By investigating the evolution of shale gas generation,storage,adjustment and accumulation under different structural settings in superimposed basins,this study elucidates the differential accumulation mechanisms of s...By investigating the evolution of shale gas generation,storage,adjustment and accumulation under different structural settings in superimposed basins,this study elucidates the differential accumulation mechanisms of shale gas.An improved evaluation method of shale gas content evolution in superimposed basins is proposed.This method incorporates the coupling effect of key geological factors such as temperature,pressure,organic matter abundance,maturity,and pore characteristics on the content and occurrence state of shale gas,as well as the configuration relationship between shale gas generation and storage throughout geological history.Using this approach,the gas evolution histories of the Longmaxi Formation shales in wells N201 and PY1 are reconstructed under varying geological conditions.The Longmaxi Formation shales in these wells are dominated by typeⅠkerogen,with original total organic carbon(TOCo)contents of 6.20 wt% and 4.92 wt%,respectively,indicating differences in the initial material basis for gas generation.At the maximum burial depth of approximately 5000 m,the Longmaxi Formation shale in well N201 exhibits a formation pressure coefficient of 2.05,an organic matter maturity of 2.2%,and organic pores accounting for 68%of the total porosity.The gas generation quantity(Qg)reaches 19.24 m3,while the gas storage capacity(Qs)is 4.30 m3.The actual total gas content(Qa),constrained by Qs,is 4.30 m3,with free gas comprising 94%.Following relatively moderate tectonic uplift,the Qa in well N201 decreases to 4.03 m3,with free gas accounting for 63%.In contrast,the Longmaxi Formation shale in well PY1 reached a maximum burial depth of 6300 m,associated with a formation pressure coefficient of 1.62,organic matter maturity of 2.5%,and organic pore proportion of 67%.Here,Qg is 16.87 m3,and both Qs and Qa are 3.65 m3,with free gas accounting for 98%.After intense tectonic uplift,Qa declines to 2.72 m3,and the proportion of free gas drops to51%.Finally,a four-stage differential accumulation model of shale gas is established:Slow gas generation and only adsorbed gas occur in stageⅠ,which is primarily controlled by TOC content;both adsorbed gas and free gas present in stageⅡ,with free gas becoming dominant;rapid gas generation and free gas predominance are controlled by temperature and porosity in stageⅢ;and gas adjustment and accumulation are primarily controlled by temperature and pressure in stageⅣ.展开更多
Welding deformation adversely affects the quality and precision of structural components,and traditional methods require significant material resources and time.Machine learning has demonstrated exceptional ac-curacy ...Welding deformation adversely affects the quality and precision of structural components,and traditional methods require significant material resources and time.Machine learning has demonstrated exceptional ac-curacy and efficiency in solving complex problems.Thus,the use of machine learning to predict welding de-formations is a novel approach.In this study,laser welding experiments were conducted on a TC4 titanium alloy to establish a welding deformation dataset.The deep neural network(DNN)and convolutional neural network(CNN)models were designed and constructed,with average prediction errors of 0.85 mm and 0.94 mm on the validation set,respectively.To further optimize the network parameters,a differential evolution algorithm was employed through mutation,crossover,and selection.The results indicated that after optimization,the pre-diction errors of the DNN and CNN models reduced to 0.75 mm and 0.85 mm,respectively.These represent accuracy improvements of 14.8%and 9.6%,respectively.The optimized models exhibited superior predictive performances for the validation set.展开更多
In reliability analyses,the absence of a priori information on the most probable point of failure(MPP)may result in overlooking critical points,thereby leading to biased assessment outcomes.Moreover,second-order relia...In reliability analyses,the absence of a priori information on the most probable point of failure(MPP)may result in overlooking critical points,thereby leading to biased assessment outcomes.Moreover,second-order reliability methods exhibit limited accuracy in highly nonlinear scenarios.To overcome these challenges,a novel reliability analysis strategy based on a multimodal differential evolution algorithm and a hypersphere integration method is proposed.Initially,the penalty function method is employed to reformulate the MPP search problem as a conditionally constrained optimization task.Subsequently,a differential evolution algorithm incorporating a population delineation strategy is utilized to identify all MPPs.Finally,a paraboloid equation is constructed based on the curvature of the limit-state function at the MPPs,and the failure probability of the structure is calculated by using the hypersphere integration method.The localization effectiveness of the MPPs is compared through multiple numerical cases and two engineering examples,with accuracy comparisons of failure probabilities against the first-order reliability method(FORM)and the secondorder reliability method(SORM).The results indicate that the method effectively identifies existing MPPs and achieves higher solution precision.展开更多
The multi-objective differential evolution(MODE)algorithm is an effective method to solve multi-objective optimization problems.However,in the absence of any information of evolution progress,the optimization strategy...The multi-objective differential evolution(MODE)algorithm is an effective method to solve multi-objective optimization problems.However,in the absence of any information of evolution progress,the optimization strategy of the MODE algorithm still appears as an open problem.In this paper,a dynamic multi-objective differential evolution algorithm,based on the information of evolution progress(DMODE-IEP),is developed to improve the optimization performance.The main contributions of DMODE-IEP are as follows.First,the information of evolution progress,using the fitness values,is proposed to describe the evolution progress of MODE.Second,the dynamic adjustment mechanisms of evolution parameter values,mutation strategies and selection parameter value based on the information of evolution progress,are designed to balance the global exploration ability and the local exploitation ability.Third,the convergence of DMODE-IEP is proved using the probability theory.Finally,the testing results on the standard multi-objective optimization problem and the wastewater treatment process verify that the optimization effect of DMODE-IEP algorithm is superior to the other compared state-of-the-art multi-objective optimization algorithms,including the quality of the solutions,and the optimization speed of the algorithm.展开更多
