels. Further analysis of the simulation results demonstrated that the sub-grid topography scheme modified the distribution of the surface energy budget components, especially at the south and southwest edges of the Tibetan Plateau, leading to the development and eastward propagation of the negative geopotential height difference and positive temperature-lapse rate difference at 700 hPa, which possibly led to an improved precipitation simulation over eastern China.

Study on wave dispersion characteristics of piezoelectric sandwich nanoplates considering surface effects

In this study,the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects(SEs).The nanoplates are composed of a composite layer reinforced by graphene and two piezoelectric surface layers.Utilizing the modified Halpin-Tsai model,the material parameters of composite layers are obtained.The displacement field is determined by the sinusoidal shear deformation theory(SSDT).The Euler-Lagrange equation is derived by employing Hamilton’s principle and the constitutive equations of piezoelectric layers considering the SEs.Subsequently,the nonlocal strain gradient theory(NSGT)is used to obtain the equations of motion.Next,the effects of scale parameters,graphene distribution,orthotropic viscoelastic foundation,and SEs on the propagation behavior are numerically examined.The results reveal that the wave frequency is a periodic function of the orthotropic angle.Furthermore,the wave frequency increases with the increase in the SEs.

Real-Time Automatic Scaling Method of Oblique Ionogram Parameters Based on Morphological Operator and Inversion Technique

Automatic scaling ionogram can get the parameters of ionogram which are vital to ionosphere detecting. In this paper, a new method is proposed to scale F2 layer trace automatically from oblique ionogram based on morphological operator and inversion technique. This method is verified through the comparison of actual detecting data with statistical analysis. The results show that the proposed automatic scaling method has high acceptable rate and is suitable for scaling oblique ionogram with different high angle wave states. It is fast and precise to fit O-mode echoes in F2 layer without the influence from F1 layer. This method could be applied in real-time ionospheric oblique sounding research with high reliability and versatility.

An Improved Method of Joint Inversion Using GPS and Gravity Observation Data

On the basis of the dislocation theory and gravity observation, a joint inversion model is presented with a fitting factor A scaling amplitudes between the gravity and GPS observation data. The test results show that the new joint model is better than that taking the scale factor ）, as a constant from the inversion result of MSE （mean square error）. In addition, the random cost method used in the inversion algorithm is revised and improved, which shows that the improved random cost method can easily get the local minimum value and greatly decrease the iteration steps.

The Mean Deviation from the Median of the Dagum Distribution

The Dagum model is particularly suitable for the analysis of the distributions of economic quantities, such as income, assets and consumption. The purpose of this note is to derive the expression of the mean deviation from the median of the Dagum distribution to study the behavior of the scale and shape parameters in terms of absolute variability and in terms of relative variability.

Concordance of Kinematics and Lensing of Elliptical Galaxies with WMAP Cosmology

We explore degeneracies in strong lensing model so to make time delay data consistent with the WMAP （Wilkinson Microwave Anisotropy Probe） cosmology. Previous models using a singular isothermal lens often yield a time delay between the observed multiple images too small than the observed value if we ＂hardwire＂ the now widely quoted post-WMAP ＂high＂ value of the Hubble constant （Ho ～71 ± 4km s^-1 Mpc^-1）. Alternatively, the lens density profile （star plus dark matter） is required to be locally steeper than r-2 （isothermal） profile near the Einstein radius （of the order 3 kpc） to fit the time delays; a naive extrapolation of a very steep profile to large radius would imply a lens halo with a scale length of the order only 3 kpc, too compact to be consistent with CDM. We explore more sophisticated, mathematically smooth, positive lens mass density profiles which are consistent with a large halo and the post-WMAP H0. Thanks to the spherical monopole degeneracy, the ＂reshuffling＂ of the mass in a lens model does not affect the quality of the fit to the image positions, amplifications, and image time delays. Even better, unlike the better-known mass sheet degeneracy, the stellar mass-to-light and the H0 value are not affected either. We apply this monopole degeneracy to the quadruple imaged time-delay system PG 1115＋080. Finally we discuss the implications of the time delay data on the newly proposed relativistic MOND theory.

Prediction of nonlocal scale parameter for carbon nanotubes

Based on the theory of nonlocal elasticity,a nonlocal shell model accounting for the small scale effect is developed for the bending characteristics of CNTs subjected to the concentrated load.With this nonlocal shell model,explicit expressions are derived for the bending solutions.To extract the proper values of nonlocal scale parameter,we have made molecular dynamics(MD) simulations for various radii and lengths of armchair and zigzag CNTs,the results of which are matched with those of nonlocal continuum model.It is found that the present nonlocal elastic shell model with its appropriate values of nonlocal scale parameter has the capability to predict the bending behavior of CNTs,which is comparable with the results of MD simulations.Moreover,exact closed form solutions for the nonlocal scale parameter for zigzag and armchair CNTs are obtained.The results show that nonlocal scale parameter is independent of the length of CNTs,and dependent on the radius of CNTs.

Bayesian inference and life testing plans for generalized exponential distribution

Recently generalized exponential distribution has received considerable attentions. In this paper, we deal with the Bayesian inference of the unknown parameters of the progressively censored generalized exponential distribution. It is assumed that the scale and the shape parameters have independent gamma priors. The Bayes estimates of the unknown parameters cannot be obtained in the closed form. Lindley’s approximation and importance sampling technique have been suggested to compute the approximate Bayes estimates. Markov Chain Monte Carlo method has been used to compute the approximate Bayes estimates and also to construct the highest posterior density credible intervals. We also provide different criteria to compare two different sampling schemes and hence to find the optimal sampling schemes. It is observed that finding the optimum censoring procedure is a computationally expensive process. And we have recommended to use the sub-optimal censoring procedure, which can be obtained very easily. Monte Carlo simulations are performed to compare the performances of the different methods and one data analysis has been performed for illustrative purposes.