A Multi-Stage Differential-Multifactorial Evolutionary Algorithm for Ingredient Optimization in the Copper Industry

Ingredient optimization plays a pivotal role in the copper industry,for which it is closely related to the concentrate utilization rate,stability of furnace conditions,and the quality of copper production.To acquire a practical ingredient plan,which should exhibit long duration time with sufficient utilization and feeding stability for real applications,an ingredient plan optimization model is proposed in this study to effectively guarantee continuous production and stable furnace conditions.To address the complex challenges posed by this integer programming model,including multiple coupling feeding stages,intricate constraints,and significant non-linearity,a multi-stage differential-multifactorial evolution algorithm is developed.In the proposed algorithm,the differential evolutionary(DE)algorithm is improved in three aspects to efficiently tackle challenges when optimizing the proposed model.First,unlike traditional time-consuming serial approaches,the multifactorial evolutionary algorithm is utilized to optimize multiple complex models contained in the population of evolutionary algorithm caused by the feeding stability in a parallel manner.Second,a repair algorithm is employed to adjust infeasible ingredient lists in a timely manner.In addition,a local search strategy taking feedback from the current optima and considering the different positions of global optimum is developed to avoiding premature convergence of the differential evolutionary algorithm.Finally,the simulation experiments considering different planning horizons using real data from the copper industry in China are conducted,which demonstrates the superiority of the proposed method on feeding duration and stability compared with other commonly deployed approaches.It is practically helpful for reducing material cost as well as increasing production profit for the copper industry.

Multi-Stage Multidisciplinary Design Optimization Method for Enhancing Complete Artillery Internal Ballistic Firing Performance

To enhance the comprehensive performance of artillery internal ballistics—encompassing power,accuracy,and service life—this study proposed a multi-stage multidisciplinary design optimization(MS-MDO)method.First,the comprehensive artillery internal ballistic dynamics(AIBD)model,based on propellant combustion,rotation band engraving,projectile axial motion,and rifling wear models,was established and validated.This model was systematically decomposed into subsystems from a system engineering perspective.The study then detailed the MS-MDO methodology,which included Stage I(MDO stage)employing an improved collaborative optimization method for consistent design variables,and Stage II(Performance Optimization)focusing on the independent optimization of local design variables and performance metrics.The methodology was applied to the AIBD problem.Results demonstrated that the MS-MDO method in Stage I effectively reduced iteration and evaluation counts,thereby accelerating system-level convergence.Meanwhile,Stage II optimization markedly enhanced overall performance.These comprehensive evaluation results affirmed the effectiveness of the MS-MDO method.

Research on Regulation Method of Energy Storage System Based on Multi-Stage Robust Optimization

To address the scheduling problem involving energy storage systems and uncertain energy,we propose a method based on multi-stage robust optimization.This approach aims to regulate the energy storage system by using a multi-stage robust optimal control method,which helps overcome the limitations of traditional methods in terms of time scale.The goal is to effectively utilize the energy storage power station system to address issues caused by unpredictable variations in environmental energy and fluctuating load throughout the day.To achieve this,a mathematical model is constructed to represent uncertain energy sources such as photovoltaic and wind power.The generalized Benders Decomposition method is then employed to solve the multi-stage objective optimization problem.By decomposing the problem into a series of sub-objectives,the system scale is effectively reduced,and the algorithm’s convergence ability is improved.Compared with other algorithms,the multi-stage robust optimization model has better economy and convergence ability and can be used to guide the power dispatching of uncertain energy and energy storage systems.

Evolution of nonmetallic inclusions in 80-t 9CrMoCoB large-scale ingots during electroslag remelting process

