PDEM-Based Response Analysis of Nonlinear Systems with Double Uncertainties

Point group identification algorithm in dynamic response analysis of nonlinear stochastic systems

Comparison of PDEM and MCS: Accuracy and efficiency

In civil and offshore engineering, the safety and serviceability of complex structures are of great concern due to the randomness involved in both external excitations and structural properties. Therefore, nonlinear stochastic dynamics of multi-dimensional complex systems plays a central role in the performance assessment of such structures. In the past decade, a new family of probability density evolution method (PDEM) was developed for this purpose. In this method, based on the principle of preservation of probability, a generalized density evolution equation was derived. In contrast to the celebrated FPK and Liouville equations, the dimension of this family of equation depends only on the number of quantities of interest instead of the dimension of the original dimension. In this paper, a newly proposed generalized F-discrepancy (GF-discrepancy) is outlined and adopted as the objective function in point selection of PDEM. By doing so, the efficiency and accuracy of PDEM could be improved and guaranteed for random variables of general distributions. Numerical examples are illustrated. Problems to be further studied are discussed.

Direct integration variance prediction of random response of nonlinear systems

In periodic forced response analysis of nonlinear structures, most of the time analytical solutions cannot be obtained due to the complex behavior of the nonlinearity and/or due to the number of nonlinear equations to be solved. Therefore, numerical methods are widely used. For periodic forced response analysis of nonlinear systems, generally Harmonic Balance Method (HBM) or Describing Function Method (DFM), which transform the nonlinear differential equations into a set of nonlinear algebraic equations, are used. In the literature, there exist several nonlinear algebraic equation solvers based on Newton’s method which have different convergence properties and computational expense. In this paper, comparison of computational performance of different nonlinear algebraic equation solvers are studied where, solvers with different convergence order are selected based on the number of Jacobian matrix and vector function evaluations. In order to compare the performance of these selected nonlinear solvers, a lumped parameter model with cubic stiffness nonlinearity is considered. Several case studies are performed and nonlinear solvers are compared to each other in terms of solution time based on error tolerance used.

Non-intrusive frequency response analysis of nonlinear systems with interval uncertainty: A comparative study

Reliability assessment of stochastic dynamical systems using physics informed neural network based PDEM

Probability density evolution method for seismic displacement-based assessment of earth retaining structures

Ground seismic response analysis based on the probability density evolution method

Surrogate modeling immersed probability density evolution method for structural reliability analysis in high dimensions

Dynamic reliability analysis of slopes based on the probability density evolution method

Limit analysis of stochastic structures in the framework of the Probability Density Evolution Method

Stochastic modeling of engineering dynamic excitations for stochastic dynamics of structures

Running trains on a long-span bridge under earthquake is an inevitable problem for the high-speed railway in seismic regions. This paper aims to investigate the seismically random dynamic behavior of train–cable stayed bridges interaction system using the probability density evolution method (PDEM). The system simultaneously involves the multi-effect of random multi-point earthquake excitations with traveling waves and random track irregularity. The multi-point earthquake excitations, composed of lateral and vertical positions, are generated by stochastic harmful functions (SHFs) and uniformly modulated into nonstationary random processes. The motion equation of such a system is established by coupling the 38-degree vehicles and bridges through the refined random wheel/rail contact relationship and accounting for the phase-lags of seismic travelling waves between pier excitations. PDEM is proven to be applicable to such time-dependent systems and is then used to transform the random excitations into a series of deterministic representative excitations with initial probability. By solving for the corresponding deterministic probability responses, various nonstationary random responses, including the time-dependent probability density evolution functions of random responses, mean values curves and standard deviations, can be obtained easily. A case study based on the cable-stayed bridge is then presented, and the results show the effectiveness and accuracy of the proposed method by comparison with Monte Carlo Simulation. Additionally, the influence of train speed and seismic intensity on the safety and reliability of trains is discussed.

This article presents an efficient method for analyzing the dynamic reliability of maglev vehicle-bridge coupled systems by combining a theoretical model with an adaptive surrogate model and the probability density evolution method (PDEM). First, a refined theoretical model of a maglev vehicle-bridge coupling system is established. Next, an adaptive surrogate model of the equivalent extreme value of the system dynamic response is established by combining an adaptive sampling method with radial basis functions. Finally, the adaptive surrogate model and PDEM are combined to further improve the efficiency of the dynamic reliability analysis. In the numerical example, the theoretical model of the maglev vehicle-guideway system was first validated by comparing with the measured data from the Shanghai high-speed maglev line. Then, by treating the controller parameters as normally distributed random variables, the accuracy and efficiency of the proposed reliability method were verified through comparison with the Monte Carlo method and the one-stage sampling surrogate model. Additionally, the impact of the randomness of each controller parameter and the coefficient of variation of the controller parameters on the system’s dynamic reliability was discussed.