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Enhancing Security and Privacy in Distributed Face Recognition Systems through Blockchain and GAN Technologies
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作者 Muhammad Ahmad Nawaz Ul Ghani Kun She +4 位作者 Muhammad Arslan Rauf Shumaila Khan Javed Ali Khan Eman Abdullah Aldakheel Doaa Sami Khafaga 《Computers, Materials & Continua》 SCIE EI 2024年第5期2609-2623,共15页
The use of privacy-enhanced facial recognition has increased in response to growing concerns about data securityand privacy in the digital age. This trend is spurred by rising demand for face recognition technology in... The use of privacy-enhanced facial recognition has increased in response to growing concerns about data securityand privacy in the digital age. This trend is spurred by rising demand for face recognition technology in a varietyof industries, including access control, law enforcement, surveillance, and internet communication. However,the growing usage of face recognition technology has created serious concerns about data monitoring and userprivacy preferences, especially in context-aware systems. In response to these problems, this study provides a novelframework that integrates sophisticated approaches such as Generative Adversarial Networks (GANs), Blockchain,and distributed computing to solve privacy concerns while maintaining exact face recognition. The framework’spainstaking design and execution strive to strike a compromise between precise face recognition and protectingpersonal data integrity in an increasingly interconnected environment. Using cutting-edge tools like Dlib for faceanalysis,Ray Cluster for distributed computing, and Blockchain for decentralized identity verification, the proposedsystem provides scalable and secure facial analysis while protecting user privacy. The study’s contributions includethe creation of a sustainable and scalable solution for privacy-aware face recognition, the implementation of flexibleprivacy computing approaches based on Blockchain networks, and the demonstration of higher performanceover previous methods. Specifically, the proposed StyleGAN model has an outstanding accuracy rate of 93.84%while processing high-resolution images from the CelebA-HQ dataset, beating other evaluated models such asProgressive GAN 90.27%, CycleGAN 89.80%, and MGAN 80.80%. With improvements in accuracy, speed, andprivacy protection, the framework has great promise for practical use in a variety of fields that need face recognitiontechnology. This study paves the way for future research in privacy-enhanced face recognition systems, emphasizingthe significance of using cutting-edge technology to meet rising privacy issues in digital identity. 展开更多
关键词 Facial recognition privacy protection blockchain GAN distributed systems
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A Novel High-Efficiency Transaction Verification Scheme for Blockchain Systems
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作者 Jingyu Zhang Pian Zhou +3 位作者 Jin Wang Osama Alfarraj Saurabh Singh Min Zhu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第5期1613-1633,共21页
Blockchain can realize the reliable storage of a large amount of data that is chronologically related and verifiable within the system.This technology has been widely used and has developed rapidly in big data systems... Blockchain can realize the reliable storage of a large amount of data that is chronologically related and verifiable within the system.This technology has been widely used and has developed rapidly in big data systems across various fields.An increasing number of users are participating in application systems that use blockchain as their underlying architecture.As the number of transactions and the capital involved in blockchain grow,ensuring information security becomes imperative.Addressing the verification of transactional information security and privacy has emerged as a critical challenge.Blockchain-based verification methods can effectively eliminate the need for centralized third-party organizations.However,the efficiency of nodes in storing and verifying blockchain data faces unprecedented challenges.To address this issue,this paper introduces an efficient verification scheme for transaction security.Initially,it presents a node evaluation module to estimate the activity level of user nodes participating in transactions,accompanied by a probabilistic analysis for all transactions.Subsequently,this paper optimizes the conventional transaction organization form,introduces a heterogeneous Merkle tree storage structure,and designs algorithms for constructing these heterogeneous trees.Theoretical analyses and simulation experiments conclusively demonstrate the superior performance of this scheme.When verifying the same number of transactions,the heterogeneous Merkle tree transmits less data and is more efficient than traditional methods.The findings indicate that the heterogeneous Merkle tree structure is suitable for various blockchain applications,including the Internet of Things.This scheme can markedly enhance the efficiency of information verification and bolster the security of distributed systems. 展开更多
关键词 Blockchain architecture transaction verification information security heterogeneous Merkle tree distributed systems
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Observer-based dynamic event-triggered control for distributed parameter systems over mobile sensor-plus-actuator networks
