Catenary Model Research Articles

ZOH-based composite neural event-triggered control of underactuated cable-laying vehicle in presence of varying depth

To achieve the autonomous cable-laying operation under the varying depth, this note investigates the path-following problem of underactuated cable-laying vehicles with constraints of the unknown actuator gain. A double-stage logical (DSL) guidance principle is developed to realize the practical laying path programming for the cable-laying vehicle. In the guidance law, the catenary model is incorporated to derive the towing distance, i.e., the horizontal projection distance between the cable landing point and the vehicle’s gravity center. That can guarantee the cable-laying operation is solidly implemented in the condition of the varying depth. As for the control part, the composite neural event-triggered control algorithm is proposed by fusing the zero-order holder (ZOH) to stabilize the track error between the target position and the actual one. The event-triggered mechanism is employed to effectively reduce the occupancy of the communication channel between sensors and controllers. Moreover, for the merits of robust neural damping and composite learning techniques, the gain uncertainty of actuators can be compensated by updating two adaptive laws online. The stability analysis of the closed-loop system is rigorously performed via Lyapunov criterion and simulation results are provided to verify the performance of the proposed scheme.

A Laplace transform approach to direct and inverse problems for multi-compartment models

Multi-compartment models described by systems of linear ordinary differential equations are considered. Catenary models are a particular class where the compartments are arranged in a chain. A unified methodology based on the Laplace transform is utilised to solve direct and inverse problems for multi-compartment models. Explicit formulas for the parameters in a catenary model are obtained in terms of the roots of elementary symmetric polynomials. A method to estimate parameters for a general multi-compartment model is also provided. Results of numerical simulations are presented to illustrate the effectiveness of the approach.

Optimization of minimum crossing distance of transmission line based on multi objective ant colony algorithm

In the test of cross span distance of transmission line, the estimation of cross span distance is not accurate, which leads to the increase of subsequent test error. Therefore, a test method of transmission line cross span distance based on a multi-objective ant colony algorithm is proposed. Statistics of the actual information of different crossovers including trees and forest areas. Considering the transmission line as a flexible cable, the objective function for estimating the cross span distance of the transmission line is constructed according to the catenary model of the flexible cable model. On this basis, the multi-objective ant colony algorithm is used to solve the function, and the optimization results of transmission line crossing distance are output. The experimental results show that the method has high accuracy, small error, short time and reliability.

Investigation and Development of a Three-Dimensional Transmission Tower-Line System Model Using Nonlinear Truss and Elastic Catenary Elements for Wind Loading Dynamic Simulation

The accuracy of transmission tower-line system simulation is highly impacted by the transmission line model and its coupling with the tower. Owing to the high geometry nonlinearity of the transmission line and the complexity of the wind loading, such analysis is often conducted in the commercial software. In most commercial software packages, nonlinear truss element is used for cable modeling, whereas the initial strain condition of the nonlinear truss under gravity loading is not directly available. Elastic catenary element establishes an analytical formulation for cable structure under distributed loading; however, the nonlinear iteration to reach convergence can be computational expensive. To derive an optimal transmission tower-line model solution with high fidelity and computational efficiency, an open-source three-dimensional model is developed. Nonlinear truss element and elastic catenary element are considered in the model development. The results of the study imply that both elements are suitable for the transmission line model; nevertheless, the initial strain in nonlinear truss element largely impacts the model accuracy and should be calibrated from the elastic catenary model. To cross-validate the developed models on the coupled transmission tower and line, a one-span eight-line system is modeled with different elements and compared with several state-of-the-art commercial packages. The results indicate that the displacement time-history root-mean-square error (RMSE) of the open-source transmission tower-line model is less than 1 % and with a 66 % computational time reduction compared with the ANSYS model. The application of the open-source package transmission tower-line model on extreme wind speed considering the aerodynamic damping is further implemented.

Wind deflection analysis of railway catenary under crosswind based on nonlinear finite element model and wind tunnel test

This paper evaluates the railway catenary's wind deflection under crosswind based on wind tunnel experiments and a nonlinear finite element model. A catenary model is constructed based on the absolute nodal coordinate formulation to describe the geometrical nonlinearity of the system. The aerodynamic forces acting on the catenary are derived according to the quasi-steady theory, and the aerodynamic coefficients are obtained by wind tunnel experiments. A procedure to generate the three-dimensional fluctuating wind field along the catenary is presented. The extreme value of the wind deflection is estimated based on a Poisson approximation of the extreme value distribution. The numerical accuracy is validated by wind tunnel experimental results of an aeroelastic catenary. The response, statistics, frequency characteristics and extreme value of the contact wire's wind deflection are investigated through numerical simulations. The analysis results indicate that the maximum wind deflection will exceed the safety limit for the analysed catenary with a turbulence intensity of more than 15%. The adjustment of some critical parameters of the catenary system can reduce the maximum wind deflection.