Multi-objective differential evolution(MODE)is a powerful and efficient population-based stochastic search technique for solving multi-objective optimization problems in many scientific and engineering fields.However,...Multi-objective differential evolution(MODE)is a powerful and efficient population-based stochastic search technique for solving multi-objective optimization problems in many scientific and engineering fields.However,premature convergence is the major drawback of MODE,especially when there are numerous local Pareto optimal solutions.To overcome this problem,we propose a MODE with a diversity enhancement(MODE-DE)mechanism to prevent the algorithm becoming trapped in a locally optimal Pareto front.The proposed algorithm combines the current population with a number of randomly generated parameter vectors to increase the diversity of the differential vectors and thereby the diversity of the newly generated offspring.The performance of the MODE-DE algorithm was evaluated on a set of 19 benchmark problem codes available from http://gffzzdcd0dfe20e794032h9x6xkqbnbvf66nbn.ffgz.tsg.suse.edu.cn/home/epnsugan/.With the proposed method,the performances were either better than or equal to those of the MODE without the diversity enhancement.展开更多
Dimensional synthesis is one of the most difficult issues in the field of parallel robots with actuation redundancy. To deal with the optimal design of a redundantly actuated parallel robot used for ankle rehabilitati...Dimensional synthesis is one of the most difficult issues in the field of parallel robots with actuation redundancy. To deal with the optimal design of a redundantly actuated parallel robot used for ankle rehabilitation, a methodology of dimensional synthesis based on multi-objective optimization is presented. First, the dimensional synthesis of the redundant parallel robot is formulated as a nonlinear constrained multi-objective optimization problem. Then four objective functions, separately reflecting occupied space, input/output transmission and torque performances, and multi-criteria constraints, such as dimension, interference and kinematics, are defined. In consideration of the passive exercise of plantar/dorsiflexion requiring large output moment, a torque index is proposed. To cope with the actuation redundancy of the parallel robot, a new output transmission index is defined as well. The multi-objective optimization problem is solved by using a modified Differential Evolution(DE) algorithm, which is characterized by new selection and mutation strategies. Meanwhile, a special penalty method is presented to tackle the multi-criteria constraints. Finally, numerical experiments for different optimization algorithms are implemented. The computation results show that the proposed indices of output transmission and torque, and constraint handling are effective for the redundant parallel robot; the modified DE algorithm is superior to the other tested algorithms, in terms of the ability of global search and the number of non-dominated solutions. The proposed methodology of multi-objective optimization can be also applied to the dimensional synthesis of other redundantly actuated parallel robots only with rotational movements.展开更多
The restructuring of the electric power market has led to complex power transmission congestion problems.Additionally,scheduled power flows in the transmission line,as well as spontaneous power exchanges have also ris...The restructuring of the electric power market has led to complex power transmission congestion problems.Additionally,scheduled power flows in the transmission line,as well as spontaneous power exchanges have also risen sharply in recent years.The proper placement of IPFC can improve the transmission line congestion problem to a great extent.This paper proposes a disparity line utilization factor(DLUF)for the optimal placement of IPFC to control the congestion in transmission lines.DLUF determines the difference between the percentages of Mega Volt Ampere utilization of each line connected to the same bus.The IPFC is placed in the lines with maximum DLUF.A multiobjective function consisting of reduction of active power loss,minimization of total voltage deviations,minimization of security margin and minimization of installed IPFC capacity is considered for the optimal tuning of IPFC using differential evolution algorithm.The proposed method is implemented for IEEE-30 bus test system under different loading conditions and the results are presented and analyzed to establish the effectiveness on the reduction of congestion.展开更多
Wire-fed laser-arc directed energy deposition(Wire-fed LA-DED)Technol.improves production speed while maintaining high quality and is particularly suited for manufacturing large,complex aluminum or titanium alloy comp...Wire-fed laser-arc directed energy deposition(Wire-fed LA-DED)Technol.improves production speed while maintaining high quality and is particularly suited for manufacturing large,complex aluminum or titanium alloy components.The geometry of the weld bead(height and width)is influenced by multiple intricate parameters and variables during the manufacturing process.Accurately predicting the weld bead shape enables precise control over the surface flatness of the part,helping to prevent defects such as lack of fusion.This significantly reduces dimensional redundancy,enhances printing efficiency,and optimizes material usage.In this study,a quadratic regression prediction model for weld bead geometry was developed using the response surface methodology(RSM),with predictions generated through several machine learning models.These models included the back-propagation neural network(BPNN),support vector regression(SVR),multi-output support vector regression(MOSVR),extreme learning machine(ELM),and a differential evolution-optimized MOSVR(DE-MOSVR)model.Grid search and cross-validation techniques were utilized to identify the optimal parameters for each model to achieve the best predictive performance.A comparison of these models was conducted,followed by an evaluation of their generalization capabilities using an additional 20 sets of test data.The most accurate predictive model was selected based on a comprehensive assessment.The results showed that the DE-MOSVR model outperformed the others,achieving mean squared error,root mean squared error,mean absolute error,and R2 values for width(height)predictions of 0.0411(0.0041),0.2028(0.0639),0.1671(0.0550),and 0.9434(0.9433),respectively.It demonstrated the smallest deviation in the validation set,with mean deviations of 1.97% and 1.68%,respectively.The model we developed was validated through the production of prototype parts,providing valuable reference and guidance for predicting and modeling weld bead morphology in the Wire-fed LA-DED process.展开更多
Differential evolution(DE)algorithms are simple and efficient evolutionary algorithms that performwell in various optimization problems.Unfortunately,they inevitably stagnate when differential evolutionary algorithms ...Differential evolution(DE)algorithms are simple and efficient evolutionary algorithms that performwell in various optimization problems.Unfortunately,they inevitably stagnate when differential evolutionary algorithms are used to solve complex problems(e.g.,real-world artificial neural network(ANN)training problems).To resolve this issue,this paper proposes a framework based on an efficient elite centroid operator.It continuously monitors the current state of the population.Once stagnation is detected,two dedicated operators,centroid-based mutation(CM)and centroid-based crossover(CX),are executed to replace the classical mutation and binomial crossover operations in DE.CM and CX are centred on the elite centroid composed of multiple elite individuals,constituting a framework consisting of elitism centroid-based operations(CMX)to improve the performance of the individuals who fall into stagnation.In CM,elite centroid provide evolutionary direction for stagnant individuals,and in CX,elite plasmoids address the limitation that stagnant individuals can only obtain limited information about the population.The CMX framework is simple enough to easily incorporate into both classically well-known DEs with constant population sizes and state-of-the-art DEs with varying populations.Numerical experiments on benchmark functions show that the proposed CMX method can significantly enhance the classical DE algorithm and its advanced variants in solving the stagnation problem and improving performance.展开更多
