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.

Prediction of stall inception in multi-stage compressors based on an eigenvalue approach

A stability model for multi-stage compressor is developed on the basis of the eigenvalue approach.This model assumes that the unsteady flow field can be decomposed into pressure,vortex and entropy waves.Besides,a linear cascade of blades is modeled by three-dimensional semi-actuator disk theory and the characteristics of steady flow field are also considered in the present model.The connection between the analytical solution for stator,rotor and gap can be established by applying mode matching approach,the relevant stability equation can be expressed in the form of matrix,while the compressor system stability can be judged by the imaginary part of the matrix eigenvalue.The capacity of the stall inception model to predict the stall inception point of multi-stage compressor is assessed against the experimental data of National Aeronautics and Space Administration(NASA) two stage fan.The theoretical results show that this model can predict the stall onset points of a two-stage fan at different operating speeds with a reasonable accuracy.

Modal Decomposition for the Analysis of the Rotor-stator Interactions in Multi-stage Compressors

A modal analysis method of the rotor-stator interactions in multistage compressors has been developed by LMFA. This method, based on a double modal decomposition of the flow over space and time, has been applied to nu- merical and experimental results of the high-speed 3Y2-stage compressor CREATE based at LMFA, Lyon-France. It reveals the presence of a very strong rotor-stator interaction which completely drives the flow at casing behind all the rotors. This modal analysis method applied to an unsteady RANS simulation permits to calculate the en- ergy of the rotor-stator interactions and to plot energetic meridian maps to explain experimental results and to analyze the interaction in the whole machine.

OPTIMUM OF PRESSURE RATIOS OF MULTI-STAGE RECIPROCATING COMPRESSOR WITH PRACTICAL INTER-COOLING

The optimum pressure ratio distribution of a multistage reciprocating compressor is presented based on the assumption, i.e. the inter stage cooling is perfect and there are no pressure losses. The optimization of the two or three stage pressure ratio is analyzed in two cases of constant heat transfer rate for the inter cooler or constant inter stage inlet temperature, based on the minimum of the sum of theoretical compression power at each stage about a multi stage reciprocating compressor. Furthermore, with an example of two stage compressor the influence on the sum of the power of each stage is analyzed when practical pressure ratio deviates from the optimum value. It is obtained that under different cooling conditions the optimum pressure ratio distribution of the multi stage compression is various, and the change of the optimum pressure ratio within a small range has little influence on the sum of the power each stage. For the two stage compression, this range can be represented as ε 1=(0 96～1 06)ε 1j .

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.

Preparation and property of seal coating for gas turbine compressor

Double-layer structure of seal coating which consisted of a Ni5Al bond coating and a Ni25 graphite top coating were prepared on steel substrate of gas turbine compressor cylinder block.Bond coating was prepared by atmospheric plasma spraying and top coating was prepared by flame spraying.The microstructure,mechanical properties and abradability of the coating were characterized by scanning elec-tron microscope(SEM),hardness tester,universal testing machine,thermal shock testing machine and abradability testing machine.The res-ults show that the overall spraying structure of the seal coating is uniform,the nickel metal phase is the skeleton supporting the entire coat-ing,and the coating is well bonded without separation.The seal coating has a bonding strength of not less than 7.7 MPa,excellent thermal stability,and thermal shock resistance cycle numbers at 500℃more than 50;the scratch length,deepest invasion depth and wear amount of the coating increase with rise of test temperature,with almost no coating adhesion,indicating that the seal coating has excellent abradability.

Numerical analysis and optimization of the inlet stage of a multi-stage high pressure compressor

An opti mization process is used to redesign blades of a high-pressure compressor.An artificial neural network (ANN) method is coupled to Navier-Stokes solvers and is applied to three different redesigns.A newrotor blade of a transonic compressor is designed by modifying thick,stacking line andinlet angle using a 3Dapproach,with a significant efficiencyi mprovement at the design point.The off-design behavior of this new compressor is also checked afterwards,which shows that the whole performance of the inlet stage is improved over a wide range of mass flow.The losses are reduced,proving the good performance of the opti mum.The whole results indicate that the opti mization method can find i mproved design and can be integrated in a design procedure.

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）.

Laves phase hydrogen storage alloys for super-high-pressure metal hydride hydrogen compressors

Ti-Cr- and Ti-Mn-based alloys were prepared to be low- and high-pressure stage metals for a double-stage super-high-pressure metal hydride hydrogen compressor. Their crystallographic characteristics and hydrogen storage properties were investigated. The alloy pair Ti0.9Zr0.1Mn1.4- Cr0.35V0.2Fe0.05/TiCr1.55Mn0.2Fe0.2 was optimized based on the comprehensive performance of the studied alloys. The product hydrogen with a pressure of 100 MPa could be produced from 4 MPa feed gas when hot oil was used as a heat reservoir.

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.