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Self-Triggered Set Stabilization of Boolean Control Networks and Its Applications 被引量:1
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作者 Rong Zhao Jun-e Feng Dawei Zhang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第7期1631-1642,共12页
Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control s... Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results. 展开更多
关键词 Boolean control networks(BCNs) output regulation self-triggered control semi-tensor product of matrices set stabilization SYNCHRONIZATION
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Cluster DetectionMethod of Endogenous Security Abnormal Attack Behavior in Air Traffic Control Network 被引量:1
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作者 Ruchun Jia Jianwei Zhang +2 位作者 Yi Lin Yunxiang Han Feike Yang 《Computers, Materials & Continua》 SCIE EI 2024年第5期2523-2546,共24页
In order to enhance the accuracy of Air Traffic Control(ATC)cybersecurity attack detection,in this paper,a new clustering detection method is designed for air traffic control network security attacks.The feature set f... In order to enhance the accuracy of Air Traffic Control(ATC)cybersecurity attack detection,in this paper,a new clustering detection method is designed for air traffic control network security attacks.The feature set for ATC cybersecurity attacks is constructed by setting the feature states,adding recursive features,and determining the feature criticality.The expected information gain and entropy of the feature data are computed to determine the information gain of the feature data and reduce the interference of similar feature data.An autoencoder is introduced into the AI(artificial intelligence)algorithm to encode and decode the characteristics of ATC network security attack behavior to reduce the dimensionality of the ATC network security attack behavior data.Based on the above processing,an unsupervised learning algorithm for clustering detection of ATC network security attacks is designed.First,determine the distance between the clustering clusters of ATC network security attack behavior characteristics,calculate the clustering threshold,and construct the initial clustering center.Then,the new average value of all feature objects in each cluster is recalculated as the new cluster center.Second,it traverses all objects in a cluster of ATC network security attack behavior feature data.Finally,the cluster detection of ATC network security attack behavior is completed by the computation of objective functions.The experiment took three groups of experimental attack behavior data sets as the test object,and took the detection rate,false detection rate and recall rate as the test indicators,and selected three similar methods for comparative test.The experimental results show that the detection rate of this method is about 98%,the false positive rate is below 1%,and the recall rate is above 97%.Research shows that this method can improve the detection performance of security attacks in air traffic control network. 展开更多
关键词 Air traffic control network security attack behavior cluster detection behavioral characteristics information gain cluster threshold automatic encoder
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The Effect of Key Nodes on theMalware Dynamics in the Industrial Control Network
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作者 Qiang Fu JunWang +1 位作者 Changfu Si Jiawei Liu 《Computers, Materials & Continua》 SCIE EI 2024年第4期329-349,共21页
As industrialization and informatization becomemore deeply intertwined,industrial control networks have entered an era of intelligence.The connection between industrial control networks and the external internet is be... As industrialization and informatization becomemore deeply intertwined,industrial control networks have entered an era of intelligence.The connection between industrial control networks and the external internet is becoming increasingly close,which leads to frequent security accidents.This paper proposes a model for the industrial control network.It includes a malware containment strategy that integrates intrusion detection,quarantine,and monitoring.Basedonthismodel,the role of keynodes in the spreadofmalware is studied,a comparisonexperiment is conducted to validate the impact of the containment strategy.In addition,the dynamic behavior of the model is analyzed,the basic reproduction number is computed,and the disease-free and endemic equilibrium of the model is also obtained by the basic reproduction number.Moreover,through simulation experiments,the effectiveness of the containment strategy is validated,the influence of the relevant parameters is analyzed,and the containment strategy is optimized.In otherwords,selective immunity to key nodes can effectively suppress the spread ofmalware andmaintain the stability of industrial control systems.The earlier the immunization of key nodes,the better.Once the time exceeds the threshold,immunizing key nodes is almost ineffective.The analysis provides a better way to contain the malware in the industrial control network. 展开更多
关键词 Key nodes dynamic model industrial control network SIMULATION
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A Method for Surveying Control Network Optimization Based on Reliability Properties 被引量:4
