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Empowering Underground Utility Tunnel Operation and Maintenance with Data Intelligence:Risk Factors,Prospects,and Challenges 被引量:1
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作者 Jie Zou Ping Wu +2 位作者 Jianwei Chen Weijie Fan Yidong Xu 《Structural Durability & Health Monitoring》 2025年第3期441-471,共31页
As an essential part of the urban infrastructure,underground utility tunnels have a long service life,complex structural performance evolution and dynamic changes both inside and outside the tunnel.These combined fact... As an essential part of the urban infrastructure,underground utility tunnels have a long service life,complex structural performance evolution and dynamic changes both inside and outside the tunnel.These combined factors result in a wide variety of disaster risks during the operation and maintenance phase,which make risk management and control particularly challenging.This work first reviews three common representative disaster factors during the operation and maintenance period:settlement,earthquakes,and explosions.It summarizes the causes of disasters,key technologies,and research methods.Then,it delves into the research on the intelligent operation and maintenance architecture for utility tunnels.Additionally,it explores the data challenges,monitoring technologies,and management platform architectures faced during the operation and maintenance process.This work provides new research perspectives for the long-term,healthy,and sustainable development of utility tunnels,which serve as the underground arteries of cities. 展开更多
关键词 Integrated utility tunnels operational hazards critical technologies intelligent maintenance smart platforms
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Research on Innovative Strategies and Application Practices for the Operation and Maintenance of Hydropower Plants
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作者 Du Li Yang Gao Huabo Zhu 《Journal of Electronic Research and Application》 2025年第4期184-189,共6页
In the context of energy structure transformation,digital and intelligent technologies have been introduced into the field of hydropower,which has accelerated the technological and equipment innovation of hydropower p... In the context of energy structure transformation,digital and intelligent technologies have been introduced into the field of hydropower,which has accelerated the technological and equipment innovation of hydropower plants.However,it has also brought severe challenges to the operation and maintenance of hydropower plants.Traditional hydropower plant operation and maintenance suffer from problems such as low efficiency,equipment aging,and high labor costs,which seriously hinder the innovation and upgrading of hydropower plant operation and maintenance.Therefore,this article focuses on the operation and maintenance of hydropower plants,summarizes a series of innovative strategies,and applies them in practice to effectively improve the operation and maintenance level of hydropower plants. 展开更多
关键词 Application practice Innovative strategy operation and maintenance Hydropower plant
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An Intelligent Operation and Maintenance System for Photovoltaic Station
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作者 Qing Yi Jiayou Sun +4 位作者 Shanying Su Houzhi Wei Ke Wang Zhihui Qi Siyu Teng 《Journal of Electronic Research and Application》 2025年第6期279-286,共8页
The rapid expansion of photovoltaic(PV)deployment poses new challenges for large-scale and distributed maintenance,particularly in fishery-PV complementary plants where panels are deployed over water surfaces.This pap... The rapid expansion of photovoltaic(PV)deployment poses new challenges for large-scale and distributed maintenance,particularly in fishery-PV complementary plants where panels are deployed over water surfaces.This paper presents the design and implementation of an intelligent operation and maintenance(O&M)system that integrates a 3D holographic digital twin cloud platform with UAV-assisted inspection and localized cleaning.The proposed system supports multi-source data acquisition,including UAV imagery,infrared sensing,and DustIQ-based soiling monitoring,and provides real-time visualization of the PV plant through 1:13D reconstruction.UAVs are employed for both autonomous inspections,covering defects such as soiling,bird droppings,bypass diode faults,and panel disconnections and targeted cleaning in small water-covered areas.Field trials were conducted at Riyue and Chebu PV plants,with small-scale UAV cleaning validation in Chebu fish ponds.Results demonstrated that the system achieves efficient task scheduling,fault detection,and localized cleaning,thereby improving O&M efficiency,reducing costs,and enabling digitalized and intelligent management for large-scale PV stations. 展开更多
关键词 Photovoltaic station Unmanned aerial vehicles operation and maintenance system
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Research on the Application of Digital Twin Technology in the Full Lifecycle Operation and Maintenance Management of Urban Road Infrastructure
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作者 Honghe Xian Jiayi Wang 《Journal of Architectural Research and Development》 2025年第6期29-35,共7页
