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Intelligent decision-making for TBM tunnelling control parameters using multi-objective optimization
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作者 Shaokang Hou Yaoru Liu +3 位作者 Jialin Yu Rujiu Zhang Li Cheng Chenfeng Gao 《Journal of Rock Mechanics and Geotechnical Engineering》 2025年第5期2943-2963,共21页
In tunnel construction,tunnel boring machine(TBM)tunnelling typically relies on manual experience with sub-optimal control parameters,which can easily lead to inefficiency and high costs.This study proposed an intelli... In tunnel construction,tunnel boring machine(TBM)tunnelling typically relies on manual experience with sub-optimal control parameters,which can easily lead to inefficiency and high costs.This study proposed an intelligent decision-making method for TBM tunnelling control parameters based on multiobjective optimization(MOO).First,the effective TBM operation dataset is obtained through data preprocessing of the Songhua River(YS)tunnel project in China.Next,the proposed method begins with developing machine learning models for predicting TBM tunnelling performance parameters(i.e.total thrust and cutterhead torque),rock mass classification,and hazard risks(i.e.tunnel collapse and shield jamming).Then,considering three optimal objectives,(i.e.,penetration rate,rock-breaking energy consumption,and cutterhead hob wear),the MOO framework and corresponding mathematical expression are established.The Pareto optimal front is solved using DE-NSGA-II algorithm.Finally,the optimal control parameters(i.e.,advance rate and cutterhead rotation speed)are obtained by the satisfactory solution determination criterion,which can balance construction safety and efficiency with satisfaction.Furthermore,the proposed method is validated through 50 cases of TBM tunnelling,showing promising potential of application. 展开更多
关键词 Tunnel boring machine(TBM) Intelligent decision-making Multi-objective optimization(MOO) control parameters
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Self-adapting control parameters modifieddifferential evolution for trajectoryplanning of manipulators 被引量:12
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作者 Lianghong WU Yaonan WANG Shaowu ZHOU 《控制理论与应用(英文版)》 EI 2007年第4期365-373,共9页
Control parameters of original differential evolution (DE) are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE for different optiinizat... Control parameters of original differential evolution (DE) are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE for different optiinization problems. According to the relative position of two different individual vectors selected to generate a difference vector in the searching place, a self-adapting strategy for the scale factor F of the difference vector is proposed. In terms of the convergence status of the target vector in the current population, a self-adapting crossover probability constant CR strategy is proposed. Therefore, good target vectors have a lower CFI while worse target vectors have a large CFI. At the same time, the mutation operator is modified to improve the convergence speed. The performance of these proposed approaches are studied with the use of some benchmark problems and applied to the trajectory planning of a three-joint redundant manipulator. Finally, the experiment results show that the proposed approaches can greatly improve robustness and convergence speed. 展开更多
关键词 Self-adapting control parameters Differential evolution Redundant manipulator Trajectory planning
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Influence of Pre-injection Control Parameters on Main-injection Fuel Quantity for an Electronically Controlled Double-valve Fuel Injection System of Diesel Engine 被引量:3
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作者 Enzhe Song Liyun Fan Chao Chen Quan Dong Xiuzhen Yun Bai 《Journal of Marine Science and Application》 2013年第3期366-373,共8页
A simulation model of an electronically controlled two solenoid valve fuel injection system for a diesel engine is established in the AMESim environment.The accuracy of the model is validated through comparison with e... A simulation model of an electronically controlled two solenoid valve fuel injection system for a diesel engine is established in the AMESim environment.The accuracy of the model is validated through comparison with experimental data.The influence of pre-injection control parameters on main-injection quantity under different control modes is analyzed.In the spill control valve mode,main-injection fuel quantity decreases gradually and then reaches a stable level because of the increase in multi-injection dwell time.In the needle control valve mode,main-injection fuel quantity increases with rising multi-injection dwell time;this effect becomes more obvious at high-speed revolutions and large main-injection pulse widths.Pre-injection pulse width has no obvious influence on main-injection quantity under the two control modes;the variation in main-injection quantity is in the range of 1 mm3. 展开更多
关键词 diesel engine double-valve fuel injection system pre-injection control parameters main-injection fuel quantity
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IMPLICIT ITERATIVE METHODS WITH VARIABLE CONTROL PARAMETERS FOR ILL-POSED OPERATOR EQUATIONS 被引量:2
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作者 贺国强 王新革 刘林先 《Acta Mathematica Scientia》 SCIE CSCD 2000年第4期485-494,共10页
This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods... This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features, especially the methods can be implemented parallelly. 展开更多
关键词 III-posed problems implicit iterative methods variable control parameters parallel algorith?
