Optimisation for multi-part flow-line configuration of reconfigurable manufacturing system using GA

To facilitate the configuration selection of reconfigurable manufacturing systems (RMS) at the beginning of every demand period, it needs to generate K (predefined number) best configurations as candidates. This paper presents a GA-based approach for optimising multi-part flow-line (MPFL) configurations of RMS for a part family. The parameters of the MPFL configuration comprise the number of workstations, the number of paralleling machines and machine type as well as assigned operation setups (OSs) for each workstation. Input requirements include an operation precedence graph for each part, relationships between operations and OSs as well as machine options for each OS. The objective is to minimise the capital cost of MPFL configurations. A 0-1 nonlinear programming model is developed to handle sharing machine utilisation over consecutive OSs for each part which is ignored in the existing approach. Then a novel GA-based approach is proposed to identify K economical solutions within a refined solution space comprising the optimal configurations associated with all feasible OS assignments. A case study shows that the best solution found by GA is better than the optimum obtained by the existing approach. The solution comparisons between the proposed GA and a particle swarm optimisation algorithm further illustrate the effectiveness and efficiency of the proposed GA approach.     

Homotopy analysis of nonlinear progressive waves in deep water

This paper describes the application of a recently developed analytic approach known as the homotopy analysis method to derive a solution for the classical problem of nonlinear progressive waves in deep water. The method is based on a continuous variation from an initial trial to the exact solution. A Maclaurin series expansion provides a successive approximation of the solution through repeated application of a differential operator with the initial trial as the first term. This approach does not require the use of perturbation parameters and the solution series converges rapidly with the number of terms. In the framework of this approach, a new technique to apply the Padé expansion is implemented to further improve the convergence. As a result, the calculated phase speed at the 20th-order approximation of the solution agrees well with previous perturbation solutions of much higher orders and reproduces the well-known characteristics of being a non-monotonic function of wave steepness near the limiting condition.     

Lagrangian finite element analysis of Newtonian fluid flows

A fully Lagrangian finite element method for the analysis of Newtonian flows is developed. The approach furnishes, in effect, a Lagrangian implementation of the compressible Navier–Stokes equations. As the flow proceeds, the mesh is maintained undistorted through continuous and adaptive remeshing of the fluid mass. The principal advantage of the present approach lies in the treatment of boundary conditions at material surfaces such as free boundaries, fluid/fluid or fluid/solid interfaces. In contrast to Eulerian approaches, boundary conditions are enforced at material surfaces ab initio and therefore require no special attention. Consistent tangents are obtained for Lagrangian implicit analysis of a Newtonian fluid flow which may exhibit compressibility effects. The accuracy of the approach is assessed by comparison of the solution for a sloshing problem with existing numerical results and its versatility demonstrated through a simulation of wave breaking. The finite element mesh is maintained undistorted throughout the computation by recourse to frequent and adaptive remeshing © 1998 John Wiley & Sons, Ltd.     

Nonlinear model order reduction based on local reduced‐order bases

A new approach for the dimensional reduction via projection of nonlinear computational models based on the concept of local reduced‐order bases is presented. It is particularly suited for problems characterized by different physical regimes, parameter variations, or moving features such as discontinuities and fronts. Instead of approximating the solution of interest in a fixed lower‐dimensional subspace of global basis vectors, the proposed model order reduction method approximates this solution in a lower‐dimensional subspace generated by most appropriate local basis vectors. To this effect, the solution space is partitioned into subregions, and a local reduced‐order basis is constructed and assigned to each subregion offline. During the incremental solution online of the reduced problem, a local basis is chosen according to the subregion of the solution space where the current high‐dimensional solution lies. This is achievable in real time because the computational complexity of the selection algorithm scales with the dimension of the lower‐dimensional solution space. Because it is also applicable to the process of hyper reduction, the proposed method for nonlinear model order reduction is computationally efficient. Its potential for achieving large speedups while maintaining good accuracy is demonstrated for two nonlinear computational fluid and fluid‐structure‐electric interaction problems. Copyright © 2012 John Wiley & Sons, Ltd.     

