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.

Multi-stage and multi-orifice throttling analysis for thermal power generating sets

Multi stage and multi orifice throttling analysis for bypass valves in thermal power generating sets is important for normal operation of power generating equipment. It is improper to exclude the factor of flow resistance from the expansion coefficient for the flow formula used for analysing the multi stage and multi orifice flow of compressible fluid, which means expansion of gas has nothing to do with resistance. The authors put forward an expanded energy equation and related formula to overcome the drawback, and use them for multi stage and multi orifice throttling analysis of compressible fluid for thermal power generating sets.

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.

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）.

Study on the hot deformation behavior of Al-Zn-Mg-Cu-Cr aluminum alloy during multi-stage hot compression

The mechanical behavior and microstructures of an Al-Zn-Mg-Cu-Cr aluminum alloy during multi-stage hot deformation were investigated by thermal stimulation test, optical microscopy, and transmission electron microscopy. The true stress vs true strain curves and the microstructure evolution of two hot deformation procedures were gained. The flow stress of the alloy studied decreases with increasing the deforming passes and declining the temperature, and the larger the temperature decline between adjacent stages, the larger the peak stress fall is. The stress-strain behavior mainly result from the dynamic recovery during deformation, the static recovery and recrystallization in the delay time, and the second phases precipitated from the matrix at high temperature.

Springback analysis and strategy for multi-stage thin-walled parts with complex geometries

Springback of a SUS321 complex geometry part formed by the multi-stage rigid-flexible compound process was studied through numerical simulations and laboratory experiments in this work.The sensitivity analysis was provided to have an insight in the effect of the evaluated process parameters.Furthermore,in order to minimize the springback problem,an accurate springback simulation model of the part was established and validated.The effects of the element size and timesteps on springback model were further investigated.Results indicate that the custom mesh size is beneficial for the springback simulation,and the four timesteps are found suited for the springback analysis for the complex geometry part.Finally,a strategy for reducing the springback by changing the geometry of the blank is proposed.The optimal blank geometry is obtained and used for manufacturing the part.

Sequential maneuvering decisions based on multi-stage influence diagram in air combat

A multi-stage influence diagram is used to model the pilot＇s sequential decision making in one on one air combat. The model based on the multi-stage influence diagram graphically describes the elements of decision process, and contains a point-mass model for the dynamics of an aircraft and takes into account the decision maker＇s preferences under uncertain conditions. Considering an active opponent, the opponent＇s maneuvers can be modeled stochastically. The solution of multistage influence diagram can be obtained by converting the multistage influence diagram into a two-level optimization problem. The simulation results show the model is effective.

Multi-stage ponds-wetlands ecosystem for effective wastewater treatment

The performance of the Dongying multi-stage ponds-wetlands ecosystem was investigated in this work. Study of the removal of different pollutants (BOD5, COD, SS, TP, TN, NH3-N, etc.) in different temperature seasons and different units in this system indicated that effluent BOD5 and SS were constant to less than 11 mg/L and 14 mg/L throughout the experimental proc- esses; but that the removal efficiencies of pollutants such as TP, TN, NH3-N, COD varied greatly with season. The higher the temperature was, the higher was the observed removal in this system. Additionally, each unit of the system functioned differently in removing pollutants. BOD5 and SS were mainly removed in the first three units (hybrid facultative ponds, aeration ponds and aerated fish ponds), whereas nitrogen and phosphates were mainly removed in hydrophyte ponds and constructed reed wetlands. The multi-stage ponds-wetlands ecosystem exhibits good potential of removing different pollutants, and the effluent quality meet several standards for wastewater reuse.

Modeling and optimization of unbalanced multi-stage logistic system

To decompose an unbalanced multi-stage logistic system to multipleindependent single-stage logistic systems, a new notion of parameterized interface distribution ispresented. For encoding the logistic pattern on each stage, the Pruefer number is used. With theimproved decoding procedure, any Pruefer number produced stochastically can be decoded to a feasiblelogistic pattern, which can match with the capacities of the nodes of the logistic system. Withthese two innovations, a new modeling method based on parameterized interface distribution and thePriifer number coding is put forward. The corresponding genetic algorithm, named as PIP-GA, can findbetter solutions and require less computational time than st-GA. Although requiring a little moreconsumption of memory, PIP-GA is still an efficient and robust method in the modeling andoptimization of unbalanced multi-stage logistic systems.

Influence of multi-stage heat treatment on the microstructure and mechanical properties of TC21 titanium alloy

Duplex-structured TC21 alloy samples were first solution-treated at a higher temperature in theα+βregion(940°C)with furnace cooling(FC),air cooling(AC),and water cooling(WC),followed by a second-stage solution treatment at a lower temperature in theα+βregion(900°C),and then finally aged at 590°C.The effects of the morphology and quantity ofαphases on the structure and properties of the TC21 alloy after the different heat treatments were analyzed.The in-situ tensile deformation process and crack propagation behavior were observed using scanning electron microscopy(SEM).The quantity of equiaxedαphases as well as the thickness of lamellarαphases reduced,the tensile strength increased firstly and then decreased,the elongation decreased with the increasing cooling rate after the first-stage solution treatment.The amount and size of lamellarαphases increased after the second-stage solution treatment because of sufficient diffusion of the alloying elements,thereby leading to increased tensile strength.The amount of dispersedαphases increased after the third-stage aging treatment owing to the increase in the nucleation rate,resulting in a noteworthy strengthening effect.After the third-stage aging treatment,the first-stage FC sample exhibited better mechanical properties because it contained more equiaxedαandβtrans phases than the first-stage AC and WC samples.

