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Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking
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作者 Xiang-long Liang Zhi-kai Yao +1 位作者 Yao-wen Ge Jian-yong Yao 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2024年第4期19-28,共10页
This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a larg... This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a large class of engineering systems,such as vehicular systems,robot manipulators and satellites.All these systems are often characterized by highly nonlinear characteristics,heavy modeling uncertainties and unknown perturbations,therefore,accurate-model-based nonlinear control approaches become unavailable.Motivated by the challenge,a reinforcement learning(RL)adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics.The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error(RISE)control approach.Different from a classical RISE control law,a tanh(·)function is utilized instead of a sign(·)function to acquire a more smooth control signal.The developed controller requires very little prior knowledge of the dynamic model,is robust to unknown dynamics and exogenous disturbances,and can achieve asymptotic output tracking.Eventually,co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom(3-DOF)manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach. 展开更多
关键词 Adaptive control Reinforcement learning uncertain mechanical systems Asymptotic tracking
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不确定需求下考虑客户差异的协同配送成本分摊策略研究
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作者 刘达 姜珊 李金孟 《工业工程》 2025年第1期90-98,共9页
多家物流企业通过协同配送展开合作,可以有效降低配送成本并促进物流运输行业的低碳发展。然而,随着客户需求和偏好的多样化发展,不同客户对于企业配送效益的贡献程度存在差异,导致协同配送企业之间的成本分摊关系愈发复杂。为此,本文... 多家物流企业通过协同配送展开合作,可以有效降低配送成本并促进物流运输行业的低碳发展。然而,随着客户需求和偏好的多样化发展,不同客户对于企业配送效益的贡献程度存在差异,导致协同配送企业之间的成本分摊关系愈发复杂。为此,本文探讨了不确定需求下考虑客户价值差异的协同配送成本分摊问题。运用鲁棒优化方法刻画客户需求不确定性,建立协同配送成本量化模型;构建客户价值评估模型,提出考虑客户价值差异的改进Shapley值法,并给出协同配送成本分摊调整策略。数值实验表明:应用本文所提的改进Shapley值法后,协同配送成本分摊的有效性和公平性得到提高。研究成果不仅从服务客户的角度丰富了现有的成本分摊理论,而且为合作企业提供了一种公平且有效的成本分摊方法。 展开更多
关键词 协同配送 不确定需求 成本分摊 客户差异 改进Shapley值
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不确定需求下冷藏集装箱低碳多式联运路径优化
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作者 苏航 李海军 《铁道运输与经济》 北大核心 2025年第1期61-69,共9页
优化冷藏集装箱多式联运路径对助力生鲜农产品运输实现降费增效具有重要作用,在既有研究的基础上,首先考虑不确定需求和碳排放的影响,引入三角模糊数表示不确定的运输需求,构建以广义物流成本最小为优化目标的路径优化模型,之后运用模... 优化冷藏集装箱多式联运路径对助力生鲜农产品运输实现降费增效具有重要作用,在既有研究的基础上,首先考虑不确定需求和碳排放的影响,引入三角模糊数表示不确定的运输需求,构建以广义物流成本最小为优化目标的路径优化模型,之后运用模糊机会约束规划理论实现模型清晰化,并对非线性项进行线性化处理,最后应用COPT7.0求解器实现模型求解,并进行案例求解、对比分析,以及碳税税率和置信水平的灵敏度分析。结果表明:冷藏集装箱多式联运可以降低生鲜农产品运输费用,提高运输效率;合理提高碳税税率可以有效促进“公转铁”,实现低碳运输;置信水平的提高有利于满足客户需求,但是由于运输能力和中转能力的限制,往往需要对运输方案进行改动,会导致运输总成本非线性增加。 展开更多
关键词 冷藏集装箱 不确定需求 碳排放 多式联运 路径优化
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不确定环境下我国人工智能产业政策的演化形成研究
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作者 朱齐宇 李白杨 +1 位作者 张心源 吴应强 《现代情报》 北大核心 2025年第2期72-86,共15页
[目的/意义]本文旨在探究我国人工智能产业政策在不确定环境下的演化路径,明确我国人工智能发展过程中工作重心的变迁与未来趋势,为人工智能产业政策进一步完善与高质量发展提供借鉴。[方法/过程]文章结合文献计量、网络分析、共现分析... [目的/意义]本文旨在探究我国人工智能产业政策在不确定环境下的演化路径,明确我国人工智能发展过程中工作重心的变迁与未来趋势,为人工智能产业政策进一步完善与高质量发展提供借鉴。[方法/过程]文章结合文献计量、网络分析、共现分析和主题结构演化等方法,分别从人工智能产业政策数量、联合发布机构和主题结构演化3个角度进行分析。[结果/结论]研究发现,我国人工智能产业政策发文数量逐年提高;中央地方政府协调统一;政策主题日益丰富,但是还存在人工智能技术创新性较低、政策平衡性欠缺、缺乏国际合作等不足。未来人工智能产业政策需要在技术创新、教育体系、就业问题和国际合作等方面进一步完善优化。 展开更多
关键词 人工智能 不确定环境 政策演化分析 主题结构演化 数字治理
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不确定态势下无人机群协同作战效能评估
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作者 孙鹏耀 黄炎焱 +1 位作者 王凯生 吴奎 《指挥控制与仿真》 2025年第1期10-22,共13页
针对不确定态势下无人机群作战效能评估问题,构建了一套基于作战过程仿真的无人机群作战效能评估方法。首先,从作战环角度分析无人机群察打任务作战过程;其次,根据作战环的各个步骤设计战法计算,结合设计的参数设置、战场态势生成与记... 针对不确定态势下无人机群作战效能评估问题,构建了一套基于作战过程仿真的无人机群作战效能评估方法。首先,从作战环角度分析无人机群察打任务作战过程;其次,根据作战环的各个步骤设计战法计算,结合设计的参数设置、战场态势生成与记录、全局进度控制器、作战数据记录等模块形成完整的无人机群察打作战过程仿真系统;然后,依据获得的作战过程仿真结果数据,构建核心效能指标与辅助效能指标,给出各指标的计算与耦合方法;最后,通过案例实验,对采用不同编配方案的无人机群进行作战过程仿真,评估分析作战效能,验证了本文方法的可行性,可实现不确定态势下无人机群作战效能的有效评估。 展开更多
