Linear n-compartment catenary models: Formulas to describe tracer amount in any compartment and identification of parameters from a concentration-time curve (original) (raw)
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Mathematical Biosciences, 1985
The parameters of catenary compartmental models are not identifiable except in special cases, e.g., where subsets of the rate constants have known values. However, an intrinsic set of parameter combinations is always identifiable, and finite ranges for all parameters can be found from these combinations. An explicit algorithm for computing the uniquely identifiable sums and products of unidentifiable parameters for this class of models is developed for the practical experimental conditions: input into and output from the first pool in the catenary chain. Upper and lower bounds on all parameters also are established algorithmically, in terms of the identifiable parameter combinations, thus permitting comprehensive analysis of any catenary model, identifiable or not, with first-pool input and output.
Pool size and mass flux bounds and quasiidentifiability relations for catenary models
Mathematical Biosciences, 1988
Closed-form algorithms were recently reported for computing the identifiable parameter combinations (structural invariants) and parameter bounds for all of the rate constants kij, of unidentifiable catenary compartmental models with input and output in pool 1 only. These results are extended here, providing bounds for unidentifiable (interval identifiable) steady state residence times, pool sizes, and mass fluxes, as well as some relationships for assessing quasiidentifiability for this class of catenary models.
Validation of a Low Fidelity Catenary Model Developed Using a Novel Optimization Algorithm
Progress in Canadian Mechanical Engineering. Volume 3, 2020
Contact wire pre-sag directly impacts the current quality collection in a high-speed railway catenary. Due to this, the initial configuration of the catenary geometry plays an important role on the dynamic performance of the railway. Therefore, accurately representing the initial equilibrium state of the catenary based on specific design requirements is crucial to obtain accurate dynamic results. Despite its importance, there are only a few publications in this area that present methods that can accommodate desired amount of presag in the contact wire and are computationally efficient. The goal of this paper is to present a catenary system that has been modelled using a novel optimization method and validate its dynamic response from its interaction with a pantograph system against the reference model results in BS EN 50318. The novel optimization methodology presented in this paper employs a gradient-based algorithm with a modified finite difference method to solve the initial equilibrium geometry of the catenary. The pantograph and catenary systems are modelled using a commercial finite element software and the post-processing of the results is done using in-house code. A penalty contact-force model is used to represent the contact behavior between the pantograph-catenary system and a threestep simulation procedure is used to achieve better convergence of results. The results from the simulation demonstrated good accordance with the reference model results in BS EN 50318.
A simplified model for railway catenary wire dynamics
European Journal of Environmental and Civil Engineering, 2016
In this paper, a simplified analytic model for the dynamic behaviour of railway catenary wire is presented. The model is discussed and validated with the help of numerical results obtained by a finite element code, for the case of a typical Italian railway installation. The simplified model is convenient from the computational point of view and is useful for sensitivity analysis. Some parametric studies have been developed by considering as free parameters the velocity and the distance of the train pantographs and looking at their effect on catenary dynamics.
Catenary Finite Element Model Initialization using Optimization
Civil-comp proceedings, 2016
The contact quality between pantograph and catenary plays a critical role on providing the required energy to power the trains traction systems. The need to study and analyze the dynamic behavior of these coupled systems as led to the development of pantograph/catenary interaction simulation software. Despite the increasing interest on the dynamical analysis of the catenary and its interaction with the pantograph, the accurate analysis of its configuration at static equilibrium becomes of most interest where its correct initial undeformed shape and correspondent undeformed mesh must be found. The initialization of the catenary, that is, the setting of the initial positions of the catenary finite element nodes have different requirements due to the different methods used in the solution of their dynamics. Furthermore, as the static configuration of the catenary provides its initial conditions for dynamic analysis it is possible that these have a significant influence on the simulation results. This is even more critical when considering the contact wire sag correct deformed shape where contact with the pantograph occurs. The work here presented proposes a catenary initialization procedure based on the definition of a fitness function to be minimized using classical gradient based optimization. The proposed methodology also opens the possibility to model catenary systems that have defects such as irregularities on its sag caused by damaged, poorly maintained or ill mounted overhead lines. Here, this irregularity can be imposed on the static equilibrium configuration of the model and the same minimization problem is set to find its corresponded undeformed shape.
Pantograph-Catenary System Modeling Using MATLAB-Simulink Algorithms
Scientific Journal of Riga Technical University. Computer Sciences, 2010
Contacts between pantograph and catenary are the most critical parts in the transmission of electrical energy for modern high-speed trains. Contact wire oscillations change combined force between pantograph and catenary, and the contact may even get lost. Therefore special pantographs and catenaries have been developed and further constructive changes are under development. A design criterion includes the permanent contact of pantograph head and contact wire at high speed and the reduction of both aero acoustic noise and wear. Because of complicated dynamic behaviour and very high costs for prototypes, all modifications and new design concepts for the pantograph/catenary system are essentially based on dynamical simulation. Traditional approaches focus on the catenary, which is modelled as set of coupled strings and/or beams, whereas simplified lumped mass models are used to describe the pantograph. Nowadays increased computer power allows considering applications with more refined pantograph modes (e.g. the elasticity of the pantograph) and active control components in innovative pantograph concepts.
Mathematical Problems in Engineering, 2015
To obtain the best operating conditions in a railway infrastructure, as the pantograph/catenary system, is a priority issue in modern railways, for a correct management and the best performance of this infrastructure. Although most of the published works on this subject are oriented to solving dynamic problems, in order to successfully address these problems a previous static study is necessary. In this paper, we present a methodology for the study of the forces in a railway catenary, according to the equations of statics equilibrium. The results of this work have allowed us to develop two iterative algorithms that calculate a simple and computationally effective lengths of the droppers, which is crucial to determine the initial structural configuration of the catenary parameter. The obtained results have led us to the implementation of a tool to obtain very precise assemblies with significant savings in maintenance, therefore still being used by ADIF, the Spanish railway administra...
Nonlinear structural models in cableway transport systems
Simulation Practice and Theory, 1999
In this paper an analysis of the nonlinear static behaviour of cable systems is developed by assuming a full nonlinear structural model of the cables based on elastic catenary results. The work is aimed at the possible application of this kind of structure to practical engineering systems such as among others ski lifts, electrical transmission lines, and cable systems in erection procedures of long-span bridges. The structural model is then implemented in a suitable computer code program able to analyse strong nonlinearities arising from low stress levels in the cables, where the uniqueness of the solution is not assured. Therefore, an appropriate simulation technique is required to capture the static equilibrium con®gurations of the cable systems subjected to a given external action. After a preliminary discussion of the relevant equations governing the behaviour of the structural model, a ®nite element analysis is developed to account for the main inherent features related to convergence and stability of the numerical algorithm used. Then, some illustrative numerical examples are developed by suitably calibrating the input data in such a way that strong nonlinearities stand out which enable the checking of the validity of the present analysis.