The rise in the use of global polyester fiber contributed to strong demand of the Terephthalic acid (TPA). The liquid-phase catalytic oxidation of p-xylene (PX) to TPA is regarded as a critical and efficient chemi...The rise in the use of global polyester fiber contributed to strong demand of the Terephthalic acid (TPA). The liquid-phase catalytic oxidation of p-xylene (PX) to TPA is regarded as a critical and efficient chemical process in industry [ 1 ]. PX oxidation reaction involves many complex side reactions, among which acetic acid combustion and PX combustion are the most important. As the target product of this oxidation process, the quality and yield of TPA are of great concern. However, the improvement of the qualified product yield can bring about the high energy consumption, which means that the economic objectives of this process cannot be achieved simulta- neously because the two objectives are in conflict with each other. In this paper, an improved self-adaptive multi-objective differential evolution algorithm was proposed to handle the multi-objective optimization prob- lems. The immune concept is introduced to the self-adaptive multi-objective differential evolution algorithm (SADE) to strengthen the local search ability and optimization accuracy. The proposed algorithm is successfully tested on several benchmark test problems, and the performance measures such as convergence and divergence metrics are calculated. Subsequently, the multi-objective optimization of an industrial PX oxidation process is carried out using the proposed immune self-adaptive multi-objective differential evolution algorithm (ISADE). Optimization results indicate that application oflSADE can greatly improve the yield of TPA with low combustion loss without degenerating TA quality.展开更多
To ensure a long-term safety and reliability of electric vehicle and energy storage system,an accurate estimation of the state of health(SOH)for lithium-ion battery is important.In this study,a method for estimating t...To ensure a long-term safety and reliability of electric vehicle and energy storage system,an accurate estimation of the state of health(SOH)for lithium-ion battery is important.In this study,a method for estimating the lithium-ion battery SOH was proposed based on an improved extreme learning machine(ELM).Input weights and hidden layer biases were generated randomly in traditional ELM.To improve the estimation accuracy of ELM,the differential evolution algorithm was used to optimize these parameters in feasible solution spaces.First,incremental capacity curves were obtained by incremental capacity analysis and smoothed by Gaussian filter to extract health interests.Then,the ELM based on differential evolution algorithm(DE-ELM model)was used for a lithium-ion battery SOH estimation.At last,four battery historical aging data sets and one random walk data set were employed to validate the prediction performance of DE-ELM model.Results show that the DE-ELM has a better performance than other studied algorithms in terms of generalization ability.展开更多
The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical pe...The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical performance,its compact form is developed herein.Through replacing the states and costates variation evolution with that of the controls,the dimension-reduced Evolution Partial Differential Equation(EPDE)only solves the control variables along the variation time to get the optimal solution,and the initial conditions for the definite solution may be arbitrary.With this equation,the scale of the resulting IVPs,obtained via the semi-discrete method,is significantly reduced and they may be solved with common Ordinary Differential Equation(ODE)integration methods conveniently.Meanwhile,the state and the costate dynamics share consistent stability in the numerical computation and this avoids the intrinsic numerical difficulty as in the indirect methods.Numerical examples are solved and it is shown that the compact form evolution equation outperforms the primary form in the precision,and the efficiency may be higher for the dense discretization.Actually,it is uncovered that the compact form of the augmented evolution equation is a continuous realization of the Newton type iteration mechanism.展开更多
Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms a...Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.展开更多
Since many aerodynamic optimization problems in the area of aeronautics contain highly nonlinear objectives and multiple local optima, it is still a challenge for most of the traditional optimization methods to find t...Since many aerodynamic optimization problems in the area of aeronautics contain highly nonlinear objectives and multiple local optima, it is still a challenge for most of the traditional optimization methods to find the global optima. In this paper, a new hybrid optimization framework based on Differential Evolution and Invasive Weed Optimization(IWO_DE/Ring) is developed, which combines global and local search to improve the performance, where a Multiple-Output Gaussian Process(MOGP) is used as the surrogate model. We first use several test functions to verify the performance of the IWO_DE/Ring method, and then apply the optimization framework to a supercritical airfoil design problem. The convergence and the robustness of the proposed framework are compared against some other optimization methods. The IWO_DE/Ringbased approach provides much quicker and steadier convergence than the traditional methods.The results show that the stability of the dynamic optimization process is an important indication of the confidence in the obtained optimum, and the proposed optimization framework based on IWO_DE/Ring is a reliable and promising alternative for complex aeronautical optimization problems.展开更多
