A finite element model for nonlinear shells of revolution

A finite element model for symmetrically loaded shells of revolution is described. The nonlinear geometric effects are accounted for by incrementing loads and iterating for equilibrium. The iteration process also allows for nonlinear materials. The shell model accounts for large strains, large rotations and shear deformation. Three example problems demonstrate the ability of this model to solve linear problems. Also, three example problems demonstrate the versatility and accuracy of this model for nonlinear problems. These nonlinear example problems are an axially loaded cylinder and an internally pressurized spherical shell that have large membrane strains, and a cylinder that deforms into a spherical shape, having large rotations.     

Semi-Markov decision models for real-time scheduling

We first present a class of real-time scheduling problems and show that these can be formulated as semi-Markov decision problems. Then we discuss two practical difficulties in solving such problems. The first is that the resulting model requires a large amount of data that is difficult to obtain; the second is that the resulting model usually has a state space that is too large for analytic consideration. Finally, we present a non-intrusive ‘knowledge acquisition’ method that identifies the states and transition probabilities that an expert uses in solving these problems. This information is then used in the semi-Markov optimization problem. A circuit board production line is used to demonstrate the feasibility of this method. The size of the state space is reduced from 2035 states to 308 by an empirical procedure. An ‘optimal’ solution is derived based on the model with the reduced state space and estimated transition probabilities. The resulting schedule is significantly better than the one used by the observed expert.     

A Constraint Programming model for food processing industry: a case for an ice cream processing facility

This paper presents a Constraint Programming (CP) scheduling model for an ice cream processing facility. CP is a mathematical optimisation tool for solving problems either for optimality (for small-size problems) or good quality solutions (for large-size problems). For practical scheduling problems, a single CP solution model can be used to optimise daily production or production horizon extending for months. The proposed model minimises a makespan objective and consists of various processing interval and sequence variables and a number of production constraints for a case from a food processing industry. Its performance was compared to a Mixed Integer Linear Programming (MILP) model from the literature for optimality, speed, and competence using the partial capacity of the production facility of the case study. Furthermore, the model was tested using different product demand sizes for the full capacity of the facility. The results demonstrate both the effectiveness, flexibility, and speed of the CP models, especially for large-scale models. As an alternative to MILP, CP models can provide a reasonable balance between optimality and computation speed for large problems.     

A COMPUTATIONAL STUDY OF EMPIRICAL DECISION HORIZONS IN INFINITE HORIZON, MULTIPERIOD NETWORK FLOW PROBLEMS

The minimum cost, multiperiod network flow model is an important optimization model for solving problems in many application areas including resource scheduling, planning and distribution. This network model describes decision making problems over time. In earlier work, we discussed the development, implementation and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method exploits the natural decomposition of multiperiod network problems, by limiting its pivoting activity to the date of the last few time periods. Both the solution CPU time and pivot count are linear in the number of time periods. For standard network optimization codes, the pivot count is linear while the solution time is approximately quadratic in the number of periods.

Here we present a computational study of the natural decomposition of, or empirical decision horizons for, an “infinite” horizon, multiperiod network model. We demonstrate the existence of such horizons for a model for which there is no guarantee of having an exact, or theoretical, decision horizon. When a problem having a sufficiently large number of time periods is solved, there is no effect on the decisions to be made for the first few time periods. Thus, the early periods' solution to a problem having an infinite number of time periods may be considered solved.     

Model reduction for nonlinear multiscale parabolic problems using dynamic mode decomposition

In this article, a model reduction technique is presented to solve nonlinear multiscale parabolic problems using dynamic mode decomposition. The multiple scales and nonlinearity bring great challenges for simulating the problems. To overcome this difficulty, we develop a model reduction method for the nonlinear multiscale dynamic problems by integrating constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with dynamic mode decomposition (DMD). CEM-GMsFEM has shown great efficiency to solve linear multiscale problems in a coarse space. However, using CEM-GMsFEM to directly solve multiscale nonlinear parabolic models involves dynamically computing the residual and the Jacobian on a fine grid. This may be very computationally expensive because the evaluation of the nonlinear term is implemented in a high-dimensional fine scale space. As a data-driven method, DMD can use observation data and give an explicit expression to accurately describe the underlying nonlinear dynamic system. To efficiently compute the multiscale nonlinear parabolic problems, we propose a CEM-DMD model reduction by combing CEM-GMsFEM and DMD. The CEM-DMD reduced model is a coarsen linear model, which avoids the nonlinear solver in the fine space. It is crucial to judiciously choose observation in DMD. Only proper observation can render an accurate DMD model. In the context of CEM-DMD, we introduce two different observations: fine scale observation and coarse scale observation. In the construction of DMD model, the coarse scale observation requires much less computation than the fine scale observation. The CEM-DMD model using the coarse scale observation gives a complete coarse model for the nonlinear multiscale dynamic systems and significantly improves the computation efficiency. To show the performance of the CEM-DMD using the different observations, we present a few numerical results for the nonlinear multiscale parabolic problems in heterogeneous porous media.     