Tabu search algorithm for flexible flow path design of unidirectional automated-guided vehicle systems

The unidirectional flow path design problem is one of the most important but difficult problems for the efficient design of automated-guided vehicle systems. As the problem was first formulated by Gaskins and Tanchoco, many researchers have studied the problem. However, the existing solution methods fail to provide an efficient solution approach. In this paper, a mathematical model for the unidirectional flow path design problem is developed. To obtain a near-to-optimal solution in reasonable computation time, a tabu search algorithm is presented. A fast construction algorithm first obtains a feasible initial solution, and a long-term memory structure and a neighbor solution generation approach are adapted to the problem characteristics and embedded in the proposed tabu search algorithm. Computational experiments show that the developed tabu search algorithm outperforms the Ko and Egbelu’s algorithm, Int J Prod Res, 41:2325–2343, (2003).     

Zone merge sequencing in an automated order picking system

This paper considers the zone automated order fulfilment systems with a number of zones linked by a main conveyor. Each zone has a number of dispensers and a buffer. Each dispenser holds one type of item and dispenses the items for an order into a buffer before the items are merged to the main conveyor. Due to variability of the mix of item types and number of items for each type in successive orders, idle time or open space on the conveyor can occur if the buffers merge the items to the conveyor sequentially. The idle time prolongs the order fulfilment duration. This paper aims to provide a solution to reduce the idle time or open space by optimising the merging sequences among zones. A model is developed to find merging sequences with minimum order fulfilment time. However, the model is strongly NP-hard. A greedy heuristic-based solution approach is thus developed. Experiment performance shows that the presented solution can reduce the order fulfilment time approximately 5% with both empirical data and simulation data. Moreover, the sensitivity analysis is conducted to measure the effect of the solution under the variation of zone numbers and order structures. Although the idle time reduction can be achieved with any number of zones and order structures, it was most significant in certain range of zone numbers and appropriate order structures.     

The design of fault tolerant systems: Prevention is better than cure

The largest threat to the efficient and safe operation of complex processes comes from erroneous actions by the humans in the system. The number of erroneous actions can be reduced and the consequences be mitigated in two principally different ways. The passive approach concentrates on how the system is designed, implemented and applied. The active approach concentrates on the system in use, as exemplified by automation in various forms, protection systems, computerised operator support, and various types of expert systems. A specific solution is to make the systems fault tolerant, i.e. forgiving of erroneous actions and able to limit the consequences through interlocks and automatic shut-down mechanisms. Yet practically all fault tolerant systems come into action after the erroneous action has occurred and has had a detectable effect. It would clearly be attractive to detect erroneous actions when they occur, possibly before they have had any effect, i.e. effectively to prevent them from happening.The paper describes the development and functioning of a system which provides an on-line detection of erroneous actions in a process domain. The system, which is called RESQ, is based on a combination of plan recognition, plan evaluation and error handling. It has been developed within the ESPRIT Project P857 ‘Graphical Dialogue Environment’, and is presently implemented for a data network. RESQ is written in Common LISP and is, with the necessary exception of a plan library, completely domain independent.     

A p-adaptive scaled boundary finite element method based on maximization of the error decrease rate

This study enhances the classical energy norm based adaptive procedure by introducing new refinement criteria, based on the projection-based interpolation technique and the steepest descent method, to drive mesh refinement for the scaled boundary finite element method. The technique is applied to p-adaptivity in this paper, but extension to h- and hp-adaptivity is straightforward. The reference solution, which is the solution of the fine mesh formed by uniformly refining the current mesh, is used to represent the unknown exact solution. In the new adaptive approach, a projection-based interpolation technique is developed for the 2D scaled boundary finite element method. New refinement criteria are proposed. The optimum mesh is assumed to be obtained by maximizing the decrease rate of the projection-based interpolation error appearing in the current solution. This refinement strategy can be interpreted as applying the minimisation steepest descent method. Numerical studies show the new approach out-performs the conventional approach.     