In mine ventilation networks,the reasonable airflow distribution is very important for the production safety and economy.Three basic problems of the natural,full-controlled and semi-controlled splitting were reviewed ...In mine ventilation networks,the reasonable airflow distribution is very important for the production safety and economy.Three basic problems of the natural,full-controlled and semi-controlled splitting were reviewed in the paper.Aiming at the high difficulty semi-controlled splitting problem,the general nonlinear multi-objectives optimization mathematical model with constraints was established based on the theory of mine ventilation networks.A new algorithm,which combined the improved differential evaluation and the critical path method(CPM)based on the multivariable separate solution strategy,was put forward to search for the global optimal solution more efficiently.In each step of evolution,the feasible solutions of air quantity distribution are firstly produced by the improved differential evolu-tion algorithm,and then the optimal solutions of regulator pressure drop are obtained by the CPM.Through finite steps iterations,the optimal solution can be given.In this new algorithm,the population of feasible solutions were sorted and grouped for enhancing the global search ability and the individuals in general group were randomly initialized for keeping diversity.Meanwhile,the individual neighbor-hood in the fine group which may be closely to the optimal solutions were searched locally and slightly for achieving a balance between global searching and local searching,thus improving the convergence rate.The computer program was developed based on this method.Finally,the two ventilation networks with single-fan and multi-fans were solved.The results show that this algorithm has advantages of high effectiveness,fast convergence,good robustness and flexibility.This computer program could be used to solve lar^e-scale~eneralized ventilation networks o^timization problem in the future.展开更多
In this paper,a global optimum-based search strategy is proposed to alleviate the situation that the differential evolution(DE)usually sticks into a stagnation,especially on complex problems.It aims to reconstruct the...In this paper,a global optimum-based search strategy is proposed to alleviate the situation that the differential evolution(DE)usually sticks into a stagnation,especially on complex problems.It aims to reconstruct the balance between exploration and exploitation,and improve the search efficiency and solution quality of DE.The proposed method is activated by recording the number of recently consecutive unsuccessful global optimum updates.It takes the feedback from the global optimum,which makes the search strategy not only refine the current solution quality,but also have a change to find other promising space with better individuals.This search strategy is incorporated with various DE mutation strategies and DE variations.The experimental results indicate that the proposed method has remarkable performance in enhancing search efficiency and improving solution quality.展开更多
A novel and effective artificial neural network(ANN) optimized using differential evolution(DE) is first introduced to provide a robust and reliable forecasting of jet grouted column diameters.The proposed computation...A novel and effective artificial neural network(ANN) optimized using differential evolution(DE) is first introduced to provide a robust and reliable forecasting of jet grouted column diameters.The proposed computational method adopts the DE algorithm to tackle the difficulties in the training and performance of neural networks and optimize the four quintessential hyper-parameters(i.e.the epoch size,the number of neurons in a hidden layer,the number of hidden layers,and the regularization parameter) that govern the neural network efficacy.This approach is further enhanced by a stochastic gradient optimization algorithm to allow ’expensive’ computation efforts.The ANN-DE is first trained using a prepared jet grouting dataset,then verified and compared with the prevalent machine learning tools,i.e.neural networks and support vector machine(SVM).The results show that,the ANN-DE outperforms the existing methods for predicting the diameter of jet grouting columns since it well balances training efficiency and model performance.Specifically,the ANN-DE achieved root mean square error(RMSE)values of 0.90603 and 0.92813 for the training and testing phases,respectively.The corresponding values were 0.8905 and 0.9006 for the optimized ANN,then,0.87569 and 0.89968 for the optimized SVM,respectively.The proposed paradigm is bound to be useful for solving various geotechnical engineering problems regardless of multi-dimension and nonlinearity.展开更多
Differential evolution (DE) is an evolutionary optimization method, which has been successfully used in many practical cases. However, DE involves large computation time, especially, when used to optimize the compur...Differential evolution (DE) is an evolutionary optimization method, which has been successfully used in many practical cases. However, DE involves large computation time, especially, when used to optimize the compurationally expensive objective function. To overcome this .difficulty, the concept of immunity based on vaccination is used to help proliferate excellent schemata and to restrain the degenerate phenomenon. To improve the effective- ness of vaccines, a new vaccine autonomous obtaining method, and a method of deciding the probability of vacci- nation are proposed. In addition, a method for modifying the search space dynamically is proposed to enhance the possibility of converging to the true global optimum. Experiments showed that the improved DE performs better than the classical DE significantly.展开更多
To determine the optimal or near optimal parameters of PID controller with incomplete derivation, a novel design method based on differential evolution (DE) algorithm is presented. The controller is called DE-PID co...To determine the optimal or near optimal parameters of PID controller with incomplete derivation, a novel design method based on differential evolution (DE) algorithm is presented. The controller is called DE-PID controller. To overcome the disadvantages of the integral performance criteria in the frequency domain such as IAE, ISE, and ITSE, a new performance criterion in the time domain is proposed. The optimization procedures employing the DE algorithm to search the optimal or near optimal PID controller parameters of a control system are demonstrated in detail. Three typical control systems are chosen to test and evaluate the adaptation and robustness of the proposed DE-PID controller. The simulation results show that the proposed approach has superior features of easy implementation, stable convergence characteristic, and good computational efficiency. Compared with the ZN, GA, and ASA, the proposed design method is indeed more efficient and robust in improving the step response of a control system.展开更多
Because of their superior problem-solving ability,nature-inspired optimization algorithms are being regularly used in solving complex real-world optimization problems.Engineering academics have recently focused on met...Because of their superior problem-solving ability,nature-inspired optimization algorithms are being regularly used in solving complex real-world optimization problems.Engineering academics have recently focused on meta-heuristic algorithms to solve various optimization challenges.Among the state-of-the-art algorithms,Differential Evolution(DE)is one of the most successful algorithms and is frequently used to solve various industrial problems.Over the previous 2 decades,DE has been heavily modified to improve its capabilities.Several DE variations secured positions in IEEE CEC competitions,establishing their efficacy.However,to our knowledge,there has never been a comparison of performance across various CEC-winning DE versions,which could aid in determining which is the most successful.In this study,the performance of DE and its eight other IEEE CEC competition-winning variants are compared.First,the algorithms have evaluated IEEE CEC 2019 and 2020 bound-constrained functions,and the performances have been compared.One unconstrained problem from IEEE CEC 2011 problem suite and five other constrained mechanical engineering design problems,out of which four issues have been taken from IEEE CEC 2020 non-convex constrained optimization suite,have been solved to compare the performances.Statistical analyses like Friedman's test and Wilcoxon's test are executed to verify the algorithm’s ability statistically.Performance analysis exposes that none of the DE variants can solve all the problems efficiently.Performance of SHADE and ELSHADE-SPACMA are considerable among the methods used for comparison to solve such mechanical design problems.展开更多