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作者 ZHANG Zhenglu DENG Yong LUO Changlin 《Geo-Spatial Information Science》 2007年第4期235-239,共5页
Surveying control network optimization design is related to standards, such as precision, reliability, sensitivity and the cost, and these standards are related closely to each other. A new method for surveying contro... Surveying control network optimization design is related to standards, such as precision, reliability, sensitivity and the cost, and these standards are related closely to each other. A new method for surveying control network simulation optimization design is proposed. This method is based on the inner reliability index of the observation values. 展开更多
关键词 surveying control network optimization design RELIABILITY redundant observation weight
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Preliminary Design of Control Network for HT-7U Tokamak Cryogenic System 被引量:2
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作者 金毅彬 庄明 白宏宇 《Plasma Science and Technology》 SCIE EI CAS CSCD 2003年第6期2035-2038,共4页
In the course of the cryoplant modernization, a control network will be set up in order to facilitate the control, the supervision, the centralized data acquisition and the alarm handling of the cryogenic system for H... In the course of the cryoplant modernization, a control network will be set up in order to facilitate the control, the supervision, the centralized data acquisition and the alarm handling of the cryogenic system for HT-7U tokamak. The paper introduces the preliminary design of control network based on the Controller Link Network for HT-7U tokamak cryogenic system. The multi-layer structure mentioned in the paper is the mainstream of automatic control. The control philosophy, the structure of the network and the components for control are also presented. 展开更多
关键词 HT-7U cryogenic system control network
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Asurvey onob vabilit of Boolean control networks 被引量:1
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作者 Kuize Zhang 《Control Theory and Technology》 EI CSCD 2023年第2期115-147,共33页
Observability is a fundamental property of a partially observed dynamical system,which means whether one can use an input sequence and the corresponding output sequence to determine the initial state.Observability pro... Observability is a fundamental property of a partially observed dynamical system,which means whether one can use an input sequence and the corresponding output sequence to determine the initial state.Observability provides bases for many related problems,such as state estimation,identification,disturbance decoupling,controller synthesis,etc.Until now,fundamental improvement has been obtained in observability of Boolean control networks(BCNs)mainly based on two methods-Edward F.Moore's partition and our observability graph or their equivalent representations found later based on the semitensor product(STP)of matrices(where the STP was proposed by Daizhan Cheng),including necessary and sufficient conditions for different types of observability,extensions to probabilistic Boolean networks(PBNs)and singular BCNs,even to nondeterministic finite-transition systems(NFTSs);and the development(with the help of the STP of matrices)in related topics,such as com-putation of smallest invariant dual subspaces of BNs containing a set of Boolean functions,multiple-experiment observability verification/decomposition in BCNs,disturbance decoupling in BCNs,etc.This paper provides a thorough survey for these topics.The contents of the paper are guided by the above two methods.First,we show that Moore's partition-based method closely relates the following problems:computation of smallest invariant dual subspaces of BNs,multiple-experiment observ-ability verification/decomposition in BCNs,and disturbance decoupling in BCNs.However,this method does not apply to other types of observability or nondeterministic systems.Second,we show that based on our observability graph,four different types of observability have been verified in BCNs,verification results have also been extended to PBNs,singular BCNs,and NFTSs.In addition,Moore's partition also shows similarities between BCNs and linear time-invariant(LTI)control systems,e.g.,smallest invariant dual subspaces of BNs containing a set of Boolean functions in BCNs vs unobservable subspaces of LTI control systems,the forms of quotient systems based on observability decomposition in both types of systems.However,there are essential differences between the two types of systems,e.g.,"all plausible definitions of observability in LTI control systems turn out to be equivalent"(by Walter M.Wonham 1985),but there exist nonequivalent definitions of observability in BCNs;the quotient system based on observability decomposition always exists in an LTI control system,while a quotient system based on multiple-experiment observability decomposition does not always exist in a BCN. 展开更多
关键词 Boolean control networks Observability-Moore's partition Observability graph Finite automaton-Semitensor product Disturbance decoupling Invariant subspace