A mixed finite element formulation for non-linear analysis of plane problems

Based on the incremental non-linear theory of solid bodies and the Hellinger-Reissncr principle, a mixed updated Lagrangian formulation of the large displacement motion of solid bodies is derived, and an associated mixed finite element model is developed. The model contains the displacements and stresses as the nodal degrees of freedom. The model is used for the large deformation elasto-plastic analysis of plane problems. In solving non-linear problems, the Newton-Raphson method with arc-length control is adopted to trace the post-buckling response. The computational steps to calculate the elasto-plastic stress increments at Gauss points in the elasto-plastic analysis by the present mixed model are described in detail. Numerical results are presented and compared with those of the displacement model and existing solutions to show the accuracy of the present mixed model in the large deformation elasto-plastic analysis of plane problems.     

Nonlinear analysis of the magnetic flux distribution in the magnetized magnet stabilized in air

A theoretical model for the relationship among magnetic quantities describing the one- versus two-dimensional field in a permanent magnet is developed. The model is applied to two problems: 1) determination of the direction of the residual magnetism and 2) finding the magnetic flux distribution in a magnet stabilized in air. The vector potential equation in a form unified for both problems is derived and transformed into a partial-difference algorithm. The numerical line-iteration procedure is described and used to solve these problems for a six-pole permanent magnet rotor of an electrical alternator.     

An efficient cycle time model for autonomous vehicle storage and retrieval systems

A computationally efficient cycle time model for conceptualizing autonomous vehicle storage and retrieval systems and comparing their performance with crane-based automated storage and retrieval systems is presented. The model is based on an iterative computational scheme exploiting random storage assumptions and queuing model approximations. Relative to earlier models, the procedure scales up efficiently for large problems thereby enabling more extensive search of a design solution space. Simulation based validation studies suggest that model accuracy is adequate for system conceptualization. The procedure is demonstrated using realistically sized sample problems.     

Frontiers in Statistical Quality Control 3

Computer model calibration is the process of determining input parameter settings to a computational model that are consistent with physical observations. This is often quite challenging due to the computational demands of running the model. In this article, we use the ensemble Kalman filter (EnKF) for computer model calibration. The EnKF has proven effective in quantifying uncertainty in data assimilation problems such as weather forecasting and ocean modeling. We find that the EnKF can be directly adapted to Bayesian computer model calibration. It is motivated by the mean and covariance relationship between the model inputs and outputs, producing an approximate posterior ensemble of the calibration parameters. While this approach may not fully capture effects due to nonlinearities in the computer model response, its computational efficiency makes it a viable choice for exploratory analyses, design problems, or problems with large numbers of model runs, inputs, and outputs.     

Implicit implementation of the stabilized non-ordinary state-based peridynamic model

This paper presents a stabilized non-ordinary state-based peridynamic model, in which the numerical instability problems induced by the zero-energy mode are overcome. The implicit discretization formulation of this model is proposed. In order to depict the progressively damaging process in coarse discretization conditions, a bilinear damage model based on the influence function is developed. An implicit implementation of the stabilized non-ordinary state-based peridynamic model is presented, in which an iterative procedure based on the secant stiffness method is used to solve the nonlinear problem. This method does not need to introduce a damping term in solving static problems, and relatively large load steps are desirable. Five numerical examples are analyzed to demonstrate the effectiveness of the present method for quantitatively simulating the quasi-static crack propagation problems.     

Proposing integrated Shannon’s entropy–inverse data envelopment analysis methods for resource allocation problem under a fuzzy environment

In this study, a two-phase methodology for resource allocation problems under a fuzzy environment is proposed. In the first phase, the imprecise Shannon’s entropy method and the acceptability index are suggested, for the first time in the literature, to select input and output variables to be used in the data envelopment analysis (DEA) application. In the second step, an interval inverse DEA model is executed for resource allocation in a short run. In an effort to exemplify the practicality of the proposed fuzzy model, a real case application has been conducted involving 16 cement firms listed in Borsa Istanbul. The results of the case application indicated that the proposed hybrid model is a viable procedure to handle input–output selection and resource allocation problems under fuzzy conditions. The presented methodology can also lend itself to different applications such as multi-criteria decision-making problems.     

