Cable Shape Research Articles

Improved algorithm for determining cable saddle pre-offsets considering the coupling effect of tower and splay saddles

By analysing the mechanical and geometrical relations between the main cable, tower, and splay saddles, and considering the coupling effect of the tower and splay saddles, an improved algorithm is proposed to determine the cable saddles pre-offsets of suspension bridges. The equilibrium relationship of the cable saddles, the compatible deformation condition, and the basic equation of the main cable shape are considered to establish several coupled non-linear equations up to 19, and the tower and splay saddle pre-offsets are obtained by solving the above equations with the Newton–Raphson method. This paper presents the initial value selection principle and the constraint conditions for solving the cable saddle pre-offsets of the plane cable suspension bridge and the calculation process ensures convergence. The calculation example demonstrates that the improved algorithm without an exact initial value can achieve excellent convergence.

An efficient surrogate model-based method for deep-towed seismic system optimization

The towing speed, cable length, towing depth, and hitch position should be optimized to improve the operational safety and efficiency of a deep-towed seismic system. However, the optimization is ineffective due to system nonlinearity and large-scale calculations. Therefore, a surrogate model-based method is proposed to simplify a deep-towed system and promote system optimization. The relationships among the towing speed, viscous drag and pitch angle of the towed vehicle are expressed using a surrogate model generated by using the artificial neural network method. Input variables of the surrogate model are related to the optimization variables through proper design variable selection, which generates an efficient explicit formulation. Additionally, a quasi-static iteration is established to speed up calculating the cable shape of the towing cable, and analytical models simplify the calculations of drag forces acting on the drogue and seismic array. Finally, the best design, such as the towing speed, cable length and hitch position, are obtained with limited cable tension and towing depth in a case study. This research provides an effective method for deep-towed seismic system optimization.

A New Method for Finding the Shape of the Main Cable in the Special Cable Plane

The main cable and suspender of the spatial special-shaped suspension bridge are in the state of spatial stress; the structural stress is more complex than that of the parallel cable plane and finding the shape of the main cable of the spatial special-shaped cable plane is more difficult. In order to solve the problem of finding the shape of the main cable of the special-shaped suspension bridge, a new calculation model and algorithm of the main cable are proposed in this paper. The new calculation model adds constraints on the transverse bridge direction coordinates of the midspan on the basis of the original calculation model. The new calculation model can timely correct the calculation errors in all directions of the control node during the main cable shape finding process and improve the calculation accuracy. The new algorithm is a hybrid algorithm. The algorithm first uses the modified quantum genetic algorithm to solve and calculate the cable end force close to the real value, and then uses the cable end force obtained by the modified quantum genetic algorithm as the initial value to iterate through the modified least squares method. In this paper, a single cable plane curved suspension bridge is taken as the research background, and the differences of different calculation models in the shape-finding calculation of the main cable of the spatial special-shaped cable plane are compared. The results show that the proposed model is more stable in the calculation process, and the proposed algorithm has high accuracy and strong adaptability.

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

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.

Cooperative Towing by Multi-Robot System That Maintains Welding Cable in Optimized Shape

As considerable amounts of welding are required during ship construction, robotic automation is being promoted. However, current welding robots do not automate work in high or narrow places. One reason is that welding cannot be performed with sufficient accuracy because a welding robot with a torch cannot tow a heavy cable and thus may go off path. This letter proposes a multi-robot system for automating the execution of long welds in high and narrow places to address this problem. In the proposed method, towing vehicles are placed along the supply cable to reduce the load on the lead welding vehicle. In confined-space welding, the cable must not be excessively loaded, and obstacles such as walls must be avoided. Under the proposed method, autonomous movement of the towing vehicles is achieved by solving an optimization problem that considers these aims and minimizes the amount of change from the estimated current cable shape. The method was evaluated through simulation and real-world tests, in which it was applied successfully to tow the cable with a welding torch in a working area of 2.6 × 10 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (simulation) and of 3.4 × 5.5 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (real-world environment) without disturbing the lead vehicle's movement.

