Methods of construction of OWA operators from data

This paper investigates the problem of obtaining the weights of the ordered weighted aggregation (OWA) operators from observations. The problem is formulated as a restricted least squares and uniform approximation problems. We take full advantage of the linearity of the problem. In the former case, a well known technique of non-negative least squares is used. In a case of uniform approximation, we employ a recently developed cutting angle method of global optimisation. Both presented methods give results superior to earlier approaches, and do not require complicated nonlinear constructions. Additional restrictions, such as degree of orness of the operator, can be easily introduced

Implementation of novel methods of global and nonsmooth optimization : GANSO programming library

We discuss the implementation of a number of modern methods of global and nonsmooth continuous optimization, based on the ideas of Rubinov, in a programming library GANSO. GANSO implements the derivative-free bundle method, the extended cutting angle method, dynamical system-based optimization and their various combinations and heuristics. We outline the main ideas behind each method, and report on the interfacing with Matlab and Maple packages.

Non-smooth optimization methods for computation of the conditional value-at-risk and portfolio optimization

We examine numerical performance of various methods of calculation of the Conditional Value-at-risk (CVaR), and portfolio optimization with respect to this risk measure. We concentrate on the method proposed by Rockafellar and Uryasev in (Rockafellar, R.T. and Uryasev, S., 2000, Optimization of conditional value-at-risk. Journal of Risk, 2, 21-41), which converts this problem to that of convex optimization. We compare the use of linear programming techniques against a non-smooth optimization method of the discrete gradient, and establish the supremacy of the latter. We show that non-smooth optimization can be used efficiently for large portfolio optimization, and also examine parallel execution of this method on computer clusters.

Experimental and numerical evaluation of forming and fracture behaviour of high strength steel

Car manufacturers are under pressure to reduce vehicle mass while maintaining comfort and passenger safety for current and future vehicles. To meet this demand the steel industry has developed Advanced High Strength Steels (AHSS) that promise higher strength and improved formability compared to conventional steel grades. Even though significant research has already been performed to evaluate the material properties and forming behaviour of most AHSS types, only a limited literature is available on their necking and fracture behaviour and the effect on formability. This paper examines and compares the thinning, necking and fracture behaviour of two AHSS and one conventional steel type, namely TRIP, DP and HSLA. Uniaxial, plane and biaxial strain conditions are investigated by tensile, cup drawing and stretch forming tests and by using numerical methods. The test results indicate that significant differences exist in necking and fracture behaviour between all three steel types.

Integral approach and numerical improvement to calculate the carbon concentration profiles in carburising process

In the present work, the carbon diffusion in steel, where the carbon diffusivity varies with the carbon content, was solved with the integral methods under the third boundary condition. The variation of carbon diffusivity in steel with the carbon content was described with two different functions ie. linear dependence and exponential dependence. The integral approximation for both cases was improved with the numerical computation to more accurately predict the carbon profiles. The integral solution is more accurate than the formulation based on the assumption of a constant diffusivity or those based on the assumption of a constant diffusivity and/or constant carbon content at part surface. It is also more easily used in practice than the numerical method to describe the carburising process and predict the carbon content at steel surface and carbon profiles in treated layer.

Selecting the individual numerical scale and prioritization method in the analytic hierarchy process : a 2-tuple fuzzy linguistic approach

The validity of the priority vector used in the analytic hierarchy process (AHP) relies on two factors: the selection of a numerical scale and the selection of a prioritization method. The traditional AHP selects only one numerical scale (e.g., the Saaty scale) and one prioritization method (e.g., the eigenvector method) for each particular problem. For this traditional selection approach, there is disagreement on which numerical scale and prioritization method is better in deriving a priority vector. In fact, the best numerical scale and the best prioritization method both rely on the content of the pairwise comparison data provided by the AHP decision makers. By defining a set of concepts regarding the scale function and the linguistic pairwise comparison matrices (LPCMs) of the priority vector and by using LPCMs to unify the format of the input and output of AHP, this paper extends the AHP prioritization process under the 2-tuple fuzzy linguistic model. Based on the extended AHP prioritization process, we present two performance measure criteria to evaluate the effect of the numerical scales and prioritization methods. We also use the performance measure criteria to develop a 2-tuple fuzzy linguistic multicriteria approach to select the best numerical scales and the best prioritization methods for different LPCMs. In this paper, we call this type of selection the individual selection of the numerical scale and prioritization method. We also compare this individual selection with traditional selection by using both random and real data and show better results with individual selection.

