Power and reversal power links for binary regressions: An application for motor insurance policyholders

In binary regression, symmetric links such as logit and probit are usually considered as standard. However, in the presence of unbalancing of ones and zeros, these links can be inappropriate and inflexible to fit the skewness in the response curve and likely to lead to misspecification. This is the case of covering some type of insurance, where it can be observed that the probability of a given binary response variable approaches zero at different rates than it approaches one. Furthermore, when usual links are considered, there is not a skewness parameter associated with the distribution chosen that, regardless of the linear predictor, is easily interpreted. In order to overcome such problems, a proposal for the construction of a set of new skew links is developed in this paper, where some of their properties are discussed. In this context, power links and their reversal versions are presented. A Bayesian inference approach using MCMC is developed for the presented models. The methodology is illustrated considering a sample of motor insurance policyholders selected randomly by gender. Results suggest that the proposed link functions are more appropriate than other alternative link functions commonly used in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Analysis of the fiber length dependence of its strength by using the weakest-link approach 1. A family of weakest-link distribution functions

This paper presents a summary and further development of the ideas proposed in the previous papers of the authors, which were dedicated to investigating the fiber scale effect (strength-length relation). In the first part of the paper, some theoretical aspects of the problem are considered; in the second one, an application to the processing of test datasets is discussed. As distinct from our previous publications, two types of defects (“technological,” i.e., existing before loading, and load-dependent) and two types of influence of the number of defects on the fiber strength are considered; the probability of absence of defects is also taken into account. We consider a specimen as a sequence of n elements of the same length. It is supposed that there are defects in K of them, 0 ≤ K ≤ n. Two cases are considered: K is a random variable or a random process K (t). In the second case, the increase in K and the failure of a specimen is described as a Markov chain whose matrix of transition probabilities depends on the current value of the loading process, described as some (increasing to infinity) sequence {x₁, x₂, …, x_t,…}. Three versions of relationships between the specimen strength and the number of defective elements are considered for both the cases. Thus, six probability structures are introduced, and different versions of distribution functions and the corresponding models are considered. The methods for estimating the model parameters, the results obtained in processing glass, flax, carbon fiber, and carbon bundle datasets, as well as a comparison of different models, are presented in the second part of the paper. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 685–696, September–October, 2008.     

Compressive Properties of Pultruded Composites

The compressive properties of E-glass fiber/polyester resin matrix pultruded composites were measured using a short-block compression test fixture. Twenty specimens were tested in the pultrusion (longitudinal) direction and twenty more specimens in the transverse direction. Six specimens were tested at 30, 45, and 60° orientations to the pultrusion direction. Compressive properties such as the compressive modulus, compressive strength, Poisson ratio, and compressive failure strain were measured for both 6.3 and 12.7 mm thick pultruded sheet materials. The test specimens were rectangular with a length of 44.4 mm, width of 25.4 mm, and gage length of 25.4 mm. The test fixture was initially validated by measuring the axial strain distribution across the width of the specimen; from the beginning of loading up to the final failure, the distribution of strains across the specimen width was found to be very uniform. Back-to-back strain gages were also mounted on representative specimens. The end shortening was also measured on all specimens. The compressive strength data were analyzed both for the longitudinal and transverse directions using a two-parameter Weibull, lognormal, and normal distributions. The compressive properties are presented as functions of the specimen orientation angle for both thicknesses.     

A computationally efficient method for modeling flexible robots based on the assumed modes method

In this paper a simple method to obtain the analytical model of a flexible robot is presented, which turns out to be more efficient, from a computational point of view, than the classic assumed modes method.The presented method consists of using appropriate linear combinations of the modes of each link as basis functions to evaluate the deflection, in such a way as to minimize the dependency of the position of the generic link on the Lagrangian variables of the previous links. Hence, the number of terms of the inertia matrix and of the Coriolis and centrifugal vectors is significantly reduced. First, the model is derived, provided that the links are homogeneous and with constant cross-section, by analytically or otherwise by numerically calculating the parameters of the closed-form expression of the Lagrangian function of the generic link supposed free; afterwards, the analytical dynamic model of the whole robot is obtained by using an iterative interconnection algorithm, which can be easily implemented by using a symbolic manipulation language.The simplicity and efficiency of the proposed method is illustrated by considering the analytic expression of the kinetic energy of the end-effector in different cases and with significant comparison examples.     

