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Recent advancement of flow-induced piezoelectric vibration energy harvesting techniques:principles,structures,and nonlinear designs 被引量:4
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作者 Dongxing CAO Junru WANG +2 位作者 Xiangying GUO S.K.LAI Yongjun SHEN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2022年第7期959-978,共20页
Energy harvesting induced from flowing fluids(e.g.,air and water flows)is a well-known process,which can be regarded as a sustainable and renewable energy source.In addition to traditional high-efficiency devices(e.g.... Energy harvesting induced from flowing fluids(e.g.,air and water flows)is a well-known process,which can be regarded as a sustainable and renewable energy source.In addition to traditional high-efficiency devices(e.g.,turbines and watermills),the micro-power extracting technologies based on the flow-induced vibration(FIV)effect have sparked great concerns by virtue of their prospective applications as a self-power source for the microelectronic devices in recent years.This article aims to conduct a comprehensive review for the FIV working principle and their potential applications for energy harvesting.First,various classifications of the FIV effect for energy harvesting are briefly introduced,such as vortex-induced vibration(VIV),galloping,flutter,and wake-induced vibration(WIV).Next,the development of FIV energy harvesting techniques is reviewed to discuss the research works in the past three years.The application of hybrid FIV energy harvesting techniques that can enhance the harvesting performance is also presented.Furthermore,the nonlinear designs of FIV-based energy harvesters are reported in this study,e.g.,multi-stability and limit-cycle oscillation(LCO)phenomena.Moreover,advanced FIV-based energy harvesting studies for fluid engineering applications are briefly mentioned.Finally,conclusions and future outlook are summarized. 展开更多
关键词 vibration-driven energy harvesting flow-induced vibration(FIV) piezoelectric approach nonlinear design
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Parameterized design of nonlinear feedback controllers for servo positioning systems 被引量:1
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作者 Cheng Guoyang Jin Wenguang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第3期593-599,共7页
To achieve fast, smooth and accurate set point tracking in servo positioning systems, a parameterized design of nonlinear feedback controllers is presented, based on a so-called composite nonlinear feedback (CNF) co... To achieve fast, smooth and accurate set point tracking in servo positioning systems, a parameterized design of nonlinear feedback controllers is presented, based on a so-called composite nonlinear feedback (CNF) control technique. The controller designed here consists of a linear feedback part and a nonlinear part. The linear part is responsible for stability and fast response of the closed-loop system. The nonlinear part serves to increase the damping ratio of closed-loop poles as the controlled output approaches the target reference. The CNF control brings together the good points of both the small and the large damping ratio cases, by continuously scheduling the damping ratio of the dominant closed-loop poles and thus has the capability for superior transient performance, i.e. a fast output response with low overshoot. In the presence of constant disturbances, an integral action is included so as to remove the static bias. An explicitly parameterized controller is derived for servo positioning systems characterized by second-order model. Practical application in a micro hard disk drive servo system is then presented, together with some discussion of the rationale and characteristics of such design. Simulation and experimental results demonstrate the effectiveness of this control design methodology. 展开更多
关键词 control systems nonlinear feedback parameterized design servo tracking disturbance.
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Non-fragile Observer Design for Fractional-order One-sided Lipschitz Nonlinear Systems 被引量:1
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作者 Yong-Hong Lan Wen-Jie Li +1 位作者 Yan Zhou Yi-Ping Luo 《International Journal of Automation and computing》 EI CSCD 2013年第4期296-302,共7页
This paper is concerned with the problem of the full-order observer design for a class of fractional-order Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using an i... This paper is concerned with the problem of the full-order observer design for a class of fractional-order Lipschitz nonlinear systems. By introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach, the sufficient condition for asymptotic stability of the full-order observer error dynamic system is presented. The stability condition is obtained in terms of LMI, which is less conservative than the existing one. A numerical example demonstrates the validity of this approach. 展开更多
关键词 FRACTIONAL-ORDER nonlinear system observer design indirect Lyapunov approach linear matrix inequality (LMI).