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Integrated Optimization of Structure and Control Parameters for the Height Control System of a Vertical Spindle Cotton Picker 被引量:1
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作者 Xingzheng Chen Congbo Li +2 位作者 Rui Hu Ning Liu Chi Zhang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2021年第6期405-416,共12页
Vertical picking method is a predominate method used to harvest cotton crop.However,a vertical picking method may cause spindle bending of the cotton picker if spindles collide with stones on the cotton field.Thus,how... Vertical picking method is a predominate method used to harvest cotton crop.However,a vertical picking method may cause spindle bending of the cotton picker if spindles collide with stones on the cotton field.Thus,how to realize a precise height control of the cotton picker is a crucial issue to be solved.The objective of this study is to design a height control system to avoid the collision.To design it,the mathematical models are established first.Then a multi-objective optimization model represented by structure parameters and control parameters is proposed to take the pressure of chamber without piston,response time and displacement error of the height control system as the opti-mization objectives.An integrated optimization approach that combines optimization via simulation,particle swarm optimization and simulated annealing is proposed to solve the model.Simulation and experimental test results show that the proposed integrated optimization approach can not only reduce the pressure of chamber without piston,but also decrease the response time and displacement error of the height control system. 展开更多
关键词 Cotton picker Height control system Structure parameters control parameters Integrated optimization
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Harmony search algorithm with differential evolution based control parameter co-evolution and its application in chemical process dynamic optimization 被引量:1
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作者 范勤勤 王循华 颜学峰 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第6期2227-2237,共11页
A modified harmony search algorithm with co-evolutional control parameters(DEHS), applied through differential evolution optimization, is proposed. In DEHS, two control parameters, i.e., harmony memory considering rat... A modified harmony search algorithm with co-evolutional control parameters(DEHS), applied through differential evolution optimization, is proposed. In DEHS, two control parameters, i.e., harmony memory considering rate and pitch adjusting rate, are encoded as a symbiotic individual of an original individual(i.e., harmony vector). Harmony search operators are applied to evolving the original population. DE is applied to co-evolving the symbiotic population based on feedback information from the original population. Thus, with the evolution of the original population in DEHS, the symbiotic population is dynamically and self-adaptively adjusted, and real-time optimum control parameters are obtained. The proposed DEHS algorithm has been applied to various benchmark functions and two typical dynamic optimization problems. The experimental results show that the performance of the proposed algorithm is better than that of other HS variants. Satisfactory results are obtained in the application. 展开更多
关键词 harmony search differential evolution optimization CO-EVOLUTION self-adaptive control parameter dynamic optimization
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Determination of temperature distribution and control parameter in a two-dimensional parabolic inverse problem with overspecified data 被引量:1
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作者 李福乐 张洪谦 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第10期1-7,共7页
In this paper, we present a new algorithm to solve a two-dimensional parabolic inverse problem with a source parameter, which appears in many physical phenomena. A linearized compact difference scheme for this problem... In this paper, we present a new algorithm to solve a two-dimensional parabolic inverse problem with a source parameter, which appears in many physical phenomena. A linearized compact difference scheme for this problem is constructed using the finite difference method. The discretization accuracy is second-order in time and fourth-order in space. We obtain the unique solvability and present an alternating direction implicit algorithm to solve this difference scheme. The results of numerical experiments are presented to demonstrate the accuracy of this algorithm. 展开更多
关键词 control parameter temperature distribution finite difference scheme SOLVABILITY
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Relative Content of Phenoxyethanol and p-Hydroxyacetophenone in Water Phase of Oil-water Systems and Teir Relevant Control Parameters 被引量:1
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作者 Xiaoling Qiao Ping Cao +7 位作者 Yuanhua Cong Chunbo Feng Zhitao Chen Xuepu Li Lingling Zhang Qin Zhu Zheng Wang Xinran Li 《China Detergent & Cosmetics》 2016年第4期43-49,共7页
