Box Complex Method Research Articles

INFLUENCE OF MERIDIONAL SHAPING ON THE COLLAPSE STRENGTH OF FRP DOMES

Parabolic and cubic splines together with circular arcs are used to approximate the meridional shapes of multisegmental, axisymmetric, externally pressurized domes. Bifurcation buckling, axisymmetric collapse and fibre first ply failure are considered as possible mechanisms of dome collapse. The objective is to maximize the lowest collapse pressure for a constant wall thickness, given the material and the through thickness lamination sequence. The optimization procedure is based on the complex method of Box and the geometrically nonlinear analysis uses the classical lamination theory. The largest increase in the failure load is obtained for segments made out of circular arcs. A generalized ellipse is also used as a possible meridional profile.

A nonlinear goal programming model for multistage, multiobjective decision problems with application to grouping and loading problem in a flexible manufacturing system

A multistage multiobjective decision problem is formulated as a nonlinear goal programming model. The solution algorithm which uses Box-Complex method is presented. The model formation and computational aspects are illustrated on the integrated grouping and loading problem of a flexible manifacturing system.

Iterative solution of multicomponent permeator model equations

Countercurrent and recycle permeator model equations require a trial and error (iterative) solution procedure. Although the iterative calculations are simple for a binary system, the calculations for a multicomponent system are greatly complicated because there are M - 1 independent mole fractions in an M component system. This paper describes a systematic method to find the multicomponent solution vector using a direct search maximization routine which is a modification of the complex method of Box.

Search for optimal torispherical end closures under buckling constraints

The optimal geometries of externally-pressurized torispherical end closures, having a prescribed weight, are sought under static stability criteria. End closures are obtained which will withstand maximum or minimum buckling pressures. Their response to initial axisymmetric imperfections is examined and compared to that of hemispherical closures of the same weight and material properties. A direct search technique, known as the complex method of Box ( Comput. J. 8, 45–52, 1965), is used together with the BOSOR 5 Code as a solver.

On the Use of Nonlinear Programming in Real Time Control of Process Industries

In process industries there is an increasing trend in the -use of computers anchor distributed digital control. The invention of powerful 16 hit and 32 bit microprocessors is opening avenues for realising advanced control algorithms in practice and control of plant with distributed intelligence. Over the years, considerable work has been done towards evolving an appropriate configuration 1 of distributed digital control system for plant control. In many system configurations a computer has been chosen at the upper tier for carrying out plant optimization and management information report generation, leaving the regulatory control and monitoring functions to the processors in the bottom 2 , Optimization of an operating process unit performed in real time with an on line process control computer has a number of significant advantages over an optimization executed by an off-line computer. While the concept of Dynamic Matrix Control 3 to address the control of a plant at its economic optimum is new, the concept of process control computer assisting optimization by moving one set of operating conditions to another is well accepted in industry. A good account of this use of static optimization in computer control of process industries is available in reference 4. If. Two popular techniques e. g linear and nonlinear programming have found place in the on line optimization task 4 . Since the mathematical model of the plant and the constaint functions are nonlinear 5 , it is appropriate to use nonlinear programming technique to carry out the on line optimization. Various algorithms are available for solving nonlinear programming (NLP) problem 7 . An account of user experience on some of them is available in reference 8. Desirable features of NLP software has been discussed by Lasdon 9 . A brief description of the performance of M.J. Box's complex method for on line optimization is available in reference 10. This paper is conceited with making a brief survey of current industrial practice of real time plant optimization using nonlinear programming techniques. An account of desirable features of a good nonlinear programming software and relationship of software packages for on line execution from various data sources e.g, historical data base of the plant, operator data entry, input from Research and development activities will be included. The performance of various techniques e.g. successive linear programming (SLP) or Method of approximation programming (MAP), generalised reduced gradient (GRG) and complex method of M.J. Box will he evaluated in the context of on line application. Case studies from petroleum industries and thermal power plant will be chosen for this purpose.