Multi-Stage Hierarchical Channel Allocation in UAV-Assisted D2D Networks:A Stackelberg Game Approach

UAV-assisted D2D networks can provide auxiliary communication for areas with poor communication facilities by using the characteristics of easy deployment of unmanned aerial vehicle(UAV),then it becomes a promising technology.However,the coexistence of UAV and D2D aggravates the conflict of spectrum resources.In addition,when the UAV performs the communication service,it will inevitably cause the location change,which will make the original channel allocation no longer applicable.Inspired by the influence of frequent channel switching on channel allocation,we define the communication utility as a tradeoff between the throughput and channel switching cost.In the considered model,we investigate the multi-stage hierarchical spectrum access problem with maximizing aggregate communication utilities in UAV-assisted D2D networks.In particular,due to the hierarchical feature of the considered network,we adopt Stackelberg game to formulate this spectrum access problem where both the throughput and channel switching cost are considered.We prove that the proposed game has a stable Stackelberg equilibrium(SE),and the heterogeneous network based channel allocation(HN-CA)algorithm is proposed to achieve the desired solution.Simulation results verify the validity of the proposed game and show the effectiveness of the HN-CA algorithm.

Spatial acoustic emission evolution of red sandstone during multi-stage triaxial deformation

Multi-stage triaxial compression tests for cylindrical red sandstone specimens(diameter of 50 mm,height of 100 mm) were carried out with a rock mechanics testing system and spatial acoustic emission(AE) locations were obtained by adopting an AE monitoring system.Based on spatial AE distribution evolution of red sandstone during multi-stage triaxial deformation,the relation between spatial AE events and triaxial deformation of red sandstone was analyzed.The results show that before peak strength,the spatial AE events are not active and distribute stochastically in the specimen,while after peak strength,the spatial AE events are very active and focus on a local region beyond final microscopic failure plane.During multi-stage triaxial deformation with five different confining pressures,the spatial AE distribution evolution in the red sandstone was obtained.The obtained spatial AE locations of red sandstone at the final confining pressure agree very well with the ultimate failure experimental mode.Finally,the influence of confining pressure on the spatial AE evolution characteristics of red sandstone during triaxial deformation was discussed.The AE behavior of red sandstone during multi-stage triaxial deformation is interpreted in the light of the Kaiser effect,which has a significant meaning for predicting the unstable failure of engineering rock mass.

Process design for multi-stage stretch forming of aluminium alloy aircraft skin

A process design approach for multi-stage stretch forming was proposed by combining the strain distribution method and finite element method(FEM)to determine the minimum stage number and deformation amount of each stage.The strain distribution method was used to calculate the deformation amount of each stage and evaluate the formability through a safety criterion.FE simulation was taken as an analysis tool to reveal the deformation behaviour,to predict the strain contour and to determine the process parameters at each stage.To evaluate the effect of heat treatment after pre-strain on occurrence of deformation defects during the subsequent deformation,a multi-stage uniaxial tension test for 2B06 aluminium alloy sheet was carried out.A case study demonstrates that the approach has high reliability and good practicability.

Development of a 4 MV Laser-Triggered Multi-Stage Switch

A 22-stage 4 MV laser-triggered multistage multi-channel switch （LTS） was designed according to the hypothesis that the well-proportioned electrical field distribution is helpful in reducing the jitter of delay. Field distribution in the switch section is regulated by a metal field regulation ring and several gradient rings. In order to reduce the jitter further, a SFB/N2 mixture is chosen as the switching medium. The generalized standard deviation of the self-breakdown voltage and the deviation of the average value from the prediction is less than 4.4% and 13% respectively. Linearity of the self-breakdown voltage is better than 0.95. Triggered by a laser pulse of 35 mJ/3 ns, the delay is about 26 ns at a working voltage of 85±3% USB （Self-breakdown Voltage）. Maximum deviation of delay is less than =t=2.5 ns. Jitter is less than 1.5 ns. The delay and jitter decrease with the increase in the working ratio （the ratio of working voltage to USB）, pressure or voltage.

Dynamic performance of cable-stayed bridge tower with multi-stage pendulum mass damper under wind excitations——I:Theory

In this paper, wind-induced vibration control of a single column tower of a cable-stayed bridge with a multi- stage pendulum mass damper （MSPMD） is investigated. Special attention is given to overcoming space limitations for installing the control device in the tower and the effect of varying natural frequency of the towers during construction. First, the finite element model of the bridge during its construction and the basic equation of motion of the MSPMD are introduced. The equation of motion of the bridge with the MSPMD under along-wind excitation is then established. Finally, a numerical simulation and parametric study are conducted to assess the effectiveness of the control system for reducing the wind-induced vibration of the bridge towers during construction. The numerical simulation results show that the MSPMD is practical and effective for reducing the along-wind response of the single column tower, can be installed in a small area of the tower, and complies with the time-variant characteristics of the bridge during its entire construction stage.