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作者 穆文英 庄波 邱芳 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期237-243,共7页
We develop a policy of observer-based dynamic event-triggered state feedback control for distributed parameter systems over a mobile sensor-plus-actuator network.It is assumed that the mobile sensing devices that prov... We develop a policy of observer-based dynamic event-triggered state feedback control for distributed parameter systems over a mobile sensor-plus-actuator network.It is assumed that the mobile sensing devices that provide spatially averaged state measurements can be used to improve state estimation in the network.For the purpose of decreasing the update frequency of controller and unnecessary sampled data transmission, an efficient dynamic event-triggered control policy is constructed.In an event-triggered system, when an error signal exceeds a specified time-varying threshold, it indicates the occurrence of a typical event.The global asymptotic stability of the event-triggered closed-loop system and the boundedness of the minimum inter-event time can be guaranteed.Based on the linear quadratic optimal regulator, the actuator selects the optimal displacement only when an event occurs.A simulation example is finally used to verify that the effectiveness of such a control strategy can enhance the system performance. 展开更多
关键词 distributed parameter systems event-triggered control mobile sensors mobile actuators
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An Augmented Jacobian Method for Power Flow Analysis of Weakly Looped Distribution Systems with PV Buses
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作者 陈星莺 余昆 单渊达 《Journal of Southeast University(English Edition)》 EI CAS 2002年第3期216-220,共5页
A power flow analysis method for weakly looped distribution systems with PV buses is proposed in this paper. The proposed method is computationally more efficient and more robust compared with the conventional compens... A power flow analysis method for weakly looped distribution systems with PV buses is proposed in this paper. The proposed method is computationally more efficient and more robust compared with the conventional compensation methods. The robustness is achieved by embedding the boundary conditions of loops and PV buses into the Jacobian matrix. The computational efficiency is achieved by the carefully designed factorization of Jacobian matrix. Test results on a 33 bus system are presented. 展开更多
关键词 power flow radial distribution systems weakly loops PV bus
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Cloud Control Systems 被引量:13
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作者 Yuanqing Xia 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI 2015年第2期134-142,共9页
The concept of cloud control systems is discussed in this paper, which is an extension of networked control systems (NCSs). With the development of internet of things (IOT), the technology of NCSs has played a key rol... The concept of cloud control systems is discussed in this paper, which is an extension of networked control systems (NCSs). With the development of internet of things (IOT), the technology of NCSs has played a key role in IOT. At the same time, cloud computing is developed rapidly, which provides a perfect platform for big data processing, controller design and performance assessment. The research on cloud control systems will give new contribution to the control theory and applications in the near future. © 2014 Chinese Association of Automation. 展开更多
关键词 Big data Cloud computing Computation theory Control systems Control theory Controllers Data handling Distributed computer systems Embedded systems Internet of things
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Exponential stabilization of distributed parameter switched systems under dwell time constraints
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作者 鲍乐平 费树岷 翟军勇 《Journal of Southeast University(English Edition)》 EI CAS 2013年第4期389-394,共6页
The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the ... The exponential stabilization problem for finite dimensional switched systems is extended to the infinite dimensional distributed parameter systems in the Hilbert space. Based on the semigroup theory, by applying the multiple Lyapunov function method, the exponential stabilization conditions are derived. These conditions are given in the form of linear operator inequalities where the decision variables are operators in the Hilbert space; while the stabilization properties depend on the switching rule. Being applied to the two-dimensional heat switched propagation equations with the Dirichlet boundary conditions, these linear operator inequalities are transformed into standard linear matrix inequalities. Finally, two examples are given to illustrate the effectiveness of the proposed results. 展开更多
关键词 distributed parameter switched systems exponential stabilization multiple Lyapunov function linear operator inequalities dwell time
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Fundamental Issues in Networked Control Systems 被引量:8
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作者 Magdi S.Mahmoud a Mutaz M.Hamdan 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第5期902-922,共21页