基金funded by the Sinopec Science and Technology Project(No.P23132)the AAPG Foundation Grants-inAid Program(No.18644937)。
摘要By investigating the evolution of shale gas generation,storage,adjustment and accumulation under different structural settings in superimposed basins,this study elucidates the differential accumulation mechanisms of shale gas.An improved evaluation method of shale gas content evolution in superimposed basins is proposed.This method incorporates the coupling effect of key geological factors such as temperature,pressure,organic matter abundance,maturity,and pore characteristics on the content and occurrence state of shale gas,as well as the configuration relationship between shale gas generation and storage throughout geological history.Using this approach,the gas evolution histories of the Longmaxi Formation shales in wells N201 and PY1 are reconstructed under varying geological conditions.The Longmaxi Formation shales in these wells are dominated by typeⅠkerogen,with original total organic carbon(TOCo)contents of 6.20 wt% and 4.92 wt%,respectively,indicating differences in the initial material basis for gas generation.At the maximum burial depth of approximately 5000 m,the Longmaxi Formation shale in well N201 exhibits a formation pressure coefficient of 2.05,an organic matter maturity of 2.2%,and organic pores accounting for 68%of the total porosity.The gas generation quantity(Qg)reaches 19.24 m3,while the gas storage capacity(Qs)is 4.30 m3.The actual total gas content(Qa),constrained by Qs,is 4.30 m3,with free gas comprising 94%.Following relatively moderate tectonic uplift,the Qa in well N201 decreases to 4.03 m3,with free gas accounting for 63%.In contrast,the Longmaxi Formation shale in well PY1 reached a maximum burial depth of 6300 m,associated with a formation pressure coefficient of 1.62,organic matter maturity of 2.5%,and organic pore proportion of 67%.Here,Qg is 16.87 m3,and both Qs and Qa are 3.65 m3,with free gas accounting for 98%.After intense tectonic uplift,Qa declines to 2.72 m3,and the proportion of free gas drops to51%.Finally,a four-stage differential accumulation model of shale gas is established:Slow gas generation and only adsorbed gas occur in stageⅠ,which is primarily controlled by TOC content;both adsorbed gas and free gas present in stageⅡ,with free gas becoming dominant;rapid gas generation and free gas predominance are controlled by temperature and porosity in stageⅢ;and gas adjustment and accumulation are primarily controlled by temperature and pressure in stageⅣ.
基金Supported by Defense Industrial Technology Development Program of China(Grant No.JCKY2021605B015).
摘要Welding deformation adversely affects the quality and precision of structural components,and traditional methods require significant material resources and time.Machine learning has demonstrated exceptional ac-curacy and efficiency in solving complex problems.Thus,the use of machine learning to predict welding de-formations is a novel approach.In this study,laser welding experiments were conducted on a TC4 titanium alloy to establish a welding deformation dataset.The deep neural network(DNN)and convolutional neural network(CNN)models were designed and constructed,with average prediction errors of 0.85 mm and 0.94 mm on the validation set,respectively.To further optimize the network parameters,a differential evolution algorithm was employed through mutation,crossover,and selection.The results indicated that after optimization,the pre-diction errors of the DNN and CNN models reduced to 0.75 mm and 0.85 mm,respectively.These represent accuracy improvements of 14.8%and 9.6%,respectively.The optimized models exhibited superior predictive performances for the validation set.
基金National Natural Science Foundation of China(No.52375236)Fundamental Research Funds for the Central Universities of China(No.23D110316)。
摘要In reliability analyses,the absence of a priori information on the most probable point of failure(MPP)may result in overlooking critical points,thereby leading to biased assessment outcomes.Moreover,second-order reliability methods exhibit limited accuracy in highly nonlinear scenarios.To overcome these challenges,a novel reliability analysis strategy based on a multimodal differential evolution algorithm and a hypersphere integration method is proposed.Initially,the penalty function method is employed to reformulate the MPP search problem as a conditionally constrained optimization task.Subsequently,a differential evolution algorithm incorporating a population delineation strategy is utilized to identify all MPPs.Finally,a paraboloid equation is constructed based on the curvature of the limit-state function at the MPPs,and the failure probability of the structure is calculated by using the hypersphere integration method.The localization effectiveness of the MPPs is compared through multiple numerical cases and two engineering examples,with accuracy comparisons of failure probabilities against the first-order reliability method(FORM)and the secondorder reliability method(SORM).The results indicate that the method effectively identifies existing MPPs and achieves higher solution precision.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.61903010 and 61890930-5)Beijing Outstanding Young Scientist Program(Grant No.BJJWZYJH01201910005020)Beijing Natural Science Foundation(Grant No.KZ202110005009).
摘要The multi-objective differential evolution(MODE)algorithm is an effective method to solve multi-objective optimization problems.However,in the absence of any information of evolution progress,the optimization strategy of the MODE algorithm still appears as an open problem.In this paper,a dynamic multi-objective differential evolution algorithm,based on the information of evolution progress(DMODE-IEP),is developed to improve the optimization performance.The main contributions of DMODE-IEP are as follows.First,the information of evolution progress,using the fitness values,is proposed to describe the evolution progress of MODE.Second,the dynamic adjustment mechanisms of evolution parameter values,mutation strategies and selection parameter value based on the information of evolution progress,are designed to balance the global exploration ability and the local exploitation ability.Third,the convergence of DMODE-IEP is proved using the probability theory.Finally,the testing results on the standard multi-objective optimization problem and the wastewater treatment process verify that the optimization effect of DMODE-IEP algorithm is superior to the other compared state-of-the-art multi-objective optimization algorithms,including the quality of the solutions,and the optimization speed of the algorithm.
