Random Irregularities Research Articles

An efficient model for the dynamic vehicle-track-bridge-soil interaction system

A semi-analytical approach based on a lumped parameter model is presented for the analysis of the dynamic interaction system of train, track, bridge, and subsoil. Herein, the bridge and the track are modeled as Euler–Bernoulli beams, which are connected through the viscoelastic track bed. The viscoelastic supports of the bridge model capture the flexibility and damping of the subsoil below the foundations. Complex modal expansion of the deformation approximates the response of the non-classically damped bridge-soil subsystem, while a Rayleigh–Ritz approximation is used to efficiently describe the track deflection. To achieve the coupling of the mechanical equations of these subsystems, a variant of component mode synthesis (CMS) is applied. The mass–spring–damper (MSD) system representing the moving train is coupled to the resulting system of equations for the track-bridge-soil subsystem by a discrete substructuring technique (DST). Geometric track irregularities describing the deviation of the track from perfectly straight and smooth are accounted for by random irregularity profile functions. The results of the proposed model are compared with a finite element model to validate the modeling approach. In an application example, the effects of track irregularities and the influence of the track on the dynamic response of a bridge are discussed. The comparison of results with and without soil–structure interaction of the bridge outlines the great influence of the subsoil properties on the dynamic response in case of resonance.

Performance assessment of pantograph and overhead system based on a vertical coupling dynamics model of the railway system

The increase of train speed leads to a violent vibration of the pantograph and overhead system. To evaluate the interaction performance of the pantograph and overhead system, a whole railway dynamics model including the track, vehicle, pantograph, and overhead system is established. The overhead system is represented by the finite element approach using the analytical formulas of nonlinear cable and truss elements. The vehicle is modeled by a multi-rigid-body system with a pantograph installed on its roof. A beam element with elastic foundations is used to model the track, which possesses harmonic and random irregularities. An iterative algorithm is implemented to solve the nonlinear behavior of the coupling model. The nonlinearities in the deformation of overhead system, the contact of the pantograph and contact line, and the contact of the vehicle-track are properly considered. Several numerical simulations are implemented to systematically investigate the influence of the vehicle-track vibration on the dynamic behavior of pantograph and overhead system. The results indicate that the vehicle-track vibration induced by the rail irregularities with large amplitude or certain wavelength can significantly aggravate the interaction performance of pantograph and overhead system.

Modeling of ionospheric scintillation

A signal, such as from a GNSS satellite or microwave sounding system, propagating in the randomly inhomogeneous ionosphere, experiences chaotic modulations of its amplitude and phase. This effect is known as scintillation. This article reviews basic theoretical concepts and simulation strategies for modeling the scintillation phenomenon. We focused our attention primarily on the methods connected with the random phase screen model. For a weak scattering regime on random ionospheric irregularities, a single-phase screen model enables us to obtain the analytic expression for phase and intensity scintillation indices, as well as the statistical quantities characterizing the strength of scintillation-related fades and distortions. In the case of multiple scattering, the simulation with multiple phase screens becomes a handy tool for obtaining these indices. For both scattering regimes, the statistical properties of the ionospheric random medium play an important role in scintillation modeling and are discussed with an emphasis on related geometric aspects. As an illustration, the phase screen simulation approaches used in the global climatological scintillation model GISM are briefly discussed.

Dynamic Characteristics of Metro Vehicle under Thermal Deformation of Long-Span Cable-Stayed Bridge