Algorithm for Locating the Datum Strand of a Suspension Bridge Considering the Influence of Friction and the Change in Tangent Point of the Cable Saddle

In order to accurately simulate the position of the saddle in the analysis and calculation of a suspension bridge, and then obtain the accurate shape of the datum strand in the construction site, this paper puts forward a calculation method on the position of the saddle and the geometric shape of the datum strand on the basis of considering the friction between the main cable and the saddle. Firstly, the calculation method of friction between the main cable and cable saddle is proposed and the formula of the deviation between the coordinates of the initial position and that of the equilibrium position of the cable saddle is derived. Then, through theoretical derivation, the calculation program of cable geometric shape considering the change in saddle tangent point is compiled. Combined with the analytical algorithm, the concept of temperature telescopic bar is introduced, and a simulation method of the cable saddle and datum strand is given, which is suitable for the combination of finite element analysis and numerical algorithm. Finally, the reliability of the algorithm is verified by the comparison of a numerical example, and by changing the value of friction, the influence of friction on the saddle position and the datum strand geometric shape is analyzed.

Experimental and simulation analysis of the initial shape of a large-span air-supported membrane structure

In recent years, air-supported membrane structures have been widely used in China’s environmental protection of closed coal yards and in sports stadiums. There have been breakthroughs year by year in the numbers constructed, unit area, and span. At present, the largest span of an air-supported membrane structure coal shed has reached 198 m. As the span increases, the force-bearing performance of the structure is more closely related to its shape. In this paper, based on a 225m×198m×66m(Length × width × height) long-span air-supported membrane structure test model, the form-finding and state-finding analysis of the air-supported membrane structure with longitudinal and transverse cable nets were carried out, and the results were compared with the forming test results. The results show that the prestressed state of the structure obtained by the state-finding analysis is closer to the test results. However, there is a specific difference with the target height. At the same time, the form-finding analysis can accurately find the target height, but the structure’s cable force and section shape are quite different from the test results.

In-plane modal behavior of a single shallow flexible cable with an intermediate transverse elastic support

Cross-tie solution has been successfully applied in field to mitigate undesirable bridge stay cable vibrations, especially for cables on modern long-span cable-stayed bridges which typically have long length and relative thick cross section. In evaluating the effectiveness of the cross-tie solution and analyzing dynamic response of the formed cable network, the taut cable assumption has been used in most existing studies. Nevertheless, cable sag and bending stiffness could have non-negligible influence in networks consisting of long cables with relatively large diameter. Since a transverse cross-tie provides an elastic constraint to a vulnerable cable by connecting it with its neighbors, to fully comprehend the impact of cable sag and bending stiffness on the dynamic behavior of shallow-cable networks, it is imperative to scrutinize their effect on the behavior of a shallow cable with a transverse elastic constraint within the span. In the current study, by using the linear theory of shallow cables, an analytical model for the in-plane dynamics of a single flexible low-sag cable with an intermediate transverse elastic support is proposed. The impact of the intermediate support stiffness, location, cable bending stiffness, and sag on the in-plane modal response of the studied cable system are examined. Results show that the presence of an intermediate transverse elastic support breaks the symmetry and anti-symmetry of the original cable mode shapes, which renders the influence of sag extends to all cable modes. Further, the level of such a mode shape distortion would determine whether or not modal cross-over would occur. For any given intermediate support location, it is found that there always exists a specific level of intermediate support stiffness of which the cable sag corresponding to the occurrence of modal cross-over would be independent of cable bending stiffness. By reducing or increasing the intermediate support stiffness to be lower or higher than this specific level, the increase of cable bending stiffness would either delay modal cross-over to occur at a larger cable sag or advance its occurrence at a smaller cable sag. Reducing the intermediate support stiffness would render a local mode to evolve into a global mode, and the presence of cable bending stiffness and sag is found to allow this mode evolution to occur when a more flexible intermediate support is used.

