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analytical algorithm for Capacities of Classical and Classical-Quantum Channels

IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第3期69卷 1381-1393页

作者： Hayashi, Masahito Southern Univ Sci & Technol Shenzhen Inst Quantum Sci & Engn Shenzhen Nanshan Peoples R China

We derive an analytical algorithm for the channel capacity of a classical channel without any iteration, while its existing algorithms require iterations and the number of iterations depends on the required precision level. Hence, our algorithm is its first analytical algorithm for this task without any iteration, while this algorithm needs several conditions for the channel. We apply the obtained algorithm to examples, and see how the obtained algorithm works in these examples. Then, we extend it to the channel capacity of a classical-quantum (cq-) channel. Many existing studies proposed algorithms for a cq-channel and all of them require iterations. Our extended analytical algorithm has also no iteration, and outputs the exactly optimum value.

关键词： Channel capacity Approximation algorithms STEM Mathematical models Complexity theory Iterative algorithms Upper bound Mutual information maximization channel capacity classical-quantum channel analytical algorithm

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Main beam positioning and posture analysis under the hinge influence for suspension bridges with short extended spans in the splicing construction state: An analytical algorithm

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ENGINEERING STRUCTURES 2025年 326卷

作者： Zhang, Wen-ming Wang, Zhen-ping Zhang, Xiao-yi Tian, Gen-min Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 210096 Peoples R China

In suspension bridges with short extended spans, the main beam in the side spans is usually installed before that in the main span. Splicing of the main beam in the main and side spans is commonly performed at the site of towers after the main beam erection is completed in the main span, in order to reduce the main beam construction period. The position and posture of the main beam in the side spans are determined by the line shape of the main span. In the splicing construction state, some beam segments in the main beam are still connected by hinges. The number and position of hinges will affect the line shape of the main beam in the main span. As the line shape varies, the position and inclination angle of the end face of the main beam change accordingly at the site of the splice, further affecting the construction schedule and precision. Addressing the above issue, this study proposes an analytical algorithm for solving the main beam's line shape and internal force, considering the number and position of hinges. Using the known parameters of the completed bridge state, the main cable deformation, main beam deformation, hanger inclination, and tower saddle pre-offset are successively derived. Governing equations are constructed based on different conditions: conservation of unstrained length of main cable in different spans, compatibility between hanger forces and hanger deformation, closure of span lengths, closure of elevation differences, and force equilibrium in the main beam. These governing equations are combined into one objective function, and the basic unknown parameters are solved as a programming problem. Once the above parameters are derived, the line shape of the main beam and inclination angle and position of the beam-end face at the splice site are calculated. The proposed method is then applied to a suspension bridge with short extended spans with a span length layout of 100 m+ 1080 m+ 100 m as a verification.

关键词： Suspension bridge Short extended spans Splicing construction state Line shape analytical algorithm

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An analytical algorithm for assessing dynamic characteristics of a triple-tower double-cable suspension bridge

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STRUCTURAL ENGINEERING AND MECHANICS 2024年第4期90卷 325-343页

作者： Zhang, Wen-ming Chen, Yu-peng Wang, Shi-han Lu, Xiao-fan Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 211189 Peoples R China Southeast Univ State Key Lab Safety Durabil & Hlth Operat Long Sp Nanjing 210096 Peoples R China

Triple -tower double -cable suspension bridges have increased confinement stiffness imposed by the main cable on the middle tower, which has bright application prospects. However, vertical bending and torsional vibrations of the double -cable and the girder are coupled in such bridges due to the hangers. In particular, the bending vibration of the towers in the longitudinal direction and torsional vibrations about the vertical axis influence the vertical bending and torsional vibrations of the stiffening girders, respectively. The conventional analytical algorithm for assessing the dynamic features of the suspension bridge is not directly applicable to this type of bridge. This study attempts to mitigate this problem by introducing an analytical algorithm for solving the triple -tower double -cable suspension bridge's natural frequencies and mode shapes. D'Alembert's principle is employed to construct the differential equations of the vertical bending and torsional vibrations of the stiffening girder continuum in each span. Vibrations of stiffening girders in each span are interrelated via the vibrations of the main cables and the bridge towers. On this basis, the natural frequencies and mode shapes are derived by separating variables. The proposed algorithm is then applied to an engineering example. The natural frequencies and mode shapes of vertical bending and torsional vibrations derived by the analytical algorithm agreed well with calculations via the finite element method. The fundamental frequency of vertical bending and first- and second -order torsion frequencies of double -cable suspension bridges are much higher than those of single -cable suspension bridges. The analytical algorithm has high computational efficiency and calculation accuracy, which can provide a reference for selecting appropriate structural parameters to meet the requirements of dynamics during the preliminary design.

