Parameters optimization of selected casting processes using teaching–learning-based optimization algorithm

In the present work, mathematical models of three important casting processes are considered namely squeeze casting, continuous casting and die casting for the parameters optimization of respective processes. A recently developed advanced optimization algorithm named as teaching–learning-based optimization (TLBO) is used for the parameters optimization of these casting processes. Each process is described with a suitable example which involves respective process parameters. The mathematical model related to the squeeze casting is a multi-objective problem whereas the model related to the continuous casting is multi-objective multi-constrained problem and the problem related to the die casting is a single objective problem. The mathematical models which are considered in the present work were previously attempted by genetic algorithm and simulated annealing algorithms. However, attempt is made in the present work to minimize the computational efforts using the TLBO algorithm. Considerable improvements in results are obtained in all the cases and it is believed that a global optimum solution is achieved in the case of die casting process.     

On the membrane approximation in isothermal film casting

In this work, a one-dimensional model for isothermal film casting is studied. Film casting is an important engineering process to manufacture thin films and sheets from a highly viscous polymer melt. The model equations account for variations in film width and film thickness, and arise from thinness and kinematic assumptions for the free liquid film. The first aspect of our study is a rigorous discussion of the existence and uniqueness of stationary solutions. This objective is approached via the argument principle, exploiting the homotopy invariance of a family of analytic functions. As our second objective, we analyze the linearization of the governing equations about stationary solutions. It is shown that solutions for the associated boundary-initial value problem are given by a strongly continuous semigroup of bounded linear operators. To reach this result, we cast the relevant Cauchy problem in a more accessible form. These transformed equations allow us insight into the regularity of the semigroup, thus yielding the validity of the spectral mapping theorem for the semigroup and the spectrally determined growth property.     

Effect of viscoelastic relaxation modes on stability of extrusion film casting process modeled using multi-mode Phan-Thien-Tanner constitutive equation

Extrusion film casting (EFC) is a commercially important process that is used to produce a significant quantity of polymer films, sheets and coatings for both industrial and household applications. Recently, we have demonstrated the influence of polymer chain architecture on the extent of necking under isothermal as well as non-isothermal film casting operation for commercially relevant polyolefin based materials [1], [2], [3], [4]. In the present research, we focus on another instability that frequently occurs in high-speed EFC process called as draw resonance. Draw resonance manifests itself as an instability that causes periodic fluctuations in both the width as well as thickness of the extruded molten film above a critical draw ratio (DR). In this work, we have carried out a linear stability analysis of the isothermal EFC process using a multi-mode Phan-Thien-Tanner (PTT) constitutive equation to determine the onset of draw resonance. We show that as the number of relaxation modes is increased there is a dramatic change in the stability regions. In particular, there is a marked variation in the stability regions obtained by simulating the multi-mode model and those obtained by taking averaged relaxation time of the modes. Additionally, as the number of faster-relaxing modes in a multi-mode spectrum is progressively increased, the process becomes increasingly stable as the level of elasticity in the melt decreases. Finally, the addition of a long relaxation mode in a multi-mode spectrum is akin to adding a long chain branch to a linear polymer that leads to a reduction in film necking and in many cases to enhanced process stability.     

Optimal die shape for film casting

We consider an isothermal model for the film casting process. The aim of this study is to determine a shape of the die that leads to a uniform thickness of the film. Thanks to a decoupling of the equations for the thickness and the velocities of the film, we are able to solve the reverse thickness equation. This reverse equation describes the dependence of the shape of the die on the desired final thickness.     