In emulsion system, micro-organisms survive in water phase, thus concentration of preservative in water phase directly reflects to anti-fungi efficacy. As preservative easily migrates into oil phase, it reduces preser... In emulsion system, micro-organisms survive in water phase, thus concentration of preservative in water phase directly reflects to anti-fungi efficacy. As preservative easily migrates into oil phase, it reduces preservative efficacy. A common solution is to increase preservative amount in the whole system. However this way always brings safety issues as preservative is a major allergen. Another effective but safety way is to prohibit preservative migrating into oil phase. In cosmetic research area, phenoxyethanol (PE) and p-Hydroxyacetophenone (p-HAP) pair gradually emerges to be a popular preservative candidate. Thus this new preservative system has been focused as the research object in this work. The relative contents (C) of both PE (CPE) and p-HAP (Cp-HAP) in water phase has been carefully determined. Eight commonly used oils have been further employed to check CPE and Cp-HAP in different oil-water system. The other infuence parameters such as polyols, processing parameters are also investigated. Results shows squalane, petrolatum, silicone oil and hydrogenated polyisobutene might be good oil phase candidates for formulation when using PE and p-HAP preservative system. In these oil systems, PE and p-HAP are mainly located in water phase. Besides, increasing percentage of 1, 3-butylene glycol, shortening homogenization time or adding preservatives at the end of processing under lower temperature could effectively increase effective content preservatives in water phase, either. 展开更多
关键词 PRESERVATIVE phenoxyethanol p-Hydroxyacetophenone relative content control parameter
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Optimization of control parameters for petroleum waste composting
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作者 MA Ying ZHANG Jia yao +1 位作者 WONG Ming Hung WU Wen zhong 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2001年第4期385-390,共6页
Composting is being widely employed in the treatment of petroleum waste. The purpose of this study was to find the optimum control parameters for petroleum waste in-vessel composting. Various physical and chemical par... Composting is being widely employed in the treatment of petroleum waste. The purpose of this study was to find the optimum control parameters for petroleum waste in-vessel composting. Various physical and chemical parameters were monitored to evaluate their influence on the microbial communities present in composting. The CO2 evolution and the number of microorganisms were measured as the activity of composting. The results demonstrated that the optimum temperature, pH and moisture content were 56.5 - 59.5 degreesC, 7.0 - 8.5 and 55 % - 60%, respectively. Under the optimum conditions, the removal efficiency of petroleum hydrocarbon reached 83.29% after 30 days composting. 展开更多
关键词 OPTIMIZATION control parameters petroleum waste COMPOSTING
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Evolvement regularity of signal control parameters of urban road in cold region
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作者 蒋贤才 苏小红 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2009年第6期873-878,共6页
In snow-icy road environment, the survey data indicate that the largest decrease in traffic flow running characters occurs when snow and ice begin to accumulate on the road surface. Saturation flow is decreased by 16%... In snow-icy road environment, the survey data indicate that the largest decrease in traffic flow running characters occurs when snow and ice begin to accumulate on the road surface. Saturation flow is decreased by 16% , speed is decreased by 30% , and start-up lost time is increased by 27%. Based on the signal control theory of HCM and Webster, the character values of traffic flow in different urban road environments were investigated, and the evolvement regularity of signal control parameters such as cycle, split, green time, offset, yellow time and red time in snow-icy road environment was analyzed. The impact factors and the changes in the scope of signal control parameters were achieved. Simulation results and practical application show that the signal control plan of road enviromnent without snow and ice will increase the vehicle delay, stop length and traffic congestion in snow-icy road environment. Thus, the traffic signal control system should address a suitable signal control plan based on different road environments. 展开更多
关键词 evolvement regularity of signal control parameter traffic simulation cold region urban road
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Influence of Control Parameters on the Competition Between Spiral Waves and Target Waves
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作者 钱郁 李伟 +2 位作者 黄晓东 弭元元 张朝阳 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第8期307-312,共6页