基金Project(No.0521010020)supported by the A*Star(Agency for Science,Technology and Research),Singapore
摘要Multi-objective differential evolution(MODE)is a powerful and efficient population-based stochastic search technique for solving multi-objective optimization problems in many scientific and engineering fields.However,premature convergence is the major drawback of MODE,especially when there are numerous local Pareto optimal solutions.To overcome this problem,we propose a MODE with a diversity enhancement(MODE-DE)mechanism to prevent the algorithm becoming trapped in a locally optimal Pareto front.The proposed algorithm combines the current population with a number of randomly generated parameter vectors to increase the diversity of the differential vectors and thereby the diversity of the newly generated offspring.The performance of the MODE-DE algorithm was evaluated on a set of 19 benchmark problem codes available from http://gffzzdcd0dfe20e794032h9x6xkqbnbvf66nbn.ffgz.tsg.suse.edu.cn/home/epnsugan/.With the proposed method,the performances were either better than or equal to those of the MODE without the diversity enhancement.
基金Supported by National Natural Science Foundation of China(Grant No.51175029)Beijing Municipal Natural Science Foundation of China(Grant No.3132019)
摘要Dimensional synthesis is one of the most difficult issues in the field of parallel robots with actuation redundancy. To deal with the optimal design of a redundantly actuated parallel robot used for ankle rehabilitation, a methodology of dimensional synthesis based on multi-objective optimization is presented. First, the dimensional synthesis of the redundant parallel robot is formulated as a nonlinear constrained multi-objective optimization problem. Then four objective functions, separately reflecting occupied space, input/output transmission and torque performances, and multi-criteria constraints, such as dimension, interference and kinematics, are defined. In consideration of the passive exercise of plantar/dorsiflexion requiring large output moment, a torque index is proposed. To cope with the actuation redundancy of the parallel robot, a new output transmission index is defined as well. The multi-objective optimization problem is solved by using a modified Differential Evolution(DE) algorithm, which is characterized by new selection and mutation strategies. Meanwhile, a special penalty method is presented to tackle the multi-criteria constraints. Finally, numerical experiments for different optimization algorithms are implemented. The computation results show that the proposed indices of output transmission and torque, and constraint handling are effective for the redundant parallel robot; the modified DE algorithm is superior to the other tested algorithms, in terms of the ability of global search and the number of non-dominated solutions. The proposed methodology of multi-objective optimization can be also applied to the dimensional synthesis of other redundantly actuated parallel robots only with rotational movements.
摘要The restructuring of the electric power market has led to complex power transmission congestion problems.Additionally,scheduled power flows in the transmission line,as well as spontaneous power exchanges have also risen sharply in recent years.The proper placement of IPFC can improve the transmission line congestion problem to a great extent.This paper proposes a disparity line utilization factor(DLUF)for the optimal placement of IPFC to control the congestion in transmission lines.DLUF determines the difference between the percentages of Mega Volt Ampere utilization of each line connected to the same bus.The IPFC is placed in the lines with maximum DLUF.A multiobjective function consisting of reduction of active power loss,minimization of total voltage deviations,minimization of security margin and minimization of installed IPFC capacity is considered for the optimal tuning of IPFC using differential evolution algorithm.The proposed method is implemented for IEEE-30 bus test system under different loading conditions and the results are presented and analyzed to establish the effectiveness on the reduction of congestion.
基金supported by Natural Science Foundation of Shandong Province(Grant No.ZR202212010161)Natural Science Foundation of Qingdao(Grant No.23-2-1-83-zyyd-jch)+1 种基金Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515110116)the National Natural Science Foundation of China(Grant No.52405359).
摘要Wire-fed laser-arc directed energy deposition(Wire-fed LA-DED)Technol.improves production speed while maintaining high quality and is particularly suited for manufacturing large,complex aluminum or titanium alloy components.The geometry of the weld bead(height and width)is influenced by multiple intricate parameters and variables during the manufacturing process.Accurately predicting the weld bead shape enables precise control over the surface flatness of the part,helping to prevent defects such as lack of fusion.This significantly reduces dimensional redundancy,enhances printing efficiency,and optimizes material usage.In this study,a quadratic regression prediction model for weld bead geometry was developed using the response surface methodology(RSM),with predictions generated through several machine learning models.These models included the back-propagation neural network(BPNN),support vector regression(SVR),multi-output support vector regression(MOSVR),extreme learning machine(ELM),and a differential evolution-optimized MOSVR(DE-MOSVR)model.Grid search and cross-validation techniques were utilized to identify the optimal parameters for each model to achieve the best predictive performance.A comparison of these models was conducted,followed by an evaluation of their generalization capabilities using an additional 20 sets of test data.The most accurate predictive model was selected based on a comprehensive assessment.The results showed that the DE-MOSVR model outperformed the others,achieving mean squared error,root mean squared error,mean absolute error,and R2 values for width(height)predictions of 0.0411(0.0041),0.2028(0.0639),0.1671(0.0550),and 0.9434(0.9433),respectively.It demonstrated the smallest deviation in the validation set,with mean deviations of 1.97% and 1.68%,respectively.The model we developed was validated through the production of prototype parts,providing valuable reference and guidance for predicting and modeling weld bead morphology in the Wire-fed LA-DED process.
基金funded by National Special Project Number for International Cooperation under Grant 2015DFR11050the Applied Science and Technology Research and Development Special Fund Project of Guangdong Province under Grant 2016B010126004.
摘要Differential evolution(DE)algorithms are simple and efficient evolutionary algorithms that performwell in various optimization problems.Unfortunately,they inevitably stagnate when differential evolutionary algorithms are used to solve complex problems(e.g.,real-world artificial neural network(ANN)training problems).To resolve this issue,this paper proposes a framework based on an efficient elite centroid operator.It continuously monitors the current state of the population.Once stagnation is detected,two dedicated operators,centroid-based mutation(CM)and centroid-based crossover(CX),are executed to replace the classical mutation and binomial crossover operations in DE.CM and CX are centred on the elite centroid composed of multiple elite individuals,constituting a framework consisting of elitism centroid-based operations(CMX)to improve the performance of the individuals who fall into stagnation.In CM,elite centroid provide evolutionary direction for stagnant individuals,and in CX,elite plasmoids address the limitation that stagnant individuals can only obtain limited information about the population.The CMX framework is simple enough to easily incorporate into both classically well-known DEs with constant population sizes and state-of-the-art DEs with varying populations.Numerical experiments on benchmark functions show that the proposed CMX method can significantly enhance the classical DE algorithm and its advanced variants in solving the stagnation problem and improving performance.