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Controller design of uncertain nonlinear systems based on T-S fuzzy model 被引量:1
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作者 Songtao ZHANG Shizhen BAI 《控制理论与应用(英文版)》 EI 2009年第2期139-143,共5页
A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input vari... A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group (EMORG) is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective. 展开更多
关键词 Controller design Uncertain nonlinear systems T-S fuzzy model
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Multi-parameter Sensitivity Analysis and Application Research in the Robust Optimization Design for Complex Nonlinear System 被引量:4
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作者 MA Tao ZHANG Weigang +1 位作者 ZHANG Yang TANG Ting 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2015年第1期55-62,共8页
The current research of complex nonlinear system robust optimization mainly focuses on the features of design parameters, such as probability density functions, boundary conditions, etc. After parameters study, high-d... The current research of complex nonlinear system robust optimization mainly focuses on the features of design parameters, such as probability density functions, boundary conditions, etc. After parameters study, high-dimensional curve or robust control design is used to find an accurate robust solution. However, there may exist complex interaction between parameters and practical engineering system. With the increase of the number of parameters, it is getting hard to determine high-dimensional curves and robust control methods, thus it's difficult to get the robust design solutions. In this paper, a method of global sensitivity analysis based on divided variables in groups is proposed. By making relevant variables in one group and keeping each other independent among sets of variables, global sensitivity analysis is conducted in grouped variables and the importance of parameters is evaluated by calculating the contribution value of each parameter to the total variance of system response. By ranking the importance of input parameters, relatively important parameters are chosen to conduct robust design analysis of the system. By applying this method to the robust optimization design of a real complex nonlinear system-a vehicle occupant restraint system with multi-parameter, good solution is gained and the response variance of the objective function is reduced to 0.01, which indicates that the robustness of the occupant restraint system is improved in a great degree and the method is effective and valuable for the robust design of complex nonlinear system. This research proposes a new method which can be used to obtain solutions for complex nonlinear system robust design. 展开更多
关键词 complex nonlinear system global sensitivity analysis robust optimization design grouped variables
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Non-derivative solution to nonlinear dynamic optimal design of class two for deformation network monitoring
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作者 陶华学 郭金运 《中国有色金属学会会刊:英文版》 CSCD 2000年第4期551-554,共4页
Based on the nonlinear error equation of deformation network monitoring, the mathematical model of nonlinear dynamic optimal design of class two was put forward for the deformation network monitoring, in which the tar... Based on the nonlinear error equation of deformation network monitoring, the mathematical model of nonlinear dynamic optimal design of class two was put forward for the deformation network monitoring, in which the target function is the accuracy criterion and the constraint conditions are the network’s sensitivity, reliability and observing cost. Meanwhile a new non derivative solution to the nonlinear dynamic optimal design of class two was also put forward. The solving model uses the difference to stand for the first derivative of functions and solves the revised feasible direction to get the optimal solution to unknown parameters. It can not only make the solution to converge on the minimum point of the constraint problem, but decrease the calculating load. 展开更多
关键词 DEFORMATION network monitoring nonlinear dynamic optimal design non DERIVATIVE ANALYTIC method.