Comparative analysis of the structural order and defectiveness of reinforcing fibers on the basis of normalized values of mechanical properties

Experimental data on mechanical properties referred to their limiting values for a flawless polymer crystal with long molecular chains is used in a comparative analysis of the degree of ordering of the structure (crystallinity, orientation) and the defectiveness of the reinforcing fibers. The actual elastic moduli and limiting (theoretical) elastic modulus are used to obtain coefficients that characterize the overall order of the structure of the fibers but are independent of their defectiveness. Values of true strength in tension and the limitingly attainable or theoretical strength are used to calculate conditional coefficients that depend both on the overall order and the defectiveness of the fiber structure. The difference in the coefficients makes it possible to detect dangerous local defects that lead to fiber failure. Results are presented from calculations for more than 20 types of reinforcing fibers. Despite the approximate nature of these representations, the data that is obtained permits comparisons of different types of fibers, characterization of their quality, and evaluation of the degree of perfection of the fiber production technology.Paper presented at the IX International Conference on the Mechanics of Composite Materials, Riga, October, 1995.St. Petersburg State University for Technology and design, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 444–453, July–August, 1996.     

三维四向编织复合材料刚度和强度的理论预测

以单胞模型为基础,将三维四向编织复合材料中相同走向的纤维束视为单向复合材料,利用桥联模型确定了单向复合材料的柔度矩阵,再将具有不同材料主向的单向复合材料的刚度矩阵通过体积平均,得到了三维四向编织复合材料的总体刚度矩阵,从而得到其工程弹性常数．然后,以单向复合材料为基础,基于等应变假设和桥联模型,确定出材料内各组分（纤维束和基体）的细观应力分布,且对纤维束采用Hoffman失效准则,对基体采用Mises失效准则,预报了三维四向编织复合材料的拉伸强度．     

Theoretical and experimental investigation of anisotropic damage in textile-reinforced composite structures

In the present work, a phenomenological plane-stress damage-mechanics-based model for textile-reinforced composites is presented and its predictive capability is evaluated by carrying out a series of experimental tests. Damage variables are introduced to describe the evolution of the damage state and, as a subsequence, the degradation of material stiffness. For calculating the nonlinear stress and strain distribution of complexly loaded composites with a textile reinforcement, a special emphasis has to be placed on the interaction between the fiber failure due to the stress in the fiber direction and the matrix failure due to the transverse and shear stresses. This demands the formulation of realistic failure criteria taking into account the microstructural material behavior and different fracture modes. The new failure criteria, like the fracture mode concepts, consider these fracture modes, as well as further fracture types, in the reinforcement plane. The failure criteria are based on equations for failure surfaces in the stress space and damage thresholds in determining the stiffness degradation of the composite. The model proposed was used to characterize the strength and the failure behavior of carbon-fiber-reinforced composites. For this purpose, several unidirectional and bidirectional tests were performed to determine the specific properties of the material. The specimens were investigated by using acoustic emission techniques and strain-controlled tension and torsion tests.Russian translated published in Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 791–810, November–December, 2004.     

Method of primers in calculating the probability of destruction of a unidirectional composite material in tension

A method of primers is elaborated which allows one to calculate the distribution function of durability of a composite material in tension in the reinforcement direction. Integral and differential equations for calculating the probabilities of formation of primers and destruction of a material caused by their formation are presented. Distribution functions of material strength for the parameter of Weibull distribution of fiber strength on the interval 2.1 ≤ β _f ≤ 50.1 are calculated. From the functions, the average values and root-mean-square deviations of material strength are found. The results obtained agree well with calculations by using the structural-imitation simulation. The distribution functions of material strength with a high precision are approximated by the three-parameter Weibull distributions. The distribution parameters are approximated by the linear functions of ln (β_f). __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 6, pp. 823–838, November–December, 2007.     

