A matrix-based clustering approach for the decomposition of design problems

In matrix-based modeling, a design problem is represented by a rectangular matrix that captures the dependency relationships between design functions and parameters. To decompose such a matrix-based design problem, the two-phase method, which adapts hierarchical cluster analysis, has been proposed in literature. Yet, the clustering strategy in general is still challenging since the decomposition of design problems requires simultaneous clustering of two types of objects (i.e., design functions and parameters). In this paper, the notion of coupling is advanced by characterizing the coupling between two objects of different types. Accordingly, the two-phase method is revised via two methodical components: coupling-based dependency analysis and tree-based partitioning analysis. While the coupling-based dependency analysis concatenates different types of coupling for organizing the dependency structure, the tree-based partitioning analysis utilizes the coupling information from dependency analysis to identify design sub-problems and their interactions. Due to a better understanding of the coupling notion, the revised approach is able to simplify the algorithmic procedure and narrow down the solution search space without compromising the solution quality. Two examples (i.e., a relief valve system and a powertrain system) are used to demonstrate and justify the utility of the revised method.     

A matrix-based Bayesian approach for manufacturing resource allocation planning in supply chain management

Nowadays, the supply chain of manufacturing resources is typically a large complex network, whose management requires network-based resource allocation planning. This paper presents a novel matrix-based Bayesian approach for recommending the optimal resource allocation plan that has the largest probability as the optimal selection within the context specified by the user. A proposed matrix-based representation of the resource allocation plan provides supply chain modelling with a good basis to understand problem complexity, support computer reasoning, facilitate resource re-allocation, and add quantitative information. The proposed Bayesian approach produces the optimal, robust manufacturing resource allocation plan by solving a multi-criteria decision-making problem that addresses not only the ontology-based static manufacturing resource capabilities, but also the statistical nature of the manufacturing supply chain, i.e. probabilities of resource execution and resource interaction execution. A genetic algorithm is employed to solve the multi-criteria decision-making problem efficiently. We use a case study from manufacturing domain to demonstrate the applicability of the proposed approach to optimal manufacturing resource allocation planning.     

Nonlinearized approach to profile inversion

A method for reconstructing the index of refraction of a bounded inhomogeneous object of known geometric configuration from measured far-field scattering data is presented. This work is an extension of recent results on the direct scattering problem wherein the governing domain integral equation was solved iteratively by a successive relaxation technique. The relaxation parameters were chosen to minimize the residual error at each step. Convergence of this process was established for indices of refraction much larger than required for convergence of the Born approximation. For the inverse problem, the same technique is applied, except is this case both the index of refraction and the field are unknown. Iterative solutions for both unknowns are postulated with two relaxation parameters at each step. They are determined by simultaneously minimizing the residual errors in satisfying the domain integral equation and matching the measured data. This procedure retains the nonlinear relation between the two unknowns. Numerical results are presented for the dielectric slab. The algorithm is shown to be effective in cases where the iterative solution of the direct problem is rapidly convergent and outperforms the Born-based approaches.     

A substrate-independent lift-off approach for patterning functional surfaces

A lift-off method for creating multifunctional patterned surfaces has been devised. It entails consecutive pulsed plasmachemical deposition of a reactive bottom layer and a protective top release layer. By way of example, a bottom/top layer combination comprising pulsed plasma deposited poly(glycidyl methacrylate)/poly(pentafluorostyrene) has been shown to display selective adhesive lift-off of the latter. Application of a prepatterned adhesive template yields well-defined arrays of reactive epoxide functionality surrounded by a passive fluoropolymer background or vice versa.     

A nonholonomic approach to isoparallel problems and some applications

Isoparallel problems are a class of optimal control problems on principal fibre bundles endowed with a connection and a Riemannian metric on the base space. These problems consist of finding the shortest curve on the base among those with a given parallel transport operator. It has been shown that when the structure group of the principal bundle admits a bi-invariant metric, the normal solutions are precisely the projections of the geodesics (relative to an appropriate Riemannian metric) on the bundle. In this work we obtain a generalization of this result that holds true for any structure group, by transforming the isoparallel problem into a nonholonomic problem of a generalized type. The latter reduces to the geodesic problem if the structure group has a bi-invariant metric. We illustrate the theory with an application to the optimal control of an elastic rolling ball (the plate-ball system), relating some aspects of this problem to the dynamics of a simple pendulum. Finally, we indicate how the study of locomotion of microorganisms can benefit from this approach. This work shows how optimal control and generalized nonholonomic mechanics are related within the context of Lagrangian reduction.     