Static, stability and dynamic characteristics of asymmetric bi-directional functionally graded sandwich tapered elastic arches in thermo-mechanical environments

This research paper investigates the in-plane static, stability and dynamic characteristics of tapered Timoshenko bi-directional functionally graded (BDFG) sandwich curved elastic arches (symmetric and asymmetric) in thermo-mechanical environments using the differential quadrature element method (DQEM). Physical properties such as Young's modulus, the mass density, Poisson's ratio and the thermal expansion coefficient are defined to vary both with respect to temperature and position while shear deformation, axial deformation, and rotary inertia effects are incorporated in the analysis. Different types of arches namely circular, parabolic, catenary, elliptic and sinusoidal models are modelled by having non-uniform cross-section and the BDFG properties. General functions are used to vary the physical properties through the thickness and length of the curved. Incorporating the influence of having a thermal environment for simplified models, the current methodology for studying such structures is verified by comparing the results with previously published literature and finite element software simulations. The effect of the temperature rise, physical properties variation and geometrical parameters (such as the ratio of thickness to length, the opening angle and non-uniform cross-section) on the static deformation, buckling load and free vibration characteristics of BDFG arches with metal/ceramics in the inner surface and ceramics/metal in the outer surface of the arch is investigated. In addition, the mechanical behaviour of sandwich arches for various combinations such as homogeneous or FG for outer skins and the inner core is presented under thermo-mechanical loadings.

Identifiability of linear compartmental models: The singular locus

This work addresses the problem of identifiability, that is, the question of whether parameters can be recovered from data, for linear compartmental models. Using standard differential algebra techniques, the question of whether a given model is generically locally identifiable is equivalent to asking whether the Jacobian matrix of a certain coefficient map, arising from input-output equations, is generically full rank. A natural next step is to study the set of parameter values where the Jacobian matrix drops in rank, which we refer to as the locus of non-identifiable parameter values, or, for short, the singular locus. In this work, we give a formula for coefficient maps in terms of acyclic subgraphs of the model's underlying directed graph and, then, study the case when the singular locus is defined by a single equation, the singular-locus equation. We prove that the singular-locus equation can be used to determine when submodels are generically locally identifiable. We also determine the singular-locus equation for two families of linear compartmental models, cycle and mammillary (star) models with input and output in a single compartment. We also state a conjecture for the corresponding equation for a third family: catenary (path) models. Finally, we introduce the identifiability degree, which is the number of parameter values that map to a generic input-output data vector. This degree was previously computed for mammillary and catenary models, and here we determine this degree for cycle models.

Geometry deviation effects of railway catenaries on pantograph\u2013catenary interaction: a case study in Norwegian Railway System

This paper presents a non-contact measurement of the realistic catenary geometry deviation in the Norwegian railway network through a laser rangefinder. The random geometry deviation is included in the catenary model to investigate its effect on the pantograph–catenary interaction. The dispersion of the longitudinal deviation is assumed to follow a Gaussian distribution. A power spectrum density represents the vertical deviation in the contact wire. Based on the Monte Carlo method, several geometry deviation samples are generated and included in the catenary model. A lumped mass pantograph with flexible collectors is employed to reproduce the high-frequency behaviours. The stochastic analysis results indicate that the catenary geometry deviation causes a significant dispersion of the pantograph–catenary interaction response. The contact force standard deviations measured by the inspection vehicle are within the scope of the simulation results. A critical cut-off frequency that covers 1/16 of the dropper interval is suggested to fully describe the effect of the catenary geometry deviation on the contact force. The statistical minimum contact force is recommended to be modified according to the tolerant contact loss rate at high frequency. An unpleasant interaction performance of the pantograph–catenary can be expected at the catenary top speed when the random catenary geometry deviation is included.

Hardware-in-the-loop pantograph tests using analytical catenary models

Pantograph hardware-in-the-loop (HIL) testing is an experimental method in which a physical pantograph is excited by an actuator which reproduces the movement of a virtual catenary. This paper proposes a new method that uses analytical catenary models for HIL tests. The approach is based on an iterative scheme until achieving a steady-state regime. Some of the method's advantages include its ability to consider the delay in the control and communication system and its applicability to a wide range of analytical catenary models. The proposed algorithm was validated both numerically and experimentally. The experimental results obtained in the HIL pantograph tests were compared with those obtained from pure numerical simulations using a linear pantograph model and showed good accuracy with pantograph running at different speeds.