基金Supported by the Shanghai Second Polytechnic University Key Discipline Construction-Control Theory & Control Engineering(No.XXKPY1609)the National Natural Science Foundation of China(61422303)+1 种基金Shanghai Talent Development Funding(H200-2R-15111)2017 Shanghai Second Polytechnic University Cultivation Research Program of Young Teachers(02)
摘要The rise in the use of global polyester fiber contributed to strong demand of the Terephthalic acid (TPA). The liquid-phase catalytic oxidation of p-xylene (PX) to TPA is regarded as a critical and efficient chemical process in industry [ 1 ]. PX oxidation reaction involves many complex side reactions, among which acetic acid combustion and PX combustion are the most important. As the target product of this oxidation process, the quality and yield of TPA are of great concern. However, the improvement of the qualified product yield can bring about the high energy consumption, which means that the economic objectives of this process cannot be achieved simulta- neously because the two objectives are in conflict with each other. In this paper, an improved self-adaptive multi-objective differential evolution algorithm was proposed to handle the multi-objective optimization prob- lems. The immune concept is introduced to the self-adaptive multi-objective differential evolution algorithm (SADE) to strengthen the local search ability and optimization accuracy. The proposed algorithm is successfully tested on several benchmark test problems, and the performance measures such as convergence and divergence metrics are calculated. Subsequently, the multi-objective optimization of an industrial PX oxidation process is carried out using the proposed immune self-adaptive multi-objective differential evolution algorithm (ISADE). Optimization results indicate that application oflSADE can greatly improve the yield of TPA with low combustion loss without degenerating TA quality.
摘要To ensure a long-term safety and reliability of electric vehicle and energy storage system,an accurate estimation of the state of health(SOH)for lithium-ion battery is important.In this study,a method for estimating the lithium-ion battery SOH was proposed based on an improved extreme learning machine(ELM).Input weights and hidden layer biases were generated randomly in traditional ELM.To improve the estimation accuracy of ELM,the differential evolution algorithm was used to optimize these parameters in feasible solution spaces.First,incremental capacity curves were obtained by incremental capacity analysis and smoothed by Gaussian filter to extract health interests.Then,the ELM based on differential evolution algorithm(DE-ELM model)was used for a lithium-ion battery SOH estimation.At last,four battery historical aging data sets and one random walk data set were employed to validate the prediction performance of DE-ELM model.Results show that the DE-ELM has a better performance than other studied algorithms in terms of generalization ability.
基金supported by the National Nature Science Foundation of China under Grant No.11902332。
摘要The augmented evolution equation is established under the framework of the Variation Evolving Method(VEM)that seeks optimal solutions by solving the transformed Initial-Value Problems(IVPs).To improve the numerical performance,its compact form is developed herein.Through replacing the states and costates variation evolution with that of the controls,the dimension-reduced Evolution Partial Differential Equation(EPDE)only solves the control variables along the variation time to get the optimal solution,and the initial conditions for the definite solution may be arbitrary.With this equation,the scale of the resulting IVPs,obtained via the semi-discrete method,is significantly reduced and they may be solved with common Ordinary Differential Equation(ODE)integration methods conveniently.Meanwhile,the state and the costate dynamics share consistent stability in the numerical computation and this avoids the intrinsic numerical difficulty as in the indirect methods.Numerical examples are solved and it is shown that the compact form evolution equation outperforms the primary form in the precision,and the efficiency may be higher for the dense discretization.Actually,it is uncovered that the compact form of the augmented evolution equation is a continuous realization of the Newton type iteration mechanism.
基金supported in part by the National Key Research and Development Program of China(2018AAA0100100)the National Natural Science Foundation of China(61906001,62136008,U21A20512)+1 种基金the Key Program of Natural Science Project of Educational Commission of Anhui Province(KJ2020A0036)Alexander von Humboldt Professorship for Artificial Intelligence Funded by the Federal Ministry of Education and Research,Germany。
摘要Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.
基金supported by the Aeronautical Science Foundation of China (Nos.20151452021 and 20152752033)the National Natural Science Foundation of China (No.61300159)+1 种基金the Natural Science Foundation of Jiangsu Province of China (No.BK20130808)China Postdoctoral Science Foundation (No.2015M571751)
摘要Since many aerodynamic optimization problems in the area of aeronautics contain highly nonlinear objectives and multiple local optima, it is still a challenge for most of the traditional optimization methods to find the global optima. In this paper, a new hybrid optimization framework based on Differential Evolution and Invasive Weed Optimization(IWO_DE/Ring) is developed, which combines global and local search to improve the performance, where a Multiple-Output Gaussian Process(MOGP) is used as the surrogate model. We first use several test functions to verify the performance of the IWO_DE/Ring method, and then apply the optimization framework to a supercritical airfoil design problem. The convergence and the robustness of the proposed framework are compared against some other optimization methods. The IWO_DE/Ringbased approach provides much quicker and steadier convergence than the traditional methods.The results show that the stability of the dynamic optimization process is an important indication of the confidence in the obtained optimum, and the proposed optimization framework based on IWO_DE/Ring is a reliable and promising alternative for complex aeronautical optimization problems.
