Asymptotic Properties of a Probabilistic‐Statistical Model of Particle Classification in Hydrocyclones

The peculiarities of practical implementation of a probabilistic‐statistical model for a hydrodynamic stage of particle classification process of liquid‐solid polydisperse systems in cylinder‐conic hydrocyclones of small size have been investigated. Within reasonable assumptions, stationary solutions of the Fokker‐Planck‐Kolmogorov kinetic equation were obtained for the considered separation process. In order to describe changes in characteristics of suspension separation in hydrocyclones it was proposed to use stationary distributions, which parameters depend not only on hydraulic and dynamic features of flows inside an apparatus, but also are determined by relative magnitudes of the impact of particle classification and centrifugal forces in comparison with the intensity of random perturbations.     

Comprehensive Pareto Efficiency in robust counterpart optimization

In this paper, an innovative concept named Comprehensive Pareto Efficiency is introduced in the context of robust counterpart optimization, which consists of three sub-concepts: Pareto Robust Optimality (PRO), Global Pareto Robust Optimality (GPRO) and Elite Pareto Robust Optimality (EPRO). Different algorithms are developed for computing robust solutions with respect to these three sub-concepts. As all sub-concepts are based on the Probability of Constraint Violation (PCV), formulations of PCV under different probability distributions are derived and an alternative way to calculate PCV is also presented. Numerical studies are drawn from two applications (production planning problem and orienteering problem), to demonstrate the Comprehensive Pareto Efficiency. The numerical results show that the Comprehensive Pareto Efficiency has important significance for practical applications in terms of the evaluation of the quality of robust solutions and the analysis of the difference between different robust counterparts, which provides a new perspective for robust counterpart optimization.     

Semiparametric analysis of clustered interval-censored survival data with a cure fraction

A generalization of the semiparametric Cox’s proportional hazards model by means of a random effect or frailty approach to accommodate clustered survival data with a cure fraction is considered. The frailty serves as a quantification of the health condition of the subjects under study and may depend on some observed covariates like age. One single individual-specific frailty that acts on the hazard function is adopted to determine the cure status of an individual and the heterogeneity on the time to event if the individual is not cured. Under this formulation, an individual who has a high propensity to be cured would tend to have a longer time to event if he is not cured. Within a cluster, both the cure statuses and the times to event of the individuals would be correlated. In contrast to some models proposed in the literature, the model accommodates the correlations among the observations in a more natural way. A multiple imputation estimation method is proposed for both right-censored and interval-censored data. Simulation studies show that the performance of the proposed estimation method is highly satisfactory. The proposed model and method are applied to the National Aeronautics and Space Administration’s hypobaric decompression sickness data to investigate the factors associated with the occurrence and the time to onset of grade IV venous gas emboli under hypobaric environments.     

On optimality and duality for multiple-objective optimization under generalized type I univexity

In this paper, we deal with the multiple-objective optimization problems, considering an improved definition of generalized type I univex function. Some optimality conditions as well as some duality relations are established.     

Multiobjective evolutionary algorithm based on multimethod with dynamic resources allocation

In the last two decades, multiobjective optimization has become main stream and various multiobjective evolutionary algorithms (MOEAs) have been suggested in the field of evolutionary computing (EC) for solving hard combinatorial and continuous multiobjective optimization problems. Most MOEAs employ single evolutionary operators such as crossover, mutation and selection for population evolution. In this paper, we suggest a multiobjective evolutionary algorithm based on multimethods (MMTD) with dynamic resource allocation for coping with continuous multi-objective optimization problems (MOPs). The suggested algorithm employs two well known population based stochastic algorithms namely MOEA/D and NSGA-II as constituent algorithms for population evolution with a dynamic resource allocation scheme. We have examined the performance of the proposed MMTD on two different MOPs test suites: the widely used ZDT problems and the recently formulated test instances for the special session on MOEAs competition of the 2009 IEEE congress on evolutionary computation (CEC’09). Experimental results obtained by the suggested MMTD are more promising than those of some state-of-the-art MOEAs in terms of the inverted generational distance (IGD)-metric on most test problems.     