In order to study the influence of thermal deformation of long-span cable- stayed bridge (LSCSB) on the dynamic characteristics of metro vehicle on the bridge, based on the theory of vehicle-track coupled dynamics, the rigid-flexible coupled dynamic model of metro vehicle-track-LSCSB system is established by using finite element method and multi-rigid-body dynamics. Adopting this model, the deformation of LSCSB subject to temperature is analyzed, then the comprehensive effect of track random irregularity and rail deformation caused by temperature load is considered to study the dynamic characteristics of metro vehicle running through the bridge, and finally the influences of temperature increment and running speed on concerned dynamic indices of vehicle are studied. The results show that the LSCSB deforms obviously subject to temperature load, and the overall performance is that the cooling is arched, and the heating is bent, and the shape variable changes almost linearly with the temperature load. According to the parameters studied in this paper, the rail deformation caused by temperature load increases the wheel-rail vertical force, derailment coefficient and wheel load reduction rate by 1.5%, 3.1% and 5% respectively. The vertical acceleration of the vehicle body decreases by 2.4% under the cooling condition, while increases by 3.7% under the heating condition. The dynamic response of the bridge changes under temperature load. The maximum vertical and horizontal displacement in the middle of the main beam span are 6.24 mm and 2.19 mm respectively, and the maximum vertical and horizontal acceleration are 1.29 cm/s2 and 2.54cm/s2 respectively. The derailment coefficient and vertical acceleration of vehicle body are more affected by temperature load, and the wheel load reduction rate and wheel-rail vertical force are more affected by speed. The conclusion of this paper provides a reference for subsequent scholars to study the influence of thermal deformation on the dynamic response of vehicles on LSCSB.

The Influence of Track Structure Parameters on the Dynamic Response Sensitivity of Heavy Haul Train-LVT System

Background: In order to study the applicability of Low Vibration Track (LVT) in heavy-haul railway tunnels, this paper carried out research on the dynamic effects of LVT heavy-haul railway wheels and rails and provided a technical reference for the structural design of heavy-haul railway track structures. Methods: Based on system dynamics response sensitivity and vehicle-track coupling dynamics, the stability of the upper heavy-haul train, the track deformation tendency, and the dynamic response sensitivity of the vehicle-track system under the influence of random track irregularity and different track structure parameters were calculated, compared and analyzed. Results: Larger under-rail lateral and vertical structural stiffness can reduce the dynamic response of the rail system. The vertical and lateral stiffness under the block should be set within a reasonable range to achieve the purpose of reducing the dynamic response of the system, and beyond a certain range, the dynamic response of the rail system will increase significantly, which will affect the safety and stability of train operation. Conclusions: Considering the changes of track vehicle body stability coefficients, the change of deformation control coefficients, and the sensitivity indexes of dynamic performance coefficients to track structure stiffness change, the recommended values of the vertical stiffness under rail, the lateral stiffness under rail, the vertical stiffness under block, and the lateral stiffness under block are, respectively 160 kN/mm, 200 kN/mm, 100 kN/mm, and 200 kN/mm.

Failure analysis of fatigue damage for fastening clips in the ballastless track of high-speed railway considering random track irregularities

In order to study the influence of wheel-rail random dynamic interaction on the fatigue damage for fastening clips, a three-dimensional (3-D) high-speed railway vehicle-track coupling random dynamics model is established based on the random theory of the probability density evolution method (PDEM). The number theoretic method (NTM) and stochastic harmonic functions (SHF) are employed to generate the representative random track irregularities. Furthermore, a refined finite element model of WJ-8 fastening system is established, and the stress time history results of the clips are obtained based on the co-simulation analysis. Eventually, the rain-flow counting is introduced to study the influence of random track irregularities on fatigue damage of fastening clips combined with cumulative damage theory and the S-N curve of the clips. The results show that, the dynamic characteristics and stochastic probability evolution mechanism of the vehicle-track random system considering random track irregularities, as well as the evolution characteristics of the fatigue failure probability of clips with service time are accurately reproduced based on PDEM. Significantly, the fatigue damage of fastening clips caused by one vehicle passing by follows the lognormal distribution with a mathematical expectation of 2.35 × 10-8 and a variance of 1.48 × 10-12. The 95% confidence interval of mathematical expectation is [7.05 × 10-9, 5.89 × 10-7] and the 95% confidence interval of variance is [1.37 × 10-13, 1.59 × 10-11]. Additionally, the longer the service time of the fastening system, the more serious the fatigue damage of the clips and the greater the fatigue failure probability.