关键词 无人机群 不确定态势 作战过程仿真 作战循环 作战效能
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真实、虚构及不确定性——村上春树《小城与不确定性的墙》的叙事学分析
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作者 张一楠 吴雨平 《常熟理工学院学报》 2025年第1期117-124,共8页
日本当代作家村上春树的长篇新作《小城与不确定性的墙》通过讲述真实和虚构两个世界中离奇曲折的故事情节和不断变化的人物关系,表现了当今社会的不确定性及人们普遍存在的孤独、迷惘和焦虑不安,并对如何应对这些问题提出了自己的独特... 日本当代作家村上春树的长篇新作《小城与不确定性的墙》通过讲述真实和虚构两个世界中离奇曲折的故事情节和不断变化的人物关系,表现了当今社会的不确定性及人们普遍存在的孤独、迷惘和焦虑不安,并对如何应对这些问题提出了自己的独特思考。这部作品采用变化的第一人称视角、“故事时间”和“叙事时间”的巧妙安排、“消解”与“隐喻”的叙事范式等一系列叙事策略,提升了小说的审美品格,深化了小说的主题。 展开更多
关键词 村上春树 《小城与不确定性的墙》 叙事策略
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碳交易机制下考虑需求不确定的多式联运路径优化
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作者 段力伟 高慧艳 《铁道运输与经济》 北大核心 2025年第1期40-52,共13页
为促进多式联运“降本减碳”及明确碳交易机制和不确定需求对多式联运路径选择的影响,构建了碳交易机制下考虑货运量不确定性的多式联运路径优化不确定机会约束规划模型,运用不确定理论转化为确定性模型,采用引入移民机制的遗传算法求... 为促进多式联运“降本减碳”及明确碳交易机制和不确定需求对多式联运路径选择的影响,构建了碳交易机制下考虑货运量不确定性的多式联运路径优化不确定机会约束规划模型,运用不确定理论转化为确定性模型,采用引入移民机制的遗传算法求解。通过算例探讨碳配额及分配方式、碳交易价格和不确定需求对货运企业联运方案、成本结构和碳排放量的综合影响。结果表明:碳交易机制有效引导货运企业选择低碳联运方式,减少碳排放18.4%;在低成本均衡场景中采用免费分配与80%及90%比例的混合分配方式时和高配额场景中采用3种分配方式时,企业能同时降低碳排放和总成本,实现经济与环境双赢;货运量不确定时,企业更偏好稳定且低碳的运输方式如铁路或铁水联运,并通过增加成本投入应对不确定风险。 展开更多
关键词 多式联运 路径优化 不确定需求 不确定机会约束规划 碳交易机制
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面向不确定量测的鲁棒RSS定位方法
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作者 王奇 胡光 +1 位作者 李飞 陈辉 《电信科学》 北大核心 2025年第2期111-119,共9页
在基于接收信号强度(received signal strength,RSS)的定位中,传感器量测的系统偏差及锚节点位置的不确定性会对定位结果造成严重影响。对此,提出一种面向不确定量测的鲁棒定位方法。首先,针对传感器量测有偏差及锚节点位置不确定的定... 在基于接收信号强度(received signal strength,RSS)的定位中,传感器量测的系统偏差及锚节点位置的不确定性会对定位结果造成严重影响。对此,提出一种面向不确定量测的鲁棒定位方法。首先,针对传感器量测有偏差及锚节点位置不确定的定位问题,建立相应的量测模型;其次,基于经典的极大似然估计准则建立关于目标位置的估计问题;最后,对所建立的非凸位置估计问题,采用合理的近似、松弛数学手段,将其转化为凸的半正定规划问题,从而保证得到全局最优解。仿真实验表明,在不同定位场景和条件下,所提方法的定位精度相比文献中的几种定位方法均有明显的优势,最高可提升约50%,证明其能有效降低量测不确定性对定位结果的不利影响,具有良好的鲁棒性。 展开更多
关键词 接收信号强度 目标定位 不确定量测 半正定规划
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Adaptive synchronization of Chua's system with uncertain inputs 被引量:8
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作者 张健 徐红兵 王厚军 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第5期953-957,共5页
The synchronization of Chua's system, whose inputs include an unknown constant parameter, is studied in this paper. A constructive method is applied to designing an adaptive controller, in which only one variable inf... The synchronization of Chua's system, whose inputs include an unknown constant parameter, is studied in this paper. A constructive method is applied to designing an adaptive controller, in which only one variable information of the master system is needed. With the action of control signals, the parameter of the slave system will approach the corresponding unknown parameter in the master system. At the same time, the synchronization errors will also converge to zero asymptotically. Numerical simulations show that the proposed theoretical approach is very effective. 展开更多
关键词 CHAOS SYNCHRONIZATION Chua's system uncertain inputs
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Adaptive synchronization of uncertain Liu system via nonlinear input 被引量:4
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作者 胡佳 张群娇 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第2期503-506,共4页
This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with to... This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with total parameters unknown. This method is simple and can be easily designed. What is more, it improves the existing conclusions in Ref [12]. Simulation results prove that the controller is effective and feasible in the end. 展开更多
关键词 adaptive synchronization Liu system uncertain parameters nonlinear controller
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Adaptive fault-tolerant control based on boundary estimation for space robot under joint actuator faults and uncertain parameters 被引量:4
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作者 Rong-Hua Lei Li Chen 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2019年第6期964-971,共8页