The diagonalized contrast source inversion approach for elastic wave inversion

This study focuses on the inverse scattering of objects embedded in a homogeneous elastic background. The medium is probed by ultrasonic sources, and the scattered fields are observed along a receiver array. The goal is to retrieve the shape, location, and constitutive parameters of the objects through an inversion procedure. The problem is formulated using a vector integral equation. As is well-known, this inverse scattering problem is nonlinear and ill-posed. In a realistic configuration, this nonlinear inverse scattering problem involves a large number of unknowns, hence the application of full nonlinear inversion approaches such as Gauss-Newton or nonlinear gradient methods might not be feasible, even with present-day computer power. Hence, in this study we use the so-called diagonalized contrast source inversion (DCSI) method in which the nonlinear problem is approximately transformed into a number of linear problems. We will show that, by using a three-step procedure, the nonlinear inverse problem can be handled at the cost of solving three constrained linear inverse problems. The robustness and efficiency of this approach is illustrated using a number of synthetic examples.     

A Grid-based integral approach for quasilinear problems

For non-homogeneous and nonlinear problems, a major difficulty in applying the Boundary Element Method is the treatment of the volume integrals that arise. A recent proposed method, the grid-based integration method (GIM), uses a 3-D uniform grid to reduce the complexity of volume discretization, i.e., the discretization of the whole domain is avoided. The same grid is also used to accelerate both surface and volume integration. The efficiency of the GIM has been demonstrated on 3-D Poisson problems. In this paper, we report our work on the extension of this technique to quasilinear problems. Numerical results of a 3-D Helmholtz problem and a quasilinear Laplace problem on a multiply-connected domain with Dirichlet boundary conditions are presented. These results are compared with analytic solutions. The performance of the GIM is measured by plotting the L₂-norm error as a function of the overall CPU time and is compared with the auxiliary domain method in the Helmholtz problem.     

A rational approach for choosing stress terms for hybrid finite element formulations

A new approach for choosing the stress terms for a hybrid stress element is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacement. Examples using 4-node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting elements will provide the most accurate solutions. Advantages of this approach for the formulation of an axisymmetric solid are also indicated.     

A complex variable approach to electrochemical machining problems

Summary Electrochemical machining is the name given to the process of eroding metal by electrolysis. The anode in this process is a workpiece from which metal is eroded and the cathode is a shaped machine tool which is fed towards the work-piece (see Fig. 1). Erosion takes place when an electric potential is applied across the electrolyte filled gap between the tool and the workpiece. The electrolyte is pumped through the gap in order to remove the products of erosion.In this paper an attempt is made, under certain simplifying assumptions, to determine the resulting shape of the workpiece and the gap-sizes between the tool and workpiece. Basically two problems are treated in this paper; one for a plane-faced tool with complete insulation on the tool sides (see Fig. 2) and the other for an uninsulated straight sided tool (see Fig. 5). An exact complex variable technique is used and only minimal computer usage is required for final evaluations from derived analytic formulae.     

A variational approach to magnetoelastic buckling problems for systems of superconducting tori

A variational principle for the magnetoelastic stability problem of superconductors is constructed. Independently, a pair of integral equations is derived, from which the initial and the perturbed field can be computed. The integral equations are solved for in-plane buckling of a slender pair of concentric tori, and out-of-plane buckling of a slender pair of equal coaxial tori. By using the variational principle, it is shown that both cases can become unstable when the currents on the two tori are equally directed, and the pertinent buckling values are calculated. The thus obtained buckling values are compared with the results of an alternative, mathematically less rigorous, method. A good correspondence between the two methods is found (at least as long as the two tori are not too near).     

A two-stage AIS approach for grid scheduling problems

Grid workflow scheduling problem has been a research focus in grid computing in recent years. Various deterministic or meta-heuristic scheduling approaches have been proposed to solve this NP-complete problem. A perusal of published papers on the artificial immune system (AIS) reveals that most researchers use the clonal selection of B cells during the evolving processes and the affinity function of B cells to solve various optimisation problems. This research takes a different approach to the subject – firstly by applying a modified algorithm (Hu, T.C., 1961. Parallel sequencing and assembly line problem. Operations Research, 9 (6), 841–848) to sequence the job and this sequence is applied for further application. Secondly, the derived sequence is then used for machine allocations using the AIS approach. The proposed AIS apply B cells to reduce the antigens and then combining T helper cells and T suppressor cells to solve the grid scheduling problems. Our proposed methodology differs from other earlier approaches as follows: 1. A two-stage approach is applied using a fixed sequence derived from heuristic to allocate machine. 2. AIS apply B cells as bases and then T cells are employed next. T helper cells are used to help improve the solution and then T suppressor cells are generated to increase the diversity of the population. A new formula is proposed to calculate the affinity of the antibody with the antigen. The total difference of completion time of each job is applied instead of the difference of makespan of the schedule. This new AIS method can supplement the flaw of genetic algorithms (GA) using fitness as the basis and a new lifespan which will keep good diversified chromosomes within the population to extend the searching spaces. The experimental tests show that this novel AIS method is very effective when compared with other meta-heuristics such as GA, simulated annealing (SA), and ant colony optimisation (ACO).     