Evaluation of the thermal behaviour of bevelled cutting inserts using a numerical approach

The nose geometry of a hard and brittle metal cutting tool is generally modified in order to avoid the premature failure due to fracture under tensile stresses. While most research findings point to a favourable mechanical load pattern, the possible influence of the shape of the geometry on the thermal fields and the consequent changes in the stressed state of the tool seem to have attained less attention. The present work aims at establishing the thermal behaviour of bevelled tools under varying geometrical and process parameters. Data generated from statistically designed experiments and quick-stop chip samples are coupled to conduct numerical investigations using a mixed finite and boundary element solution to obtain the temperature distribution in bevelled carbide inserts. Due consideration is given to the presence of the stagnation zone and its size and shape. While the cutting forces and temperatures increased owing to the blunt shape of the tool, the possible absence of tensile stresses was found to be the likely effect of a more uniform temperature distribution resulting from a significant plastic contact on the principal flank and the consequent flank heat source. The characteristic low-temperature zones close to the nose of the conventional tool are taken over by the stagnation zone in bevelled tools. © IMechE 2007.

Damage identification of steel beams using local and global methods

Structural condition monitoring methods can be generally classified as local and global. While the global method needs only a small number of sensors to measure the low-frequency structural vibration properties, the acquired information is often not sufficiently sensitive to minor damages in a structure. Local methods, on the other hand, could be very sensitive to minor damages but their detection range is usually small. To overcome the drawbacks and take advantage of both methods, an integrated condition monitoring system has been recently developed for structural damage detection, which combines guided wave and structural vibration tests. This study aims at finding a viable damage identification method for steel structures by using this system. First, a spectral element modelling method is developed, which can simulate both wave propagation and structural vibration properties. Then the model is used in updating analysis to identify crack damage. Extensive numerical simulations and model updating works are conducted. The experimental and numerical results suggest that simply combining the objective functions cannot provide better structural damage identification. A two-stage damage identification scheme is more suitable for identifying damage in steel beams.

Integral approach and numerical improvement to calculate carbon concentration profiles in carburising

The carbon diffusion in steel, where the carbon diffusivity varies with the carbon content, was solved with the integral methods under the third boundary condition. The variation of carbon diffusivity in steel with the carbon content was described with two different functions, linear dependence and exponential dependence. The integral approximation for both cases was improved with the numerical computation to more accurately predict the carbon profiles. The integral solution is more accurate than the formulation based on the assumption of a constant diffusivity or those based on the assumption of a constant diffusivity and/or constant carbon content at part surface. It is also more easily used in practice than the numerical method to describe the carburising process and predict the carbon content at steel surface and carbon profiles in treated layer.

Tracking single bubble in Hall-Héroult aluminium cell : an experimental and numerical study

In simulations of the hydrodynamics of the multiphase flow in gas– liquid systems with finite sizes of bubbles, the important thing is to compute explicitly the time evolution of the gas–liquid interface in many engineering applications. The most commonly used methods representing this approach are: the volume of fluid and the phase field methods. The later has gained significant interest because of its capability of performing numerical computations on a fixed Cartesian grid without having to parametrise these objects (Eulerian approach) and at the same time it allows to follow the interface ( for example bubble’s shape) that change the topology. In this paper, both numerical (phase field method) and experimental results for the bubble shapes underneath a downward facing plane is presented. Experiments are carried out to see the bubble sliding motion underneath a horizontal and inclined anode. It is assumed that the bubble formed under the anode surface is deformed (flattened) due to buoyant field before it goes around the anode corner. The bubble elongates to form a tail-like shape. The change in shape of the bubble is almost instantaneous and has a significant effect on the localised hydrodynamics around the bubble, which could influence the dynamics of the flow patterns in the Hall–Héroult cell. This deformation is the main cause of the bubble wake and the induced flow field in the aluminium cell. Various parameters such as bubble size, deformation and its sliding mechanism at different surface tensions are discussed and compared with experimental results.