Dynamic Response Analysis of Medium-Speed Maglev Train with Track Random Irregularities

In order to analyze the dynamic response of medium-speed maglev train in the speed range of 0–200 km/h, the suspension performance, suspended energy consumption, and riding comfort of the train stimulated by random track irregularities are discussed in this paper. Firstly, the model of medium-speed maglev train including car body, air spring vibration isolation system, and the suspension system is established. Then, a controller based on flux inner feedback loop and PID outer feedback loop is designed for the suspension system. The established model is stimulated by the actual track power spectrum in full speed range. The simulation results show that the fluctuation of suspension gap is less than ±4 mm. Furthermore, thanks to the adding of permanent magnet, the power consumption is significantly reduced, which is of benefit to the electromagnet heating problem and on-board levitation power supply system. The riding comfort of the train moving on the irregular track using Sperling index is assessed. The experimental results validate the effectiveness of the proposed analytical calculation model of medium-speed maglev train. It is shown that medium-speed maglev train achieved good performance, significant power reduction, and satisfactory riding comfort.

Unsupervised Machine Learning-based EV Load Profile Generation for Efficient Distribution System Operation

With the popularization of EVs, learning the charging load patterns is becoming a key step for the stability of power grids. However, the randomly probable nature of EVs has brought new challenges to the scheduling, operation and planning of distribution system. Also, EV load patterns can be different from locations such as in areas where offices are located and in areas which makes it more complicated to generate EV load profiles. In this paper, we propose machine learning based EV profiling technique to better understand the information behind the random probability and irregularity of EV load. The proposed method is able to take into account the time-varying, dynamic character and the complex temporal correlation of EV loads. Through the proposed method, we develop reliable probabilistic models and generate a series of different EV load profiles. The simulation results show that EV load profiles generated by the proposed method can not only retain the temporal correlation and probability distribution nature, but also improve the accuracy of load forecast. As a result, considering a series of different EV load profiles generated by our proposed methods, the distribution system operation can take uncertainty into account when making decisions, such as safe operation of distribution network, optimal economic trade and cooperative scheduling strategy.

Full-scale test and numerical simulation of wheelset-gear box vibration excited by wheel polygon wear and track irregularity

The wheelset-gear box of high-speed train is the typical unsprung mass serving in the complex excitation environment. To investigate the independent and compounded influences of wheelset out-of-roundness, wheel polygon wear and track irregularity on the vibration performance of wheelset-gearbox system, the 1:1 high-frequency excitation test based on the rolling test rig is carried out within the speeds of 100 ∼ 500 km/h. The corresponding multi-body dynamic model is established and validated. The detailed wheel-wheel contact relations are discussed. The research results indicate that the test rig dynamic model can capture the vibration amplitude and main frequency characteristics well, especially for the vibration below 1000 Hz. For the wheelset-gearbox system without track excitation, its vibration energy is basically concentrated in the resonance region of test object. At higher speeds, the vibrations induced by wheelset and motor rotation gradually become dominant. Under excitation of the grinded polygon wear in rail wheel, the multiple-frequency vibration almost determines the system vibration level within the test speed ranges, whilst the vibration induced by the wheelset and motor rotation plays an important role only at the speed above 300 km/h. In comparison, the high-speed track random irregularity contributes very small vibration magnitude. For the axle box, the vibration amplitude composition ratios led by the excitations of wheelset out-of-roundness, rail wheel polygon wear and track irregularity are around 26.7%, 48.3% and 25% correspondingly. And for the gear box, the composition ratios reach 38.46%, 32.05% and 29.49% respectively. The wheel polygon wear has been the main excitation source in the high-frequency vibration of wheelset system, followed by the wheelset 1st-order out of round and track irregularity in sequence.

Влияние неровностей пути на вертикальные ускорения вагонов при высокоскоростном движении поездов по мостам

Objective: Obtaining differential equations of the “bridge-train” system, the solution of which allows one to identify the optimal dynamic parameters of the vehicle of high-speed rolling stock and bridge structures when rolling load moves at high speed. Methods: Derivation of differential equations of the “bridge– train” system by the analytical method. Results: Obtaining formulas for determining the acceleration of the spring borne part of rolling stock vehicles depending on track irregularities. Practical importance: Based on the results of calculations according to these formulas, a reasonable assignment of the values of camber and the possibility of assessing the effect of random irregularities of the rail track on the bridge are provided.