With the continuous development of digital technology,urban management and urban construction have undergone tremendous changes,exerting a profound impact on people’s lives.As a vital component of cities,urban road i... With the continuous development of digital technology,urban management and urban construction have undergone tremendous changes,exerting a profound impact on people’s lives.As a vital component of cities,urban road infrastructure is closely related to the daily lives of citizens.The application of digital twin technology can provide more support for the full lifecycle operation and maintenance management of urban road infrastructure,effectively improving the quality and efficiency of operation and maintenance management,ensuring the effectiveness of urban road infrastructure,and building a higher-quality urban life.Based on urban road infrastructure,this paper analyzes the application value of digital twin technology,proposes strategies for full lifecycle operation and maintenance management,and offers more references for urban construction. 展开更多
关键词 Digital twin technology Urban roads INFRASTRUCTURE Full lifecycle operation and maintenance management
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Research on Construction Operation and Maintenance Management Based on BIM Technology
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作者 Sisi Qian 《Journal of World Architecture》 2025年第1期40-46,共7页
With the rapid advancement of information technology,Building Information Modeling(BIM)is being increasingly utilized in the construction industry,demonstrating significant potential and value in construction operatio... With the rapid advancement of information technology,Building Information Modeling(BIM)is being increasingly utilized in the construction industry,demonstrating significant potential and value in construction operations and maintenance management.Based on this,this paper conducts an in-depth discussion on BIM technology in building operation and maintenance management,analyzing its challenges and countermeasures,with the aim of providing readers with useful insights and references. 展开更多
关键词 BIM technology Building operation and maintenance management Information integration
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Application and Research of Electrical Fault Diagnosis and Operation and Maintenance Technology in Mechanical and Electrical Engineering of Property Services
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作者 Runfeng Zhou 《Journal of Electronic Research and Application》 2025年第6期250-258,共9页
This paper focuses on electrical fault diagnosis and operation and maintenance technology in property service electromechanical engineering.It details core diagnostic methods,application-oriented tools,predictive main... This paper focuses on electrical fault diagnosis and operation and maintenance technology in property service electromechanical engineering.It details core diagnostic methods,application-oriented tools,predictive maintenance frameworks,and enhanced maintenance planning.It also explores wireless sensor networks,big data analytics,and design-phase applications.Case studies in construction and operation phases are presented.Challenges like legacy system retrofitting are noted,and future potential in quantum sensing and edge AI is discussed. 展开更多
关键词 Electrical fault diagnosis operation and maintenance Property service electromechanical engineering
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AI-Based Intelligent Information System Operation and Maintenance
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作者 Sihao Huang 《Journal of Electronic Research and Application》 2025年第6期65-71,共7页
This paper focuses on AI intelligence as the fundamental direction to conduct research on information system operation and maintenance(O&M).Combining current AI-supported technologies in information system O&M... This paper focuses on AI intelligence as the fundamental direction to conduct research on information system operation and maintenance(O&M).Combining current AI-supported technologies in information system O&M,it proposes O&M strategies such as intelligent fault prediction and diagnosis,intelligent system performance optimization,intelligent system security protection,and adaptive system O&M implementation.Practical applications reveal that AI intelligence technology offers significant advantages in information system O&M,effectively addressing pain points of traditional O&M techniques,such as low fault prediction rates,slow repair speeds,poor security interception,and high labor costs.This substantially enhances the effectiveness of information system O&M. 展开更多
关键词 Information system operation and maintenance INTELLIGENCE Fault prediction and diagnosis Performance optimization Security protection
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Innovative Models for Construction and Pipeline Operation and Maintenance of Water Plants Driven by Smart Water Management
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作者 Jingyi Shi 《Journal of Architectural Research and Development》 2025年第5期63-68,共6页
This article elaborates on the application of smart water management in the construction of water plants and the operation and maintenance of pipeline networks,covering all layers of the technical framework,including ... This article elaborates on the application of smart water management in the construction of water plants and the operation and maintenance of pipeline networks,covering all layers of the technical framework,including IoT perception.It introduces full chain application scenarios,such as water source monitoring.It also involves BIM,intelligent IoT device applications,breakthroughs in pipeline monitoring system construction and operation technology,as well as the economic cost-effectiveness of innovative models,evaluation index systems,system iteration and upgrading strategies,and points out limitations and future development directions. 展开更多