Optimal design of plane frames by the complex method

A general methodology for the optimization of the skeletal geometry of plane rigid frames based on a modified version of the Complex Method of Box is presented. The design routines allow multiple load cases and produce near-optimal designs that satisfy relevant provisions of the American Institute of Steel Construction's (AISC) specification. The capabilities of the proposed procedure are demonstrated by example problems of practical significance.

Deconvolution of overlapping chromatographic peaks using constrained non-linear optimization

Non-linear regression involving Gaussian, modified Gaussian or Weibull functions is currently used for deconvoluting fused chromatograms. In this paper, we report that deconvolution of fused chromatograms is a problem in constrained non-linear optimization and not an unconstrained problem as assumed by previous researchers. A modified version of the generalized exponential function is shown to fit chromatographic peaks using the Box-Complex method for constrained optimization. Previously reported problems of false fits do not occur with this method. Several deconvolutios on real size exclusion chromatographic data are shown to demonstrate the power of the technique.

A probabilistic approach to modify the complex method

Based on a probabilistic approach the Complex method of Box has been modified such that several points may be replaced in an iteration. The modified version as applied to five test problems compares favourably with the parent method. A more detailed analysis, especially in the application to multimodal functions, must be made before any generalisation.

Optimal synthesis of waste treatment plants

It is possible to simulate waste treatment plants with increasing accuracy and reliability. This study examines the application of the SEPSIM steady-state simulation program as the modelling basis of an optimal synthesis program. A modified form of Box's Complex method coupled with Fan's structural parameter method is presented and employed in the solution of the multidimensional optimization problem. The computational difficulties associated with the optimal synthesis of processing systems are discussed in some detail. It is found that an operating arrangement consisting of a trickling filter and an activated sludge system working in parallel is clearly indicated by the models as being the optimal system.

The complex method applied to optimal truss configuration

The Complex Method of Box is applied to the determination of optimal member sizes and geometric configuration for minimum weight of 3-dimensional truss structures. Design constraints include bounds on member size, joint coordinates, member stresses, Euler buckling and joint displacements. The displacement method of structural analysis is used and the system is assumed to be linearly elastic. Statically indeterminate structures under multiple loading conditions can be optimized and the sizing as well as the geometric design variables may be linked. Limited topological changes are permitted for designs which have small member forces. The design spaces for sizing and geometric variables are separated. Geometry is modified by the Complex Method and member sizes by stress ratio and a scaling procedure for stiffness. The method is applied to two numerical examples from the literature. Results indicate favourable design improvements and rates of convergence. Substantial additional improvement resulting from member deletion is demonstrated.

Optimal design of layered structures under dynamic loading

A direct search procedure is presented to treat problems of optimization of layered structures subjected to dynamic loading conditions. The procedure combines the basic idea of the complex method of Box to locate the next trial point, with a local direct pattern search of Hooke and Jeeves to insure the continuous accelerative movement toward the optimum. The method is applied to two problems of optimal design for minimum tensile stress at the interfaces in layered structures under time-harmonic loads and transient loads, respectively.

Direct Search Optimization Method

A nongradient direct search procedure is presented to treat general structural optimization problems, in which the independent design variables are discrete in nature. The procedure combines the basic ideas of the complex method of Box with the pattern search of Hooke and Jeeves. Three examples of design are considered: a framed structure and a tied cantilever beam under static loads, and a two-layered slab under dynamic loads. These examples illustrate the wide variety of structural optimization problems which can be satisfactorily treated by the method.

Synthesis of optimal processing system by an integrated approach

A general synthesis problem is defined as that of determining an optimal system structure by extracting it from an enlarged system structure generated by splitting streams into alternative routes. When the optimized splitting ratio is close to 0 or 1, one of the alternative streams can be eliminated to give the optimal synthesis. Box's Complex method, is used to solve an actual example amenable to the integrated approach.

A Computational Algorithm for Real-Time Control of System Voltage and Reactive Power Part II - Algorithm of Optimization

An efficient computational algorithm is presented for the real-time control of system voltage and reactive power on the basis of a simplified linear model. A modified version of the complex method of Box is used for the minimization of bus voltage deviation in the first phase of optimization and a numerical search technique for the reduction of transmission losses due to reactive power flows in the second phase. The numerical example for a sample practical system is also given.