Dynamic Influence of Wheel Flat on Fatigue Life of the Traction Motor Bearing in Vibration Environment of a Locomotive

Wheel flat can cause a large impact between the wheel and rail and excites a forced vibration in the locomotive and track structure systems. The working conditions and fatigue life of the motor bearings are significantly affected by the intensified wheel–rail interaction via the transmission path of the gear mesh. In this study, a fatigue life prediction method of the traction motor bearings in a locomotive is proposed. Based on the L−P theory or ISO 281 combined with the Miner linear damage theory and vehicle–track coupled dynamics, the irregular loads induced by the track random irregularity and gear mesh are considered in this proposed method. It can greatly increase the accuracy of predictions compared with the traditional prediction models of a rolling bearing life whose bearing loads are assumed to be constant. The results indicate that the periodic impact forces and larger mesh forces caused by the wheel flat will reduce the fatigue life of the motor bearings, especially when the flat length is larger than 30 mm. Using this method, the effects of the flat length and relatively constant velocity of the locomotive are analyzed. The proposed method can provide a theoretical basis to guarantee safe and reliable working for motor bearings.

Dynamic Correction of the Influence of Long Measuring Path Irregularity in Antenna Tests

This article investigates the influence of random microwave discontinuities on the characteristics of long transmission paths. This is most important for dynamic measuring stands, accompanied by multiple space movement of long transmission paths with their bending or twisting during the measurement process. In modern active electronically scanned arrays this issue also becomes relevant, due to increased requirements for the accuracy of beam shaping. The aim of this study is to develop a theoretical background and perform experimental verification for taking into account the effect of random microwave discontinuities on the transmission path characteristics. A method for correcting the effect of such irregularities is considered based on electrical length control by measuring the input reflection coefficient. Relations for the magnitude and phase of the path’s input reflection coefficient depending on the S-parameters of a long four-terminal network terminated with mismatched load are obtained and plotted. Using theory of sensitivity, the mathematical expressions of conditions were obtained to achieve maximum accuracy of measuring the electrical length of a long microwave path. The possibility of dynamic error correction in antenna measurements with a long test path caused by random microwave irregularities along it has been experimentally proved.

A Probabilistic Assessment Model for Train-Bridge Systems: Special Attention on Track Irregularities

In this paper, a probabilistic model devoted to investigating the dynamic behaviors of train-bridge systems subjected to random track irregularities is presented, in which a train-ballasted track-bridge coupled model with nonlinear wheel-rail contacts is introduced, and then a new approach for simulating a random field of track irregularities is developed; moreover, the probability density evolution method is used to describe the probability transmission from excitation inputs to response outputs; finally, extended analysis from three aspects, that is, stochastic analysis, reliability analysis, and correlation analysis, are conducted on the evaluation and application of the proposed model. Besides, compared to the Monte Carlo method, the high efficiency and the accuracy of this proposed model are validated. Numerical studies show that the ergodic properties of track irregularities on spectra, amplitudes, wavelengths, and phases should be taken into account in stochastic analysis of train-bridge interactions. Since the main contributive factors concerning different dynamic indices are rather different, different failure modes possess no obvious or only weak correlations from the probabilistic perspective, and the first-order reliability theory is suitable in achieving the system reliability.

Influence of Vehicle Number on the Dynamic Characteristics of High-Speed Train-CRTS III Slab Track-Subgrade Coupled System.

In this paper, a high-speed train–CRTS III slab track–subgrade coupled dynamic model is established. With the model, the influence of vehicle number on the dynamic characteristics of a train–CRTS III slab track–subgrade coupled system with smooth and random track irregularity conditions for conventional and vibration-reduction CRTS III slab tracks are theoretically studied and analyzed. Some conclusions are drawn from the results: (1) the largest dynamic responses of the coupled system for all items and cases are no longer changed when the vehicle number exceeds three, and three vehicles are adequate to guarantee the simulation precision to investigate the dynamic responses of the coupled system. (2) The acceleration of the car body has almost no relation with the vehicle number, and only one vehicle is needed to study the vehicle dynamics using the train–CRTS III slab track–subgrade coupled dynamic model. (3) For the conventional CRTS III slab track on a subgrade, the vehicle number has a negligible influence on the accelerations of the rail, slab, and concrete base, the positive and negative bending moments of the rail, the compressive force of the fastener, and the positive bending stress of slab, but it has a large influence on the tension force of the fastener, and the negative bending stresses of the slab and concrete base. Only one vehicle is needed to study track dynamics without considering the tension force of the fastener, the negative bending stresses of the slab and concrete base, otherwise, two or more vehicles are required. (4) For vibration reduction of the CRTS III slab track on a subgrade, the number of vehicles has some influence on the dynamic responses of all track components, and at least two vehicles are required to investigate the track dynamics.