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Optimal design theories of tuned mass dampers with nonlinear viscous damping 被引量:6
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作者 Lap-Loi Chung Lai-Yun Wu +2 位作者 Hsu-Hui Huang Chung-Hsin Chang Kuan-Hua Lien 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2009年第4期547-560,共14页
Optimal design theory for linear tuned mass dampers (TMD) has been thoroughly investigated, but is still under development for nonlinear TMDs. In this paper, optimization procedures in the time domain are proposed f... Optimal design theory for linear tuned mass dampers (TMD) has been thoroughly investigated, but is still under development for nonlinear TMDs. In this paper, optimization procedures in the time domain are proposed for design of a TMD with nonlinear viscous damping. A dynamic analysis of a structure implemented with a nonlinear TMD is conducted first. Optimum design parameters for the nonlinear TMD are searched using an optimization method to minimize the performance index. The feasibility of the proposed optimization method is illustrated numerically by using the Taipei 101 structure implemented with TMD. The sensitivity analysis shows that the performance index is less sensitive to the damping coefficient than to the frequency ratio. Time history analysis is conducted using the Taipei 101 structure implemented with different TMDs under wind excitation. For both linear and nonlinear TMDs, the comfort requirements for building occupants are satisfied as long as the TMD is properly designed. It was found that as the damping exponent increases, the relative displacement of the TMD decreases but the damping force increases. 展开更多
关键词 optimal design theory tuned mass damper (TMD) nonlinear performance index sensitivity analysis Taipei 101
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Nonlinear Programming Based Preamble Design for OFDM Systems
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作者 Ce-Wu Lu Xiao-Jun Liu +1 位作者 Yu-Jun Kuang Guang-You Fang 《Journal of Electronic Science and Technology of China》 2008年第1期25-28,共4页
A new preamble structure and design method for orthogonal frequency division multiplexing(OFDM)systems is described,which results a two-symbol long training preamble.The preamble contains four parts,the first part i... A new preamble structure and design method for orthogonal frequency division multiplexing(OFDM)systems is described,which results a two-symbol long training preamble.The preamble contains four parts,the first part is the same as the third,and the four parts are calculated by using nonlinear programming(NLP)model such that the moving correlation of the preamble results a steep rectangular-like pulse of certain width,whose step-down indicates the timing offset.Simulation results in AWGN channel are given to evaluate the perf o rmance of the proposed preamble design. 展开更多
关键词 nonlinear programming orthogonal frequency division multiplexing preamble design symbolsynchronization.
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H2 and H-Feedback Control Design for Nonlinear Gene Networks via Successive Galerkin’s Approximation
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作者 Alexander W. Bae 《Computational Molecular Bioscience》 2022年第2期95-108,共14页
This paper presents a design method of H<sub>2</sub> and H<sub>∞</sub>-feedback control loop for nonlinear smooth gene networks that are in control affine form. Formulaic solution methodology ... This paper presents a design method of H<sub>2</sub> and H<sub>∞</sub>-feedback control loop for nonlinear smooth gene networks that are in control affine form. Formulaic solution methodology for solving the nonlinear partial differential equations, namely the Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations through successive Galerkin’s approximation is implemented and the results are compared. Throughout the implementation, there were several caveats that need to be further resolved for practical applications in general cases. Such issues and the clarification of causes are mathematically established and reviewed. 展开更多
关键词 Gene Regulatory Network GMA System Galerkin’s Approximation Feedback design of Biomolecular Systems Hamilton-Jacobi Equation nonlinear Control
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具有时滞与状态约束的一类非线性系统自适应跟踪控制
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作者 范永青 李培龙 《西安邮电大学学报》 2026年第1期128-136,共9页