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Applications of Graph Theory to Gross Error Detection for GPS Geodetic Control Networks 被引量:1
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作者 Samwel Simon Katambi 《Geo-Spatial Information Science》 2002年第4期26-31,共6页
This paper describes a broad perspective of the application of graph theory to establishment of GPS control networks whereby the GPS network is considered as a connected and directed graph with three components.In thi... This paper describes a broad perspective of the application of graph theory to establishment of GPS control networks whereby the GPS network is considered as a connected and directed graph with three components.In this algorithm the gross error detection is undertaken through loops of different spanning trees using the "Loop Law" in which the individual components Δ X, Δ Y and Δ Z sum up to zero.If the sum of the respective vector components ∑X,∑Y and ∑Z in a loop is not zero and if the error is beyond the tolerable limit (ε>w),it indicates the existence of gross errors in one of the baselines in the loop and therefore the baseline must be removed or re_observed.After successful screening of errors by graph theory,network adjustment can be carried out.In this paper,the GPS data from the control network established as reference system for the HP Dam at Baishan county in Liaoning province is presented to illustrate the algorithm. 展开更多
关键词 GPS control network quality criteria graph theory directed graph spanning tree fundamental loop incident matrix gross error
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Morgan's problem of Boolean control networks 被引量:1
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《Control Theory and Technology》 EI CSCD 2017年第4期316-326,共11页
This paper investigates the Morgan's problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is co... This paper investigates the Morgan's problem of Boolean control networks. Based on the matrix expression of logical functions, two key steps are proposed to solve the problem. First, the Boolean control network is converted into an output- decomposed form by constructing a set of consistent outputfriendly subspaces, and a necessary and sufficient condition for the existence of the consistent output-friendly subspaces is obtained. Secondly, a type of state feedback controllers are designed to solve the Morgan's problem if it is solvable. By solving a set of matrix equations, a necessary and sufficient condition for converting an output-decomposed form to an input-output decomposed form is given, and by verifying the output controllability matrix, the solvability of Morgan's problem is obtained. 展开更多
关键词 Boolean control network Morgan's problem regular subspace y-friendly subspace semi-tensor product ofmatrices
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Antidepressants combined with psychodrama improve the coping style and cognitive control network in patients with childhood trauma-associated major depressive disorder 被引量:1
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作者 Ren-Qiang Yu Huan Tan +6 位作者 Er-Dong Wang Jie Huang Pei-Jia Wang Xiao-Mei Li Han-Han Zheng Fa-Jin Lv Hua Hu 《World Journal of Psychiatry》 SCIE 2022年第8期1016-1030,共15页
BACKGROUND The use of antidepressant therapy alone has a limited efficacy in patients with childhood trauma-associated major depressive disorder(MDD).However,the effectiveness of antidepressant treatment combined with... BACKGROUND The use of antidepressant therapy alone has a limited efficacy in patients with childhood trauma-associated major depressive disorder(MDD).However,the effectiveness of antidepressant treatment combined with psychodrama in these patients is unclear.AIM To evaluate the effectiveness of antidepressant treatment combined with psychodrama.METHODS Patients with childhood trauma-associated MDD treated with antidepressants were randomly assigned to either the psychodrama intervention(observation group)or the general health education intervention(control group)and received combination treatment for 6 mo.The observation group received general health education given by the investigator together with the“semi-structured group intervention model”of Yi Shu psychodrama.A total of 46 patients were recruited,including 29 cases in the observation group and 17 cases in the control group.Symptoms of depression and anxiety as well as coping style and resting-state functional magnetic resonance imaging were assessed before and after the intervention.RESULTS Symptoms of depression and anxiety,measured by the Hamilton Depression Scale,Beck Depression Inventory,and Beck Anxiety Inventory,were reduced after the intervention in both groups of patients.The coping style of the observation group improved significantly in contrast to the control group,which did not.In addition,an interaction between treatment and time in the right superior parietal gyrus node was found.Furthermore,functional connectivity between the right superior parietal gyrus and left inferior frontal gyrus in the observation group increased after the intervention,while in the control group the connectivity decreased.CONCLUSION This study supports the use of combined treatment with antidepressants and psychodrama to improve the coping style of patients with childhood trauma-associated MDD.Functional connectivity between the superior parietal gyrus and inferior frontal gyrus was increased after this combined treatment.We speculate that psychodrama enhances the internal connectivity of the cognitive control network and corrects the negative attention bias of patients with childhood trauma-associated MDD.Elucidating the neurobiological features of patients with childhood trauma-associated MDD is important for the development of methods that can assist in early diagnosis and intervention. 展开更多