Mathematical modeling of articulated passenger train spatial vibrations

The problem of high-speed railway transport development is important for Ukraine. In many countries articulated trains are used for this purpose. As the connections between cars in such a train differ from each other, to investigate its dynamic characteristics not a separate car, but a full train vibrations model is necessary. The article is devoted to the development of the mathematical model for articulated passenger train spatial vibrations. The considered train consists of 7 cars: one motor-car, one transitional car, three articulated cars, one more transitional car and again one motor-car. Differential equations of the train motion along the track of arbitrary shape are set in the form of Lagrange’s equations of the second kind. All the necessary design features of the vehicles are taken into account. Articulated cars have common bogies with adjoining cars and a transfer car and the cars are united by the hinge. The operation of the central hinge between two cars is modeled using springs and dampers acting in the horizontal and vertical directions. Four dampers between two adjacent car-bodies act as dampers for pitching and hunting and are represented in the model by viscous damping. The system of 257 differential equations of the second order is set, which describes the articulated train motion along straight, curved, and transitional track segments with taking into account random track irregularities. On the basis of the obtained mathematical model the algorithm and computational software has been developed to simulate a wide range of cases including all possible combinations of parameters for the train elements and track technical state. The study of the train self-exited vibrations has shown the stable motion in all the range of the considered speeds (40 km/h – 180 km/h). The results obtained at the train motion along the track maintained for the speedy motion have shown that all the dynamic characteristics and ride quality index insure train safe motion and comfortable conditions for the travelling passengers.

Lateral girder displacement effect on the safety and comfortability of the high-speed rail train operation

Rail irregularity presents a major threat to the high-speed train (HST) safety on a high-speed rail (HSR) bridge. Lateral bridge deformation has a significant impact on geometric parameters of the rail. In this paper, the influence of lateral bridge deformation on the train operation on the HSR bridge is investigated. Variational calculus is employed to establish the analytical mapping between the lateral bridge and rail deformation. By superimposing the mapped rail deformation and initial random rail irregularity, the composed rail unevenness under lateral bridge deformation is obtained. Thereafter, by adopting the dynamical model of the train-track-bridge coupling system (TTBCS), the dynamic behaviour of the train moving across the HSR track-bridge system is analysed. Based on safety and comfortability control indicators of the HST operation, effects of different types of lateral bridge deformations with various amplitudes on the train’s operation performances are investigated. The results indicate that the bilateral girder’s mutual translation has the most significant impact on the train’s operation. When the HST is moving with the velocity of 350 km/h, lateral bridge deformation amplitude thresholds are suggested as 17.43 and 8.12 mm to ensure the safety and comfortability of the HST operation, respectively. The obtained results can provide beneficial pointers for HSR bridge design.

A two-step framework for stochastic dynamic analysis of uncertain vehicle-bridge system subjected to random track irregularity

This paper presents a two-step probabilistic framework for stochastic dynamic analysis of the coupled vehicle-bridge system (VBS) involving both uncertain parameters and random track irregularity. Firstly, an explicit time-domain method is extended to evaluate the conditional response statistics of the VBS subjected to random irregularity at specific parameter points, and an efficient spectral representation-based formulation is proposed to calculate the excitation correlation matrix required in the analysis. Then, the total response statistics are further evaluated by Gaussian integration of the conditional ones based on the total probability theorem, and an efficient dimension-adaptive algorithm is proposed to collocate the required quadrature points. In the numerical examples, the proposed method is used to study a typical VBS model with both deterministic or random parameters; several other existing methods are employed to illustrate the advantages of the proposed method. The results indicate that the proposed framework is an accurate and efficient method for stochastic dynamic analysis of the vehicle-bridge interaction problem.