针对具有输入时滞和状态约束的一类非线性自适应系统,提出一种基于障碍Lyapunov函数与模糊切换控制的自适应跟踪控制方法。该方法利用Pade近似对输入时滞进行补偿,引入平滑切换函数构造连续控制律,确保系统状态始终满足预设约束条件。同... 针对具有输入时滞和状态约束的一类非线性自适应系统,提出一种基于障碍Lyapunov函数与模糊切换控制的自适应跟踪控制方法。该方法利用Pade近似对输入时滞进行补偿,引入平滑切换函数构造连续控制律,确保系统状态始终满足预设约束条件。同时,设计基于状态误差的模糊逻辑控制器,通过模糊规则提高控制精度,并增强系统的鲁棒性。为降低计算复杂度,采用参数自适应律对隶属函数向量的范数进行在线更新,有效简化了模糊系统的设计。所提控制方案无需先验系统模型信息,可适应多种复杂非线性动态特性。仿真实验以倒立摆系统为例,在不同输入时滞条件下验证了该方法的有效性,结果表明该控制器具有良好的跟踪性能、稳定性和约束保持能力。 展开更多
关键词 模糊控制 非线性控制系统 输入延迟 输出约束 反推设计技术 切换函数
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基于非线性能量阱的海洋平台地震减振控制
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作者 杜兴宇 陈为 张宝琳 《青岛科技大学学报(自然科学版)》 2026年第1期116-124,共9页
海洋平台在地震的作用下会产生持续剧烈的振动,该振动会导致结构受到损耗,影响人员安全。提出一种基于非线性能量阱(nonlinear energy sink,NES)的海洋平台振动控制方法。建立了地震作用下基于NES的海洋导管架平台动力学模型。给出了NES... 海洋平台在地震的作用下会产生持续剧烈的振动,该振动会导致结构受到损耗,影响人员安全。提出一种基于非线性能量阱(nonlinear energy sink,NES)的海洋平台振动控制方法。建立了地震作用下基于NES的海洋导管架平台动力学模型。给出了NES和TMD优化设计方案,得到地震载荷下NES和TMD的最优参数。最后,从平台结构刚度有无损耗以及系统初值角度,对NES和TMD的控制效果进行分析对比。结果表明:NES可以显著提高海洋平台稳定性;与TMD相比,NES具有更好的抗失谐性,抑制平台振动效果更好。 展开更多
关键词 非线性能量阱(NES) 振动控制 海洋平台 优化设计
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基于有限元方法的石化建筑物抗爆设计分析
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作者 王昌 黄钰 +1 位作者 王伟 吴凯锋 《山东化工》 2026年第2期204-207,共4页
随着石化工业规模的扩大,爆炸事故的潜在风险显著增加。为降低爆炸对建筑物及人员安全的威胁,本文以某石油终端控制室为研究对象,采用有限元方法(FEM)结合Midas Gen软件进行抗爆设计分析。研究表明,相较于传统等效单自由度体系法,有限... 随着石化工业规模的扩大,爆炸事故的潜在风险显著增加。为降低爆炸对建筑物及人员安全的威胁,本文以某石油终端控制室为研究对象,采用有限元方法(FEM)结合Midas Gen软件进行抗爆设计分析。研究表明,相较于传统等效单自由度体系法,有限元法能够更精确地模拟爆炸荷载下结构的非线性动态响应,并有效分析多层建筑中构件间的协同作用。本研究不仅验证了有限元法在抗爆设计中的适用性,还为复杂石油化工建筑物的抗爆优化提供了有益的技术参考。 展开更多
关键词 石化爆炸 石油化工建筑物 抗爆设计 有限元法 非线性动态响应
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Optimal State Estimation and Fault Diagnosis for a Class of Nonlinear Systems 被引量:2
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作者 Hamed Kazemi Alireza Yazdizadeh 《IEEE/CAA Journal of Automatica Sinica》 EI CSCD 2020年第2期517-526,共10页
This study proposes a scheme for state estimation and,consequently,fault diagnosis in nonlinear systems.Initially,an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault.B... This study proposes a scheme for state estimation and,consequently,fault diagnosis in nonlinear systems.Initially,an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault.By utilizing Lyapunov's direct method,the observer is proved to be optimal with respect to a performance function,including the magnitude of the observer gain and the convergence time.The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman(HJB)equation.The approximation is determined via an online trained neural network(NN).Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals.In this case,for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation(FDI).Simulation results of a singlelink flexible joint robot(SLFJR)electric drive system show the effectiveness of the proposed methodology. 展开更多
关键词 Differential geometry fault detection and isolation(FDI) fault diagnosis neural network(NN) nonlinear observer and filter design optimal state estimation
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Low-alpha optics design for SSRF 被引量:3
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作者 WANG Xin TIAN Shunqiang LIU Guimin 《Nuclear Science and Techniques》 SCIE CAS CSCD 2010年第3期134-140,共7页
In this paper,short pulse radiation in Shanghai Synchrotron Radiation Facility(SSRF)is generated by the low momentum compaction factor(α_C)optics,and three kinds of the low-α_C optics are found,with the very lowα_C... In this paper,short pulse radiation in Shanghai Synchrotron Radiation Facility(SSRF)is generated by the low momentum compaction factor(α_C)optics,and three kinds of the low-α_C optics are found,with the very lowα_C being adopted by reducing dispersion in the straight section to negative value in the SSRF.Energy acceptance is selected as objective functions in nonlinear optimization rather than the second orderα_C or other nonlinear driving terms.The optimal result is improved step-by-step by randomly setting harmonic sextupole strengths.Two optics modes,i.e.low positiveα_C and low negativeα_C,are analyzed.In order to get a large energy acceptance and only one stable point in longitudinal phase space,the low negativeα_C optics is taken as an operation mode for the short pulse radiation in the SSRF. 展开更多
关键词 上海同步辐射装置 光学设计 光源 阿尔法 二阶非线性 动量压缩因子 优化目标函数 脉冲辐射
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Robust Adaptive Actuator Failure Compensation for a Class of Uncertain Nonlinear Systems 被引量:3