In combination with theoretical calculations,experiments were conducted to investigate the evolution behavior of nonmetallic inclusions(NMIs)during the manufacture of large-scale heat-resistant steel ingots using 9CrMoCoB heat-resistant steel and CaF_(2)–CaO–Al_(2)O_(3)–SiO_(2)–B_(2)O_(3)electroslag remelting(ESR)-type slag in an 80-t industrial ESR furnace.The main types of NMI in the consumable electrode comprised pure alumina,a multiphase oxide consisting of an Al_(2)O_(3)core and liquid CaO–Al_(2)O_(3)–SiO_(2)–MnO shell,and M_(23)C_(6)carbides with an MnS core.The Al_(2)O_(3)and MnS inclusions had higher precipitation temperatures than the M_(23)C_(6)-type carbide under equilibrium and nonequilibrium solidification processes.Therefore,inclusions can act as nucleation sites for carbide layer precipitation.The ESR process completely removed the liquid CaO–Al_(2)O_(3)–SiO_(2)–MnO oxide and MnS inclusion with a carbide shell,and only the Al_(2)O_(3)inclusions and Al_(2)O_(3)core with a carbide shell occupied the remelted ingot.The M_(23)C_(6)-type carbides in steel were determined as Cr_(23)C_(6)based on the analysis of transmission electron microscopy results.The substitution of Cr with W,Fe,or/and Mo in the Cr_(23)C_(6)lattice caused slight changes in the lattice parameter of the Cr_(23)C_(6)carbide.Therefore,Cr_(21.34)Fe_(1.66)C_(6),(Cr_(19)W_(4)C_(6),Cr_(18.4)Mo_(4.6)C_(6),and Cr_(16)Fe_(5)Mo_(2)C_(6)can match the fraction pattern of Cr_(23)C_(6)carbide.The Al_(2)O_(3)inclusions in the remelted ingot formed due to the reduction of CaO,SiO_(2),and MnO components in the liquid inclusion.The increased Al content in liquid steel or the higher supersaturation degree of Al_(2)O_(3)precipitation in the remelted ingot than that in the electrode can be attributed to the evaporation of CaF_(2)and the increase in CaO content in the ESR-type slag.

Trace Elements of Multi-stage Minerals and Titanite U-Pb Dating for the Gneisses from Liansan Island,Sulu UHPM Belt

Gneisses with anatectic characteristics from the Liansan island in the Sulu UHPM(ultra-high pressure metamorphic)belt were studied for petrography,titanite U-Pb dating and mineral geochemistry.Three origins of garnets are distinguished:metamorphic garnet,peritectic garnet and anatectic garnet,which are formed in the stages of peak metamorphism,retrograde anatexis and melt crystallization,respectively.The euhedral titanite has a high content of REE and high Th/U ratios,which is interpreted as indicating that it was newly-formed from an anatectic melt.The LA-ICP-MS titanite U-Pb dating yields 214-217 Ma ages for the titanite(melt)crystallization.The distribution of trace elements varies in response to the different host minerals at different stages.At the peak metamorphic stage,Y and HREE are mainly hosted by garnet,Ba and Rb by phengite,Sr,Nb,Ta,Pb,Th,U and LREE by allanite and Y,U and HREE by zircon.During partial melting,Y,Pb,Th,U and REE are released into the melt,which causes a dramatic decline of these element contents in the retrograde minerals.Finally,titanite absorbs most of the Nb,U,LREE and HREE from the melt.Therefore,the different stages of metamorphism have different mineral assemblages,which host different trace elements.

Overview of multi-stage charging strategies for Li-ion batteries

To reduce the carbon footprint in the transportation sector and improve overall vehicle efficiency,a large number of electric vehicles are being manufactured.This is due to the fact that environmental concerns and the depletion of fossil fuels have become significant global problems.Lithium-ion batteries(LIBs)have been distinguished themselves from alternative energy storage technologies for electric vehicles(EVs) due to superior qualities like high energy and power density,extended cycle life,and low maintenance cost to a competitive price.However,there are still certain challenges to be solved,like EV fast charging,longer lifetime,and reduced weight.For fast charging,the multi-stage constant current(MSCC) charging technique is an emerging solution to improve charging efficiency,reduce temperature rise during charging,increase charging/discharging capacities,shorten charging time,and extend the cycle life.However,there are large variations in the implementation of the number of stages,stage transition criterion,and C-rate selection for each stage.This paper provides a review of these problems by compiling information from the literature.An overview of the impact of different design parameters(number of stages,stage transition,and C-rate) that the MSCC charging techniques have had on the LIB performance and cycle life is described in detail and analyzed.The impact of design parameters on lifetime,charging efficiency,charging and discharging capacity,charging speed,and rising temperature during charging is presented,and this review provides guidelines for designing advanced fast charging strategies and determining future research gaps.

Controlling oxygen content in electro-slag remelting steel by optimizing slag-steel reaction process

The thermodynamic equilibrium of deoxidation reactions between molten slag and steel was calculated using a slag-steel coupling thermodynamic model and the mass conservation model based on the ion-molecular coexistence theory.The study focused on the effects of slag composition and deoxidizer type on the oxygen content of low alloy steel during the electroslag remelting(ESR)process.The measured and predicted values of the oxygen content in remelted ingots,and the contents of FeO and MnO in slags were compared and analyzed.Results show that the measured content of total oxygen has a certain correlation with the trend of dissolved oxygen predicted by the model when using Ca-Si alloys as deoxidizer,but it is not correlated with the trend of dissolved oxygen predicted by the model when using Al as deoxidizer.The deoxidation mechanisms of Ca-Si and Al are different.Ca-Si alloy directly reacts with FeO and MnO in slag to reduce the oxygen potential of slag,hence it can inhibit the transfer of oxygen from the slag to molten steel.While,when Al deoxidizer is used,the oxygen content in steel is mainly reduced through floating up the alumina inclusions.Compared to Al,utilizing Ca-Si alloy as a deoxidizer is more effective in reducing the oxygen content and the amount of inclusions in ESR ingot.