Fracture modelling of DP780 sheets using a hybrid experimental-numerical method and two-dimensional digital image correlation

This paper is concerned with the construction of fracture envelopes of DP780 sheets using two methods: a hybrid experimental-numerical method; two-dimensional digital image correlation (2D-DIC). For the hybrid method, four types of ductile fracture tests were carried out covering a wide range of stress states on specimens: with a central hole; two symmetric circular notches; flat grooved; and diagonally double-notched. Based on the fracture strain and loading paths identified with finite element simulation, a fracture envelope was obtained by employing the three-parameter modified Mohr-Coulomb fracture model. In addition, the fracture surface strain was directly measured using 2D-DIC. Loading histories of each test were extracted from a surface element of a three dimensional finite element model. The comparison of fracture envelopes constructed by the two methods reveals that there is little difference. Thus, it can be concluded that 2D-DIC is applicable to fracture modelling of DP780 sheets despite the assumption of the plane stress condition even after necking

A new method for deriving priority weights by extracting consistent numerical-valued matrices from interval-valued fuzzy judgement matrix

It is important to derive priority weights from interval-valued fuzzy preferences when a pairwise comparative mechanism is used. By focusing on the significance of consistency in the pairwise comparison matrix, two numerical-valued consistent comparison matrices are extracted from an interval fuzzy judgement matrix. Both consistent matrices are derived by solving the linear or nonlinear programming models with the aid of assessments from Decision Makers (DMs). An interval priority weight vector from the extracted consistent matrices is generated. In order to retain more information hidden in the intervals, a new probability-based method for comparison of the interval priority weights is introduced. An algorithm for deriving the final priority interval weights for both consistent and inconsistent interval matrices is proposed. The algorithm is also generalized to handle the pairwise comparison matrix with fuzzy numbers. The comparative results from the five examples reveal that the proposed method, as compared with eight existing methods, exhibits a smaller degree of uncertainty pertaining to the priority weights, and is also more reliable based on the similarity measure. © 2014 Elsevier Inc. All rights reserved.

Slope stability charts for two-layered purely cohesive soils based on finite-element limit analysis methods

Stability charts for soil slopes, first produced in the first half of the twentieth century, continue to be used extensively as design tools, and draw the attention of many investigators. This paper uses finite-element upper and lower bound limit analysis to assess the short-term stability of slopes in which the slopematerial and subgrade foundation material have two distinctly different undrained strengths. The stability charts are proposed, and the exact theoretical solutions are bracketed to within 4.2% or better. In addition, results from the limit-equilibrium method (LEM) have been used for comparison. Differences of up to 20% were found between the numerical limit analysis and LEM solutions. It also shown that the LEM sometimes leads to errors, although it is widely used in practice for slope stability assessments.

Consensus building in a local context for the AHP-GDM with the individual numerical scale and prioritization method

The methodology for selecting the individual numerical scale and prioritization method has recently been presented and justified in the analytic hierarchy process (AHP). In this study, we further propose a novel AHP-group decision making (GDM) model in a local context (a unique criterion), based on the individual selection of the numerical scale and prioritization method. The resolution framework of the AHP-GDM with the individual numerical scale and prioritization method is first proposed. Then, based on linguistic Euclidean distance (LED) and linguistic minimum violations (LMV), the novel consensus measure is defined so that the consensus degree among decision makers who use different numerical scales and prioritization methods can be analyzed. Next, a consensus reaching model is proposed to help decision makers improve the consensus degree. In this consensus reaching model, the LED-based and LMV-based consensus rules are proposed and used. Finally, a new individual consistency index and its properties are proposed for the use of the individual numerical scale and prioritization method in the AHP-GDM. Simulation experiments and numerical examples are presented to demonstrate the validity of the proposed model.