Abstract--This paper provides a survey on modeling and theories of networked control systems (NCS). In the first part, modeling of the different types of imperfections that affect NCS is discussed. These imperfectio... Abstract--This paper provides a survey on modeling and theories of networked control systems (NCS). In the first part, modeling of the different types of imperfections that affect NCS is discussed. These imperfections are quantization errors, packet dropouts, variable sampling/transmission intervals, vari- able transmission delays, and communication constraints. Then follows in the second part a presentation of several theories that have been applied for controlling networked systems. These theories include: input delay system approach, Markovian system approach, switched system approach, stochastic system approach, impulsive system approach, and predictive control approach. In the last part, some advanced issues in NCS including decentral- ized and distributed NCS, cloud control system, and co-design of NCS are reviewed. Index Terms--Decentralized networked control systems (NCS), distributed networked control systems, network constraints, net- worked control system, quantization, time delays. 展开更多
关键词 Decentralized networked control systems(NCS) distributed networked control systems network constraints networked control system QUANTIZATION time delays
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Toward Cloud Computing QoS Architecture:Analysis of Cloud Systems and Cloud Services 被引量:20
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作者 Mohammad Hossein Ghahramani MengChu Zhou Chi Tin Hon 《IEEE/CAA Journal of Automatica Sinica》 EI CSCD 2017年第1期6-18,共13页
Cloud can be defined as a new computing paradigm that provides scalable, on-demand, and virtualized resources for users. In this style of computing, users can access a shared pool of computing resources which are prov... Cloud can be defined as a new computing paradigm that provides scalable, on-demand, and virtualized resources for users. In this style of computing, users can access a shared pool of computing resources which are provisioned with minimal management efforts of users. Yet there are some obstacles and concerns about the use of clouds. Guaranteeing quality of service QoS by service providers can be regarded as one of the main concerns for companies tending to use it. Service provisioning in clouds is based on service level agreements representing a contract negotiated between users and providers. According to this contract, if a provider cannot satisfy its agreed application requirements, it should pay penalties as compensation. In this paper, we intend to carry out a comprehensive survey on the models proposed in literature with respect to the implementation principles to address the QoS guarantee issue. © 2014 Chinese Association of Automation. 展开更多
关键词 Cloud computing Distributed computer systems System of systems systems engineering Telecommunication services Web services
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Iron stability in drinking water distribution systems in a city of China 被引量:2
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作者 NIU Zhang-bin WANG Yang +3 位作者 ZHANG Xiao-jian HE Wen-fie HAN Hong-da YIN Pei-jun 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2006年第1期40-46,共7页
A field study on the estimation and analysis of iron stability in drinking water distribution system was carried out in a city of China. The stability of iron ion was estimated by pC-pH figure. It was found that iron ... A field study on the estimation and analysis of iron stability in drinking water distribution system was carried out in a city of China. The stability of iron ion was estimated by pC-pH figure. It was found that iron ion was unstable, with a high Fe (OH)3 precipitation tendency and obvious increase in turbidity. The outer layer of the corrosion scale was compact, while the inner core was porous. The main composition of the scale was iron, and the possible compound constitutes of the outer scale were α-FeOH, γ-FeOOH, α-Fe2O3, γ-F2O3, FeCl3, while the inner were Fe3O4, FeCl2, FeCO3. According to the characteristics of the corrosion scale, it was thought that the main reason for iron instability was iron release from corrosion scale. Many factors such as pipe materials, dissolved oxygen and chlorine residual affect iron release. Generally, higher iron release occurred with lower dissolved oxygen or chlorine residual concentration, while lower iron release occurred with higher dissolved oxygen or chlorine residual concentration. The reason was considered that the passivated out layer of scale of ferric oxide was broken down by reductive reaction in a condition of low oxidants concentration, which would result more rapid corrosion of the nine and red water phenomenon. 展开更多
关键词 chlorine residual corrosion scale dissolved oxygen drinking water distribution systems iron release iron stability
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Security and Privacy Frameworks for Access Control Big Data Systems 被引量:2
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作者 Paolina Centonze 《Computers, Materials & Continua》 SCIE EI 2019年第5期361-374,共14页
