Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm

Concentrate copper grade(CCG)is one of the important production indicators of copper flotation processes,and keeping the CCG at the set value is of great significance to the economic benefit of copper flotation industrial processes.This paper addresses the fluctuation problem of CCG through an operational optimization method.Firstly,a density-based affinity propagationalgorithm is proposed so that more ideal working condition categories can be obtained for the complex raw ore properties.Next,a Bayesian network(BN)is applied to explore the relationship between the operational variables and the CCG.Based on the analysis results of BN,a weighted Gaussian process regression model is constructed to predict the CCG that a higher prediction accuracy can be obtained.To ensure the predicted CCG is close to the set value with a smaller magnitude of the operation adjustments and a smaller uncertainty of the prediction results,an index-oriented adaptive differential evolution(IOADE)algorithm is proposed,and the convergence performance of IOADE is superior to the traditional differential evolution and adaptive differential evolution methods.Finally,the effectiveness and feasibility of the proposed methods are verified by the experiments on a copper flotation industrial process.

An Enhanced Adaptive Differential Evolution Approach for Constrained Optimization Problems

Effective constrained optimization algorithms have been proposed for engineering problems recently.It is common to consider constraint violation and optimization algorithm as two separate parts.In this study,a pbest selection mechanism is proposed to integrate the current mutation strategy in constrained optimization problems.Based on the improved pbest selection method,an adaptive differential evolution approach is proposed,which helps the population jump out of the infeasible region.If all the individuals are infeasible,the top 5%of infeasible individuals are selected.In addition,a modified truncatedε-level method is proposed to avoid trapping in infeasible regions.The proposed adaptive differential evolution approach with an improvedεconstraint processmechanism(IεJADE)is examined on CEC 2006 and CEC 2010 constrained benchmark function series.Besides,a standard IEEE-30 bus test system is studied on the efficiency of the IεJADE.The numerical analysis verifies the IεJADE algorithm is effective in comparisonwith other effective algorithms.

An improved adaptive differential evolution algorithm for single unmanned aerial vehicle multitasking

Single unmanned aerial vehicle(UAV)multitasking plays an important role in multiple UAVs cooperative control,which is as well as the most complicated and hardest part.This paper establishes a threedimensional topographical map,and an improved adaptive differential evolution(IADE)algorithm is proposed for single UAV multitasking.As an optimized problem,the efficiency of using standard differential evolution to obtain the global optimal solution is very low to avoid this problem.Therefore,the algorithm adopts the mutation factor and crossover factor into dynamic adaptive functions,which makes the crossover factor and variation factor can be adjusted with the number of population iteration and individual fitness value,letting the algorithm exploration and development more reasonable.The experimental results implicate that the IADE algorithm has better performance,higher convergence and efficiency to solve the multitasking problem compared with other algorithms.

Optimal Kinematics Design of MacPherson Suspension: Integrated Use of Grey Relational Analysis and Improved Entropy Weight Method

Selecting design variables and determining optimal hard⁃point coordinates are subjective in the traditional multiobjective optimization of geometric design of vehicle suspension,thereby usually resulting in poor overall suspension kinematic performance.To eliminate the subjectivity of selection,a method transferring multiobjective optimization function into a single⁃objective one through the integrated use of grey relational analysis(GRA)and improved entropy weight method(IEWM)is proposed.First,a comprehensive evaluation index of sensitivities was formulated to facilitate the objective selection of design variables by using GRA,in which IEWM was used to determine the weight of each subindex.Second,approximate models between the variations of the front wheel alignment parameters and the design variables were developed on the basis of support vector regression(SVR)and the fruit fly optimization algorithm(FOA).Subsequently,to eliminate the subjectivity and improve the computational efficiency of multiobjective optimization(MOO)of hard⁃point coordinates,the MOO functions were transformed into a single⁃objective optimization(SOO)function by using the GRA-IEWM method again.Finally,the SOO problem was solved by the self⁃adaptive differential evolution(jDE)algorithm.Simulation results indicate that the GRA⁃IEWM method outperforms the traditional multiobjective optimization method and the original coordinate scheme remarkably in terms of kinematic performance.