Extreme response based reliability analysis of composite risers for applications in deepwater

As current oil reserves start to deplete, companies are looking to exploit deeper deposits. At these greater depths composite risers, with their high strength-to-weight ratio, reduce the effective tensions and bending moments compared to steel risers. However, there is still limited research into their behaviour, with one key missing element being a comparison with traditional riser designs which accounts for variances in material properties and wave loads. This paper therefore conducts a strength-based reliability analysis of composite catenary risers operating between 1,500 m and 4,000 m. A static global catenary model is combined with Classical Laminate Theory to determine the extreme response and its performance is verified against FEA. This response is evaluated with the Tsai-Wu failure criterion to determine first-ply failure. The effect of laminate moisture absorption on the long-term reliability of submerged composite-based risers is also investigated as it can cause a significant reduction in the strength of composite risers. The reliability analysis is conducted using the Monte Carlo Method, revealing that the composite risers perform well at 4000 m. The degradation in performance from moisture absorption becomes increasingly important at greater depths and needs further investigation for these applications.

Simulation of Mooring Line Operation in Ship Mooring

In order to simulate the process of ship mooring more accurately, catenary equations are used to model mooring lines. Use different catenary models to simulate different phases of ship mooring operation. Establish a basic elastic catenary equation of mooring line by using the micro mechanical equilibriums theory. Then, a double-catenary model of heaving line and cable with a point load, imitating the effect of an eye splice, is developed based on existing catenary models in the literature. By calculating the mooring line tension, analyze whether the tension exceeds the safety load. The simulator is verified through simulations. A set of case studies is used to verify the effectiveness and practicability of the model. Integrate and realize the three-dimensional visualization of mooring line operation in ship mooring operation. The established model can guide mooring operation of ships.

A catenary model for the analysis of arching effect in soils and its application to predicting sinkhole collapse

This paper describes a model for the prediction of sinkhole collapse for two-dimensional and axisymmetric conditions. The model explains the arching effect on the threshold of collapse by a catenary arch or dome that tries to redirect the self-weight of the unstable soil to the adjacent stable mass. The collapse mechanism considers the vertical displacement of this unstable soil mass through vertical slip planes. An adapted Krynine's construction is used for predicting Mohr–Coulomb failure conditions on the base of the catenary arches for saturated or dry conditions, whereas a simple modification is proposed for unsaturated conditions. Upward growth of sinkholes is also discussed on the basis of the model described, as well as the dependency of the stability of arches on oscillations of the water level. Some case studies and experimental evidence are presented for evaluation and application of the proposed model. It is shown that the catenary arch assumption is an efficient but simple approach for the prediction of sinkhole growth and collapse.

Validation and Analysis on Numerical Response of Super‐High‐Speed Railway Pantograph‐Catenary Interaction Based on Experimental Test

The numerical tools can be used to facilitate the design of the railway pantograph‐catenary system. The validation of the current numerical results is mostly performed at a speed slower than 350 km/h. This paper aims at the validation and analysis of the numerical results at a super‐high‐speed. The catenary model is constructed based on a nonlinear finite element approach employing the absolute nodal coordinate formulation. A multibody dynamics model is adopted to represent the pantograph. The measurement data are collected by an inspection vehicle equipped with an instrumented pantograph operating at 378 km/h in Chengdu‐Chongqing high‐speed line. Comparing the numerical simulation and the field test shows that the present pantograph‐catenary model can provide reliable numerical results at 378 km/h. The numerical analysis of pantograph‐catenary interaction at super‐high‐speed shows that the trailing pantograph performance does not comply with the assessment standard at 378 km/h. The adjustment of double‐pantograph interval and messenger wire tension can effectively improve the trailing pantograph performance.

An Investigation on the Current Collection Quality of Railway Pantograph-Catenary Systems With Contact Wire Wear Degradations

In railway pantograph-catenary systems, the contact surfaces undergo wear in long-term operations, directly affecting interaction performance and potentially deteriorating the current collection quality. The effect of contact wire wear (CWW) on the current collection quality should be evaluated to understand the system’s health status in operations. This article presents a stochastic analysis of the pantograph–catenary interaction performance with different levels of CWW based on four years of measurement data. The power spectral density (PSD) estimation is carried out on the measured CWW to obtain their frequency representations. The random time histories of CWW are generated based on the PSDs. A nonlinear finite element model of catenary with a lumped-mass pantograph is built. Using the Monte Carlo method, the stochastic analysis of pantograph-catenary contact force is carried out to investigate the distribution and dispersion of assessment indices with different levels of CWW. The results indicate that the CWW mainly affects the maximum and minimum contact forces instead of the contact force standard deviation. The optimal pantograph–catenary interaction performance is observed certain years after CWW is formed, depending on the traffic density of the railway line, which is at the second year in the presented case study. Then, the performance declines with an increase in service time. Also, higher operating speed causes a more significant dispersion in assessment indices representing a lower current collection quality, particularly at the maximum operating speed (70% of the catenary wave propagation speed).