关键词 Smart water management Construction and operation and maintenance Technical framework
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Optimization of Water Supply and Drainage System:Coordinated Development of Pipeline Network Maintenance and Sewage Plant Expansion and Operation
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作者 Jianwei Deng 《Journal of Architectural Research and Development》 2025年第5期29-35,共7页
This article focuses on the optimization of water supply and drainage systems,involving theories such as hydraulic models of pipeline systems and multi-objective collaborative optimization.It introduces the system dyn... This article focuses on the optimization of water supply and drainage systems,involving theories such as hydraulic models of pipeline systems and multi-objective collaborative optimization.It introduces the system dynamics model of sewage treatment facility expansion.Elaborating on detection technology,construction of an intelligent operation and maintenance system,and factors to be considered for sewage plant expansion,it emphasizes the importance of collaborative development and verifies benefits through the PSR model. 展开更多
关键词 Water supply and drainage system Pipeline network maintenance Expansion of sewage treatment plant
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Adaptive-length data-driven predictive control for post-operation of space robot non-cooperative target capture with disturbances 被引量:1
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作者 Peiji WANG Bicheng CAI +2 位作者 Chengfei YUE Yong ZHAO Weiren WU 《Chinese Journal of Aeronautics》 2026年第2期485-498,共14页
This paper solves the problem of model-free dual-arm space robot maneuvering after non-cooperative target capture under high control quality requirements.The explicit system model is unavailable,and the maneuvering mi... This paper solves the problem of model-free dual-arm space robot maneuvering after non-cooperative target capture under high control quality requirements.The explicit system model is unavailable,and the maneuvering mission is disturbed by the measurement noise and the target adversarial behavior.To address these problems,a model-free Combined Adaptive-length Datadriven Predictive Controller(CADPC)is proposed.It consists of a separated subsystem identification method and a combined predictive control strategy.The subsystem identification method is composed of an adaptive data length,thereby reducing sensitivity to undetermined measurement noises and disturbances.Based on the subsystem identification,the combined predictive controller is established,reducing calculating resource.The stability of the CADPC is rigorously proven using the Input-to-State Stable(ISS)theorem and the small-gain theorem.Simulations demonstrate that CADPC effectively handles the model-free space robot post operation in the presence of significant disturbances,state measurement noise,and control input errors.It achieves improved steady-state accuracy,reduced steady-state control consumption,and minimized control input chattering. 展开更多
关键词 Combined control Data-driven predictive control Post operation Predictive control systems Space non-cooperative target capture
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Cooperative robust parallel operation of multiple actuators
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作者 XU Liang XU Xiang LIU Tao 《控制理论与应用》 北大核心 2026年第1期3-11,共9页
This paper studies cooperative robust parallel operation of multiple actuators over an undirected communication graph.The plant is modeled as an uncertain linear system,and the actuators are linear and identical.Based... This paper studies cooperative robust parallel operation of multiple actuators over an undirected communication graph.The plant is modeled as an uncertain linear system,and the actuators are linear and identical.Based on the internal model principle,a distributed dynamic output feedback control law is proposed to achieve both robust output regulation of the closed-loop system and plant input sharing among the actuators.A practical example of five motors cooperatively driving an uncertain shaft under an external load torque is presented to show the effectiveness of the proposed control law. 展开更多
关键词 cooperative parallel operation multiple actuators robust output regulation CONSENSUS
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Stochastic Differential Equation-Based Dynamic Imperfect Maintenance Strategy for Wind Turbine Systems
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作者 Hongsheng Su Zhensheng Teng Zihan Zhou 《Energy Engineering》 2026年第2期229-258,共30页