A boundary element approach for non-homogeneous potential problems

This paper reports an implementation of a Boundary Element Method dealing with two-dimensional inhomogeneous potential problems. This method avoids the tedious calculation of the domain integral contributions to the boundary integral equations. This is achieved by applying approximate particular solutions which are obtained by expressing the source distribution in terms of a linear combination of radial basis functions. Numerical examples show that the method is efficient and can produce accurate results.     

A boundary element approach for non-linear boundary-value problems

A Boundary Element Method has been developed for solving nonlinear boundary-value problems. This method avoids the tedious calculation of the domain integral contributions to the boundary integral equations. This is achieved by applying approximate particular solutions which are obtained by expressing the pseudo-body force in terms of a linear combination of radial basis functions. Numerical examples show that the method is efficient and can produce accurate results.     

A hybrid-element approach to crack problems in plane elasticity

The hybrid-element concept and the complex variable technique have been adopted for constructing a special super-element to be used jointly with conventional finite elements for the analysis of elastic stress intensity factors for plane cracks. The use of the complex variable technique permits the proper consideration of the stress intensity at the crack tip, and it also leads to very efficient programming. The use of such a super-element in the finite element solution has been shown to be highly accurate when only a very coarse element mesh is used near the crack.     

A combined heuristic approach to dynamic lot sizing problems

A combined heuristic approach for dynamic lot sizing problems has been proposed. The combined heuristic is based on the performance analysis of the Silver-Meal heuristic on different problem sizes and demand patterns. The heuristic performs extremely well on average, and has a worst case performance ratio of two.     

A time-predefined local search approach to exam timetabling problems

In recent years the processing speed of computers has increased dramatically. This in turn has allowed search algorithms to execute more iterations in a given amount of real-time. Does this necessarily always lead to an improvement in the quality of final solutions? This paper is devoted to the investigation of that question. We present two variants of local search where the search time can be set as an input parameter. These two approaches are: a time-predefined variant of simulated annealing and an adaptation of the “great deluge” method. We present a comprehensive series of experiments which show that these approaches significantly outperform the previous best results (in terms of solution quality) on a range of benchmark exam timetabling problems. Of course, there is a price to pay for such better results: increased execution time. We discuss the impact of this trade-off between quality and execution time. In particular we discuss issues involving the proper estimation of the algorithm's execution time and the assessment of its importance.     

A phenomenological inversion approach for the evaluation and analysis of NDT measurement systems

The aim of this study is to equip the practitioner with a simple method for the solution of practical inverse problems in NDT. In this approach, complete modelling of the measuring system and examined samples has been avoided. Inversion is based on a first principles model describing the ‘ideal output’ of the system and on a semi-empirical ‘instrument function’ (IF). The imposed constraint on the model is that it should be invertible. The IF describes the degradation and distortions in the ideal response. The function should be shift invariant to enable adaption of the linear response theory. Expressions for resolution and dynamic range as a function of measurement system parameters have been developed.     

海底介质特性反演方法研究

海底介质特性反演一直是水声研究里很活跃的领域,本文应用两种不同的反演方法,差分进化方法(DE)和自适应下山模拟退火算法(ASSA)分别对海底介质特性进行反演,并比较了这两种算法在解决海底介质特性反演问题的优缺点,特别是通过对噪声数据和试验数据的反演发现,差分进化方法虽然是一种效率高,鲁棒性好,收敛速度快的反演算法,但是在抗噪声能力方面显然不如自适应下山模拟退火算法.     

A rational approach to mass matrix diagonalization in two‐dimensional elastodynamics

A variationally consistent methodology is presented, which yields diagonal mass matrices in two‐dimensional elastodynamic problems. The proposed approach avoids ad hoc procedures and applies to arbitrary quadrilateral and triangular finite elements. As a starting point, a modified variational principle in elastodynamics is used. The time derivatives of displacements, the velocities, and the momentum type variables are assumed as independent variables and are approximated using piecewise linear or constant functions and combinations of piecewise constant polynomials and Dirac distributions. It is proved that the proposed methodology ensures consistency and stability. Copyright © 2004 John Wiley & Sons, Ltd.