关键词： analytical algorithm double-cable dynamic characteristics free vibration suspension bridge triple-tower

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analytical algorithm for determining anchor span strand tensions in the suspension bridge's free-cable state

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STRUCTURES 2024年 65卷

作者： Zhang, Wen-ming Zhang, Xiao-yi Chen, Yu-peng Shen, Xing-hang Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 211189 Peoples R China

Anchor span strand tensions have a large bearing on the overall structural safety of the suspension bridge. Precise estimation of anchor span strand tensions and construction parameters in the free-cable state is critical for geometric form design of main cable and for realizing proper strand tensions in the completed bridge state. Given the complex geometric form of anchor span strands, calculating strand tensions remains highly challenging. To calculate strand tensions in the anchor span in the free-cable state, a system of equations is built based on geometric compatibility conditions and mechanical equilibrium conditions in the anchor span. The calculation of anchor span strand tensions in the free-cable state requires using the unstrained lengths of strands in the completed bridge state, which links the free-cable state with the completed bridge state. This study proposes an analytical algorithm for the unstrained lengths of the anchor span strands. Strand tension is calculated from the three-dimensional steering angle because the anchor span strand has a spatial geometric form. Then, the strand elongation is estimated, and the unstrained length of the strand is obtained accordingly. Based on the conservation of the unstrained lengths of strands, we further estimate the strand tension in the anchor span and the prerotation angle of the splay saddle in the free-cable state. The above calculation of parameters lays a solid foundation for suspension bridge construction. The proposed method is applied to the engineering case of the Jindong Bridge with a main span of 730 m in Kunming, China, to verify the algorithm's feasibility.

关键词： Suspension bridge Anchor span Strand tension Free-cable state analytical algorithm

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Determination of main cable shape and hanger tensions of a suspension bridge based on the measured live-load deflection of the main beam: An analytical algorithm

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ENGINEERING STRUCTURES 2022年 272卷 1页

作者： Zhang, Wen-ming Chang, Jia-qi Feng, Dan-dian Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 210096 Peoples R China

Hanger tensions and the main cable shape are key parameters of suspension bridges that must be assessed during their construction and operation phases. An analytical algorithm is proposed for assessing these parameters via the measured deflection of the main beam and tower-top displacements. First, the hanger tension increments caused by the live load are derived based on the known live load and measured deflection of the main beam. Next, the hanger tensions in the initial state are determined according to the conditions for conserving the unstrained length of each main cable segment and the force-deformation coordination of each hanger with and without the live load. Finally, the main cable shape is derived from the hanger tensions in the initial state. In contrast to the conventional method, the proposed analytical approach requires no complex dynamic equations. At the same time, the expression based on static analysis has a simpler form and higher universality and practicality. The proposed approach allows for a faster and more accurate evaluation of the suspension bridge's main cable shape and hanger tensions. The feasibility and effectiveness of the proposed method are verified for an exemplary suspension bridge with a main span of 1080 m.

关键词： Suspension bridge Hanger tension Main cable shape Live load Main beam deflection analytical algorithm

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Comparative Study of Seafloor Topography Prediction from Gravity-Geologic Method and analytical algorithm

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REMOTE SENSING 2024年第17期16卷 3154-3154页

作者： Tian, Yuwei Xu, Huan Yu, Jinhai Wang, Qiuyu Jia, Yongjun Chen, Xin Univ Chinese Acad Sci Coll Earth & Planetary Sci Key Lab Computat Geodynam Beijing 100049 Peoples R China Natl Satellite Ocean Applicat Serv Beijing 100081 Peoples R China Naval Res Inst Tianjin 300061 Peoples R China