Since the joint actuator of the space robot executes the control instructions frequently in the harsh space environment,it is prone to the partial loss of control effectiveness(PLCE)fault.An adaptive fault-tolerant co... Since the joint actuator of the space robot executes the control instructions frequently in the harsh space environment,it is prone to the partial loss of control effectiveness(PLCE)fault.An adaptive fault-tolerant control algorithm is designed for a space robot system with the uncertain parameters and the PLCE actuator faults.The mathematical model of the system is established based on the Lagrange method,and the PLCE actuator fault is described as an effectiveness factor.The lower bound of the effectiveness factors and the upper bound of the uncertain parameters are estimated by an adaptive strategy,and the estimated value is fed back to the control algorithm.Compared with the traditional fault-tolerant algorithms,the proposed algorithm does not need to predetermine the lower bound of the effectiveness factor,hence it is more in line with the actual engineering application.It is proved that the algorithm can guarantee the stability of the closed-loop system based on the Lyapunov function method.The numerical simulation results show that the proposed algorithm can not only compensate for the uncertain parameters,but also can tolerate the PLCE actuator faults effectively,which verifies the effectiveness and superiority of the control scheme. 展开更多
关键词 Space robot Actuator faults uncertain parameters Effectiveness factor Fault-tolerant control
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ROBUST GLOBAL EXPONENTIAL STABILITY OF UNCERTAIN IMPULSIVE SYSTEMS 被引量:3
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作者 刘斌 刘新芝 廖晓昕 《Acta Mathematica Scientia》 SCIE CSCD 2005年第1期161-169,共9页
By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequ... By using the quasi-Lyapunov function, some sufficient conditions of global exponential stability for impulsive systems are established, which is the basis for the following discussion. Then, by employing Riccati inequality and Hamilton-Jacobi inequality approach, some sufficient conditions of robust exponential stability for uncertain linear/nonlinear impulsive systems are derived, respectively. Finally, some examples are given to illustrate the applications of the theory. 展开更多
关键词 uncertain impulsive system interval matrix Riccati/Hamilton-Jacobi inequality global exponential stability robust global exponential stability
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Optimization of a dynamic uncertain causality graph for fault diagnosis in nuclear power plant 被引量:2
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作者 Yue Zhao Francesco Di Maio +3 位作者 Enrico Zio Qin Zhang Chun-Ling Dong Jin-Ying Zhang 《Nuclear Science and Techniques》 SCIE CAS CSCD 2017年第3期59-67,共9页
Fault diagnostics is important for safe operation of nuclear power plants(NPPs). In recent years, data-driven approaches have been proposed and implemented to tackle the problem, e.g., neural networks, fuzzy and neuro... Fault diagnostics is important for safe operation of nuclear power plants(NPPs). In recent years, data-driven approaches have been proposed and implemented to tackle the problem, e.g., neural networks, fuzzy and neurofuzzy approaches, support vector machine, K-nearest neighbor classifiers and inference methodologies. Among these methods, dynamic uncertain causality graph(DUCG)has been proved effective in many practical cases. However, the causal graph construction behind the DUCG is complicate and, in many cases, results redundant on the symptoms needed to correctly classify the fault. In this paper, we propose a method to simplify causal graph construction in an automatic way. The method consists in transforming the expert knowledge-based DCUG into a fuzzy decision tree(FDT) by extracting from the DUCG a fuzzy rule base that resumes