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ МАГНИТНОГО ВЛИЯНИЯ КОНТАКТНОЙ СЕТИ ПОСТОЯННОГО ТОКА НАПРЯЖЕНИЕМ 3 И 24 КВ НА СМЕЖНЫЕ КОММУНИКАЦИИ СВЯЗИ

The paper analyses a magnetic influence of a direct current catenary with voltages of 3 and 24 kV on adjacent communication facilities. The authors have compared the gained results with standards of magnetic interference. The have developed a model of catenary with voltages of 3 and 24 kV in the Matlab Simulink dynamic modeling environment. With the use of the model the authors have determined parameters of all key components that it is necessary to consider at analysis of magnetic compatibility of the direct current catenary with adjacent communication facilities.

Research on reliability analysis of catenary model based on the fusion particle swarm least square support vector machine algorithm

Research on reliability analysis of catenary model based on the fusion particle swarm least square support vector machine algorithm

Vibration Measurement and Wave Reflection Analysis in an Electrified Railway Catenary Based on Analytical Methods

The wave propagation property of the catenary directly affects the pantograph–catenary interaction performance. Specifically, wave reflection and transmission occurring at waveguide discontinuities, particularly at dropper junctions, directly impact the pantograph–catenary interaction performance. In this study, wave reflection occurring at the dropper junctions is investigated using both analytical and experimental approaches. First, a partial catenary model is established to analyze the catenary wave propagation by considering the wave reflections at the dropper junctions. The result indicates that the wave reflection in the contact wire (CW) affects the contact performance more significantly than that in the messenger wire. Two types of experimental tests are performed to analyze the wave reflection in the catenary—single CW and full-scale catenary tests. An analytical method considering back-and-forth reflections between the adjacent droppers is proposed to identify the actual reflection coefficients and extract the wave components from the measured data. The single CW test result shows that the dropper mass has a negligible influence on the wave reflection. The full-scale catenary test result indicates that the catenary reflection coefficient obtained from the measured data can match the design value with an acceptable error using the proposed method. Moreover, the measured data can be decomposed into wave components with different reflection orders, in which less energy is centered in the higher-reflection-order component. The proposed methods have been justified effective in reflection coefficient identification for the actual catenary structure.

Analysis of contact forces between the pantograph and the overhead conductor rail using a validated finite element model

This work presents the study of the interaction between 11 models of pantographs and 2 models of overhead conductor rails (OCR). All the models have been analysed at speeds of 70, 100 and 130 km/h. Furthermore, one of the OCR models used to carry out this study has been previously validated with experimental modal tests. The contact forces between each pantograph and catenary model is obtained in all cases. The analysis of the results reveals the contact forces are influenced by the dispersion in the length of the spans of the OCR sections and the pantograph model for speeds above 100 km/h. Thus, if pantograph resonance is not present, the lower the dispersion, the more constant the forces are. On the contrary, span length variations and the pantograph model have little influence on contact forces at low speeds. In addition, contact forces increase in the transitions between two sections of the overhead conductor rail. This phenomenom becomes more noticeable as the speed of pantograph operation increases.

Modeling of a Tethered Testbed for a VTVL Vehicle

This paper proposes an algorithm for modeling a three-dimensional tethered environment for testing vertical-take off, vertical landing vehicles. The method is able to take several geometrical configurations into account and combines the classical catenary model with the elasticity theory to predict the forces acting on the lander in quasistatic conditions, i.e., in conditions of hovering, where the motion of the vehicle is reduced. Numerical results confirm that the method is potentially able to provide real-time solutions, which can be included as feedforward contributions in the design of tethered experiments.

Study on Mooring Design and Calculation Method of Ocean Farm Based on Time-Domain Potential Flow Theory

In order to calculate the mooring force of a new semi-submerged Ocean Farm quickly and accurately, based on the unsteady time-domain potential flow theory and combined the catenary model, the control equation of mooring cable is established, and the mooring force of the platform under the wave spectrum is calculated. First of all, based on the actual situation of the ocean environment and platform, the mooring design of the platform is carried out, and the failure analysis and sensitivity analysis of the single anchor chain by the time domain coupling method are adopted: including different water depth, cycle, pretension size, anchor chain layout direction and wind speed, etc. The analysis results confirm the reliability of anchoring method. Based on this, the mooring point location of the platform is determined, the force of each anchor chain in the anchoring process is calculated, and the mooring force and the number of mooring cables are obtained for each cable that satisfies the specification, the results of this paper can provide theoretical calculation methods for mooring setting and mooring force calculation of similar offshore platforms.