In the security and privacy fields,Access Control(AC)systems are viewed as the fundamental aspects of networking security mechanisms.Enforcing AC becomes even more challenging when researchers and data analysts have t... In the security and privacy fields,Access Control(AC)systems are viewed as the fundamental aspects of networking security mechanisms.Enforcing AC becomes even more challenging when researchers and data analysts have to analyze complex and distributed Big Data(BD)processing cluster frameworks,which are adopted to manage yottabyte of unstructured sensitive data.For instance,Big Data systems’privacy and security restrictions are most likely to failure due to the malformed AC policy configurations.Furthermore,BD systems were initially developed toped to take care of some of the DB issues to address BD challenges and many of these dealt with the“three Vs”(Velocity,Volume,and Variety)attributes,without planning security consideration,which are considered to be patch work.Some of the BD“three Vs”characteristics,such as distributed computing,fragment,redundant data and node-to node communication,each with its own security challenges,complicate even more the applicability of AC in BD.This paper gives an overview of the latest security and privacy challenges in BD AC systems.Furthermore,it analyzes and compares some of the latest AC research frameworks to reduce privacy and security issues in distributed BD systems,which very few enforce AC in a cost-effective and in a timely manner.Moreover,this work discusses some of the future research methodologies and improvements for BD AC systems.This study is valuable asset for Artificial Intelligence(AI)researchers,DB developers and DB analysts who need the latest AC security and privacy research perspective before using and/or improving a current BD AC framework. 展开更多
关键词 Big data access control distributed systems SECURITY PRIVACY
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Improved control of distributed parameter systems using wireless sensor and actuator networks:An observer-based method 被引量:2
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作者 江正仙 崔宝同 +1 位作者 楼旭阳 庄波 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第4期59-65,共7页
In this paper,the control problem of distributed parameter systems is investigated by using wireless sensor and actuator networks with the observer-based method.Firstly,a centralized observer which makes use of the me... In this paper,the control problem of distributed parameter systems is investigated by using wireless sensor and actuator networks with the observer-based method.Firstly,a centralized observer which makes use of the measurement information provided by the fixed sensors is designed to estimate the distributed parameter systems.The mobile agents,each of which is affixed with a controller and an actuator,can provide the observer-based control for the target systems.By using Lyapunov stability arguments,the stability for the estimation error system and distributed parameter control system is proved,meanwhile a guidance scheme for each mobile actuator is provided to improve the control performance.A numerical example is finally used to demonstrate the effectiveness and the advantages of the proposed approaches. 展开更多
关键词 distributed parameter systems wireless sensor and actuator networks mobile actuator OBSERVER
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Improved control for distributed parameter systems with time-dependent spatial domains utilizing mobile sensor-actuator networks 被引量:2
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作者 张建中 崔宝同 庄波 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第9期7-16,共10页
A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks (MSANs) is proposed for a class of distributed parameter systems (DPSs), which are governed by diffusion partial d... A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks (MSANs) is proposed for a class of distributed parameter systems (DPSs), which are governed by diffusion partial differential equations (PDEs) with time-dependent spatial domains. Several sufficient conditions for controller performance enhancement are presented. First, the infinite dimensional operator theory is used to derive an abstract evolution equation of the systems under some rational assumptions on the operators, and a static output feedback controller is designed to control the spatial process. Then, based on Lyapunov stability arguments, guidance policies for collocated and non-collocated MSANs are provided to enhance the performance of the proposed controller, which show that the time-dependent characteristic of the spatial domains can significantly affect the design of the mobile scheme. Finally, a simulation example illustrates the effectiveness of the proposed policy. 展开更多
关键词 distributed parameter systems time-dependent spatial domains mobile actuator-sensor networks Lyapunov stability
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Leak Detection in Water Distribution Systems Using Bayesian Theory and Fisher’s Law 被引量:1
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作者 张宏伟 王丽娟 《Transactions of Tianjin University》 EI CAS 2011年第3期181-186,共6页
A leak detection method based on Bayesian theory and Fisher’s law was developed for water distribution systems. A hydraulic model was associated with the parameters of leaks (location, extent). The randomness of para... A leak detection method based on Bayesian theory and Fisher’s law was developed for water distribution systems. A hydraulic model was associated with the parameters of leaks (location, extent). The randomness of parameter values was quantified by probability density function and updated by Bayesian theory. Values of the parameters were estimated based on Fisher’s law. The amount of leaks was estimated by back propagation neural network. Based on flow characteristics in water distribution systems, the location of leaks can be estimated. The effectiveness of the proposed method was illustrated by simulated leak data of node pressure head and flow rate of pipelines in a test pipe network, and the leaks were spotted accurately and renovated on time. 展开更多