基金financially supported by the National Natural Science Foundation of China(No.51134023)
摘要In mine ventilation networks,the reasonable airflow distribution is very important for the production safety and economy.Three basic problems of the natural,full-controlled and semi-controlled splitting were reviewed in the paper.Aiming at the high difficulty semi-controlled splitting problem,the general nonlinear multi-objectives optimization mathematical model with constraints was established based on the theory of mine ventilation networks.A new algorithm,which combined the improved differential evaluation and the critical path method(CPM)based on the multivariable separate solution strategy,was put forward to search for the global optimal solution more efficiently.In each step of evolution,the feasible solutions of air quantity distribution are firstly produced by the improved differential evolu-tion algorithm,and then the optimal solutions of regulator pressure drop are obtained by the CPM.Through finite steps iterations,the optimal solution can be given.In this new algorithm,the population of feasible solutions were sorted and grouped for enhancing the global search ability and the individuals in general group were randomly initialized for keeping diversity.Meanwhile,the individual neighbor-hood in the fine group which may be closely to the optimal solutions were searched locally and slightly for achieving a balance between global searching and local searching,thus improving the convergence rate.The computer program was developed based on this method.Finally,the two ventilation networks with single-fan and multi-fans were solved.The results show that this algorithm has advantages of high effectiveness,fast convergence,good robustness and flexibility.This computer program could be used to solve lar^e-scale~eneralized ventilation networks o^timization problem in the future.
基金This work was supported by the JSPS KAKENHI(JP17K12751 and JP15K00332).
摘要In this paper,a global optimum-based search strategy is proposed to alleviate the situation that the differential evolution(DE)usually sticks into a stagnation,especially on complex problems.It aims to reconstruct the balance between exploration and exploitation,and improve the search efficiency and solution quality of DE.The proposed method is activated by recording the number of recently consecutive unsuccessful global optimum updates.It takes the feedback from the global optimum,which makes the search strategy not only refine the current solution quality,but also have a change to find other promising space with better individuals.This search strategy is incorporated with various DE mutation strategies and DE variations.The experimental results indicate that the proposed method has remarkable performance in enhancing search efficiency and improving solution quality.
基金funded by“The Pearl River Talent Recruitment Program”in 2019 for Professor Shui-Long Shen(Grant No.2019CX01G338),Guangdong Provincethe Research Funding of Shantou University for New Faculty Member(Grant No.NTF19024-2019)。
摘要A novel and effective artificial neural network(ANN) optimized using differential evolution(DE) is first introduced to provide a robust and reliable forecasting of jet grouted column diameters.The proposed computational method adopts the DE algorithm to tackle the difficulties in the training and performance of neural networks and optimize the four quintessential hyper-parameters(i.e.the epoch size,the number of neurons in a hidden layer,the number of hidden layers,and the regularization parameter) that govern the neural network efficacy.This approach is further enhanced by a stochastic gradient optimization algorithm to allow ’expensive’ computation efforts.The ANN-DE is first trained using a prepared jet grouting dataset,then verified and compared with the prevalent machine learning tools,i.e.neural networks and support vector machine(SVM).The results show that,the ANN-DE outperforms the existing methods for predicting the diameter of jet grouting columns since it well balances training efficiency and model performance.Specifically,the ANN-DE achieved root mean square error(RMSE)values of 0.90603 and 0.92813 for the training and testing phases,respectively.The corresponding values were 0.8905 and 0.9006 for the optimized ANN,then,0.87569 and 0.89968 for the optimized SVM,respectively.The proposed paradigm is bound to be useful for solving various geotechnical engineering problems regardless of multi-dimension and nonlinearity.
基金Supported by the National Natural Science Foundation of China (60736021), the National High Technology Research and Development Program of China (2006AA04Z184, 2007AA041406), and the Key Technologies R&D Program of Zhejiang Province (2006C 11066, 2006C31051).
摘要Differential evolution (DE) is an evolutionary optimization method, which has been successfully used in many practical cases. However, DE involves large computation time, especially, when used to optimize the compurationally expensive objective function. To overcome this .difficulty, the concept of immunity based on vaccination is used to help proliferate excellent schemata and to restrain the degenerate phenomenon. To improve the effective- ness of vaccines, a new vaccine autonomous obtaining method, and a method of deciding the probability of vacci- nation are proposed. In addition, a method for modifying the search space dynamically is proposed to enhance the possibility of converging to the true global optimum. Experiments showed that the improved DE performs better than the classical DE significantly.
基金the National Natural Science Foundation of China (60375001)the Scientific Research Foundation of Hunan Provincial Education Department (05B016).
摘要To determine the optimal or near optimal parameters of PID controller with incomplete derivation, a novel design method based on differential evolution (DE) algorithm is presented. The controller is called DE-PID controller. To overcome the disadvantages of the integral performance criteria in the frequency domain such as IAE, ISE, and ITSE, a new performance criterion in the time domain is proposed. The optimization procedures employing the DE algorithm to search the optimal or near optimal PID controller parameters of a control system are demonstrated in detail. Three typical control systems are chosen to test and evaluate the adaptation and robustness of the proposed DE-PID controller. The simulation results show that the proposed approach has superior features of easy implementation, stable convergence characteristic, and good computational efficiency. Compared with the ZN, GA, and ASA, the proposed design method is indeed more efficient and robust in improving the step response of a control system.
摘要Because of their superior problem-solving ability,nature-inspired optimization algorithms are being regularly used in solving complex real-world optimization problems.Engineering academics have recently focused on meta-heuristic algorithms to solve various optimization challenges.Among the state-of-the-art algorithms,Differential Evolution(DE)is one of the most successful algorithms and is frequently used to solve various industrial problems.Over the previous 2 decades,DE has been heavily modified to improve its capabilities.Several DE variations secured positions in IEEE CEC competitions,establishing their efficacy.However,to our knowledge,there has never been a comparison of performance across various CEC-winning DE versions,which could aid in determining which is the most successful.In this study,the performance of DE and its eight other IEEE CEC competition-winning variants are compared.First,the algorithms have evaluated IEEE CEC 2019 and 2020 bound-constrained functions,and the performances have been compared.One unconstrained problem from IEEE CEC 2011 problem suite and five other constrained mechanical engineering design problems,out of which four issues have been taken from IEEE CEC 2020 non-convex constrained optimization suite,have been solved to compare the performances.Statistical analyses like Friedman's test and Wilcoxon's test are executed to verify the algorithm’s ability statistically.Performance analysis exposes that none of the DE variants can solve all the problems efficiently.Performance of SHADE and ELSHADE-SPACMA are considerable among the methods used for comparison to solve such mechanical design problems.