Linear programming with imprecise data

Conventional linear programming requires the deterministic specification of all the relevant data but generally this is only known imprecisely. Several ways in which imprecision may be incorporated into the programs are discussed. These include proximate programming, inexact programming and fuzzy programming. A simple illustrative example concerned with water quality is reworked using some of the described techniques. Fuzzy programming is a particularly useful model which can handle imprecision with respect to all the parameters and can also incorporate multiple goals.     

Asymptotic properties of mixture-of-experts models

The statistical properties of the likelihood ratio test statistic (LRTS) for mixture-of-expert models are addressed in this paper. This question is essential when estimating the number of experts in the model. Our purpose is to extend the existing results for simple mixture models (Liu and Shao, 2003 [8]) and mixtures of multilayer perceptrons (Olteanu and Rynkiewicz, 2008 [9]). In this paper we first study a simple example which embodies all the difficulties arising in such models. We find that in the most general case the LRTS diverges but, with additional assumptions, the behavior of such models can be totally explicated.     

Auto-parametric semi-trivial and post-critical response of a spherical pendulum damper

The pendulum vibration damper modelled as a two degree of freedom strongly non-linear auto-parametric system is investigated. A kinematic external excitation in the suspension point is applied. The excitation is considered to be horizontal and harmonically variable in time. A semi-trivial solution and its stability are analyzed. Special attention is paid to the resonance domain. In certain domains of pendulum and excitation parameters the semi-trivial solution does not exist in this domain and various post-critical three-dimensional regimes occur. Some of them are non-stationary despite the harmonic excitation. Three different types of the resonance domain are investigated. Their main properties depend significantly on dynamic parameters of the pendulum and of the external excitation amplitude. An analytical and numerical study brings forth several recommendations for designers of these devices. Their aim is to avoid any post-critical response regimes endangering the pendulum functionality.     

Asymptotic homogenisation in linear elasticity. Part I: Mathematical formulation and finite element modelling

The asymptotic expansion homogenisation method is an excellent methodology to model physical phenomena on media with periodic microstructure and a useful technique to study the mechanical behaviour of structural components built with composite materials. In the first part of this work the authors present a detailed form of the mathematical formulation of the asymptotic expansion homogenisation for linear elasticity problems, as well the explicit mathematical equations that characterise the microstructural stress and strain fields associated with a given macrostructural equilibrium state – the localisation procedure. From this mathematical basis, the authors also present the numerical equations resulting from the finite element modelling of the asymptotic expansion homogenisation method in linear elasticity.     

Asymptotic homogenisation in linear elasticity. Part II: Finite element procedures and multiscale applications

The asymptotic expansion homogenisation (AEH) method can be used to solve problems involving physical phenomena on continuous media with periodic microstructures. In particular, the AEH is a useful technique to study of the behaviour of structural components built with composite materials. The main advantages of this approach lie on the fact that (i) it allows a significant reduction of the problem size and (ii) it has the capability to characterise stress and deformation microfields. In fact, specific equations can be developed to define these fields, in a process designated by localisation and not found on typical homogenisation methods. In the AEH methodology, overall material properties can be derived from the mechanical behaviour of selected periodic microscale representative volumes (also known as representative unit-cells, RUC). Nevertheless, unit-cell based modelling requires the control of some parameters, such as reinforcement volume fraction, geometry and distribution within the matrix material. The need for variety and flexibility leads to the development of automatic geometry generation algorithms. Additionally, the unstructured finite element meshes required by these RUC are usually non-periodic and involve the control of specific periodic boundary conditions. This work presents some numerical procedures developed in order to support finite element AEH implementations, rendering them more efficient and less user-dependent. The authors also present a numerical study of the influence of the reinforcement volume fraction on the overall material properties for a metal matrix composite (MMC) reinforced with spherical ceramic particles. A general multiscale application is shown, with both the homogenisation and localisation procedures.