关键词 Major depressive disorder Childhood trauma Yi Shu psychodrama Cognitive control network Coping style
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The Deformation Analysis of the 3D Alignment Control Network Based on the Multiple Congruence Models 被引量:1
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作者 Xudong ZHANG Wenjun CHEN +5 位作者 Xiaodong ZHANG Yajun ZHENG Bin ZHANG Shaoming WANG Jiandong YUAN Guozhen SUN 《Journal of Geodesy and Geoinformation Science》 CSCD 2023年第2期21-31,共11页
In the construction and maintenance of particle accelerators,all the accelerator elements should be installed in the same coordinate system,only in this way could the devices in the actual world be consistent with the... In the construction and maintenance of particle accelerators,all the accelerator elements should be installed in the same coordinate system,only in this way could the devices in the actual world be consistent with the design drawings.However,with the occurrence of the movements of the reinforced concrete cover plates at short notice or building deformations in the long term,the control points upon the engineering structure will be displaced,and the fitness between the subnetwork and the global control network may be irresponsible.Therefore,it is necessary to evaluate the deformations of the 3D alignment control network.Different from the extant investigations,in this paper,to characterize the deformations of the control network,all of the congruent models between the points measured in different epochs have been identified,and the congruence model with the most control points is considered as the primary or fundamental model,the remaining models are recognized as the additional ones.Furthermore,the discrepancies between the primary S-transformation parameters and the additional S-transformation parameters can reflect the relative movements of the additional congruence models.Both the iterative GCT method and the iterative combinatorial theory are proposed to detect multiple congruence models in the control network.Considering the actual work of the alignment,it is essential to identify the competitive models in the monitoring network,which can provide us a hint that,even the fitness between the subnetwork and the global control network is good,there are still deformations which may be ignored.The numerical experiments show that the suggested approaches can describe the deformation of the 3D alignment control network roundly. 展开更多
关键词 similarity transformation 3D alignment control network deformation analysis hypothesis testing iterative global congruence test iterative combinatorial theory
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Fuzzy adaptive learning control network with sigmoid membership function 被引量:1
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作者 邢杰 Xiao Deyun 《High Technology Letters》 EI CAS 2007年第3期225-229,共5页
To get simpler operation in modified fuzzy adaptive learning control network (FALCON) in some engineering application, sigmoid nonlinear function is employed as a substitute of traditional Gaussian membership functi... To get simpler operation in modified fuzzy adaptive learning control network (FALCON) in some engineering application, sigmoid nonlinear function is employed as a substitute of traditional Gaussian membership function. For making the modified FALCON learning more efficient and stable, a simulated annealing (SA) learning coefficient is introduced into learning algorithm. At first, the basic concepts and main advantages of FALCON were briefly reviewed. Subsequently, the topological structure and nodes operation were illustrated; the gradient-descent learning algorithm with SA learning coefficient was derived; and the distinctions between the archetype and the modification were analyzed. Eventually, the significance and worthiness of the modified FALCON were validated by its application to probability prediction of anode effect in aluminium electrolysis cells. 展开更多
关键词 fuzzy adaptive learning control network (FALCON) topological structure learning algorithm sigmoid function gaussian function simulated annealing (SA)
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Chinese Surveying and Control Network for Earth-Orbit Satellites and Deep Space Detection
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作者 WEI Erhu LIU Jingnan SHI Chuang 《Geo-Spatial Information Science》 2006年第1期6-12,37,共8页