The use of artificial intelligence technique for the optimisation of process parameters used in the continuous casting of steel

The productivity and quality of a continuous caster depend mainly on process parameters, i.e. casting speed, casting temperature, steel composition and cleanliness of the melt, water flow rates in the different cooling zones, etc. This work presents the development of an algorithm, which incorporates heuristic search techniques for direct application in metallurgical industries, particularly those using continuous casting process for the production of steel billets and slabs. This is done to determine the casting objectives of maximum casting rate as a function of casting constraints. These constraints are evaluated with the aid of a heat transfer and solidification model based on the finite difference technique, which has been developed and integrated with a genetic algorithm. The essential parts of continuous casting equipment, which must be subjected to monitoring, as well as a methodology of mathematical model and physical settlements in each cooling region, are presented. The efficiency of the intelligent system is assured by the optimisation of the continuous casting operation by maximum casting rate and defect-free products. This approach is applied to the real dimension of a steel continuous caster, in real conditions of operation, demonstrating that good results can be attained by using heuristic search, such as: smaller temperature gradients between sprays zones, reduction in water consumption and an increase in casting speed.     

On Optimal Control of a Free Surface Flow

We discuss an optimal control approach for a 2D Stokes flow with a free surface. The aim is to optimize the shape of a polymer film by adjusting the ambient pressure in a casting process. The resulting minimization problem is solved by the method of steepest descent. Numerical results will be presented. Furthermore we state the adjoint system for the Lagrangian formalism. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

One-dimensional stock cutting: optimization of usable leftovers in consecutive orders

Central European Journal of Operations Research - This paper deals with usable leftovers (UL) in one-dimensional stock cutting in consecutive orders. UL are leftovers longer than a certain...     

Adjoint Based Optimization of a Free Surface Flow for Film Casting

Motivated by the industrial process of film casting, we discuss an optimal control approach for a viscous free surface flow that is asymptotically described by 2d Stokes equations. The aim is to optimize the shape of the free boundaries by adjusting the ambient pressure. A PDE-constrained optimization problem is set up, where the free surfaces are described as graphs. The first-order optimality system is derived via the Lagrangian formalism. The resulting minimization problem is solved by a steepest descent method, where the gradient is expressed in terms of the adjoint variables. Numerical results are presented. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

实值函数与某些覆盖性质

In the paper [properties defined with semi-continuous functions and some related spaces',Houston J.Math.,2015,41(3):1097–1106] properties(U L)~(wl)_m,(U L)~K_m and(U L)_m were defined and it was shown that spaces having these properties coincide with countably paracompact spaces,countably mesocompact spaces and countably metacompact spaces,respectively.In this paper,we continue with the study on the relationship between properties defined with real-valued functions and some covering properties.Some characterizations of countably compact spaces and pseudo-compact spaces in terms of real-valued functions are obtained.     

Application of bacterial colony chemotaxis optimization algorithm and RBF neural network in thermal NDT/E for the identification of defect parameters

The identification of defect parameters in thermal non-destructive test and evaluation (NDT/E) was considered as a kind of inverse heat transfer problem (IHTP). However, it can be further considered as a shape optimization problem, and then a structure design optimization problem, and the design results should meet the surface temperature profile of the apparatus with defects. A bacterial colony chemotaxis (BCC) optimization algorithm and a radial basis function (RBF) neural network (NN) are applied to the thermal NDT/E for the identification of defects parameters. The RBFNN is a precise and convenient surrogate model for the time costly finite element computation, which obtains the surface temperature with different defect parameters. The BCC optimization algorithm is derivatively-free, and the convergence speed is fast. Then a simple but complete multi-disciplinary design optimization (MDO) framework is constructed for the sake of generality and flexibility. This method is applied to a simple verification case and the result is acceptable. The algorithm is also compared with the particle swarm optimization (PSO) algorithm, and the BCC algorithm can access the optimum with faster speed.     

A nondestructive experimental approach for heat flux determination on direct‐chill cast aluminium alloy billet surface

In this paper a new nondestructive experimental method for the determination of the billet surface heat flux in direct‐chill casting of aluminium alloys is presented. The new measurement method is based on measurements of the water film temperatures along the billet surface and determination of the local heat flux from the energy balance. Experiments using the new technique are carried out in a real plant environment. The results are used for the validation of a computational model of the process.     