In this paper we systematically investigate the influence of control parameters on the competition results between spiral waves and target waves. Driving frequency f , amplitude A and injection area n of the input sig... In this paper we systematically investigate the influence of control parameters on the competition results between spiral waves and target waves. Driving frequency f , amplitude A and injection area n of the input signals are three important parameters and the competition results between spiral waves and target waves are influenced by these three parameters remarkably. Based on these understandings we can control spiral waves effectively by suitable combination these parameters to generate faster target waves. And the effective controllable parameter regions are also studied. 展开更多
关键词 spiral wave and target wave COMPETITION controllable parameter region
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Robust formation tracking control for multi-agent systems with control parameter uncertainties
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作者 Jian LIAO Yu KUANG +5 位作者 Kai MAO Bin XIN Ying HE Jingli HUANG Fanglin HAN Delin LUO 《Science China(Technological Sciences)》 2025年第8期289-290,共2页
In recent years,multi-agent systems(MASs)formation tracking control(FTC)technology has achieved substantial advancements and has become a prominent research area due to its widespread applications in various fields,su... In recent years,multi-agent systems(MASs)formation tracking control(FTC)technology has achieved substantial advancements and has become a prominent research area due to its widespread applications in various fields,such as multi-unmanned aerial vehicle(multi-UAV)systems[1]and multiautonomous underwater vehicle(multi-AUV)systems[2].The consensusbased approach has evolved into the principal method for MASs’FTC because of its advantages,including rigorous logical deduction,easily solvable control parameters,and strong universal performance. 展开更多
关键词 multi agent systems rigorous logical deductioneasily robust formation tracking control consensus based approach control parameter uncertainties multi unmanned aerial vehicle systems consensusbased approach multiautonomous underwater vehicle multi auv systems
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Control Parameters Design Procedure for Multi-Converters DC Power System Considering Dynamic Interaction Between Converters
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作者 Xueshen Zhao Lin Zhu +4 位作者 Li Guo Xialin Li Zhi Wang Hao Lu Chengshan Wang 《CSEE Journal of Power and Energy Systems》 2025年第2期724-738,共15页
Due to dynamic interaction between converters, design of control parameters of multi-converters medium-voltage DC (MVDC) power system is much more complicated than of a single-converter situation. Open-loop and closed... Due to dynamic interaction between converters, design of control parameters of multi-converters medium-voltage DC (MVDC) power system is much more complicated than of a single-converter situation. Open-loop and closed-loop transfer functions considering control-loops dynamic interaction between converters are developed, which are suitable for studying influence of control parameters on system stability. With the above transfer functions, a system-level control parameter design proce-dure for dynamic stability (e.g., oscillation frequency and damping factor) of system is proposed. If there are many converters, computational burden of system-level control parameters design procedure will be huge. For this reason, a control parameter sharing method is further proposed in this paper, which is based on dynamic interaction mechanism between converters. In this sharing method, control parameters of equivalent reduced-order model of the system are shared with each converter, so calculation burden of control parameters of system is reduced significantly. Consequently, dynamic stability of the system can be designed by equivalent reduced-order model. Experiments are conduced to validate the system-level control parameter design procedure. 展开更多
关键词 control parameters design procedure dynamic interaction medium-voltage DC(MVDC)power system sharing principle
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Parameter identification and high order active disturbance rejection control of electro-hydraulic servo motor system
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作者 WANG Xiaojing GAO Wentao +1 位作者 ZHANG Yuxuan SUN Yuwei 《High Technology Letters》 2025年第3期280-287,共8页
An enhanced least mean square(LMS)error identification algorithm integrated with Kalman filtering is proposed to resolve accuracy degradation induced by nonlinear dynamics and parameter uncertainties in continuous rot... An enhanced least mean square(LMS)error identification algorithm integrated with Kalman filtering is proposed to resolve accuracy degradation induced by nonlinear dynamics and parameter uncertainties in continuous rotary electro-hydraulic servo systems.This enhancement accelerates convergence and improves accuracy compared with traditional LMS.A fifth-order identification mod-el is developed based on valve-controlled hydraulic motors,with parameters identified using Kalman filter state estimation and gradient smoothing.The results indicate that the improved LMS effectively enhances parameter identification.An advanced disturbance rejection controller(ADRC)is de-signed,and its performance is compared with an optimal proportional integral derivative(PID)con-troller through Simulink simulations.The results show that the ADRC fulfills the control specifications and expands the system’s operational bandwidth. 展开更多
