Safety evaluation of a vehicle–bridge interaction system using the pseudo-excitation method

A method for analysing the vehicle–bridge interaction system with enhanced objectivity is proposed in the paper, which considers the time-variant and random characteristics and allows finding the power spectral densities (PSDs) of the system responses directly from the PSD of track irregularity. The pseudo-excitation method is adopted in the proposed framework, where the vehicle is modelled as a rigid body and the bridge is modelled using the finite element method. The vertical and lateral wheel–rail pseudo-excitations are established assuming the wheel and rail have the same displacement and using the simplified Kalker creep theory, respectively. The power spectrum function of vehicle and bridge responses is calculated by history integral. Based on the dynamic responses from the deterministic and random analyses of the interaction system, and the probability density functions for three safety factors (derailment coefficient, wheel unloading rate, and lateral wheel axle force) are obtained, and the probabilities of the safety factors exceeding the given limits are calculated. The proposed method is validated by Monte Carlo simulations using a case study of a high-speed train running over a bridge with five simply supported spans and four piers.

Research on probability statistics of train running safety indices based on pseudo-excitation method

In order to explore the random nature of high-speed railway train operation safety indices, the pseudo-excitation method, extreme value theory, and non-stationary harmonic superposition theory are used in this paper to study the statistics of train operation safety indices. The pseudo-excitation load formulation for track irregularity is obtained by the pseudo-excitation method, and the resulting non-stationary random vibration problem is transformed into a deterministic time history problem. The pseudo-excitation method is used to establish the dynamic equations of motion, and the separation iteration method is used to solve the equations, so as to obtain the power spectral density of the wheel-rail interaction forces. The wheel-rail interaction forces are obtained by using a modulation function and the harmonic superposition method. By fitting an extreme value distribution, the maximum values of the train running safety indices are explored. The proposed numerical approach is validated experimentally using the data from a 24.6 m long simply supported concrete bridge by studying the extreme value distributions of driving safety indices. Additional numerical simulation are conducted for varying train speeds and bridge spans. The results show that the Gumbel distribution can fit the extreme value of driving safety parameters for different speeds and different bridge span lengths. It is observed that the higher the speed, the sharper the extreme value distribution of train running safety indices, and the larger the train running safety index values corresponding to 99.87% confidence level. The corresponding extreme values at the 99.87% confidence level are greater than the maximum value of each time-domain sample.

Dynamic Reliability Evaluation by First-Order Reliability Method Integrated with Stochastic Pseudo Excitation Method

The stochastic pseudo excitation method (SPEM), which is based on the principle of pseudo excitation method (PEM), is introduced to represent the randomness of dynamic input in which the amplitude of excitation is adopted as a random variable. Based on the mathematic definition of power spectral density, a physical interpolation of the SPEM is discussed. Even if one random variable is involved in calculation, the effects of the uncertainties are required to be investigated. The SPEM offers a simple but quite effective way to solve the dynamic reliability problem. Through integrating the new algorithm into first-order reliability method (FORM), the dynamic reliability of uncertain structure subjected to random excitation is studied. A linear oscillator with three types of white noise is adopted to verify the SPEM for dynamic reliability of linear random vibration analysis. Also, the accuracy and efficiency of SPEM to handle the multi-degree-of-freedom structure is investigated in this paper.

A framework combining pseudo-excitation method and two-and-a-half-dimensional finite element method for random ground vibrations induced by high-speed trains

A framework is developed in this article to predict the nonstationary random ground vibrations induced by high-speed trains, by combining the pseudo-excitation method with the two-and-a-half-dimensional finite element method. This development contains two steps. First, the power spectral density of the wheel–rail dynamic force is accurately obtained through the combination of the pseudo-excitation method and a vehicle–slab-track–ground theoretical model. Second, the nonstationary random ground vibrations are efficiently solved by combining the pseudo-excitation method and the two-and-a-half-dimensional finite element method, where the power spectral density of the wheel–rail dynamic force obtained in the former step is used to constitute the pseudo-loads. In the numerical examples, the accuracy and efficiency of the proposed approach are validated through the comparison to the fast three-dimensional random method for train–track–soil system developed previously. The results show that the proposed approach can predict the train-induced random ground vibrations with sufficient accuracy and has three-to-five times increase in efficiency in comparison to the fast three-dimensional random method.

Random Characteristics of Vehicle-Bridge System Vibration by an Optimized Pseudo Excitation Method

The pseudo excitation method (PEM) is improved for its efficiency by incorporating the self-adaptive Gauss integration (SGI) technology as a new combining integration. The PEM can transform the random rail irregularities into some pseudo harmonic excitation, which is a mature approach to deal with the random excitation for vehicle–bridge systems. The SGI was used to distinguish the significant from the insignificant parts of an integral section for the random excitation frequency on the stochastic response of the system, thereby reducing the computational effort required for the random vibration analysis of the system. Also, the SGI can intelligently handle the recognized integral section, by subdividing the important sections into several necessary frequency points, making rough decomposition, and allowing the unimportant regions to be eliminated. Based on selected frequency points, the deterministic pseudo harmonic excitations were generated, and then the standard deviation (SD) of the time history for the system was calculated by the PEM. The vehicle subsystem was simulated as a 23-degree of freedom model, and the bridge subsystem as a three-dimensional finite element model. The time-varying power spectral density (PSD) plots of the system were presented. Besides, the cumulative distribution function (CDF) of the response was calculated using Poisson’s crossing assumption. The random characteristics for the vehicle–bridge vibrations for different speeds and rail irregularities were calculated.

Simultaneous optimization of control parameters and placements of piezoelectric patches for active structural acoustic control of shell structures under random excitation

Simultaneous optimization of multiple parameters of an active structural acoustic control system under random force excitation is presented in this article. A method integrating the pseudo excitation method, finite element method, and boundary element method is proposed to analyze the random acoustic radiation. The active structural acoustic control of randomly vibrating structures is developed using the velocity feedback control scheme with the help of the pseudo excitation method. The acoustic design optimization model is proposed, in which the auto power spectral density of sound pressure is taken as the objective function and the placements of actuators/sensors as well as control gains are assigned as design variables. Taking into account the operational efficiency and control cost, the number of actuators/sensors and the total actuation energy are considered as constraints. A simulated annealing algorithm is employed for the optimization problem with discrete and continuous variables coexisting. Numerical examples are given to demonstrate the effectiveness of the proposed methods and the programs, and several key factors on the optimized designs are also discussed.