On the fibration of augmented link complements

We study the fibration of augmented link complements. Given the diagram of an augmented link we associate a spanning surface and a graph. We then show that this surface is a fiber for the link complement if and only if the associated graph is a tree. We further show that fibration is preserved under Dehn filling on certain components of these links. This last result is then used to prove that within a very large class of links, called locally alternating augmented links, every link is fibered.     

Effect of antioxidant distribution in polycaprolactam on the variation of strength and deformability at elevated temperatures

The effect of quinhydrone distribution over the cross section on the strength and deformability at elevated temperatures has been investigated for specimens of polycaprolactam. The optimum concentrations of quinhydrone in the surface layer of polycaprolactam retaining maximum strength over an extended period in a hot-air medium have been determined. The most probable areas of formation and localization of structural defects under thermal action have been established.Mekhanika Polimerov, Vol. 3, No. 2, pp. 296–301, 1967     

Effect of certain technological factors on residual stress formation in stiffened glass-reinforced plastic shells

Conclusions Residual stress formation in stiffened composite shells has a nonmonotonic character determined by the fabrication technology, by the structural geometry and by the relations between the thermophysical and mechanical characteristics of the materials of which the individual elements are composed. For a given temperature regime a residual stress distribution favorable with respect to strength can be obtained by using auxiliary devices with specially selected properties.Moscow Power-Engineering Institute. Translated from Mekhanika Polimerov, No. 1, pp. 34–39, January–February, 1978.     

Cutting of aramide fiber-reinforced plastics by Co2 laser

Comparative characteristics of aramide fiber reinforced plastics (AFRP) made by laser cutting or machining are presented. It is found that the strength of the specimens cut out by laser is 4–25% higher, while the moisture absorption is at least 2 times lower as compared to those cut out by machining. The deviation of the cutting edge size for AFRP 2 mm thick does not exceed 0.4 mm. Calculated and experimental data are given. The possibilities and conditions of cutting the AFRP up to 6 mm thick are determined.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 375–384, May–June, 1999.     

Determining Knotsw and Links by Cyclic Branched Coverings

It is well known that different knots or links in the 3-sphere can have homeomorphic n-fold cyclic branched coverings. We consider the following problem: for which values of nis a knot of link determined by itsn-fold cyclic branched covering? We consider the class of hyperbolic resp.2π/n-hyperbolic links. The isometry or symmetry groups of such links are finite, and their n-fold branched coverings are hyperbolic 3-manifolds. Our main result states that if ndoes not divide the order of the finite symmetry group of such a link, then the link is determined by its n-fold branched covering. In a sense, the result is best possible; the key argument of its proof is algebraic using some basic result about finite p-groups. The main result applies, for example, to the cyclic branched coverings of the 2-bridge links; in particular, it gives a classification of the maximally symmetricD₆-manifolds which are exactly the 3-fold branched coverings of the 2-bridge links.     

Experimental Validation of RVE Based Failure Simulations of Macro-Porous Materials

Connections between inhomogeneities and the failure behavior of brittle material may be investigated by finite element simulations of representative volume elements. Representative volume elements are typically subjected to periodic boundary conditions. Moreover, representative volume elements are often chosen as planar, i. e., two dimensional in order to reach reasonable statistics with regard to random distributions of inhomogeneities. The significance of such strongly simplified simulations needs to be validated, especially if the matrix failure is potentially dominated by defects, as is the case, e. g., in macro-porous ceramics. We propose a quasi-periodic concept to design specimens with cylindrical pores, which reproduce the stress state in a two dimensional representative volume element. This is achieved by a partial periodic replication of the region of interest. We suggest that material models used in simulations can be assessed by comparison between simulated and experimentally observed failure. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mechanism by which tension on the fibrous filler affects the structure and the strength of wound glass-plastics