A fast simulation algorithm for the wheel profile wear of high-speed trains considering stochastic parameters

A fast calculation algorithm for the wear evolution of wheel profiles is proposed and results presented with a high-speed train as an example. The dynamics simulation includes the calculation of the vehicle running on a short straight track with random irregularities and the vehicle passing various curves without track excitation. The penetration curves of wheel/rail contact are assumed as the shape of wear distribution in a contact patch, which are calculated after the update of wheel profiles and interpolated in each step of wear calculation. The total wheel wear is the sum of the wear caused by track irregularities and the wear under smooth tracks, such as the straight and curved lines. After each dynamic simulation, several loops for wear calculation and profile update are carried out to smooth the wear curve. Simulation results show that the calculated distribution and average of the wear depth and the equivalent conicity in a reprofile cycle are in good agreement with the measured results. The predicted and measured wear shapes agree reasonably well in the area near the tape circle. Moreover, the proposed method is at least 15 times faster than the traditional wear calculation method and it can consider the influences of the stochastic parameters of the wheel/rail contact.

Nanostructure regularity in white beetle scales for stability and strong optical scattering [Invited

Cyphochilus white beetle scales exhibit exceptionally strong light scattering power that originates from their regular random fibrillar network nanostructure. The structure is believed to be formed by late-stage spinodal decomposition in a lipid membrane system. However, the structure is characterized by nonconstant mean curvatures and appreciable anisotropy, which are not expected from late-stage spinodal decomposition, so that the surface free energy is not minimized. Nevertheless, a high degree of regularity represented by the relatively uniform fibril dimensions and smooth fibril surfaces in the structure may result from a process similar to spinodal decomposition. In this study, we investigate the role of regularity in the Cyphochilus white beetle scale structure in realizing strong light scattering. Irregularity is computationally introduced into the structure in a systematic fashion such that its anisotropy is preserved and its surface area is kept constant. Calculations show that optical scattering power decreases as irregularity increases with a high sensitivity. This effect happens because, remarkably, irregularity on a scale much smaller than the wavelength destroys anisotropy in optical diffusion. Thus, the result shows that the in vivo process in Cyphochilus white beetle scales utilizes structural regularity and anisotropy to achieve strong light scattering at a tolerable surface free energy. In typical fabrication of random media, irregularity and multiple length scales typically increase surface area, so that durability of the nanostructures may be negatively affected. Our study indicates that regularity in anisotropic random nanostructures can achieve strong light scattering with a moderate surface free energy.

Investigations on the influence of prestressed concrete creep on train-track-bridge system

In response to long-term operation of prestressed concrete railway bridges, the girder body will arch because of creep, which may influence the running stability of high-speed trains. Usually, the deformation of the rail-bridge system under the creep effect is calculated by a finite element model with the rail geometry deformation input as additional irregularity. The original irregularity is superimposed to the coupled system of the train and bridge to calculate the dynamic response of the system. However, such a strategy is time-consuming and cannot accurately integrate the uncertainty of the original rail irregularity. This paper presents an analytical formula for predicting the rail deformation caused by concrete creep. The rail deformation caused by the bridge upper arch can be quickly predicted by the creep amplitude of the bridge. The creep deformation of the rail is applied as an irregularity excitation to the train-track-bridge coupled system (TTBCS). In addition to creep irregularities, original random irregularities also exist on the track. The Karhunen-Loéve expansion method is adopted to represent the random track irregularity that considers creep deformation. The results achieve good agreement with the initial samples. Subsequently, the TTBCS model is established to analyze the dynamic responses of different train speeds and different bridge creep deformations using a stochastic dynamic analysis method. This method achieves very high agreement with the Monte Carlo method, and the error rate of the mean bridge displacement calculated by both methods under the same working conditions was only 0.0351%. Finally, the upper probability limit value of the creep of the bridge is put forward: at a speed of a high-speed train of 350 km/h, the creep upper arch limit is only 7 mm. These probability limits at different train speeds have guiding significance for the design, maintenance, and repair of the actual medium–high-speed railway concrete supported beam bridge.