关键词 water distribution systems LEAK DETECTION EPANET Fisher's law Bayesian theory back propagationneural network
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Sliding mode control of uncertain systems with distributed time-delay: parameter-dependent Lyapunov functional approach 被引量:2
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作者 Ligang WU Changhong WANG Huijun GAO Qingshuang ZENG 《控制理论与应用(英文版)》 EI 2006年第2期159-167,共9页
The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional ... The robust stability and robust sliding mode control problems are studied for a class of linear distributed time-delay systems with polytopic-type uncertainties by applying the parameter-dependent Lyapunov functional approach combining with a new method of introducing some relaxation matrices and tuning parameters, which can be chosen properly to lead to a less conservative result. First, a sufficient condition is proposed for robust stability of the autonomic system; next, the sufficient conditions of the robust stabilization controller and the existence condition of sliding mode are developed. The results are given in terms of linear matrix inequalities (LMIs), which can be solved via efficient interior-point algorithms. A numerical example is presented to illustrate the feasibility and advantages of the proposed design scheme. 展开更多
关键词 Parameter-dependent Lyapunov functional Distributed delay systems Sliding mode control Robust stabilization Linear matrix inequalities (LMIs)
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Partial Least Squares Regression Model to Predict Water Quality in Urban Water Distribution Systems 被引量:1
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作者 骆碧君 赵元 +1 位作者 陈凯 赵新华 《Transactions of Tianjin University》 EI CAS 2009年第2期140-144,共5页
The water distribution system of one residential district in Tianjin is taken as an example to analyze the changes of water quality.Partial least squares(PLS) regression model,in which the turbidity and Fe are regarde... The water distribution system of one residential district in Tianjin is taken as an example to analyze the changes of water quality.Partial least squares(PLS) regression model,in which the turbidity and Fe are regarded as control objectives,is used to establish the statistical model.The experimental results indicate that the PLS regression model has good predicted results of water quality compared with the monitored data.The percentages of absolute relative error(below 15%,20%,30%) are 44.4%,66.7%,100%(turbidity) and 33.3%,44.4%,77.8%(Fe) on the 4th sampling point;77.8%,88.9%,88.9%(turbidity) and 44.4%,55.6%,66.7%(Fe) on the 5th sampling point. 展开更多
关键词 water distribution systems water quality TURBIDITY FE partial least squares regression
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Performance Analysis of WLAN Medium Access Control Protocols in Simulcast Radio-Over-Fiber-Based Distributed Antenna Systems 被引量:5
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作者 LI Jianqiang FAN Yuting CHEN Hao LU Xun XU Kun 《China Communications》 SCIE CSCD 2014年第5期37-48,共12页
The performance of three wireless local-area network(WLAN) media access control(MAC) protocols is investigated and compared in the context of simulcast radioover-fiber-based distributed antenna systems(RoF-DASs) where... The performance of three wireless local-area network(WLAN) media access control(MAC) protocols is investigated and compared in the context of simulcast radioover-fiber-based distributed antenna systems(RoF-DASs) where multiple remote antenna units(RAUs) are connected to one access point(AP) with different-length fiber links.The three WLAN MAC protocols under investigation are distributed coordination function(DCF) in basic access mode,DCF in request/clear to send(RTS/CTS) exchange mode,and point coordination function(PCF).In the analysis,the inter-RAU hidden nodes problems and fiber-length difference effect are both taken into account.Results show that adaptive PCF mechanism has better throughput performances than the other two DCF modes,especially when the inserted fiber length is short. 展开更多
关键词 radio-over-fiber wireless localarea network distributed antenna systems medium access control simulcast
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Assessment on reliability of water quality in water distribution systems 被引量:1
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作者 伍悦滨 田海 王龙岩 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2004年第5期481-484,共4页