Conclusions 1. We have studied how the structure of glass-plastics wound with twisted threads is affected by tension on the fibrous filler. The trend of changes in fiber content and porosity, as well as an increasingly nonuniform distribution of the reinforcing filler over the thickness, has been established.2. The effect of a nonuniform filler distribution over the thickness on the tensile strength has been evaluated. The calculated and the experimental curve of strength as a function of the tension have been compared, the former taking into account variable porosity, fiber content, and nonuniformity of fiber distribution over the thickness.3. It has been demonstrated that the change in the strength characteristics of a wound glass-plastic as a function of the tension on the reinforcing filler during winding is due to a combined complex effect of such factors as the overall fiber content and porosity, a nonuniform fiber distribution over the thickness, the fiber orientation, and the degree of mechanical damage in threads due to their interaction with the active components of the winding machine.Report presented at the Third All-Union Conference on Polymer Mechanics. Riga, November 10–12, 1976.Translated from Mekhanika Polimerov, No. 3, pp. 439–444, May–June, 1977.     

Telecommunication Network Capacity Design for Uncertain Demand

The expansion of telecommunication services has increased the number of users sharing network resources. When a given service is highly demanded, some demands may be unmet due to the limited capacity of the network links. Moreover, for such demands, telecommunication operators should pay penalty costs. To avoid rejecting demands, we can install more capacities in the existing network. In this paper we report experiments on the network capacity design for uncertain demand in telecommunication networks with integer link capacities. We use Poisson demands with bandwidths given by normal or log-normal distribution functions. The expectation function is evaluated using a predetermined set of realizations of the random parameter. We model this problem as a two-stage mixed integer program, which is solved using a stochastic subgradient procedure, the Barahona's volume approach and the Benders decomposition.     

A new boundary element technique for solving plane problems of linear elasticity: 1. Theory

A new boundary elements technique for solving plane problems of linear elasticity theory is described. The method is based upon the Muskhelishvili complex variable representation of the displacement and stress fields involving two independent complex functions. These functions are represented by complex Cauchy integrals where the path of integration is taken around the external boundary of the solid. Two complex density functions appearing in the integrands of the Cauchy integrals are represented by spline functions and these are determined by the application of appropriate boundary conditions. The theory presented is suitable only for bounded simply-connected regions.     

Importance Link Function Estimation for Markov Chain Monte Carlo Methods

Abstract

This article focuses on improving estimation for Markov chain Monte Carlo simulation. The proposed methodology is based upon the use of importance link functions. With the help of appropriate importance sampling weights, effective estimates of functionals are developed. The method is most easily applied to irreducible Markov chains, where application is typically immediate. An important conceptual point is the applicability of the method to reducible Markov chains through the use of many-to-many importance link functions. Applications discussed include estimation of marginal genotypic probabilities for pedigree data, estimation for models with and without influential observations, and importance sampling for a target distribution with thick tails.     

Analysis of the fracture of fiber composites on the basis of the statistical theory of branching processes

A statistical theory of branching processes is used to examine models of the localized and delocalized fracture of fiber composites. It is shown that despite the differences between the two types of models, both can be reduced to the same generalized Markov process. A new fracture criterion to be used for all types of models is proposed. The use of this criterion makes it possible to theoretically describe a new structural effect — the dependence of the breaking stress of a composite specimen on its cross-sectional area. In the limiting case of an infinitely large cross-sectional area, the breaking stress calculated on the basis of the proposed approach turns out to be equal to that calculated using previous models. The breaking stress for specimens of finite dimensions turns out to be lower than for specimens of infinite size. This result is due to the nonlinear dependence of the probability of fiber rupture on the additional overstresses that develop in the composite during local microscopic fractures. The results that are obtained should be taken into account in the calculation of the strength of structurally reinforced composites and small structural elements made of composite materials.Kompozit Research Center, St. Petersburg, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 795–807, November–December, 1996.