TRANSFORM-ANN for online optimization of complex industrial processes: Casting process as case study

Artificial Neural Networks (ANNs) are well known for their credible ability to capture non-linear trends in scientific data. However, the heuristic nature of estimation of parameters associated with ANNs has prevented their evolution into efficient surrogate models. Further, the dearth of optimal training size estimation algorithms for the data greedy ANNs resulted in their overfitting. Therefore, through this work, we aim to contribute a novel ANN building algorithm called TRANSFORM aimed at simultaneous and optimal estimation of ANN architecture, training size and transfer function. TRANSFORM is integrated with three standalone Sobol sampling based training size determination algorithms which incorporate the concepts of hypercube sampling and optimal space filling. TRANSFORM was used to construct ANN surrogates for a highly non-linear industrially validated continuous casting model from steel plant. Multiobjective optimization of casting model to ensure maximum productivity, maximum energy saving and minimum operational cost was performed by ANN assisted Non-dominated Sorting Genetic Algorithms (NSGA-II). The surrogate assisted optimization was found to be 13 times faster than conventional optimization, leading to its online implementation. Simple operator's rules were deciphered from the optimal solutions using Pareto front characterization and K-means clustering for optimal functioning of casting plant. Comprehensive studies on (a) computational time comparisons between proposed training size estimation algorithms and (b) predictability comparisons between constructed ANNs and state of art statistical models, Kriging Interpolators adds to the other highlights of this work. TRANSFORM takes physics based model as the only input and provides parsimonious ANNs as outputs, making it generic across all scientific domains.     

混沌粒子群神经网络在上证指数预测中的应用

上证指数预测是一个非常复杂的非线性问题,为了提高对上证指数预测的准确性,本文采用基于混沌粒子群(CPSO)算法对BP神经网络算法改进的方法来进行预测.BP神经网络算法目前已经应用到预测、聚类、分类等许多领域,取得了不少的成果.但自身也有明显的缺点,比如易陷入局部极小值、收敛速度慢等.用混沌粒子群算法改进BP神经网络算法的基本思想是用混沌粒子群算法优化BP神经网络算法的权值和阈值,在粒子群算法中加入混沌元素,提高粒子群算法的全局搜索能力.对上证指数预测的结果表明改进后的预测方法,具有更好的准确性.     

A method of making specimens of free varnish films for physicomechanical testing

The author describes a method of preparing film specimens of a required shape by casting varnish in an open mold.All-Union Scientific-Research Institute of Electromechanics, Moscow Region. Translated from Mekhanika Polimerov, No. 2, pp. 372–373, March–April, 1974.     

An Asynchronous Distributed Expectation Maximization Algorithm for Massive Data: The DEM Algorithm

The family of expectation--maximization (EM) algorithms provides a general approach to fitting flexible models for large and complex data. The expectation (E) step of EM-type algorithms is time-consuming in massive data applications because it requires multiple passes through the full data. We address this problem by proposing an asynchronous and distributed generalization of the EM called the distributed EM (DEM). Using DEM, existing EM-type algorithms are easily extended to massive data settings by exploiting the divide-and-conquer technique and widely available computing power, such as grid computing. The DEM algorithm reserves two groups of computing processes called workers and managers for performing the E step and the maximization step (M step), respectively. The samples are randomly partitioned into a large number of disjoint subsets and are stored on the worker processes. The E step of DEM algorithm is performed in parallel on all the workers, and every worker communicates its results to the managers at the end of local E step. The managers perform the M step after they have received results from a γ-fraction of the workers, where γ is a fixed constant in (0, 1]. The sequence of parameter estimates generated by the DEM algorithm retains the attractive properties of EM: convergence of the sequence of parameter estimates to a local mode and linear global rate of convergence. Across diverse simulations focused on linear mixed-effects models, the DEM algorithm is significantly faster than competing EM-type algorithms while having a similar accuracy. The DEM algorithm maintains its superior empirical performance on a movie ratings database consisting of 10 million ratings. Supplementary material for this article is available online.     

