TESTING SPHERICITY IN A GMANOVA-MANOVA MODEL WITH NORMAL ERROR

This article presents a statistic for testing the sphericity in a GMANOVA- MANOVA model with normal error. It is shown that the null distribution of this statistic is beta and its nonnull distribution is given in series form of beta distributions.

Mechanism and Method of Testing Fracture Toughness and Impact Absorbed Energy of Ductile Metals by Spherical Indentation Tests

To address the problem of conventional approaches for mechanical property determination requiring destructive sampling, which may be unsuitable for in-service structures, the authors proposed a method for determining the quasi-static fracture toughness and impact absorbed energy of ductile metals from spherical indentation tests (SITs). The stress status and damage mechanism of SIT, mode I fracture, Charpy impact tests, and related tests were frst investigated through fnite element (FE) calculations and scanning electron microscopy (SEM) observations, respectively. It was found that the damage mechanism of SITs is diferent from that of mode I fractures, while mode I fractures and Charpy impact tests share the same damage mechanism. Considering the diference between SIT and mode I fractures, uniaxial tension and pure shear were introduced to correlate SIT with mode I fractures. Based on this, the widely used critical indentation energy (CIE) model for fracture toughness determination using SITs was modifed. The quasi-static fracture toughness determined from the modifed CIE model was used to evaluate the impact absorbed energy using the dynamic fracture toughness and energy for crack initiation. The efectiveness of the newly proposed method was verifed through experiments on four types of steels: Q345R, SA508-3, 18MnMoNbR, and S30408.

ASYMPTOTIC DISTRIBUTION OF LIKELIHOOD RATIO STATISTIC FOR TESTING SPHERICTY IN GROWTH CURVE MODELS

In this paper, asymptotic expansions of the distribution of the likelihood ratio statistic for testing sphericity in a crowth curve model have been derived in the null and nonnull cases when the alternatives are dose to the null hypothesis. These expansions are given in series form of beta distributions.

ONE-WAY MULTIVARIATE REPEATED MEASUREMENTS ANALYSIS OF VARIANCE MODEL

The one-way multivariate repeated measurements analysis of variance (1-way MRM ANOVA) model for complete data and the sphericity test are studied.

New Inverse Method for Determining Uniaxial Flow Properties by Spherical Indentation Test

The spherical indentation test has been successfully applied to inversely derive the tensile properties of small regions in a non-destructive way.Current inverse methods mainly rely on extensive iterative calculations,which yield a considerable computational costs.In this paper,a database method is proposed to determine tensile flow properties from a single indentation force-depth curves to avoid iterative simulations.Firstly,a database that contain numerous indentation force-depth curves is established by inputting varied Ludwic material parameters into the indentation finite elements model.Secondly,for a given experimental indentation curve,a mean square error(MSE)is designated to evaluate the deviation between the experimental curve and each curve in the database.Finally,the true stresses at a series of plastic strain can be acquired by analyzing these deviations.To validate this new method,three different steels,i.e.A508,2.25Cr1 Mo and 316L are selected.Both simulated indentation curves and experimental indentation curves are used as inputs of the database to inversely acquire the flow properties.The result indicates that the pro-posed approach provides impressive accuracy when simulated indentation curves are used,but is less accurate when experimental curves are used.This new method can derive tensile properties in a much higher efficiency compared with traditional inverse method and are therefore more adaptive to engineering application.

ON SOME TESTS FOR ELLIPTICAL SYMMETRY

In this paper, some test statistics of Kolmogorov type and Cramer-von Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and any fixed alternative. The asymptotic properties of Bootstrap approximation are investigated.Furthermore, for computational reasons, an approximation for the statistics, based on number theoretic method, is suggested.

Sphericity and Identity Test for High-dimensional Covariance Matrix Using Random Matrix Theory

This paper addresses the issue of testing sphericity and identity of high-dimensional population covariance matrix when the data dimension exceeds the sample size.The central limit theorem of the first four moments of eigenvalues of sample covariance matrix is derived using random matrix theory for generally distributed populations.Further,some desirable asymptotic properties of the proposed test statistics are provided under the null hypothesis as data dimension and sample size both tend to infinity.Simulations show that the proposed tests have a greater power than existing methods for the spiked covariance model.