scholarly journals The Effect of High-Frequency Parametric Excitation on a Stochastically Driven Pantograph-Catenary System

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
R. H. Huan ◽  
W. Q. Zhu ◽  
F. Ma ◽  
Z. H. Liu
Keyword(s):  
Parametric Excitation ◽  
High Frequency ◽  
High Speed ◽  
Transition Probability ◽  
Kolmogorov Equation ◽  
System Response ◽  
Appreciable Effect ◽  
Transition Probability Density ◽  
Stationary Response ◽  
Catenary System

In high-speed electric trains, a pantograph is mounted on the roof of the train to collect power through contact with an overhead catenary wire. The effect of fast harmonic and parametric excitation on a stochastically driven pantograph-catenary system is studied in this paper. A single-degree-of-freedom model of the pantograph-catenary system is adopted, wherein the stiffness of the nonlinear spring has a time-varying component characterized by both low and high frequencies. Using perturbation and harmonic averaging, a Fokker-Planck-Kolmogorov equation governing the stationary response of the pantograph-catenary system is set up. Based on the transition probability density of the stationary response, it is found that even small high-frequency parametric excitation has an appreciable effect on the system response. Among other things, it shifts the resonant frequency and often changes the response characteristics markedly.

The stationary moments of Poisson-driven non-linear dynamical systems

1982 ◽  
Vol 19 (3) ◽  
pp. 702-706
Author(s):  
Charles E. Smith ◽  
Loren Cobb
Keyword(s):  
Dynamical Systems ◽  
Probability Density ◽  
Stochastic Systems ◽  
Transition Probability ◽  
Kolmogorov Equation ◽  
Transition Probability Density ◽  
Linear Dynamical Systems ◽  
Stationary Density ◽  
Non Linear ◽  
Noise Input

Moment recursion relations have previously been derived for the stationary probability density functions of continuous-time stochastic systems with Wiener (white noise) input. These results are extended in this paper to the case of Poisson (shot noise) input. The non-linear dynamical systems are expressed, in general, as stochastic differential equations, with an independent increment input. The transition probability density function evolves according to the appropriate Kolmogorov equation. Moments of the stationary density are obtained from the Fourier transform of the stationary density. The moment relations can be used to estimate the parameters of linear and non-linear stochastic systems from empirical moments, given either Wiener or Poisson input.

On the first-exit time problem for temporally homogeneous Markov processes

1976 ◽  
Vol 13 (1) ◽  
pp. 39-48 ◽  
Author(s):  
Henry C. Tuckwell
Keyword(s):  
Recurrence Relations ◽  
Diffusion Processes ◽  
Transition Probability ◽  
Exit Time ◽  
Model Neuron ◽  
Kolmogorov Equation ◽  
First Exit Time ◽  
Transition Probability Density ◽  
Homogeneous Markov Process ◽  
Time Problem

Using an integral equation of Darling and Siegert in conjunction with the backward Kolmogorov equation for the transition probability density function, recurrence relations are derived for the moments of the time of first exit of a temporally homogeneous Markov process from a set in the phase space. The results, which are similar to those for diffusion processes, are used to find the expectation of the time between impulses of a Stein model neuron.

scholarly journals The Nonlinear Behaviour of a Pantograph Current Collector Suspension

1999 ◽  
Author(s):  
L. Drugge ◽  
T. Larsson ◽  
A. Berghuvud ◽  
A. Stensson
Keyword(s):  
High Speed ◽  
Current Collector ◽  
System Response ◽  
Nonlinear Behaviour ◽  
High Speed Train ◽  
Nonlinear Characteristics ◽  
Catenary System ◽  
Parameter Values ◽  
Force Excitation ◽  
Dynamic Phenomena

Abstract The pantograph-catenary system is a critical component for trains required to run at higher speeds. The pantograph often includes nonlinear characteristics and the scope of this work is to investigate if nonlinear dynamic phenomena can occur in an existing design. A model of a pantograph suspension subsystem has been developed according to physical parameter values of the head suspension of the Schunk WBL88/X2 pantograph, providing electric power to the Swedish high-speed train X2. Studies of the system response for different force excitation show both harmonic, subharmonic and chaotic behaviour for the investigated parameter regions.

Stochastic Averaging of Quasi-Nonintegrable-Hamiltonian Systems

1997 ◽  
Vol 64 (1) ◽  
pp. 157-164 ◽  
Author(s):  
W. Q. Zhu ◽  
Y. Q. Yang
Keyword(s):  
Nonlinear System ◽  
Probability Density ◽  
Hamiltonian Systems ◽  
Present Method ◽  
Transition Probability ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Kolmogorov Equation ◽  
Transition Probability Density ◽  
System Method

A stochastic averaging method is proposed to predict approximately the response of multi-degree-of-freedom quasi-nonintegrable-Hamiltonian systems (nonintegrable Hamiltonian systems with lightly linear and (or) nonlinear dampings and subject to weakly external and (or) parametric excitations of Gaussian white noises). According to the present method, a one-dimensional approximate Fokker-Planck-Kolmogorov equation for the transition probability density of the Hamiltonian can be constructed and the probability density and statistics of the stationary response of the system can be readily obtained. The method is compared with the equivalent nonlinear system method for stochastically excited and dissipated nonintegrable Hamiltonian systems and extended to a more general class of systems. An example is given to illustrate the application and validity of the present method and the consistency of the present method and the equivalent nonlinear system method.