Water leaving the treatment works is usually of a high quality but its properties change during the transportation stage. Increasing awareness of the quality of the service provided within the water industry today and... Water leaving the treatment works is usually of a high quality but its properties change during the transportation stage. Increasing awareness of the quality of the service provided within the water industry today and assessing the reliability of the water quality in a distribution system has become a major significance for decision on system operation based on water quality in distribution networks. Using together a water age model, a chlorine decay model and a model of acceptable maximum water age can assess the reliability of the water quality in a distribution system. First, the nodal water age values in a certain complex distribution system can be calculated by the water age model. Then, the acceptable maximum water age value in the distribution system is obtained based on the chlorine decay model. The nodes at which the water age values are below the maximum value are regarded as reliable nodes. Finally, the reliability index on the percentile weighted by the nodal demands reflects the reliability of the water quality in the distribution system. The approach has been applied in a real water distribution network. The contour plot based on the water age values determines a surface of the reliability of the water quality. At any time, this surface is used to locate high water age but poor reliability areas, which identify parts of the network that may be of poor water quality. As a result, the contour water age provides a valuable aid for a straight insight into the water quality in the distribution system. 展开更多
关键词 reliability of water quality reliability index maximum water age contour water age water distribution systems
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Optimal switching policy for performance enhancement of distributed parameter systems based on event-driven control 被引量:1
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作者 穆文英 崔宝同 +1 位作者 楼旭阳 李纹 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第7期211-217,共7页
This paper aims to improve the performance of a class of distributed parameter systems for the optimal switching of actuators and controllers based on event-driven control. It is assumed that in the available multiple... This paper aims to improve the performance of a class of distributed parameter systems for the optimal switching of actuators and controllers based on event-driven control. It is assumed that in the available multiple actuators, only one actuator can receive the control signal and be activated over an unfixed time interval, and the other actuators keep dormant. After incorporating a state observer into the event generator, the event-driven control loop and the minimum inter-event time are ultimately bounded. Based on the event-driven state feedback control, the time intervals of unfixed length can be obtained. The optimal switching policy is based on finite horizon linear quadratic optimal control at the beginning of each time subinterval. A simulation example demonstrate the effectiveness of the proposed policy. 展开更多
关键词 distributed parameter systems optimal switching policy EVENT-DRIVEN
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Kinetics of Chlorine Decay in Water Distribution Systems 被引量:1
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作者 周建华 薛罡 +2 位作者 赵洪宾 汪永辉 郭美芳 《Journal of Donghua University(English Edition)》 EI CAS 2004年第1期140-145,共6页
A combined first and second-order model, which includes bulk decay and wall decay, was developed to describe chlorine decay in water distribution systems. In the model the bulk decay has complex relationships with tot... A combined first and second-order model, which includes bulk decay and wall decay, was developed to describe chlorine decay in water distribution systems. In the model the bulk decay has complex relationships with total organic carbon (TOC), the initial chlorine concentration and the temperature. Except for the initial stages they can be simplified into a linear increase with TOC, a linear decrease with initial chlorine concentration and an exponential relationship with the temperature. The model also explains why chlorine decays rapidly in the initial stages. The parameters of model are determined by deriving the best fitness with experimental data. And the accuracy of model has been verified by using the experimental data and the monitoring data in a distribution system. 展开更多
关键词 water distribution systems chlorine decay bulk decay wall decay
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STATIONARY DISTRIBUTIONS OF INFINITE PARTICLE SYSTEMS WITH NONCOMPACT STATE SPACE. 被引量:2
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作者 陈木法 《Acta Mathematica Scientia》 SCIE CSCD 1989年第1期7-19,共13页
This paper deals with the preblem of existence and uniqueness of the stationary distributions (abbr., s. d.'s) for the processes constructed in [4] .The main results are stated in § 1. For the reader's co... This paper deals with the preblem of existence and uniqueness of the stationary distributions (abbr., s. d.'s) for the processes constructed in [4] .The main results are stated in § 1. For the reader's convenience we first restate the existence theorems (Theorem 1 and 2) of the processes given in [4]. Then two existence theorems (Theorem 3 and 4) and a uniqueness theorem (Theorem 5) for the s. d.'s of the processes are presented. The last result (Theorem 6), as an application of the previous ones, is about the Schlgl model which comes from nonequilibrium statisticali physics. The details of the proofs of Theorem 3—6 are given in § 2—4. 展开更多
关键词 PRO STATIONARY DISTRIBUTIONS OF INFINITE PARTICLE systems WITH NONCOMPACT STATE SPACE
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