关键词 electro-hydraulic servo system tracking differentiator filter minimum mean square error identification advanced disturbance rejection controller nonlinear feedback control law extended state observer parameter optimal proportional integral derivative control
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Optimization and Configuration of Control Parameters to Enhance Small-signal Stability of Hybrid LCC-MMC HVDC System 被引量:7
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作者 Chunyi Guo Peng Cui Chengyong Zhao 《Journal of Modern Power Systems and Clean Energy》 SCIE EI CSCD 2022年第1期213-221,共9页
This paper investigates the small-signal stability of the hybrid high-voltage direct current(HVDC)transmission system.The system is composed of line commutated converter(LCC)as rectifier and modular multi-level conver... This paper investigates the small-signal stability of the hybrid high-voltage direct current(HVDC)transmission system.The system is composed of line commutated converter(LCC)as rectifier and modular multi-level converter(MMC)as inverter under weak AC grid condition.Firstly,the impact of short-circuit ratio(SCR)at inverter side on the system stability is investigated by eigen-analysis,and the key control parameters which have major impact on the dominant mode are identified by the participation factor and sensitivity analysis.Then,considering the quadratic index and damping ratio characteristic,an objective function for evaluating the system stability is developed,and an optimization and configuration method for control parameters is presented by the utilization of Monte Carlo method.The eigenvalue results and the electromagnetic transient(EMT)simulation results show that,with the optimized control parameters,the small-signal stability and the dynamic responses of the hybrid system are greatly improved,and the hybrid system can even operate under weak AC grid condition. 展开更多
关键词 Hybrid high-voltage direct current(HVDC) line commutated converter(LCC) modular multi-level converter(MMC) optimization of control parameter
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Control Parameter Optimization of Thermostatically Controlled Loads Using a Modified State-queuing Model 被引量:5
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作者 Yuqing Bao Peipei Chen +1 位作者 Minqiang Hu Xuemei Zhu 《CSEE Journal of Power and Energy Systems》 SCIE CSCD 2020年第2期394-401,共8页
Thermostatically controlled loads(TCLs)are one of the best candidates to participate in direct load control(DLC).However,little attention is given to the parameter optimization of the TCLs control system due to the co... Thermostatically controlled loads(TCLs)are one of the best candidates to participate in direct load control(DLC).However,little attention is given to the parameter optimization of the TCLs control system due to the complexity of the TCLs’dynamics.In this paper,the parameters of the feedback control system based on the direct compressor control mechanism(DCCM)are optimized using the modified state-queuing(SQ)model,which can provide good characterizaton and greatly simplifies the dynamics of the TCLs.The simulation results verify the effectiveness of the proposed method. 展开更多
关键词 control parameters optimization direct compressor control mechanism genetic algorithm
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QPSO-ILF-ANN-based optimization of TBM control parameters considering tunneling energy efficiency 被引量:3
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作者 Xinyu WANG Jian WU +6 位作者 Xin YIN Quansheng LIU Xing HUANG Yucong PAN Jihua YANG Lei HUANG Shuangping MIAO 《Frontiers of Structural and Civil Engineering》 SCIE EI CSCD 2023年第1期25-36,共12页
In recent years, tunnel boring machines (TBMs) have been widely used in tunnel construction. However, the TBM control parameters set based on operator experience may not necessarily be suitable for certain geological ... In recent years, tunnel boring machines (TBMs) have been widely used in tunnel construction. However, the TBM control parameters set based on operator experience may not necessarily be suitable for certain geological conditions. Hence, a method to optimize TBM control parameters using an improved loss function-based artificial neural network (ILF-ANN) combined with quantum particle swarm optimization (QPSO) is proposed herein. The purpose of this method is to improve the TBM performance by optimizing the penetration and cutterhead rotation speeds. Inspired by the regularization technique, a custom artificial neural network (ANN) loss function based on the penetration rate and rock-breaking specific energy as TBM performance indicators is developed in the form of a penalty function to adjust the output of the network. In addition, to overcome the disadvantage of classical error backpropagation ANNs, i.e., the ease of falling into a local optimum, QPSO is adopted to train the ANN hyperparameters (weight and bias). Rock mass classes and tunneling parameters obtained in real time are used as the input of the QPSO-ILF-ANN, whereas the cutterhead rotation speed and penetration are specified as the output. The proposed method is validated using construction data from the Songhua River water conveyance tunnel project. Results show that, compared with the TBM operator and QPSO-ANN, the QPSO-ILF-ANN effectively increases the TBM penetration rate by 14.85% and 13.71%, respectively, and reduces the rock-breaking specific energy by 9.41% and 9.18%, respectively. 展开更多