Experimental research on submarine cable monitoring method based on MEMS sensor

In the context of the global energy internet, ocean power transmission has become the preferred method between coastal cities in various countries. However, it is easy to destroy the submarine cable due to anchoring, thus affecting the long-term use. Therefore, early detection of hidden dangers and timely maintenance can effectively reduce the huge cost of cable failure. In this article, we introduce a monitoring system based on MEMS-IMU to evaluate the possible damage of the submarine cable. Firstly, we give the structure of the system and the process of judging the health status. Secondly, we build the mathematical model to reconstruct the cable shape and analyze the torsion. Finally, experiments are conducted to ensure the accuracy and feasibility of the method. In this article, we introduces a monitoring system based on MEMS-IMU to evaluate the possible damage of the submarine cable. Firstly, we give the structure of the system and the process of judging the health status. Secondly, we build the mathematical model to reconstruct the cable shape and analyze the torsion. Finally, experiments and sea trial are conducted to ensure the accuracy and feasibility of the method. • The article puts forward the idea of a submarine cable monitoring system based on MEMS-IMU sensor array. • The article proposes the arc model to reconstruct the cable shape and the judgment basis for torsion. • The article conducts experiments to verify the monitoring accuracy and the feasibility of deep-sea applications.

UAV-based bridge geometric shape measurement using automatic bridge component detection and distributed multi-view reconstruction

UAV cameras combined with image-based reconstruction are promising non-contact tools for bridge shape inspection while computational efficiency is low, particularly on large-scale image sets. This paper describes an efficient image-based reconstruction pipeline for bridge geometry measurements. A full bridge three-dimensional reconstruction task is decomposed into multiple distributed tasks of reconstructing bridge sub-models using sub-image sets. A deep learning-based object detection method combined with Euclidean clustering is proposed to automatically generate cropped sub-image sets. An image mask generation technique based on 3D-to-2D mesh projection is used to keep valid pixels for camera pose estimation. The proposed method was validated in a laboratory test for arch shape measurement and in a field test for suspension cable shape measurement. The results show significant improvement about computational efficiency without accuracy reduction, compared with conventional image reconstruction methods.

Computer-aided optimal design for flexible cable in aerospace products based on dynamic analogy modeling

Due to large, complex deformations, the accurate design of cables has become a major problem in the manufacturing of aerospace products. The current design method often leads to large products, uncertain centroids, and poor reliability. To solve these problems, a computer-aided optimal design method for flexible cables was proposed based on dynamic analogy modeling. A nonlinear optimization model was established by combining Cosserat theory and the minimum potential energy principle. The total deformation energy was considered as the optimization object, and Euler parameters were used as control variables to describe the cable geometric shape. Considering the length and bending radius requirements, the normalized form of the cable constraints was expressed by the cross-section position and orientation matrix. An efficient method to solve this problem using finite element discretization and the primitive dual interior point method was proposed. A digital wiring module was developed based on an open source geometry kernel system, and a cable geometry test bench was built. To verify our model, a satellite wiring simulation example was implemented using the module, SolidWorks, and the test bench. Our method achieved the optimal design for the cable length and geometric shape. A theoretical and technical foundation for effectively solving the problem of large cable manufacturing errors and realizing the lightweight design of aerospace products was outlined.

Vibration of two in-plane simply supported bending cables interconnected by a flexible cross-link

ABSTRACT Most of the existing analytical solutions to the vibration of cable networks interconnected by cross-ties are developed based on string theory, where the effect of cable bending rigidity on cable vibration is ignored. However, the bending rigidity of cables strongly influences the natural frequencies and vibration mode shapes of short and stout cables and long cables at higher modes. Hence, this paper considers cable bending rigidity to form a closed-form solution that can be used in determining the natural frequencies and mode shapes of cable networks. The analytical solution of the cable network model with hinged-end boundary conditions is derived. It can be combined with other existing techniques to analyze the dynamic behaviors of a two-cable network with partly fixed supports. The analytical solution derived from this paper can be degenerated to the same solution without considering the cable bending rigidity in previous studies. The accuracy of this analytical solution considering cable bending rigidity is verified by finite element analysis. The effects of bending rigidity on the vibration frequencies and modes of the cable network with inclined and flexible cross-link are investigated in detail. This analytical solution can be applied to backward analysis to identify the cable tension of a two-cable network with partly fixed supports.