Multi-Stage Improvement of Marine Predators Algorithm and Its Application

The metaheuristic algorithms are widely used in solving the parameters of the optimization problem.The marine predators algorithm(MPA)is a novel population-based intelligent algorithm.Although MPA has shown a talented foraging strategy,it still needs a balance of exploration and exploitation.Therefore,a multi-stage improvement of marine predators algorithm(MSMPA)is proposed in this paper.The algorithm retains the advantage of multistage search and introduces a linear flight strategy in the middle stage to enhance the interaction between predators.Predators further away from the historical optimum are required to move,increasing the exploration capability of the algorithm.In the middle and late stages,the searchmechanism of particle swarmoptimization(PSO)is inserted,which enhances the exploitation capability of the algorithm.This means that the stochasticity is decreased,that is the optimal region where predators jumping out is effectively stifled.At the same time,self-adjusting weight is used to regulate the convergence speed of the algorithm,which can balance the exploration and exploitation capability of the algorithm.The algorithm is applied to different types of CEC2017 benchmark test functions and threemultidimensional nonlinear structure design optimization problems,compared with other recent algorithms.The results show that the convergence speed and accuracy of MSMPA are significantly better than that of the comparison algorithms.

基于Multi-Stage DEA模型的中国细羊毛生产技术效率实证分析

以内蒙古等4省区为例，采用基于规模报酬可变假设的产出主导型Muhi-StageDEA模型，对2001～2010年中国细羊毛生产技术效率进行了测算和分析。研究结果表明，中国细羊毛生产技术效率不高，存在显著的技术效率损失；细羊毛生产在总体上出现了纯技术效率下降和规模效率提高并存的现象，2008年以来纯技术效率提高对细羊毛生产技术效率改善的促进作用逐渐增强，而细羊毛生产规模效率则呈现出了一定的下降趋势；各省区细羊毛生产技术效率存在较大差异，细羊毛生产的规模效率均要高于纯技术效率，规模效率仍是影响各省区细羊毛生产技术效率改善和提高的主要因素。最后提出改善和提高中国细羊毛生产技术效率的政策建议。

Triangular Au-Ag framework nanostructures prepared by multi-stage replacement and their spectral properties

Triangular Au-Ag framework nanostructures （TFN） were synthesized via a multi-step galvanic replacement reaction （MGRR） of single-crystalline triangular silver nanoplates in a chlorauric acid （HAuCl4） solution at room temperature. The morphological, compositional, and crystal structural changes involved with reaction steps were analyzed by using transmission electron microscopy（TEM）, energy-dispersive X-ray spectrometry （EDX）, and X-ray diffraction. TEM combined with EDX and selected area electron diffraction confirmed the replacement of Ag with Au. The in-plane dipolar surface plasmon resonance （SPR） absorption band of the Ag nanoplates locating initially at around 700 nm gradually redshifted to 1 100 nm via a multi-stage replacement manner after 7 stages. The adding amount of HAuCl4 per stage influenced the average redshift value per stage, thus enabled a fine tuning of the in-plane dipolar band. A proposed formation mechanism of the original Ag nanoplates developing pores while growing Au nanoparticles covering this underlying structure at more reaction steps was confirmed by exploiting surface-enhanced Raman scattering （SERS）.

Microstructural evolution and phase transformation during partial remelting of in-situ Mg_2Si_p/AM60B composite

The microstructural evolution and phase transformations during partial remelting of in-situ Mg2Sip/AM60B composite modified by SiC and Sr were investigated. The results indicate that SiC and Sr are effective for refining primary α-Mg grains and Mg2Si particles. After being partially remelted, a semisolid microstructure with small and spheroidal primary α-Mg particles can be obtained. The microstructural evolution during partial remelting can be divided into four stages： the initial rapid coarsening, structural separation, spheroidization and final coarsening, which are essentially caused by the phase transformations of β→α, α＋β→L and α→L, α→L, and α→L and L→α, respectively. The Mg2Si particles have not obvious effect on the general microstructural evolution steps, but can slower the evolution progress and change the coarsening mechanism. During partial remelting, Mg2Si particles first become blunt and then become spheroidal because of melting of their edges and corners, and finally are coarsened owing to Ostwald ripening.