the used symptoms at the basis of the FDT. Genetic algorithm(GA) is, then, used for the optimization of the FDT, by performing a wrapper search around the FDT: the set of symptoms selected during the iterative search are taken as the best set of symptoms for the diagnosis of the faults that can occur in the system. The effectiveness of the approach is shown with respect to a DUCG model initially built to diagnose 23 faults originally using 262 symptoms of Unit-1 in the Ningde NPP of the China Guangdong Nuclear Power Corporation. The results show that the FDT, with GA-optimized symptoms and diagnosis strategy, can drive the construction of DUCG and lower the computational burden without loss of accuracy in diagnosis. 展开更多
关键词 DYNAMIC uncertain CAUSALITY GRAPH Fault diagnosis Classification Fuzzy DECISION tree GENETIC algorithm Nuclear power plant
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Backstepping synchronization of uncertain chaotic systems by a single driving variable 被引量:1
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作者 吕翎 张庆灵 郭治安 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第2期498-502,共5页
In this paper a parameter observer and a synchronization controller are designed to synchronize unknown chaotic systems with diverse structures. Based on stability theory the structures of the observer and the control... In this paper a parameter observer and a synchronization controller are designed to synchronize unknown chaotic systems with diverse structures. Based on stability theory the structures of the observer and the controller are presented. The unknown Coullet system and Rossler system are taken for examples to demonstrate that the method is effective and feasible. The artificial simulation results show that global synchronization between the unknown Coullet system and the Rossler system can be achieved by a single driving variable with co-operation of the observer and the controller, and all parameters of the Coullet system can be identified at the same time. 展开更多
关键词 backstepping synchronization parameter identification uncertain Coullet system Rossler system
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Cluster synchronization of uncertain complex networks with desynchronizing impulse 被引量:1
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作者 蔡国梁 姜胜芹 +1 位作者 蔡水明 田立新 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第12期109-116,共8页
Cluster synchronization of nonlinear uncertain complex networks with desynchronizing impulse is explored. First of all, a feedback controller is employed, based on the Lyapunov stability theorem and Lipschitz conditio... Cluster synchronization of nonlinear uncertain complex networks with desynchronizing impulse is explored. First of all, a feedback controller is employed, based on the Lyapunov stability theorem and Lipschitz condition, to guarantee that the uncertain complex networks with desynchronizing impulse synchronize with an object trajectory. Furthermore, a synchronizing impulse controller is presented, which is more efficiently and directly used to achieve the cluster synchronization. Finally, numerical examples are examined to show the effectiveness of the proposed methods. 展开更多
关键词 uncertain complex networks desynchronizing impulse cluster synchronization
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Collective Intelligence and Uncertain Knowledge Representation in Cloud Computing 被引量:1
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作者 刘玉超 张海粟 +2 位作者 马于涛 李德毅 陈桂生 《China Communications》 SCIE CSCD 2011年第6期58-66,共9页