Addressing the limitations of inadequate stochastic disturbance characterization during wind turbine degradation processes that result in constrained modeling accuracy,replacement-based maintenance practices that devi... Addressing the limitations of inadequate stochastic disturbance characterization during wind turbine degradation processes that result in constrained modeling accuracy,replacement-based maintenance practices that deviate from actual operational conditions,and static maintenance strategies that fail to adapt to accelerated deterioration trends leading to suboptimal remaining useful life utilization,this study proposes a Time-Based Incomplete Maintenance(TBIM)strategy incorporating reliability constraints through stochastic differential equations(SDE).By quantifying stochastic interference via Brownian motion terms and characterizing nonlinear degradation features through state influence rate functions,a high-precision SDE degradation model is constructed,achieving 16%residual reduction compared to conventional ordinary differential equation(ODE)methods.The introduction of age reduction factors and failure rate growth factors establishes an incomplete maintenance mechanism that transcends traditional“as-good-as-new”assumptions,with the TBIM model demonstrating an additional 8.5%residual reduction relative to baseline SDE approaches.A dynamic maintenance interval optimization model driven by dual parameters—preventive maintenance threshold R_(p) and replacement threshold R_(r)—is designed to achieve synergistic optimization of equipment reliability and maintenance economics.Experimental validation demonstrates that the optimized TBIM extends equipment lifespan by 4.4%and reducesmaintenance costs by 4.16%at R_(p)=0.80,while achieving 17.2%lifespan enhancement and 14.6%cost reduction at R_(p)=0.90.This methodology provides a solution for wind turbine preventive maintenance that integrates condition sensitivity with strategic foresight. 展开更多
关键词 Stochastic differential equations(SDE) imperfect maintenance condition-based maintenance(CBM) time-based maintenance(TBM) reliability constraint wind turbine
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A hierarchical and role-driven digital twin system with applications to complex chemical process operation
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作者 Xinyu Tao Runjie Yao +3 位作者 Lingyu Zhu Changrui Xie Muqian Zhang Xi Chen 《Chinese Journal of Chemical Engineering》 2026年第1期302-313,共12页
Digital twin technology brings more opportunities and challenges to chemical engineering in both academic and industry.A complex process could have multiple digitalization needs,including simulation,monitoring,operato... Digital twin technology brings more opportunities and challenges to chemical engineering in both academic and industry.A complex process could have multiple digitalization needs,including simulation,monitoring,operator training,etc.;thus,a hierarchical digital twin would be a comprehensive solution to that.In this study,a novel and general framework of the digital twin is proposed for operations in process industry.With the hierarchical structure,the framework can handle various tasks driven by different roles in process industry,including managers,engineers,and operators.To complete these tasks,the framework consists of three modules:OAS(Operation Analysis System),OMS(Operation Monitoring System),and OTS(Operator Training System).Each module focuses on one unique type of demand from the staff,as well as interactions among them enabling efficient data sharing.Based on the hierarchical framework,a digital twin system is applied for one complex industrial nitration process,which successfully enhances the operation efficiency and safety in several industrial scenarios with different demands. 展开更多
关键词 Digital twin Hierarchical framework Role-driven Process operation Process modeling&optimization operator training system
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Lines Across Horizons Hainan's island-wide special customs operations are redefining boundaries to elevate opening-up
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作者 Yang Hangjun 《China Report ASEAN》 2026年第3期16-19,共4页
On December 18,2025, Hainan Free Trade Port (Hainan FTP) officially began islandwide special customs operations.Although only two months have passed since this landmark step, the shift is already visible everywhere—f... On December 18,2025, Hainan Free Trade Port (Hainan FTP) officially began islandwide special customs operations.Although only two months have passed since this landmark step, the shift is already visible everywhere—from the bustling flow of international passengers at Haikou Meilan International Airport to the steady stream of cargo vessels calling at Yangpu Port, and even in the sustained attention investors are paying to “Hainan-related” stocks.Together, these signals point to one clear conclusion:China’s largest special economic zone has entered a new phase of development. 展开更多
关键词 free trade port Special Customs operations Hainan Free Trade Port Islandwide Special Customs operations International Passengers cargo vessels INVESTORS Opening up
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An Agentic Artificial Intelligence Observer for Predictive Maintenance in Electrolysers
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作者 Abiodun Abiola Francisca Segura +1 位作者 JoséManuel Andújar Antonio Javier Barragán 《Computer Modeling in Engineering & Sciences》 2026年第3期718-749,共32页