Seafloor topography prediction can fill in sea areas without ship sounding data. However, the dependence of various topographic prediction algorithms on ship soundings varies significantly. Hence, this study explores the impact of the number and distributions of ship soundings on topographic prediction using the gravity-geologic method (GGM) and an analytical algorithm. Firstly, this study investigates the influence of ship sounding coverage on the two algorithms. The simulation results demonstrate that increasing coverage from 5.40% to 31.80%, coupled with more uniform distributions across the study area, substantially reduces the RMS error of the GGM. Specifically, the RMS error decreases from 238.68 m to 42.90 m, an improvement of 82.03%. The analytical algorithm maintains a consistent RMS error of 40.39 m because it does not depend on ship soundings. Furthermore, we select a 1 degrees x 1 degrees sea area (134.8 degrees-135.8 degrees E, 30.0 degrees-31.0 degrees N), and the ship soundings are divided into two control groups, Part I and Part II, with coverages of 8.19% and 33.19%, respectively. When Part II is used for calculation, the RMS error of the GGM decreases from 204.17 m to 126.95 m compared to when Part I is used, while the analytical algorithm exhibits an RMS error of 167.94 m. The findings indicate that the prediction accuracy of the GGM is significantly affected by ship soundings, whereas the analytical algorithm is more stable and independent of ship soundings. Based on simulation experiments and realistic examples, when the effective ship soundings coverage exceeds 30%, the GGM may have more advantages. Conversely, the analytical algorithm may be better. This suggests that effectively combining and utilizing different algorithms based on the ship sounding coverage can improve the accuracy of topographic prediction. This will provide a basis for integrating multiple algorithms to construct a global seafloor topography model.

关键词： seafloor topography gravity anomaly analytical algorithm gravity-geologic method numerical simulation

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Assessment of maximum and minimum hanger forces in a triple-cable suspension bridge under live load: analytical algorithm with manta ray foraging optimization

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STRUCTURES 2024年 64卷

作者： Zhang, Wen-ming Liao, Jian-bin Chen, Yu-peng Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 211189 Peoples R China

Triple-cable suspension bridges (TCSBs) are widely used in sea-crossing, island-linking projects with extra-long spans and ultra-wide decks. Their safe operation requires sufficient resistance of all bridge components (towers, cables, girders, and hangers) to static/dead and cyclic/live loads. Therefore, reliable assessment of maximum and minimum axial forces acting on each hanger is topical. This study proposes an analytical algorithm for assessing the internal forces and deformations of a TCSB. Specific steps and formulae for solving the coefficients are described by taking the estimation of girder response under random eccentric line loading as an example. Parameters of the suspension bridge under dead load are treated as known quantities. Actual engineering scenarios, including girder displacements along the bridge, are analyzed and discussed in detail. Basic unknown quantities are determined via governing equations under conditions of elevation differences' closure and conservation of main cables' unstressed lengths, yielding direct solutions for deformations of the main cables, girder, towers, and hangers. The proposed analytical model's feasibility is verified via the finite element method. Optimal solutions to the above equations are derived by the manta ray foraging optimization (MRFO) algorithm to find the most unfavorable load distributions for all vehicle lanes of the bridge and the maximum and minimum axial forces of random hangers. Finally, the proposed method is successfully applied to a TCSB with a 1600 m main span under two operating conditions. The most unfavorable load distributions and the maximum and minimum axial forces of hangers at the mid-span and at the quarter-span point are estimated. The calculation results are compared against those obtained by the influence surface method, showing their good correlation and superiority of the proposed method in computation workload.

关键词： Triple -cable suspension bridge Live load analytical algorithm Axial hanger force Internal force Displacement Most unfavorable load Influence surface Left span

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Suspension bridge deformation and internal forces under the concentrated live load: analytical algorithm

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ENGINEERING STRUCTURES 2021年 248卷 113271-113271页

作者： Zhang, Wen-ming Chang, Jia-qi Lu, Xiao-fan Tian, Gen-min Li, Jin-guo Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 210096 Peoples R China Tongji Architectural Design Grp Co Ltd Shanghai 200092 Peoples R China