The lasting evolution of computing environment, software engineering and interaction methods leads to cloud computing. Cloud computing changes the configuration mode of resources on the Internet and all kinds of resou... The lasting evolution of computing environment, software engineering and interaction methods leads to cloud computing. Cloud computing changes the configuration mode of resources on the Internet and all kinds of resources are virtualized and provided as services. Mass participation and online interaction with social annotations become usual in human daily life. People who own similar interests on the Internet may cluster naturally into scalable and boundless communities and collective intelligence will emerge. Human is taken as an intelligent computing factor, and uncertainty becomes a basic property in cloud computing. Virtualization, soft computing and granular computing will become essential features of cloud computing. Compared with the engineering technological problems of IaaS (Infrastructure as a service), PaaS (Platform as a Service) and SaaS (Software as a Service), collective intelligence and uncertain knowledge representation will be more important frontiers in cloud computing for researchers within the community of intelligence science. 展开更多
关键词 collective intelligence social annotation common sense uncertain knowledge representation
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Robust Adaptive Path Following for Underactuated Surface Vessels with Uncertain Dynamics 被引量:3
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作者 Wei Meng Chen Guo Yang Liu 《Journal of Marine Science and Application》 2012年第2期244-250,共7页
A robust adaptive control strategy was developed to force an underactuated surface vessel to follow a reference path,despite the presence of uncertain parameters and unstructured uncertainties including exogenous dist... A robust adaptive control strategy was developed to force an underactuated surface vessel to follow a reference path,despite the presence of uncertain parameters and unstructured uncertainties including exogenous disturbances and measurement noise.The reference path can be a curve or a straight line.The proposed controller was designed by using Lyapunov’s direct method and sliding mode control and backstepping techniques.Because the sway axis of the vessel was not directly actuated,two sliding surfaces were introduced,the first one in terms of the surge motion tracking errors and the second one for the yaw motion tracking errors.The adaptive control law guaranteed the uniform ultimate boundedness of the tracking errors.Numerical simulation results were provided to validate the effectiveness of the proposed controller for path following of underactuated surface vessels. 展开更多
关键词 underactuated surface vessels path following uncertain parameters ROBUSTNESS adaptive control
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Extracting and Measuring Uncertain Biomedical Knowledge from Scientific Statements 被引量:3
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作者 Xin Guo Yuming Chen +1 位作者 Jian Du Erdan Dong 《Journal of Data and Information Science》 CSCD 2022年第2期6-30,共25页
Purpose:Given the information overload of scientific literature,there is an increasing need for computable biomedical knowledge buried in free text.This study aimed to develop a novel approach to extracting and measur... Purpose:Given the information overload of scientific literature,there is an increasing need for computable biomedical knowledge buried in free text.This study aimed to develop a novel approach to extracting and measuring uncertain biomedical knowledge from scientific statements.Design/methodology/approach:Taking cardiovascular research publications in China as a sample,we extracted subject-predicate-object triples(SPO triples)as knowledge units and unknown/hedging/conflicting uncertainties as the knowledge context.We introduced information entropy(IE)as potential metric to quantify the uncertainty of epistemic status of scientific knowledge represented at subject-object pairs(SO pairs)levels.Findings:The results indicated an extraordinary growth of cardiovascular publications in China while only a modest growth of the novel SPO triples.After evaluating the uncertainty of biomedical knowledge with IE,we identified the Top 10 SO pairs with highest IE,which