The relationship between the surveying and contro l network(CSN) for earth-orbit satellite and spatial geodesy, and the relationshi p between the CSN for deep space celestial bodies and detectors, and deep space detec... The relationship between the surveying and contro l network(CSN) for earth-orbit satellite and spatial geodesy, and the relationshi p between the CSN for deep space celestial bodies and detectors, and deep space detection are briefly summarized, and so are the basic technical needs of the de ep space surveying and control network(DSN). Then, the techniques, the constitue nts and the distributing of Chinese satellite CSN (CSCSN) and other radio observ ing establishments in China are introduced. Lastly, with the primary CSCSN and o ther observing establishments, some projects for China to rebuild a more perfect CSCSN, and to establish a DSN are analyzed and stated. 展开更多
关键词 satellite surveying and control network DSN microwave radio radar LLR DSCCs radio observation space-based station
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A New Intrusion Detection Algorithm AE-3WD for Industrial Control Network
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作者 Yongzhong Li Cong Li +1 位作者 Yuheng Li Shipeng Zhang 《Journal of New Media》 2022年第4期205-217,共13页
In this paper,we propose a intrusion detection algorithm based on auto-encoder and three-way decisions(AE-3WD)for industrial control networks,aiming at the security problem of industrial control network.The ideology o... In this paper,we propose a intrusion detection algorithm based on auto-encoder and three-way decisions(AE-3WD)for industrial control networks,aiming at the security problem of industrial control network.The ideology of deep learning is similar to the idea of intrusion detection.Deep learning is a kind of intelligent algorithm and has the ability of automatically learning.It uses self-learning to enhance the experience and dynamic classification capabilities.We use deep learning to improve the intrusion detection rate and reduce the false alarm rate through learning,a denoising AutoEncoder and three-way decisions intrusion detection method AE-3WD is proposed to improve intrusion detection accuracy.In the processing,deep learning AutoEncoder is used to extract the features of high-dimensional data by combining the coefficient penalty and reconstruction loss function of the encode layer during the training mode.A multi-feature space can be constructed by multiple feature extractions from AutoEncoder,and then a decision for intrusion behavior or normal behavior is made by three-way decisions.NSL-KDD data sets are used to the experiments.The experiment results prove that our proposed method can extract meaningful features and effectively improve the performance of intrusion detection. 展开更多
关键词 Industrial control network security intrusion detection deep learning AutoEncoder three-way decision
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基于Control Net网通讯的传输方式研究及应用
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作者 郑明辉 李伟 陈梦竹 《港工技术》 2020年第S02期32-34,共3页
在散货码头控制系统中,受场区控制设备安装范围影响,结合整体网络设备的统一性,控制网设备选型往往受到一定的影响,控制网的多模光纤传输距离与控制网覆盖范围成为网络传输过程中的一个问题。本文通过控制网络在距离长、限制多的情况下... 在散货码头控制系统中,受场区控制设备安装范围影响,结合整体网络设备的统一性,控制网设备选型往往受到一定的影响,控制网的多模光纤传输距离与控制网覆盖范围成为网络传输过程中的一个问题。本文通过控制网络在距离长、限制多的情况下的优化搭接,解决多模光纤控制网远距离传输方式。 展开更多
关键词 控制网 优化 数据传输 control net
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Disrupted functional connectivity of default mode network and executive control network in patients with vascular cognitive impairment, no dementia
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作者 Tan Zhao Jianping Jia 《Journal of Translational Neuroscience》 2017年第3期39-48,共10页
Objective: To investigate functional connectivity within default mode network (DMN) and ex-ecutive control network (ECN) in vascular cognitive im-pairment, no dementia (VCIND). Methods: Twenty-eight VCIND pati... Objective: To investigate functional connectivity within default mode network (DMN) and ex-ecutive control network (ECN) in vascular cognitive im-pairment, no dementia (VCIND). Methods: Twenty-eight VCIND patients and sixteen healthy controls were recruit-ed. A seed-based connectivity analysis was performed us-ing data from resting-state functional magnetic resonance imaging (fMRI). Based on previous fndings, posteriorcingulate cortex (PCC) and dorsolateral prefrontal cortex (DLPFC) were chosen as regions of interest to study these networks.One-sample t-test and two-sample t-test were used for statistical analysis. Results: Compared with thecontrols, the VCIND group exhibited increased functional activity in such DMN regions as the left inferior temporal gyrus, parahippocampal gyrus, and medial frontal gyrus. The VCIND group had decreased functional connectivity of DMN at right superior frontal gyrus, left mid-cingu-late area, the medial part of left superior frontal gyrus, and bilateral medial frontal gyrus. The VCIND group also showed decreased functional connectivity of ECN pri-marilyat left inferior parietal gyrus, right angular gyrus, right middle occipital gyrus, and right middle frontal cor-tex. Conclusions: Increased functional connectivity with-in DMN and decreased functional connectivity within ECN suggested dysfunction of these two networks, which mightbe associated with the cognitive defcitsin patients with VCIND. These fndingsmay help usunderstandthe pathogenesis and clinical characteristics of VCIND. 展开更多
关键词 vascular cognitive impairment (VCI) VCI no dementia (VCIND) functional connectivity de-fault mode network executive control network