Multiple pole residue approach for 3D BEM analysis of mathematical degenerate and non‐degenerate materials

In this paper we develop an alternative boundary element method (BEM) formulation for the analysis of anisotropic three‐dimensional (3D) elastic solids. Our implementation is based on the derivation of explicit expressions for the fundamental solution displacements and tractions, of general validity for any class of anisotropic materials, by means of Stroh formalism and Cauchy's residue theory. The resulting fundamental solution remains valid for mathematical degenerate cases when Stroh's eigenvalues are coincident, meanwhile it does not exhibit numerical instabilities for quasi‐degenerate cases when Stroh's eigenvalues are nearly equal. A multiple pole residue approach is followed, leading to general explicit expressions to evaluate the traction fundamental solution for poles of m‐multiplicity. Despite the existence of general displacement solutions in the literature, and for the sake of completeness, the same approach as for the traction solution is considered to derive the displacement fundamental solution as well. Based on these solutions, an explicit BEM approach for the numerical solution of 3D linear elastic problems for solids with general anisotropic behavior is presented. The analysis of cracked anisotropic solids is also considered. Details on the numerical implementation and its validation for degenerate cases are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

A class of parallel multiple‐front algorithms on subdomains

A class of parallel multiple‐front solution algorithms is developed for solving linear systems arising from discretization of boundary value problems and evolution problems. The basic substructuring approach and frontal algorithm on each subdomain are first modified to ensure stable factorization in situations where ill‐conditioning may occur due to differing material properties or the use of high degree finite elements (p methods). Next, the method is implemented on distributed‐memory multiprocessor systems with the final reduced (small) Schur complement problem solved on a single processor. A novel algorithm that implements a recursive partitioning approach on the subdomain interfaces is then developed. Both algorithms are implemented and compared in a least‐squares finite‐element scheme for viscous incompressible flow computation using h‐ and p‐finite element schemes. Copyright © 2003 John Wiley & Sons, Ltd.     

2D simulation of the deformation of pH-sensitive hydrogel by novel strong-form meshless random differential quadrature method

The objective of presented work is to simulate the response of 2D hydrogel when subjected to the varying pH of buffer solution and initial fixed-charge concentration inside the hydrogel. The novelty of the work is that this is the first attempt to perform the 2D simulation of pH-responsive hydrogel by novel strong-form meshless method, such as random differential quadrature (RDQ) method. The analytical equations, derived for the hydrogel deformation in the x and y directions, are numerically verified by the square shaped hydrogel disc. The jumps in the distributions of ionic concentrations and electrical potential, across the interface between solution and hydrogel, are effectively captured by the RDQ method. A novel approach is proposed to correctly impose natural boundary conditions for non-uniform boundary. The effects of solution pH and initial fixed-charge concentration on the hydrogel swelling are also successfully investigated.     

Adaptive multiresolution refinement with distance fields

This paper describes a multiresolution approach to field modeling that can be used with any meshfree or mesh‐based method for adaptive solution refinement. The refined solution is represented as a superposition of a coarse (unrefined) solution and a sequence of refinements that provide additional degrees of freedom with higher spatial or functional resolution. Each refinement is treated as a solution to a boundary‐value problem within a specified refinement window. The proposed approach is based on the meshfree method with distance fields (Comput. Mech. 2000; 25 :305–316, Eng. Comput. 2002; 18 (4):295–311) and guarantees C^m continuity of the refined solutions with matching or non‐matching grids. The method does not restrict the shape of the refinement window and does not place any constraints on the type of basis functions, or relative position and resolution of the refinement grids. Combining the proposed approach with hierarchical space decompositions and a posteriori error estimators results in an effective tool for automatic solution refinement. Carefully chosen numerical examples illustrate the power and advantages of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

A note on the series solution of the solitary wave problem

Summary Previousnumerical calculations have indicated that the series solution of the solitary wave problem is an asymptotic series rather than a convergent series. In this Note a new approach to obtain this series solution is proposed which makes it possible to show, solelyanalytically, that it must necessarily be so.     

A solution via generalised intergral transform technique for the simultaneous transport processes during combustion of wood cylinders

A non‐linear moving boundary diffusion problem is proposed as a simple model for the heat transfer during combustion of wood cylinders. Such a problem is solved here by applying the generalized integral transform technique. A new filtering strategy, denoted as local‐instantaneous filter, is used in order to accelerate the convergence of the series‐solution obtained with the present hybrid numerical–analytical technique. We show that the use of such filtering approach reduces the stiffness of the system of ordinary differential equations, resultant from the integral transformation of the original problem. Hence, subroutines based on simpler and faster methods can be used for the solution of such systems. Results are presented in the paper for the combustion of cylinders of different sizes and involving different initial moisture contents and densities. The effects on the solution of different models available in the literature for the evaluation of thermal conductivity and specific heat are also addressed on the paper. Copyright © 2000 John Wiley & Sons, Ltd.     

