Methods for uncertainty propagation in life cycle assessment

Life cycle assessment (LCA) calculates the environmental impact of a product over its entire life cycle. Uncertainty analysis is an important aspect in LCA, and is usually performed using Monte Carlo sampling. In this study, Monte Carlo sampling, Latin hypercube sampling, quasi Monte Carlo sampling, analytical uncertainty propagation and fuzzy interval arithmetic were compared based on e.g. convergence rate and output statistics. Each method was tested on three LCA case studies, which differed in size and behaviour. Uncertainty propagation in LCA using a sampling method leads to more (directly) usable information compared to fuzzy interval arithmetic or analytical uncertainty propagation. Latin hypercube and quasi Monte Carlo sampling provide more accuracy in determining the sample mean than Monte Carlo sampling and can even converge faster than Monte Carlo sampling for some of the case studies discussed in this paper.     

Domain reduction for Benders decomposition based global optimization

While domain reduction has been successfully applied in branch-and-bound based global optimization over the last two decades, it has not been systematically studied for decomposition based global optimization, which is usually more efficient for problems with decomposable structures. This paper discusses integration of domain reduction in Benders decomposition based global optimization, specifically, generalized Benders decomposition (GBD) and nonconvex generalized Benders decomposition (NGBD). Revised GBD and NGBD frameworks are proposed to incorporate bound contraction operations or/and range reduction calculations, which can reduce the variable bounds and therefore improve the convergence rate and expedite the solution of nonconvex subproblems. Novel customized bound contraction problems are proposed for GBD and NGBD, and they are easier to solve than the classical bound contraction problems because they are defined on reduced variable spaces. The benefits of the proposed methods are demonstrated through a gas production operation problem and a power distribution system design problem.     

Three-level designs: Evaluation and comparison for screening purposes

Since their introduction by Box and Hunter, resolution criteria have been widely used when comparing regular fractional factorials designs. In this article, we investigate how a generalized resolution criterion can be used to assess some recently developed three-level screening designs, such as definitive screening designs (DSDs) and screening designs from weighing matrices. The aim of this paper is to capture the projection properties of those three-level screening designs, complementing the work of Deng and Tang, who used generalized resolution and minimum aberration criteria for ranking different two-level designs, particularly Plackett-Burman and other nonregular factorial designs. An advantage of generalized resolution, extended here to work on three-level designs, is that it offers a useful criterion for ranking three-level screening designs, whereas the Deng and Tang resolution is used mainly for the assessment of two-level designs. In addition, we applied a projection estimation capacity (PEC) criterion to select three-level screening designs with desirable properties. Practical examples and the best projections of the designs are presented in tables.     

Mechanical buckling of two-dimensional functionally graded cylindrical shells surrounded by Winkler–Pasternak elastic foundation

In this research, buckling analysis of a two-dimensional, functionally graded, cylindrical shell that has been embedded in an outer elastic medium in the presence of combined axial and transverse loading based on third-order shear deformation shell theory is numerically investigated. Variations of the shell properties are considered to be continuous through length and thickness. Winkler–Pasternak foundation and simply supported boundary conditions have been applied. The problem has been solved using the generalized differential quadrature method. Geometrical, load, and foundation parameters beside functionally graded power indexes effects on the critical buckling load have been studied.     

Finding better weight functions for generalized Shepard's operator on infinite intervals

In this paper, we investigate the difference of Shepard's generalized operators S _σ from the approximated set of data for various weight functions σ. Bounds are given for the sizes of the ‘bumps’ shown on the graph of S _σ for σ(d)=1/d in dimension N=1, and the best weight function σ for practical use is proposed.     

Calculation of Coupling Coefficients of Coupled Reactors Theory Using the Generalized Perturbation Theory

Recently, rigorous multi-point equations are derived using the region-wise importance functions to produce fission neutrons. Since the coupling coefficients used in these multi-point equations are calculated with the weight of these importance functions but not the adjoint function used in the conventional perturbation theory, errors due to the change of the flux is introduced in the coupling coefficients for a perturbed system if the unperturbed flux is used.

It is shown that using the generalized perturbation theory, the coupling coefficients using the unperturbed flux can be obtained taking into account the first order change of the flux due to the perturbation, and the same accuracy as the conventional perturbation theory in which the adjoint function is used can be obtained in the case of one-point reactor.     

Thermo-mechanical vibration analysis of rotating nonlocal nanoplates applying generalized differential quadrature method

In this study, thermal and small-scale effects on the flapwise bending vibrations of a rotating nanoplate, which can be the basis of nano-turbine design, have been analyzed. The nano-turbine is made of an orthotropic nanoplate with a setting angle that is modeled based on the classical plate theory (CPT) with cantilever boundary conditions. The axial forces are also included in the model as the true spatial variation due to the rotation and temperature change. The governing equations and boundary conditions are derived according to Hamilton's principle and the governing equations are solved with the aid of the generalized differential quadrature method. The effects of small-scale parameter, nondimensional angular velocity, temperature change, and setting angles in the first four nondimensional frequencies are discussed. Due to the consideration of the rotating effects, results of this study are applicable in nano-machines, such as nano-motors, nano-rotor, and other rotating nano-structures. Also, by considering the effect of thermal loading on rotation of a nanoplate, the results are useful in the design of nano-turbines.     

ORDERING FUZZY SETS BY CONSENSUS CONCEPT AND FUZZY RELATION EQUATIONS

A general class of consensus measures of fuzzy sets is introduced in this paper. It is shown that, while the consensus measures are valuations but neither isotone nor antitone with respect to the lattice structure induced by the pointwise maximum and minimum operations to the set of all the fuzzy sets on a nonempty crisp set, they are antitone valuations with respect to the lattice structure induced by the generalized sharpening relation to a quotient set of the set of fuzzy sets. It is also shown that the solutions of a finite fuzzy relation equation that have the maximum consensus measure can be characterized through the join operation of the latter lattice in terms of the maximum solution and some of the minimal solutions of the equation.     

Induced continuous Choquet integral operators and their application to group decision making

With respect to multi-attribute group decision making, in this study two induced continuous Choquet integral operators named as the induced continuous Choquet weighted averaging (ICCWA) operator and the induced continuous Choquet geometric mean (ICCGM) operator are defined, which reflect the interactive characteristics between elements. Meantime, some associated desirable properties are studied to provide assurance in applications. In order to globally reflect the interactions between elements, we further define the probabilistic generalized semivalue ICCWA (PGS-ICCWA) operator and the probabilistic generalized semivalue ICCGM (PGS-ICCGM) operator. If the information about the weights of experts and attributes is incompletely known, the models for the optimal fuzzy measures on experts set and on attribute set based on consistency principle and TOPSIS method are respectively established. Moreover, an approach to uncertain multi-attribute group decision making with incomplete weight information and interactive conditions is developed. Finally, a numerical example is provided to illustrate the practicality and feasibility of the developed procedure.