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Discussion on Selection of Control Network Layout Scheme for Super Large Bridge
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作者 ZHANG Zhenji WU Hao CUI Jinghan 《外文科技期刊数据库(文摘版)工程技术》 2021年第2期277-282,共6页
With the rapid and comprehensive development of China's high-speed railway passenger transport, China's railway bridge construction has also made rapid progress. The high demand of bridge construction urges us... With the rapid and comprehensive development of China's high-speed railway passenger transport, China's railway bridge construction has also made rapid progress. The high demand of bridge construction urges us to have a high standard of construction quality, among which the layout of bridge construction control network and the calculation of construction lofting points are very important links. High-precision construction control network and accurate calculation are the necessary prerequisites for high-quality construction. This pap summarizes that selection of control network layout plan and the key points of quality control in the process. 展开更多
关键词 BRIDGE control network plane control elevation control
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Control Net网络在电厂水处理系统中的应用 被引量:7
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作者 张双城 《自动化仪表》 CAS 2005年第12期53-54,共2页
AB公司的PLC产品的网络功能强大,在实际应用中,可以根据不同情况灵活的运用,Control Net网络在华能太仓电厂水处理系统中得到成功应用,本文介绍在一期工程,二期扩建工程以及一期和二期之间的互连过程中,Control Net网络的应用。
关键词 PIE control-net 网络技术
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Accuracy Control Method of Long Distance Tunnel Plane Control Network
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作者 CHEN Xin 《外文科技期刊数据库(文摘版)工程技术》 2021年第6期339-342,共7页
With the continuous acceleration of the urbanization process, the development of underground space around the rapid development, rail transit tunnel construction is increasingly perfect. In recent years, the construct... With the continuous acceleration of the urbanization process, the development of underground space around the rapid development, rail transit tunnel construction is increasingly perfect. In recent years, the construction of long and ultra-long distance tunnels is becoming more and more common, and the accuracy requirements are constantly improving. As one of the important difficulties affecting the penetration accuracy, the improvement of the tunnel underground plane control network accuracy is the key issue discussed in this paper. By introducing three methods to improve the accuracy and applying new technology to the long distance tunnel construction survey, combined with the project construction example, it is analyzed that the above three methods can improve the accuracy of the underground plane control network of long distance tunnel, meet the requirement of through-through control, and ensure the quality of the project. 展开更多
关键词 long distance tunnel downhole plane control network PRECISION penetration accuracy adjustment
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Problems and Suggestions in the Use of Track Control Network of Beijing Zhangjiakou High Speed Railway
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作者 LI Fan ZHONG Zhuogang +1 位作者 WANG Jiahui ZHENG Shunhang 《外文科技期刊数据库(文摘版)工程技术》 2021年第9期811-815,共8页
The Beijing-Zhangjiakou high-speed railway starts from Beijingbei railway station and ends at Zhangjiakou station, Zhangjiakou city. Changping workshop of high-speed railway of Beijing track maintenance division has t... The Beijing-Zhangjiakou high-speed railway starts from Beijingbei railway station and ends at Zhangjiakou station, Zhangjiakou city. Changping workshop of high-speed railway of Beijing track maintenance division has the jurisdiction of about 122.3km (including Yanqing railway). According to the site situation, this paper summarizes and analyzes the problems in the use of the track control network (CPIII) in this section, and puts forward some improvement suggestions based on the experience, hoping to provide some enlightenment for the design of the high-speed railway precision measurement network in the future. 展开更多
关键词 Beijing-Zhangjiakou high-speed railway Beijing track maintenance division rail control network
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Best bounds on the distance between 3-direction quartic box spline surface and its control net 被引量:2
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作者 ZENG Xiao-ming ZHOU Guo-rong YANG Lian-qiang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2013年第2期147-157,共11页
We present the best bounds on the distance between 3-direction quartic box spline surface patch and its control net by means of analysis and computing for the basis functions of 3-direction quartic box spline surface.... We present the best bounds on the distance between 3-direction quartic box spline surface patch and its control net by means of analysis and computing for the basis functions of 3-direction quartic box spline surface.Both the local bounds and the global bounds are given by the maximum norm of the first differences or second differences or mixed differences of the control points of the surface patch. 展开更多
关键词 Box spline BOUND parametric surface basis function differences of control point.
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