Suspension bridge is a flexible structure, which responses to live loads are quite complicated due to the coupling of several factors. In this paper, an analytical algorithm is proposed for estimating the deformation and internal forces of earth-anchored suspension bridges under the concentrated live load. Based on the known parameters of the completed bridge and the live load, the deformation of the main cable, the deformation of the girder, the relationship between the main cable and the girder, and the deformation of towers are successively analyzed. Next, four categories of governing equations are set up, namely, the conservation of the unstrained length of each main cable segment, the force and deformation coordination of each hanger, the closure of length and elevation difference in each span, and the mechanical balance of the girder. The total number of governing equations is equal to that of basic unknown parameters. Finally, all the governing equations are incorporated into an objective function, and the programming solution is carried out. The values of the basic unknown parameters are determined so that all the governing equations hold true simultaneously. Based on this, all other parameters are derived and the deformed state of the structure is expressed. The proposed method's feasibility and effectiveness are verified by its application to an earth-anchored suspension bridge with a main span of 1080 m. Both the deformation and internal forces under the live load are accurately estimated using the proposed analytical algorithm, which agree well with the finite element analysis.

关键词： Suspension bridge Concentrated live load Structural deformation Internal force Governing equation analytical algorithm

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Improved analytical algorithm for Magnetic Field of End Windings in 300Mvar Synchronous Condenser

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IEEE ACCESS 2021年 9卷 85885-85893页

作者： Zhu, Erhang Liang, Yanping Han, Xiao Bian, Xu Wang, Chenguang Harbin Univ Sci & Technol Coll Elect & Elect Engn Harbin 150080 Peoples R China

The magnetic field of end windings affects the leakage reactance of end windings and the eddy current losses of end structures in the large electrical machine. With the rising of single-machine capacity, such effect becomes more obvious. However, due to the complexity of end structures of large electrical machine, it will cause difficulty in meshing and long calculation time to calculate the magnetic field of end windings by using 3-D finite element method (FEM). In order to calculate the magnetic field of end windings quickly and accurately, an improved analytical algorithm (IAA) is proposed based on the mirror image principle, which takes into account the influence of stator back core and air-gap on the magnetic field of end windings by adding the fictitious boundary current and air-gap current, respectively. Taking a 300Mvar synchronous condenser (SC) as an example, the boundary current, air-gap current and magnetic field of end windings are calculated. Then, the influence of stator back core and stator involute segment current on the magnetic field of end windings are analyzed, which provides a theoretical support for the design and optimization of SC. To validate the accuracy of IAA, the calculation result is compared with 3-D FEM.

关键词： Windings Magnetic fields Stator cores Stator windings Magnetic cores Mirrors Air gaps Synchronous condenser magnetic field analytical algorithm mirror image stator back core

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Main Cable Shape-Finding and Live Load Response of the Suspension Bridge with Central Buckles: An analytical algorithm

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JOURNAL OF BRIDGE ENGINEERING 2023年第11期28卷 04023084-04023084页

作者： Zhang, Wen-ming Shen, Xing-hang Chang, Jia-qi Southeast Univ Key Lab Concrete & Prestressed Concrete Struct Minist Educ Nanjing 211189 Peoples R China

The stiffness of suspension bridges, which are flexible systems composed of main cables and stiffening beams, is frequently increased by adding one or more pairs of central buckles in the midspan. This study examined a suspension bridge with flexible central buckles, proposing a set of analytical calculation methods for the shape-finding of the main cable under dead load and the structural deformation and internal forces under any uniform live loads. The proposed method is based on the known bridge design parameters. First, the suspender and central buckle tension of each hanging point of the stiffening beam was determined by the multipoint rigid support continuous beam method. After assigning these tensions to the suspenders and the central buckles, the multisegment catenary theory was used to derive the equation for each main cable segment in turn. The constraint equation was established through the closure condition of the height difference within the span. The equation was then transformed into an objective function to be programmatically solved, determining the completed bridge state. To determine the live load response of the bridge, the deformation and position relationships of the main cable, main beam, and bridge towers were analyzed in sequence, with known live load parameters. Five types of constraint equations were established through the conservation of the unstrained length of each main cable segment, the coordination of the force and deformation of each suspender, the coordination of the force and deformation of each central buckle, the closure of span length and height difference in each span, and the force balance of the main beam. Then, they were converted into an objective function to be programmatically solved, leading to the live load response of the structure. Finally, a case study of a suspension bridge with a main span of 1,050 m was used to verify the feasibility and effectiveness of the proposed method. The structural deformation and intern

关键词： Suspension bridge Flexible central buckle Main cable shape Uniform live load Structural deformation Internal force Constraint equation analytical algorithm

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