Application of linear active disturbance rejection control for photoelectric tracking system

Dynamic characteristics and tracking precision are studied in the photoelectric tracking system and a linear active disturbance rejection control( LADRC) scheme is proposed for position loop. A current and speed controller is designed by a transfer function model,which is obtained by adaptive differential evolution. Model error,friction and nonlinear factor existing in position loop are treated as ‘disturbance',which is estimated and compensated by generalized proportional integral( GPI)observer. Comparative results are provided to demonstrate the remarkable performance of the proposed method. It turns out that the proposed scheme is successful and has superior features,such as quick dynamic response,low overshoot and high tracking precision. Furthermore,with the proposed method,friction is suppressed effectively.

AERODYNAMIC OPTIMIZATION DESIGN OF LOW ASPECT RATIO TRANSONIC TURBINE STAGE

The advanced optimization method named as adaptive range differential evolution （ARDE） is developed. The optimization performance of ARDE is demonstrated using a typical mathematical test and compared with the standard genetic algorithm and differential evolution. Combined with parallel ARDE, surface modeling method and Navier-Stokes solution, a new automatic aerodynamic optimization method is presented. A low aspect ratio transonic turbine stage is optimized for the maximization of the isentropic efficiency with forty-one design variables in total. The coarse-grained parallel strategy is applied to accelerate the design process using 15 CPUs. The isentropic efficiency of the optimum design is 1.6% higher than that of the reference design. The aerodynamic performance of the optimal design is much better than that of the reference design.

Estimating Effective Reproduction Number for SIR Compartmental Model:A Stochastic Evolutionary Approach

Compatmental pandemic models have become a significant tool in the battle against disease outbreaks.Despite this,pandemic models sometimes require extensive modification to accuately reflect the actual epidemic condition The Susceptble-Infectious-Removed(SIR)model,in particular,contains two primary parameters:the infectious rate parameter ρ and the removal rate parameter r,in addition to additional unknowns such as the initial infectious population.Adding to the complexity,there is an obvious challenge to tack the evolution of these parameters,especially ρ and γ,over time which leads to the estimation of the reproduction number for the paticular time window,^(κ)T.This reproduction mumber may provide better understanding on the efectiveness of isolation or control measures.The changing ^(κ)T values(evolving over time window)will lead to even more possible parameter scenanios.Given the present Coronavirus Disease 2019(COVID-19)pandemic,a stochastic optimization stategy is proposed to ft the model on the basis of parameter changes over timne.Solutions are encoded to reflet the changing parameters of Tρ and γT,alwing the changing ^(κ)T to be estimated.In our approach,an Adaptive Differential Evolution(ADE)and Paricle Swam Optimization(PSO)are used to ft the curves into previously recorded data.ADE eliminates the need to tume the parameters of the Differential Evolution(DE)to balance the exploitation and exploration in the solution space.Results show that the proposed optimized model can generally ft the cuves well albeit high variance in the solutions.

Strip width spread prediction in rough rolling process based on mechanism modeling and optimization

Aiming at the problems of low accuracy and poor robustness that existed in the current hot rolling strip width spread model,an improved strip spread prediction model based on a material forming mechanism and Bayesian optimized adaptive differential evolution algorithm(BADE)was proposed.At first,we improved the original spread mechanism model by adding the weight and bias term to enhance the model robustness based on rolling temperature.Then,the BADE algorithm was proposed to optimize the improved spread mechanism model.The optimization algorithm is based on a novel adaptive differential evolution algorithm,which can effectively achieve the global optimal solution.Finally,the prediction performances of five machine learning algorithms were compared in experiments.The results show that the prediction accuracy of the improved spread model is obviously better than that of the machine learning algorithms,which proves the effectiveness of the proposed method.

A Multilevel Splitting Algorithm for Quick Sampling

To reduce intermediate levels of splitting process and enhance sampling accuracy, a multilevel splitting algorithm for quick sampling is proposed in this paper. Firstly, the selected area of the elite set is expanded to maintain the diversity of the samples. Secondly, the combined use of an adaptive difference evolution algorithm and a local searching algorithm is proposed for the splitting procedure. Finally, a suite of benchmark functions are used for performance testing. The results indicate that the convergence rate and stability of this algorithm are superior to those of the classical importance splitting algorithm and an adaptive multilevel splitting algorithm.