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作者 Mahnaz Hashemi Javad Askari +1 位作者 Jafar Ghaisari Marzieh Kamali 《International Journal of Automation and computing》 EI CSCD 2017年第6期719-728,共10页
This paper presents a robust adaptive state feedback control scheme for a class of parametric-strict-feedback nonlinear systems in the presence of time varying actuator failures. The designed adaptive controller compe... This paper presents a robust adaptive state feedback control scheme for a class of parametric-strict-feedback nonlinear systems in the presence of time varying actuator failures. The designed adaptive controller compensates a general class of actuator failures without any need for explicit fault detection. The parameters, times, and patterns of the considered failures are completely unknown. The proposed controller is constructed based on a backstepping design method. The global boundedness of all the closed-loop signals is guaranteed and the tracking error is proved to converge to a small neighborhood of the origin. The proposed approach is employed for a two-axis positioning stage system as well as an aircraft wing system. The simulation results show the correctness and effectiveness of the proposed robust adaptive actuator failure compensation approach. 展开更多
关键词 Time varying actuator failure nonlinear systems robust adaptive control compensation backstepping design method
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Lattice design and optimization of the SSRF storage ring with super-bends 被引量:2
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作者 田顺强 姜伯承 +2 位作者 周巧根 冷用斌 赵振堂 《Nuclear Science and Techniques》 SCIE CAS CSCD 2014年第1期6-11,共6页
In the near future,the Phase-Ⅱ beamline project of Shanghai Synchrotron Radiation Facility(SSRF)will be implemented and some dipoles in the storage ring will be replaced by high field dipoles(super-bend),so as to lea... In the near future,the Phase-Ⅱ beamline project of Shanghai Synchrotron Radiation Facility(SSRF)will be implemented and some dipoles in the storage ring will be replaced by high field dipoles(super-bend),so as to leave room for short straight sections.In this way,the brightness of the hard x-ray emitted from the super-bends can be enhanced,and more insertion devices can be installed.In this paper,super-bends of two lengths are discussed and the corresponding lattices are presented. 展开更多
关键词 上海同步辐射装置 储存环 弯曲 优化 光源 设计 SSRF 硬X射线
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Seismic design of Xiluodu ultra-high arch dam 被引量:4
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作者 Ren-kun Wang Lin Chen Chong Zhang 《Water Science and Engineering》 EI CAS CSCD 2018年第4期288-301,共14页
The 285.5 m-high Xiluodu Arch Dam is located in a seismic region along the Jinsha River in China, where the horizontal components of peak ground accelerations for design and checking earthquakes have been estimated to... The 285.5 m-high Xiluodu Arch Dam is located in a seismic region along the Jinsha River in China, where the horizontal components of peak ground accelerations for design and checking earthquakes have been estimated to be 0.355 g and 0.423 g, respectively( g is the gravitational acceleration). The ground motion parameters of design and checking earthquakes are defined by exceedance probabilities of 2% over 100 years and 1% over 100 years, respectively. The dam shape was first selected and optimized through static analysis of the basic load combinations, and then adjusted after taking into account the seismic loads. The dam should be operational during and after the design earthquake with or without minor repairs, and maintain local and global stabilities during an extreme earthquake. Both linear elastic dynamic analysis and nonlinear dynamic analysis considering radiation damping, contraction joints, and material nonlinearity were conducted to assess the stress in the arch dam.The dynamic analysis shows that the maximum dynamic compressive stresses are less than the allowable levels, while the area with tensile stress over the limit is less than 15% of the dam surface and the maximum contraction openings range from 10 mm to 25 mm. The arch dam has sufficient earthquake-resistance capacity and meets the safety requirements. Nevertheless, steel reinforcement has been provided at the dam toe and in the zones of high tensile stress on the dam surface out of extra precaution. 展开更多