Effect of ball milling on microstructural evolution during partial remelting of6061 aluminum alloy prepared by cold-pressing of alloy powders

The effect of ball milling on the microstructural evolution was investigated during partial remelting of 6061 aluminum alloy prepared by cold-pressing of atomized alloy powders.The results indicate that the microstructural evolution of 6061 aluminum alloy can be divided into three stages,the dissolution of eutectic phases and the coarsening and growth behavior of the resulting grains,structural separation and spheroidization of primary particles,and the final coarsening behavior of the particles.Compared with the alloy without ball milling,ball milling accelerates the first stage of microstructural evolution due to the energy stored in the powders,but the latter two stages are slowed down because of the formation of large-sized powders.Moreover,the finer the as-cold-pressed microstructure is,the smaller and more spherical the primary particles in the final semisolid microstructure are.Furthermore,properly elevating the heating temperature is beneficial for obtaining small and spheroidal particles.

Mathematical Model for Electroslag Remelting Process

A mathematical model, including electromagnetic field equation, fluid flow equation, and temperature field equation, was established for the simulation of the electroslag remelting process. The distribution of temperature field was obtained by solving this model. The relationship between the local solidification time and the interdendritic spacing during the ingot solidification process was established, which has been regarded as a criterion for the evaluation of the quality of crystallization. For a crucible of 950 mm in diameter, the local solidification time is more than 1 h at the center of the ingot with the longest interdendritic spacing, whereas it is the shortest at the edge of the ingot according to the calculated results. The model can be used to understand the ESR process and to predict the ingot quality.

Characteristics of Al_2O_3, MnS, and TiN inclusions in the remelting process of bearing steel

The Al_2O_3, MnS, and TiN inclusions in bearing steel will deteriorate the steel's mechanical properties. Therefore, elucidating detailed characteristics of these inclusions in consumable electrode during the electroslag remelting process is important for achieving a subsequently clean ingot. In this study, a confocal scanning violet laser microscope was used to simulate the remelting process and observe, in real time, the behaviors of inclusions. The obtained images show that, after the temperature exceeded the steel solidus temperature, MnS and TiN inclusions in the specimen began to dissolve. Higher temperatures led to faster dissolution, and the inclusions disappeared before the steel was fully liquid. In the case of an observed Al_2O_3 inclusion, its shape changed from angular to a smooth ellipsoid in the region where the solid and liquid coexisted and it began to dissolve as the temperature continued to increase. This dissolution was driven by the difference in oxygen potential between the inclusion and the liquid steel.

Effect of slag on oxide inclusions in carburized bearing steel during industrial electroslag remelting

Industrial experiments with three types of slags were performed to investigate the effect of slag on oxide inclusions during electroslag remelting(ESR) process. G20CrNi2Mo bearing steel was used as the consumable electrode and remelted using a 2400-kg industrial furnace. The results showed that most inclusions in the electrode were low-melting-point CaO-MgO-Al_2O_3. After ESR, all the inclusions in ingots were located outside the liquid region. When the slag consisted of 65.70 wt% CaF_2, 28.58 wt% Al_2O_3, and 4.42 wt% CaO was used, pure Al_2O_3 were the dominant inclusions in ingot, some of which presented a clear trend of agglomeration. When the ingot was remelted by a multi-component slag with 16.83 wt% CaO, a certain amount of sphere CaAl_4O_7 inclusions larger than 5 μm were generated in ingot. The slag with 8.18 wt% CaO exhibited greater capacity to control the inclusion characteristics. Thermodynamic calculations indicated that the total Ca and Mg in ingots were attributed from the relics in electrode and strongly influenced by the slag composition. The formation of ingot inclusions was calculated by FactSage^(TM) 7.0, and the results were basically in accordance with the observed inclusions, indicating that a quasi-thermodynamic equilibrium could be obtained in the metal pool.

Characteristics of inclusions in high-Al steel during electroslag remelting process

The characteristics of inclusions in high-A1 steel refmed by electroslag remelting （ESR） were investigated by image analysis, scanning electron microscopy （SEM）, and energy-dispersive spectrometry （EDS）. The results show that the size of almost all the inclusions observed in ESR ingots is less than 5 μm. Inclusions smaller than 3 μm take nearly 75% of the total inclusions observed in each ingot. Inclu- sions observed in ESR ingots are pure AIN as dominating precipitates and some fine spherical Al2O3 inclusions with a size of 1 μm or less. It is also found that protective gas operation and slag deoxidation treatment during ESR process have significant effects on the number of inclusions smaller than 2μm but little effects on that of inclusions larger than 2 μm. Thermodynamic calculations show that AIN inclusions are unable to precipitate in the liquid metal pool under the present experimental conditions, while the precipitation of AlN inclusions could take place at the solidifying front due to the microsegregation orAl and N in liquid steel during solidification.