A Method of Fitting the Regression Curve E(y) = α + δx + βρ x

In the curve E(y) = α + δx + βρ ^x , the estimation of the parameter ρ is of vital importance. Shah and Pate1 [2] have described a least-squares solution by using tables. A simple approach of finding a quick estimate of ρ with high efficiency is discussed here in detail. A table is given in order to simplify the calculation of the estimate. Two Chemical Engineering examples are discussed to illustrate the method.     

Computation of resonant modes for axisymmetric Maxwell cavities using hp‐version edge finite elements

The computation of the resonant frequencies for closed cavities is not a trivial task: Multi‐materials and sharp corners all give rise to highly singular eigenfunctions. However, an approach using hp‐finite elements is well suited to such problems and, with the correct combination of h‐ and p‐refinements, it yields the theoretically predicated exponential rates of convergence. In this paper, we present a novel approach to the solution of axisymmetric cavity problems which uses a hierarchic H¹ and H (curl) conforming finite element basis. A selection of numerical examples is included and these demonstrate that the exponential rates of convergence are achieved in practice. Copyright © 2005 John Wiley & Sons, Ltd.     

Hierarchical model reduction at multiple scales

A hierarchical model reduction approach aimed at reducing computational complexity of non‐linear homogenization at multiple scales is developed. The method consists of the following salient features: (1) formulation of non‐linear unit cell problems at multiple scales in terms of eigendeformation modes that a priori satisfy equilibrium equations at multiple scales and thus eliminating the need for costly solution of discretized non‐linear equilibrium, (2) the ability to control the discretization of the eigendeformation modes at multiple scales to maintain desired accuracy, and (3) hierarchical solution strategy that requires sequential solution of single‐scale problems. A two‐scale formulation is verified against an one‐dimensional model problem for which an analytical solution can be obtained and a three‐scale formulation is validated against tube crash experiments. Copyright © 2009 John Wiley & Sons, Ltd.     

End Effects in the Three-Omega Method to Measure Gas Thermal Conductivity

A two-dimensional analytical solution is derived for the three-omega method for measurement of thermal conductivity of materials with a fine wire. The analytical solution includes the wire heat capacity and the effect of heat losses from the ends of the wire. To derive the solution, finite Fourier transforms are applied in the direction parallel to the wire axis. The solution is compared with a one-dimensional solution and experimental data. It is found that heat losses from the wire ends have a significant effect on the 3ω components at low frequency and tend to be less important at high frequency. Moreover, it is shown that two-dimensional effects will be severe for nano-scale wires, even if the wire length-to-diameter ratio is very large.     

Cohesive stresses and size effect in quasi-brittle materials

A novel approach to the derivation of Bažant’s size effect law is presented. Contrarily to the original Lagrangian derivation which hinged on energetic consideration, a Newtonian approach based on local stress intensity factors is presented. Through this approach, it is shown that Bažant’s size effect law is the first (and dominant) term in a series expansion for the nominal stress. Furthermore, analytical expressions forB are derived for selected specimen geometries.     

Bayes approach in RDT using accelerated and long-term life data

A common problem of reliability demonstration testing (RDT) is the magnitude of total time on test required to demonstrate reliability to the consumer’s satisfaction, particularly in the case of high reliability components. One solution is the use of accelerated life testing (ALT) techniques. Another is to incorporate prior beliefs, engineering experience, or previous data into the testing framework. This may have the effect of reducing the amount of testing required in the RDT in order to reach a decision regarding conformance to the reliability specification. It is in this spirit that the use of a Bayesian approach can, in many cases, significantly reduce the amount of testing required.We demonstrate the use of this approach to estimate the acceleration factor in the Arrhenius reliability model based on long-term data given by a manufacturer of electronic components (EC). Using the Bayes approach we consider failure rate and acceleration factor to vary randomly according to some prior distributions. Bayes approach enables for a given type of technology the optimal choice of test plan for RDT under accelerated conditions when exacting reliability requirements must be met. These requirements are given by a hypothetical consumer by two different ways. The calculation of posterior consumer’s risk is demonstrated in both cases.The test plans are optimum in that they take into account Var{λ|data}, posterior risk, E{λ|data}, Median λ or other percentiles of λ at data observed at the accelerated conditions. The test setup assumes testing of units with time censoring.