Numerical modelling of melt-conditioned direct-chill casting

Melt conditioned direct-chill (MC-DC) casting is a novel technology which combines direct-chill (DC) casting with a high shear device directly immersed in the sump for in situ microstructural control. A numerical model of melt-conditioned direct-chill casting (MC-DC) is presented in this paper. This model is based on a finite volume continuum model using a moving reference frame (MRF) to enforce fluid rotation inside the rotor-stator region and is numerically stable within the range of processing conditions. The boundary conditions for the heat transfer include the effects of the hot-top, the aluminium mould, and the direct chill. This model is applied to the casting of two alloys: aluminium-based A6060 and magnesium-based AZ31. Results show that MC-DC casting modifies the temperature profile in the sump, resulting in a larger temperature gradient at the solidification front and a shorter local solidification time. The increased heat extraction rate due to forced convection in the sump is expected to contribute to a finer, more uniform grain structure in the as-cast billet.     

An effective heuristic algorithm to minimise stack shuffles in selecting steel slabs from the slab yard for heating and rolling

Steel production is a multi-stage process. A slab yard serves as a buffer between the continuous casting stage and the steel rolling stage. Steel slabs are stored in stacks in the yard. Shuffling is needed when picking up a slab for heating and rolling, if it is not in the top position of a stack. This paper studies the problem of selecting appropriate slabs in the yard for a given rolling schedule so as to minimise the total shuffling cost. The study uses the hot strip rolling mill in Shanghai Baoshan Iron and Steel Complex as an application background. We propose a new heuristic algorithm to solve the problem. This is a two-phase algorithm that first generates an initial feasible solution and then improves it using local search. The new algorithm is compared with the algorithm in use on randomly generated test problems and on real data. Experimental results show that the proposed algorithm yields significant better solutions. The average improvement over the old algorithm is 15%.     

Full transversal matroids, strict gammoids, and the matroid components problem

We provide two algorithms for finding dependence graphs both in a full transversal matroid and in its dual, a strict gammoid. The first algorithm is based on directed paths in the directed graph associated with a strict gammoid; its complexity is O(|L|(|V-L|+|E|)), where L is the link-set of the gammoid. The second algorithm is based on a special property of Gaussian elimination in a matrix of indeterminates representing a full transversal matroid; it complexity is o(m²n), where m is the rank of the matroid and n the cardinality of the underlying set. We provide an algorithm for listing all bases in, and calculating the Whitney and Tutte polynomials for, a full transversal matroid or a strict gammoid. The complexity of this algorithm is 0(N(n-m) (|E| + m²)), where N is the number of bases.     

Evidential evolving Gustafson–Kessel algorithm for online data streams partitioning using belief function theory

A new online clustering method called E2GK (Evidential Evolving Gustafson–Kessel) is introduced. This partitional clustering algorithm is based on the concept of credal partition defined in the theoretical framework of belief functions. A credal partition is derived online by applying an algorithm resulting from the adaptation of the Evolving Gustafson–Kessel (EGK) algorithm. Online partitioning of data streams is then possible with a meaningful interpretation of the data structure. A comparative study with the original online procedure shows that E2GK outperforms EGK on different entry data sets. To show the performance of E2GK, several experiments have been conducted on synthetic data sets as well as on data collected from a real application problem. A study of parameters’ sensitivity is also carried out and solutions are proposed to limit complexity issues.     

A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian

In this paper, we focus on the proposed algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition that it has been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, An algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition, Appl. Math. Comput. 178 (2006) 502–509]. Firstly, we show that the algorithm may not lead to the optimal solution in some cases. Secondly, we propose a new algorithm for solving the presented model by Ghodousian and Khorram (2006), as mentioned above. In fact, it modifies the presented algorithm in the Ghodousian and Khorram’s paper. Also, this algorithm is extended to the presented model by Khorram and Ghodousian [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886.] with max-av composition. Finally, some numerical examples are given for illustrating the purposes.