The stationary moments of Poisson-driven non-linear dynamical systems

1982 ◽  
Vol 19 (03) ◽  
pp. 702-706
Author(s):  
Charles E. Smith ◽  
Loren Cobb
Keyword(s):  
Dynamical Systems ◽  
Probability Density ◽  
Stochastic Systems ◽  
Transition Probability ◽  
Kolmogorov Equation ◽  
Transition Probability Density ◽  
Linear Dynamical Systems ◽  
Stationary Density ◽  
Non Linear ◽  
Noise Input

Moment recursion relations have previously been derived for the stationary probability density functions of continuous-time stochastic systems with Wiener (white noise) input. These results are extended in this paper to the case of Poisson (shot noise) input. The non-linear dynamical systems are expressed, in general, as stochastic differential equations, with an independent increment input. The transition probability density function evolves according to the appropriate Kolmogorov equation. Moments of the stationary density are obtained from the Fourier transform of the stationary density. The moment relations can be used to estimate the parameters of linear and non-linear stochastic systems from empirical moments, given either Wiener or Poisson input.

On the first-exit time problem for temporally homogeneous Markov processes

1976 ◽  
Vol 13 (01) ◽  
pp. 39-48 ◽  
Author(s):  
Henry C. Tuckwell
Keyword(s):  
Recurrence Relations ◽  
Diffusion Processes ◽  
Transition Probability ◽  
Exit Time ◽  
Model Neuron ◽  
Kolmogorov Equation ◽  
First Exit Time ◽  
Transition Probability Density ◽  
Homogeneous Markov Process ◽  
Time Problem

Using an integral equation of Darling and Siegert in conjunction with the backward Kolmogorov equation for the transition probability density function, recurrence relations are derived for the moments of the time of first exit of a temporally homogeneous Markov process from a set in the phase space. The results, which are similar to those for diffusion processes, are used to find the expectation of the time between impulses of a Stein model neuron.

Stochastic Averaging of Quasi-Nonintegrable-Hamiltonian Systems Under Poisson White Noise Excitation

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Y. Zeng ◽  
W. Q. Zhu
Keyword(s):  
Probability Density ◽  
Hamiltonian Systems ◽  
Transition Probability ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Degree Of Freedom ◽  
Kolmogorov Equation ◽  
Transition Probability Density ◽  
Poisson White Noise ◽  
Van Der Pol Oscillators

A stochastic averaging method for predicting the response of multi-degree-of-freedom quasi-nonintegrable-Hamiltonian systems (nonintegrable-Hamiltonian systems with lightly linear and (or) nonlinear dampings subject to weakly external and (or) parametric excitations of Poisson white noises) is proposed. A one-dimensional averaged generalized Fokker–Planck–Kolmogorov equation for the transition probability density of the Hamiltonian is derived and the probability density of the stationary response of the system is obtained by using the perturbation method. Two examples, two linearly and nonlinearly coupled van der Pol oscillators and two-degree-of-freedom vibro-impact system, are given to illustrate the application and validity of the proposed method.

Power Spectral Density of Nonlinear System Response: The Recursion Method

1993 ◽  
Vol 60 (2) ◽  
pp. 358-365 ◽  
Author(s):  
R. Vale´ry Roy ◽  
P. D. Spanos
Keyword(s):  
Broad Class ◽  
Formal Solution ◽  
Power Series Expansion ◽  
Kolmogorov Equation ◽  
System Response ◽  
Lanczos Algorithm ◽  
Spectral Densities ◽  
Recursion Method ◽  
Approximate Form ◽  
Single Well

Spectral densities of the response of nonlinear systems to white noise excitation are considered. By using a formal solution of the associated Fokker-Planck-Kolmogorov equation, response spectral densities are represented by formal power series expansion for large frequencies. The coefficients of the series, known as the spectral moments, are determined in terms of first-order response statistics. Alternatively, a J-fraction representation of spectral densities can be achieved by using a generalization of the Lanczos algorithm for matrix tridiagonalization, known as the “recursion method.” Sequences of rational approximations of increasing order are obtained. They are used for numerical calculations regarding the single-well and double-well Duffing oscillators, and Van der Pol type oscillators. Digital simulations demonstrate that the proposed approach can be quite reliable over large variations of the system parameters. Further, it is quite versatile as it can be used for the determination of the spectrum of the response of a broad class of randomly excited nonlinear oscillators, with the sole prerequisite being the availability, in exact or approximate form, of the stationary probability density of the response.

HFTViz: Visualization for the exploration of high frequency trading data

2021 ◽  
pp. 147387162110649
Author(s):  
Javad Yaali ◽  
Vincent Grégoire ◽  
Thomas Hurtut
Keyword(s):  
Portfolio Management ◽  
High Frequency ◽  
High Speed ◽  
High Frequency Trading ◽  
Domain Experts ◽  
Risk Return ◽  
Visualization Tools ◽  
Liquidity Measures ◽  
Trading Volumes

High Frequency Trading (HFT), mainly based on high speed infrastructure, is a significant element of the trading industry. However, trading machines generate enormous quantities of trading messages that are difficult to explore for financial researchers and traders. Visualization tools of financial data usually focus on portfolio management and the analysis of the relationships between risk and return. Beside risk-return relationship, there are other aspects that attract financial researchers like liquidity and moments of flash crashes in the market. HFT researchers can extract these aspects from HFT data since it shows every detail of the market movement. In this paper, we present HFTViz, a visualization tool designed to help financial researchers explore the HFT dataset provided by NASDAQ exchange. HFTViz provides a comprehensive dashboard aimed at facilitate HFT data exploration. HFTViz contains two sections. It first proposes an overview of the market on a specific date. After selecting desired stocks from overview visualization to investigate in detail, HFTViz also provides a detailed view of the trading messages, the trading volumes and the liquidity measures. In a case study gathering five domain experts, we illustrate the usefulness of HFTViz.

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