Generalization of the ordinary state-based peridynamic model for isotropic linear viscoelasticity

This paper presents a generalization of the original ordinary state-based peridynamic model for isotropic linear viscoelasticity. The viscoelastic material response is represented using the thermodynamically acceptable Prony series approach. It can feature as many Prony terms as required and accounts for viscoelastic spherical and deviatoric components. The model was derived from an equivalence between peridynamic viscoelastic parameters and those appearing in classical continuum mechanics, by equating the free energy densities expressed in both frameworks. The model was simplified to a uni-dimensional expression and implemented to simulate a creep-recovery test. This implementation was finally validated by comparing peridynamic predictions to those predicted from classical continuum mechanics. An exact correspondence between peridynamics and the classical continuum approach was shown when the peridynamic horizon becomes small, meaning peridynamics tends toward classical continuum mechanics. This work provides a clear and direct means to researchers dealing with viscoelastic phenomena to tackle their problem within the peridynamic framework.     

Robust and efficient direction identification for groupwise additive multiple-index models and its applications

This paper concerns robust and efficient direction identification for a groupwise additive multiple-index model, in which each additive function has a single-index structure. Interestingly, without involving non-parametric approach, we show that the directions of all the index parameter vectors can be recovered by a simple linear composite quantile regression (CQR). As a specific application, a iterative-free CQR estimation procedure for the partially linear single-index model is proposed. Furthermore, it can also be used to develop a penalized CQR procedure for variable selection in the high-dimensional settings. The new method has superiority in robustness and efficiency by inheriting the advantage of the CQR approach. Simulation results and real-data analysis also confirm our method.     

Honest confidence regions and optimality in high-dimensional precision matrix estimation

We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters p can be much larger than the sample size. We show that the novel estimator achieves minimax rates in supremum norm and the low-dimensional components of the estimator have a Gaussian limiting distribution. These results hold uniformly over the class of precision matrices with row sparsity of small order \(\sqrt{n}/\log p\) and spectrum uniformly bounded, under a sub-Gaussian tail assumption on the margins of the true underlying distribution. Consequently, our results lead to uniformly valid confidence regions for low-dimensional parameters of the precision matrix. Thresholding the estimator leads to variable selection without imposing irrepresentability conditions. The performance of the method is demonstrated in a simulation study and on real data.     

Testing the hypothesis of a block compound symmetric covariance matrix for elliptically contoured distributions

In this paper, the authors study the problem of testing the hypothesis of a block compound symmetry covariance matrix with two-level multivariate observations, taken for m variables over u sites or time points. Through the use of a suitable block-diagonalization of the hypothesis matrix, it is possible to obtain a decomposition of the main hypothesis into two sub-hypotheses. Using this decomposition, it is then possible to obtain the likelihood ratio test statistic as well as its exact moments in a much simpler way. The exact distribution of the likelihood ratio test statistic is then analyzed. Because this distribution is quite elaborate, yielding a non-manageable distribution function, a manageable but very precise near-exact distribution is developed. Numerical studies conducted to evaluate the closeness between this near-exact distribution and the exact distribution show the very good performance of this approximation even for very small sample sizes and the approach followed allows us to extend its validity to situations where the population distributions are elliptically contoured. A real-data example is presented and a simulation study is also conducted.     

Bandwidth selection in kernel density estimation for interval-grouped data

When interval-grouped data are available, the classical Parzen–Rosenblatt kernel density estimator has to be modified to get a computable and useful approach in this context. The new nonparametric grouped data estimator needs of the choice of a smoothing parameter. In this paper, two different bandwidth selectors for this estimator are analyzed. A plug-in bandwidth selector is proposed and its relative rate of convergence obtained. Additionally, a bootstrap algorithm to select the bandwidth in this framework is designed. This method is easy to implement and does not require Monte Carlo. Both proposals are compared through simulations in different scenarios. It is observed that when the sample size is medium or large and grouping is not heavy, both bandwidth selection methods have a similar and good performance. However, when the sample size is large and under heavy grouping scenarios, the bootstrap bandwidth selector leads to better results.     

A Method for Performance Degradation Modeling Based upon the Accelerated Experiment

Performance degradation modeling plays an important role in prognostics and health management of mechanical system. Influenced by the complex structure of the hydraulic pump and the limited experiment standards, it is hard to establish an appropriate performance degradation model. To fulfill current requirements, a method for establishing the performance degradation model based on accelerated experiment is proposed. In order to describe the general trend of the degradation, the double-stress exponential model is firstly established as the theoretical degradation model. On this basement, combined with the characteristics of the experiment, the accelerating coefficient is settled; meanwhile, the procedures for assuring the model parameters are presented. Furthermore, based on the accelerated experiment of the hydraulic pump under various stresses, the performance degradation model is finally established. Result of the experimental analysis indicates that the proposed method is applicable and the presented model is effective to measure the performance degradation of pump.     

Catastrophic Failure of a Steel Chimney in a Lime Plant

Failure analysis of a steel chimney used in a lime plant was carried out. The chimney broke from two different locations during a storm. During the site visit, it was observed that the chimney was dislodged from weld joints. The chimney was made up of hot rolled mild steel plates. Investigations were carried out on the failed chimney plate and welding between plates. The investigation consists of visual observation, chemical analysis, characterization of macro- and microstructures, measurement of hardness, tensile property tests and energy-dispersive spectroscopy (EDS). Calculation of wind load at the location of breakage was also carried out. EDS analysis revealed entrapment of slag inside weld. Overall analysis suggested that the failure took place due to selection of improper reconditioning technique as well as poor workmanship in welding.     

Design Optimization of Composite Prosthetic Tubes Using GA-ANN Algorithm Considering Tsai-Wu Failure Criteria

The investigation of possible failures in composite materials is a matter of very great importance, and the Tsai-Wu criterion is an effective criterion for analyzing those flaws in anisotropic materials and defining whether the material at a given load will or will not suffer structural failure. In this study, an optimization procedure is proposed to minimize the maximum value of Tsai-Wu of laminated composite tubes subject to axial loading. Artificial neural networks and genetic algorithms are chosen as optimization tools. The results of this study show that the developed algorithm converges faster. Then, the maximum Tsai-Wu value is used as the objective function and the fiber orientations are the constraints in the optimization process. The results yielded by them are compared and discussed. Optimal results are compared with respect to the usual initial design. The design approach is recommended for structures where composites are the key load-carrying members such as orthopedic prosthesis.     

Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations

The novelty of this paper is the use of an efficient beam theory for bending, free vibration and buckling analysis of functionally graded material (FGM) beams on two-parameter elastic foundation. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the beam without requiring any shear correction factor. Due to porosities, possibly occurring inside FGMs during fabrication, it is therefore necessary to consider the vibration, bending and buckling behaviors of beams having porosities in this work. The equation of motion for FGM beams is obtained through Hamilton’s principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. The validity of the present theory is investigated by comparing some of the present in literature. It can be concluded that the proposed theory is accurate and simple in solving the bending, free vibration and buckling behaviors of FGM sandwich beams.