implied the epistemic status pluralism.Visual presentation of the SO pairs overlaid with uncertainty provided a comprehensive overview of clusters of biomedical knowledge and contending topics in cardiovascular research.Research limitations:The current methods didn’t distinguish the specificity and probabilities of uncertainty cue words.The number of sentences surrounding a given triple may also influence the value of IE.Practical implications:Our approach identified major uncertain knowledge areas such as diagnostic biomarkers,genetic polymorphism and co-existing risk factors related to cardiovascular diseases in China.These areas are suggested to be prioritized;new hypotheses need to be verified,while disputes,conflicts,and contradictions need to be settled.Originality/value:We provided a novel approach by combining natural language processing and computational linguistics with informetric methods to extract and measure uncertain knowledge from scientific statements. 展开更多
关键词 uncertain knowledge Information entropy Natural language processing Cardiovascular diseases China
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Scheduling for Uncertain Data Broadcast in Mobile Networks 被引量:1
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作者 许华杰 李国徽 +1 位作者 胡小明 余艳玮 《Journal of Southwest Jiaotong University(English Edition)》 2009年第3期192-198,共7页
With the increasing popularity of wireless sensor network and GPS ( global positioning system), uncertain data as a new type of data brings a new challenge for the traditional data processing methods. Data broadcast... With the increasing popularity of wireless sensor network and GPS ( global positioning system), uncertain data as a new type of data brings a new challenge for the traditional data processing methods. Data broadcast is an effective means for data dissemination in mobile networks. In this paper, the def'mition of the mean uncertainty ratio of data is presented and a broadcasting scheme is proposed for uncertain data dissemination. Simulation results show that the scheme can reduce the uncertainty of the broadcasted uncertain data effectively at the cost of a minor increase in data access time, in the case of no transmission error and presence of transmission errors. As a result, lower uncertainty of data benefits the qualifies of the query results based on the data. 展开更多
关键词 Mobile networks uncertain data BROADCAST SCHEDULING
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Uncertain Modal Analysis of Unmanned Aircraft Composite Landing Gear 被引量:1
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作者 CHEN Xiao ZHANG Xin +1 位作者 LI Chunping LI Darang 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2020年第5期694-701,共8页
Through taking uncertain mechanical parameters of composites into consideration,this paper carries out uncertain modal analysis for an unmanned aircraft landing gear.By describing correlated multi-dimensional mechanic... Through taking uncertain mechanical parameters of composites into consideration,this paper carries out uncertain modal analysis for an unmanned aircraft landing gear.By describing correlated multi-dimensional mechanical parameters as a convex polyhedral model,the modal analysis problem of a composite landing gear is transferred into a linear fractional programming(LFR)eigenvalue solution problem.As a consequent,the extreme-point algorithm is proposed to estimate lower and upper bounds of eigenvalues,namely the exact results of eigenvalues can be easily obtained at the extreme-point locations of the convex polyhedral model.The simulation results show that the proposed model and algorithm can play an important role in the eigenvalue solution problem and possess valuable engineering significance.It will be a powerful and effective tool for further vibration analysis for the landing gear. 展开更多
关键词 landing gear COMPOSITE uncertain convex polyhedral model modal analysis
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