Main Cable Shape of Short Span in Three-Tower Suspension Bridge

The main cable is one of the essential components of the suspension bridge; accurate calculation of the main cable shape is crucial in constructing a suspension bridge. This paper solves the challenge of the main cable shape for a “short span” in a three-tower suspension bridge by the analytical method of the ideal bridge shape and empty cable shape of the main cable. Feng Chu suspension bridge Xiangyang is taken as a prototype. This paper discusses the main cable shape and anchor-span tension control method in the construction stage of the main cable analyzes the deflection and stress characteristics of the main tower in the hoisting stage of the stiffening beam. The influence of pushing the cable saddle on the main tower provides accurate control of the main cable shape. Design sag and span of the main cable were taken as the known quantities. The sectional catenary equation is used to deduce and iteratively calculate the completed bridge alignment. The completed bridge alignment was taken as the target, the iterative calculation method of main cable bridge alignment and empty cable alignment compiles the corresponding program with MATLAB software. The calculation values of the unstressed length of the main cable, the pre-deflection of the saddle, and the mid-span sag of the empty cable are compared with the design values. The results show that the calculation accuracy of the program is high.

Improved Algorithm to Determine the Composite Circular Curve Splay Saddle Position

By analyzing the main cable shape of the suspension bridge and the mechanical and geometric relationship between the main cable and the cable saddle, an improved algorithm is established for determining the position of the composite circular curve splay saddle. The geometric conditions of the main cable and saddle are considered to establish the equations, and the position of the composite circular curve splay saddle is obtained by solving only a one-dimensional nonlinear equation with the dichotomy method. The algorithm yields the solution interval of the dichotomy method to achieve the solution of the nonlinear equation, and the calculation process ensures convergence without any initial value. Several examples demonstrate that the improved algorithm can achieve excellent convergence.

User expectations and perceptions towards new public transport infrastructure: evaluating a cable car in Bogotá

Cable cars are a viable alternative to improve citizens’ accessibility in zones with limitations on urban public transport supply due to the topography. In Latin America, such systems have recently been implemented in zones with high levels of poverty and vulnerability. Although the social implications of their implementation are relevant, individual expectations of these systems and how current changes in travel conditions and quality of life are perceived have not been widely reported in the literature. This paper aims to evaluate users’ expectations and perceptions of a new cable car in the southern periphery of Bogotá (Colombia). We conducted a panel survey before (n = 341) and after (n = 301) the cable car started operations to evaluate the ranking of preferences toward a set of possible benefits of the project. We estimated discrete choice models to analyze the statistical differences between the expectations and perceptions before and after changes. Results suggest that travel time reductions, comfort improvements, and in-vehicle security are the benefits most valued by the users. Even though the project meets expectations of these aspects, it seems to fall short in expectations of reductions of pollution. Individuals’ experience with the cable car shapes their perceptions of the system. We found that perceptions differ between those who have used the service at least once and those who never did. Policy implications derived from this study might be of interest to decision-makers seeking to guarantee the public acceptability of urban projects.

FEM-Based Shape-Finding and Force-Assessment of Suspension Bridges via Completed Loop Adjustment

Abstract Finding the main cable shape is an essential step in the design and construction of suspension bridges. In this paper, shape-finding and force-assessment of suspension bridges based on loo...

Cable Force Determination Using Phase-Based Video Motion Magnification and Digital Image Correlation

The mode shape-aided method provides a simple and effective way for cable force determination, which, however, requires accurate parameter identification of the cable structure. This paper proposes a phase-based video motion magnification to process the image sequences of a cable. Digital image correlations were engaged to measure the dynamic displacement–time history, through tracking the surface characteristic features of the cable. Thereafter, a frequency–domain decomposition technique was applied to extract the natural frequency and mode shape of the cable from the displacement–time history measurements. The identified cable mode shapes, along with a tensioned pinned-pinned cable model, were used to estimate the cable force. The accuracy of the proposed methodology was subsequently verified through laboratory testing on an inclined cable model and field testing on a typical hanger cable of a real-world arch bridge. Overall, the study results indicated that the proposed methodology could expediently and cost-effectively estimate the tension forces of a cable with reasonably acceptable identification accuracy.