This paper presents an artificial intelligence(AI)-based observer that combines fuzzy logic and neural networks to detect abnormalities in sensors embedded in an electrolyser.Electrolysers are hydrogen production plan... This paper presents an artificial intelligence(AI)-based observer that combines fuzzy logic and neural networks to detect abnormalities in sensors embedded in an electrolyser.Electrolysers are hydrogen production plants that require effective maintenance to guarantee suitable operation,prevent degradation,and avoid loss of efficiency.In this sense,predictive maintenance arises as one of the most advisable techniques for maintenance in electrolysers by using sensor data to predict potential abnormalities.However,if the sensor fails,there will be an incorrect forecasting of abnormalities.Among the different types of operational faults that sensors can present are drift-related faults,which are probably the most difficult to detect due to a slow but progressive loss of accuracy in measurements.Another problem with predictive maintenance is that it often requires enormous training data,which is not available at the early stage of plant operation.The developed fuzzy system is responsible for detecting faulty readings arising from drift sensor signals,while the neural network complements the function of the fuzzy system by predicting sensor signals when enough training data are available.The AI-based observer and the fuzzy rules are validated in an experimental case study with a 1 Nm^(3)/h electrolyser.The selected variables are electrolyser temperature and efficiency.Experimental results show that the rules of the fuzzy component of the AI-based observer guarantee an accuracy of±0.25 within the range of 0 to 1,and the neural network component predicted correct sensor values with a root mean square error(RMSE)as low as 0.0016.The authors’approach helps to determine drift faults without additional sensors or components installed in the plant. 展开更多
关键词 Electrolysis plant predictive maintenance artificial intelligence-based observer fuzzy system long short-term memory(LSTM) neural network
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An Integrated Approach to Condition-Based Maintenance Decision-Making of Planetary Gearboxes: Combining Temporal Convolutional Network Auto Encoders with Wiener Process
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作者 Bo Zhu Enzhi Dong +3 位作者 Zhonghua Cheng Xianbiao Zhan Kexin Jiang Rongcai Wang 《Computers, Materials & Continua》 2026年第1期661-686,共26页
With the increasing complexity of industrial automation,planetary gearboxes play a vital role in largescale equipment transmission systems,directly impacting operational efficiency and safety.Traditional maintenance s... With the increasing complexity of industrial automation,planetary gearboxes play a vital role in largescale equipment transmission systems,directly impacting operational efficiency and safety.Traditional maintenance strategies often struggle to accurately predict the degradation process of equipment,leading to excessive maintenance costs or potential failure risks.However,existing prediction methods based on statistical models are difficult to adapt to nonlinear degradation processes.To address these challenges,this study proposes a novel condition-based maintenance framework for planetary gearboxes.A comprehensive full-lifecycle degradation experiment was conducted to collect raw vibration signals,which were then processed using a temporal convolutional network autoencoder with multi-scale perception capability to extract deep temporal degradation features,enabling the collaborative extraction of longperiod meshing frequencies and short-term impact features from the vibration signals.Kernel principal component analysis was employed to fuse and normalize these features,enhancing the characterization of degradation progression.A nonlinear Wiener process was used to model the degradation trajectory,with a threshold decay function introduced to dynamically adjust maintenance strategies,and model parameters optimized through maximum likelihood estimation.Meanwhile,the maintenance strategy was optimized to minimize costs per unit time,determining the optimal maintenance timing and preventive maintenance threshold.The comprehensive indicator of degradation trends extracted by this method reaches 0.756,which is 41.2%higher than that of traditional time-domain features;the dynamic threshold strategy reduces the maintenance cost per unit time to 55.56,which is 8.9%better than that of the static threshold optimization.Experimental results demonstrate significant reductions in maintenance costs while enhancing system reliability and safety.This study realizes the organic integration of deep learning and reliability theory in the maintenance of planetary gearboxes,provides an interpretable solution for the predictive maintenance of complex mechanical systems,and promotes the development of condition-based maintenance strategies for planetary gearboxes. 展开更多
关键词 Temporal convolutional network autoencoder full lifecycle degradation experiment nonlinear Wiener process condition-based maintenance decision-making fault monitoring
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Preparation of digital-encoded and analog-encoded quantum states corresponding to matrix operations
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作者 Kaitian Gao Youlong Yang Zhenye Du 《Chinese Physics B》 2026年第1期332-344,共13页