Microstructure evolution of ZA72 magnesium alloy during partial remelting

The application of some semi-solid forming magnesium alloys is restricted due to their weak mechanical properties. To improve the mechanical properties, it is necessary to research the regularity and theory of semi-solid microstructure evolution of the alloy. In this study, microstructure evolution of ZA72 alloy during the partial remelting, and the effect of holding temperature and holding time on the semi-solid microstructure evolution of ZA72 magnesium alloy were investigated by means of OM, SEM and EDS analysis. The results indicate that the microstructure with small and spheroidal semi-solid particles which are available for thixo-forming can be obtained using proper heating parameters. After being isothermally treated at between 580 and 610 ℃ for 30 min, the equivalent size and shape factor of primary solid phase of ZA72 alloy decrease gradually, while the liquid volume fraction increases. When isothermally treated at 600 ℃ and held for different times from 15 to 60 min, with the increase of holding time, the equivalent size of primary particles decreases at first and then increases gradually; while the shape factor decreases gradually. The best heat treatment parameters in this experiment are to hold at 610 ℃for 30 min. Compared with as-cast ZA72 alloy, the sizes of the eutectic phase and second a-Mg phase obtained in semi-solid state are smaller due to the higher solidification rate and the higher under-cooling degree than as-cast state. These decrease the fracture probability during tensile stress and improve the properties of the ZA72 alloy by semi-solid forming.

Effect of Laser Remelting on the Microstructure and Corrosion Resistance of Plasma Sprayed Fe-based Coating

Fe-based amorphous and nanocrystalline coatings were fabricated by air plasma spraying. The coatings were further treated by laser remelting process to improve their microstructure and properties. The corrosion resistance of the as-sprayed and laser-remelted coatings in 3.5wt% NaC1 and 1 mol/L HCI solutions was evaluated by electrochemical polarization analysis. It was found that laser-remelted coating appeared much denser than the as-sprayed coating. However, laser-remelted coating contains much more nanocrystalline grains than the as-sprayed coatings, resulting from the lower cooling rate in laser remelting process compared with plasma spraying process. Electrochemical polarization results indicated that the laser-remelted coating has great corrosion resistance than the as-sprayed coating because of its dense structure.

Effect of TiO_2 on the viscosity and structure of low-fluoride slag used for electroslag remelting of Ti-containing steels

The viscosity of CaF_2-CaO-Al_2O_3-MgO-（TiO_2） slag was measured using a rotating crucible viscometer. Raman spectroscopy analysis was performed to correlate the viscosity to slag structure. The viscosity of the slag was found to decrease with increasing TiO_2 content in the slag from 0 to 9.73wt%. The activation energy decreased from 95.16 kJ /mol to 79.40 kJ /mol with increasing TiO_2 content in the slag. The introduction of TiO_2 into the slag played a destructive role in Al-O-Al structural units and Q^4 units by forming simpler structural units of Q^2 and Ti_2O_6^（4-） chain. The amount of Al-O-Al significantly decreased with increasing TiO_2 content. The relative fraction of Q^4 units in the [AlO_4]^（5-）-tetrahedral units shows a decreasing trend, whereas the relative fraction of Q^2 units and Ti_2O_6^（4-） chain increases with increasing TiO_2 content accordingly. Consequently, the polymerization degree of the slag decreases with increasing TiO_2 content. The variation in slag structure is consistent with the change in measured viscosity.

Formation of Liquid Pools Entrapped within Solid Grains of ZA27 Alloys during Partial Remelting

The investigations were performed into the formation processes of liquid pools entrapped within solid grains of three ZA27 alloys, produced respectively by either grain refinement, or traditional permanent casting or mechanical stirring, during partial remelting at semisolid temperature of 460℃. The results show that the rapid coalescence of primary grains due to merging of secondary arms during the initial stage of partial remelting is the main cause for the formation of the entrapped liquid pools. This coalescence resulted in that a high quality of eutectics, especially the 77 phase, was entrapped within the grains, and then remelted to form liquid pools during the subsequent heating. In addition, the growth of the η phase decomposed from the primary α' phase and β phase and the subsequent remelting is another cause for the refined and permanent mould casting alloys. Furthermore, the agglomeration of the solid grains also resulted in the entrapment of liquid in the interior of grains.