Real-time trace of riser profile and stress with numerical inclinometers

In this paper, the methodology for the real-time tracing of riser profile and bending moment by multiple inclinometers along the riser is presented with the assumption that its top (by GPS; global positioning system) and bottom (anchoring) points are known. The riser is modelled as a series of slender-beam segments and at each time step, the riser nodal points are progressively traced. For riser x-y-z displacement and bending-moment tracing, quadratic and cubic interpolation functions for each line element between two neighboring bi-axial inclinometers are employed with respect to the global and generalized coordinate systems. Analytical solutions are derived for the instantaneous riser profile and bending moment at each line's mid-point. To validate the developed riser-monitoring algorithms, a FPSO (floating production storage offloading) system with SCR (steel catenary riser) or SLWR (steel lazy wave riser) was simulated for 1-yr and 50-yr collinear wind-wave-current storm conditions with 45-deg heading and the corresponding numerical sensor signals were inputted to the algorithms for reproducing the real-time riser profiles and bending stresses. Based on the comparisons between the algorithm-predicted and actual values, the developed method is validated. The methodology can be applied to any kinds and shapes of lines and cables too. • The real-time tracing of riser profile and bending moment by multiple numerical inclinometers along the riser is presented. • Analytical solution using numerical inclinometer is derived for the instantaneous riser node displacement. • The analytic curved line length formula in 3D space is derived. • Simplified analytic formula for the bending moment at the mid-point of each riser segment is suggested.

Gravity stiffness of a three-tower suspension bridge: Analytical solution via double-span bridge reduction to a single-span one with elastic constraints

Suspension bridge’s main cable under live load undergoes deformation depending on its gravity stiffness, i.e., work done against gravity under the initial dead load. In three-tower suspension bridges (3TSB), the middle tower's effect on the main cable's gravity stiffness is crucial but hard to assess. In this paper, the 3TSB model was simplified to the 2TSB with elastic constraints. The main cable shape was then calculated via the ratio between the simply supported beam's bending moment and the horizontal force component. The 2TSB model results were used to derive the 3TSB main cable's deflection using the middle tower's stiffness under vertical load. The analytical formula for gravity stiffness of 3TSB was derived by matching the latter with the simply supported beam's deflection formula. For a case-study 3TSB with main spans of 248 m + 1060 m + 1360 m + 380 m, analytical predictions were verified by FEM numerical results obtained via ANSYS. Linear relationships between live load and increments of the main cable's deflection and horizontal force component were derived. Besides, the main cable's deflection under live load can be reduced by increasing its sag-to-span ratio and cross-sectional area.

A Novel Shape Finding Method for the Main Cable of Suspension Bridge Using Nonlinear Finite Element Approach

The determination of the final cable shape under the self-weight of the suspension bridge enables its safe construction and operation. Most existing studies solve the cable shape segment-by-segment in the Lagrangian coordinate system. This paper develops a novel shape finding method for the main cable of suspension bridge using nonlinear finite element approach with Eulerian description. The governing differential equations for a three-dimensional spatial main cable is developed before a one-dimensional linear shape function is introduced to solve the cable shape utilizing the Newton iteration method. The proposed method can be readily reduced to solve the two-dimensional parallel cable shape. Two iteration layers are required for the proposed method. The shape finding process has no need for the information of the cable material or cross section using the present technique. The commonly used segmental catenary method is compared with the present method using three cases study, i.e., a 1666-m-main-span earth-anchored suspension bridge with 2D parallel and 3D spatial main cables as well as a 300-m-main-span self-anchored suspension bridge with 3D spatial main cables. Numerical studies and iteration results show that the proposed shape finding technique is sufficiently accurate and operationally convenient to achieve the target configuration of the main cable.