A mixed integer linear programming solution for single hoist multi-degree cyclic scheduling with reentrance

This article considers single hoist multi-degree cyclic scheduling problems with reentrance. Time window constraints are also considered. Firstly, a mixed integer programming model is formulated for multi-degree cyclic hoist scheduling without reentrance, referred to as basic lines in this article. Two valid inequalities corresponding to this problem are also presented. Based on the model for basic lines, an extended mixed integer programming model is proposed for more complicated scheduling problems with reentrance. Phillips and Unger's benchmark instance and randomly generated instances are applied to test the model without reentrance, solved using the commercial software CPLEX. The efficiency of the model is analysed based on computational time. Moreover, an example is given to demonstrate the effectiveness of the model with reentrance.     

A Bayesian Approach to Controlling Percent Defective A Model and Application

The purpose of this paper is to develop a general model for controlling the percent defective of an ongoing production process. The model is developed in a Bayesian decision theory framework so that, using dynamic programming, optimal (least cost) control decisions can be found. An application of the model to a real world production process is described in detail. The problems of estimating the model parameters are discussed along with some approaches to overcoming the estimation problems. Finally, the optimal control policies for the real world process are presented and are shown to be straightforward and easily implemented.     

Explicit model of dual programming and solving method for a class of separable convex programming problems

An objective function for a dual model of nonlinear programming problems is an implicit function with respect to Lagrangian multipliers. This study aims to address separable convex programming problems. An explicit expression with respect to Lagrangian multipliers is derived for the dual objective function. The exact solution of the dual model can be achieved because an explicit objective function is more exact than an approximated objective function. Then, a set of improved Lagrangian multipliers can be used to obtain the optimal solution of the original nonlinear programming model. A corresponding dual programming and explicit model (DP-EM) method is proposed and applied to the structural topology optimization of continuum structures. The solution efficiency of the DPEM is compared with the dual sequential quadratic programming (DSQP) method and method of moving asymptotes (MMA). The results show that the DP-EM method is more efficient than the DSQP and MMA.     

基于Vague集的国有企业并购多属性拍卖决策研究

在分析国有企业并购中凸显问题的基础上,构建了国有企业并购多属性拍卖决策的属性集,提出了基于Vague集理论的国有企业并购多属性拍卖决策的一般模型。该决策模型相较传统的模糊集决策模型更具灵活性和实用性,为国有企业并购多属性拍卖决策提供了一种新的思路,总结提炼了国有企业并购多属性拍卖的决策控制要点。     

The Estimation of Parameters in Nonlinear,Implicit Models

The estimation of parameters in nonlinear algebraic models is considered for a general class of problems. Included are problems where both the independent and dependent variables are subject to error and problems where the model is algebraically implicit. The maximum likelihood principle leads to an equality constrained minimization problem. An algorithm to achieve this minimization is obtained through the use of Lagrange multipliers.     

MOAPPS 1.0: Aggregate production planning using the multiple-objective tabu search

In recent years, there has been a trend in the research community to solve large-scale complex planning and design problems using the modern heuristics optimization techniques (i.e. tabu search, genetic algorithms, etc.). This is mainly due to unsuitability of the classical solution techniques in many circumstances. Depending upon the assumptions made and the modelling approach used, aggregate production planning (APP) problems can be quite complex and large scale. Therefore, there is a need to investigate the suitability of modern heuristics for their solution. In this paper, the multiple-objective APP problem is formulated as a pre-emptive goal-programming model and solved by a specially developed multiple-objective tabu search algorithm. The mathematical formulation is built upon Masud and Hwang's model (original model) due to its extensibility characteristics. The present model extents their model by including subcontracting and setup decisions. The multiple-objective tabu search algorithm is applied to both the original and extended model. Results obtained from the solution of the original model are then compared. It is observed that the multiple-objective tabu search algorithm can be used as an alternative solution mechanism for solving APP problems. During this study, an object-oriented program is also developed using C++. This software is named as MOAPPS 1.0 (Multiple Objective Aggregate Production Planning Software).     

Modeling errors due to Timoshenko approximation in damage identification

The use of accurate computational models for damage identification problems may lead to prohibitive costs. Damage identification problems are often characterized as inverse ill-posed problems. Thus, the use of approximate models such as simplified physical and/or reduced-order models typically yields misleading results. In this paper, we carry out a preliminary study on a particular simplified physical model, the Timoshenko beam model in the context of damage identification. The actual beam is a two-dimensional relatively high aspect ratio (thickness/length) beam with a distributed damage that is modeled as a spatially varying Young modulus. We state the problem in the Bayesian framework for inverse problems and carry out approximative marginalization over the related modeling errors. The numerical experiments suggest that the proposed approach yields more stable results than using the Timoshenko beam model as an accurate model. Due to the severity of the Timoshenko approximation, however, the posterior error estimates of the proposed approach are not always feasible in the probabilistic sense.