关键词 tunnel boring machine control parameter optimization quantum particle swarm optimization artificial neural network tunneling energy efficiency
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A Numerical Algorithm for Determination of a Control Parameter in Two-dimensional Parabolic Inverse Problems 被引量:1
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作者 Akbar Mohebbi 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2015年第1期213-224,共12页
Numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications. In this study we present a high order scheme for determining unknown... Numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications. In this study we present a high order scheme for determining unknown control parameter and unknown solution of two-dimensional parabolic inverse problem with overspe- cialization at a point in the spatial domain. In this approach, a compact fourth-order scheme is used to discretize spatial derivatives of equation and reduces the problem to a system of ordinary differential equations (ODEs). Then we apply a fourth order boundary value method to the solution of resulting system of ODEs. So the proposed method has fourth order of accuracy in both space and time components and is unconditionally stable due to the favorable stability property of boundary value methods. The results of numerical experiments are presented and some comparisons are made with several well-known finite difference schemes in the literature. Also we will investigate the effect of noise in data on the approximate solutions. 展开更多
关键词 compact finite difference scheme boundary value method control parameter parabolic inverseproblem temperature over=specification high accuracy noise
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Enhancing the Performance of JADE Using Two-phase Parameter Control Scheme and Its Application 被引量:1
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作者 Qin-Qin Fan Yi-Lian Zhang +1 位作者 Xue-Feng Yan Zhi-Huan Wang 《International Journal of Automation and computing》 EI CSCD 2018年第4期462-473,共12页
The search efficiency of differential evolution (DE) algorithm is greatly impacted by its control parameters. Although many adaptation/self-adaptation techniques can automatically find suitable control parameters fo... The search efficiency of differential evolution (DE) algorithm is greatly impacted by its control parameters. Although many adaptation/self-adaptation techniques can automatically find suitable control parameters for the DE, most techniques are based on pop- ulation information which may be misleading in solving complex optimization problems. Therefore, a self-adaptive DE (i.e., JADE) using two-phase parameter control scheme (TPC-JADE) is proposed to enhance the performance of DE in the current study. In the TPC-JADE, an adaptation technique is utilized to generate the control parameters in the early population evolution, and a well-known empirical guideline is used to update the control parameters in the later evolution stages. The TPC-JADE is compared with four state-of-the-art DE variants on two famous test suites (i.e., IEEE CEC2005 and IEEE CEC2015). Results indicate that the overall performance of the TPC-JADE is better than that of the other compared algorithms. In addition, the proposed algorithm is utilized to obtain optimal nutrient and inducer feeding for the Lee-Ramirez bioreactor. Experimental results show that the TPC-JADE can perform well on an actual dynamic optimization problem. 展开更多
关键词 Differential evolution(DE)algorithm evolutionary computation dynamic optimization control parameter adaptation chemical processes.
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STUDY ON THE METHOD OF CONSTRUCTING RATIONAL CUBIC CURVES AND CURVED SURFACE INCLUDING CONTROLLING PARAMETERS
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作者 孙兰凤 高天真 +1 位作者 梁艳书 陈健 《Transactions of Tianjin University》 EI CAS 1998年第1期31-36,共6页
By adopting the method of controlling parameters this paper describes the construction of various kinds of cubic curve segment and curved surface fragment with rational and non rational parameters, and discusses the ... By adopting the method of controlling parameters this paper describes the construction of various kinds of cubic curve segment and curved surface fragment with rational and non rational parameters, and discusses the relationship between controlling parameters, weighted factors and types, kinds and characteristics of curve segments and curved surface fragments. A mathematical method is provided for CAGD with abundant connotations, broad covering region, convenience, flexibility and direct simplicity. 展开更多
关键词 controlling parameter weighted factor rational and non rational curve segment curved surface fragment matrix of parametric coefficient
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