Efficient implementation of fundamental matrix operations on quantum computers,such as matrix products and Hadamard operations,holds significant potential for accelerating machine learning algorithms.A critical prereq... Efficient implementation of fundamental matrix operations on quantum computers,such as matrix products and Hadamard operations,holds significant potential for accelerating machine learning algorithms.A critical prerequisite for quantum implementations is the effective encoding of classical data into quantum states.We propose two quantum computing frameworks for preparing the distinct encoded states corresponding to matrix operations,including the matrix product,matrix sum,matrix Hadamard product and division.Quantum algorithms based on the digital encoding computing framework are capable of implementing the matrix Hadamard operation with a time complexity of O(poly log(mn/ε))and the matrix product with a time complexity of O(poly log(mnl/ε)),achieving an exponential speedup in contrast to the classical methods of O(mn)and O(mnl).Quantum algorithms based on the analog-encoding framework are capable of implementing the matrix Hadamard operation with a time complexity of O(k_(1)√mn·poly log(mn/ε))and the matrix product with a time complexity of O(k_(2)√1·poly log(mnl/ε)),where k_(1)and k_(2)are coefficients correlated with the elements of the matrix,achieving a square speedup in contrast to the classical counterparts.As applications,we construct an oracle that can access the trace of a matrix within logarithmic time,and propose several algorithms to respectively estimate the trace of a matrix,the trace of the product of two matrices,and the trace inner product of two matrices within logarithmic time. 展开更多
关键词 quantum algorithm matrix operation digital and analog-encoded states quantum computing
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Research on Operation Strategies of Trade Publishing Knowledge Service Platform Based on the SICAS Model:A Case Study of CITIC Academy
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作者 WANG Jun ZHOU Xiaoyi 《Cultural and Religious Studies》 2026年第1期13-21,共9页
Amidst evolving user behavior driven by the development of the internet,enhancing the operational quality of trade publishing knowledge service platforms has become a significant challenge for publishing institutions.... Amidst evolving user behavior driven by the development of the internet,enhancing the operational quality of trade publishing knowledge service platforms has become a significant challenge for publishing institutions.To address this issue,this paper employs a combined approach of theoretical analysis and case study,introducing the SICAS(Sense-Interest-Connection-Action-Share)user consumption behavior analysis model and selecting“CITIC Academy”as the case study subject.It systematically examines and summarizes the platform’s operational practices and specific strategies,aiming to offer strategic insights and practical references for the operational improvement and sustainable,high-quality development of trade publishing knowledge service platforms. 展开更多
关键词 trade publishing knowledge service platform SICAS model operation strategy CITIC Academy
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Unit Commitment with Concentrating Solar Power Considering Operational Risk and Frequency Dynamic Constraints
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作者 Yuchen Fang Ershun Du +3 位作者 Haiyang Jiang Fei Liu Xu Tian Ning Zhang 《CSEE Journal of Power and Energy Systems》 2026年第1期230-243,共14页
The large-scale integration of power electronic interface-based renewable energy with intermittency and uncertainty poses severe challenges for power system secure operation,especially frequency security.Determining t... The large-scale integration of power electronic interface-based renewable energy with intermittency and uncertainty poses severe challenges for power system secure operation,especially frequency security.Determining the system frequency regulation ability under contingency is an open problem.To bridge this gap,a unit commitment(UC)to concentrate solar power considering operational risk and frequency dynamic constraints(RFUC-CSP)is proposed in this paper.A concentrating solar power(CSP)plant with renewable energy characteristics and synchronous units is employed to improve renewable energy utilization and provide frequency support.Firstly,an analytical operational risk model is established to quantify the operational risk under renewable energy integration.Then,the frequency dynamic response characteristic of the system is considered to construct frequency security constraints.A novel RFUC-CSP framework is formulated by incorporating operational risk and frequency security constraints into the UC model,which can allocate operational flexibility of power systems by optimizing the admissible uncertainty level to reduce operational risk.The effectiveness of the proposed RFUC-CSP model is demonstrated by case studies on the modified IEEE 30-bus and IEEE RTS-79 system,and the cost-effectiveness of the CSP plant is quantified. 展开更多
关键词 Concentrating solar power frequency dynamics operational risk power system inertia unit commitment
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Splitting of Operations for Di-Associative Algebras and Tri-Associative Algebras
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作者 Wen TENG Xiansheng DAI 《Journal of Mathematical Research with Applications》 2026年第1期21-32,共12页
Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algeb... Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras. 展开更多
关键词 dendriform algebra di-associative algebra quad-dendriform algebra tri-associative algebra six-dendriform algebra relative averaging operator
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