关键词 Seismic design nonlinear dynamic analysis Dam shape optimization Seismic strengthening Xiluodu arch dam
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Research on the Optimization Approach for Cargo Oil Tank Design Based on the Improved Particle Swarm Optimization Algorithm 被引量:1
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作者 姜文英 林焰 +1 位作者 陈明 于雁云 《Journal of Shanghai Jiaotong university(Science)》 EI 2015年第5期565-570,共6页
Based on the improved particle swarm optimization(PSO) algorithm,an optimization approach for the cargo oil tank design(COTD) is presented in this paper.The purpose is to design an optimal overall dimension of the car... Based on the improved particle swarm optimization(PSO) algorithm,an optimization approach for the cargo oil tank design(COTD) is presented in this paper.The purpose is to design an optimal overall dimension of the cargo oil tank(COT) under various kinds of constraints in the preliminary design stage.A non-linear programming model is built to simulate the optimization design,in which the requirements and rules for COTD are used as the constraints.Considering the distance between the inner shell and hull,a fuzzy constraint is used to express the feasibility degree of the double-hull configuration.In terms of the characteristic of COTD,the PSO algorithm is improved to solve this problem.A bivariate extremum strategy is presented to deal with the fuzzy constraint,by which the maximum and minimum cargo capacities are obtained simultaneously.Finally,the simulation demonstrates the feasibility and effectiveness of the proposed approach. 展开更多
关键词 cargo oil tank optimization design nonlinear programming improved particle swarm optimization(PSO)algorithm fuzzy constraint construction feasibility degree
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Adaptive robust dissipative designs on straight path control for underactuated ships 被引量:3
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作者 Li Tieshan Yang Yansheng Hong Biguang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2006年第1期177-181,共5页
An adaptive robust control algorithm for ship straight path control system in the presence of both modeling uncertainties and the bounded disturbances is proposed. Motivated by the backstepping approach, the algorithm... An adaptive robust control algorithm for ship straight path control system in the presence of both modeling uncertainties and the bounded disturbances is proposed. Motivated by the backstepping approach, the algorithm is developed by using the dissipation theory, such that the resulting dosed-loop system is both strictly dissipative and asymptotically adaptively stable for all admissible uncertainties. Also, it is able to steer an underactuated ship along a prescribed straight path with ultimate bounds under external disturbances induced by wave, wind and ocean current. When there are no disturbances, the straight path control can be implemented in a locally asymptotically stable manner. Simulation results on an ocean-going training ship ‘YULONG' are presented to validate the effectiveness of the algorithm. 展开更多
关键词 underactuated ship straight path control nonlinear system adaptive backstepping design robust control.
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OPTIMUM DESIGN OF FLEXIBLE PAVEMENT STRUCTURE BY FLEXIPLEX TOLERANCE METHOD
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作者 黄卫 《Journal of Southeast University(English Edition)》 EI CAS 1991年第1期70-76,共7页
The optimum design for flexible pavement structure is studied by using themethod of mathematical programming.The mathematical model is founded on the basisof“Design Code of Highway Flexible Pavement”issued by the Mi... The optimum design for flexible pavement structure is studied by using themethod of mathematical programming.The mathematical model is founded on the basisof“Design Code of Highway Flexible Pavement”issued by the Ministry of Communica-tions of China.The objective function is the cost of pavement structure.The optimal solu-tions of the mathematical model were searched successfully by flexiplex tolerance method.The relevant program has been developed on DPS-8 and IBM-PC computers.And thecalculated results show good convergence and accuracy for engineering applications. 展开更多
关键词 FLEXIBLE PAVEMENTS OPTIMUM designS nonlinear PROGRAMMING
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