Sufficient crosswind stability is an important criterion in the approval process of railway vehicles. However, crosswind stability is in conflict with demands for light-weight constructions (especially cabin cars) and higher driving velocities. In many countries, the approval process foresees stability predictions based on worst case scenarios, where uncertainties are taken into account by means of safety factors and comparison with reference vehicles. This procedure is a burden for innovations and hinders the interoperability of railway vehicles.
The aim of our study is the development of models that allow for a quantification of the influence of random disturbances and to develop appropriate computational procedures.
The stochastic model takes uncertainties in the aerodynamic coefficients (random variables) into account. The gust load is described by a model with positive random variables for the gust amplitude and duration and a stochastic process for the fluctuations due to aerodynamic turbulence. A similar model has been recently applied to design calculations of wind turbines. Track disturbances are described as a stationary Gaussian process, for which spectral characteristics are available from measurements. The stochastic processes are discretized using appropriate decomposition techniques.
The stochastic model described above is linked with a complete model of a cabin car, which is obtained with a multi-body system simulation software. This model includes non-linear effects that stem mainly from the wheel/rail contact, bump stops and spring characteristics.
Given the stochastic description and the detailed multi-body system model, a brute force computation of the overturning probability by means of direct Monte Carlo simulation is impossible due to the large amount of CPU time needed. Therefore, sensitivity based screening is applied in order to reduce the model size and the number of stochastic parameters and metamodels are applied.
The obtained results in form of overturning probabilities give valuable hints for the actual safety level and permit a correction of the deterministic characteristic wind curves and the standardized deterministic computational procedures for crosswind stability.

 
Source: BorgWarner Turbo Systems

This project investigates the stability of rotors that are supported by sleeve bearings. To this end, nonlinear models of sleeve bearings are combined with various models of turbocharger rotors. The multi-body simulations should help to gain a better understanding of the stability properties of rotor-bearing-systems and yield better predictions of the domains of instability.

Polynomial chaos expansions of response quantities have been widely used in Computational Stochastic Mechanics and are well documented. Introduced in conjunction with a truncated Karhunen-Loeve-representation of the input random field, they represent global approximations in the Hilbert space of functions of (usually standard Gaussian) random variables. However, the global approximation character may lead to inefficient convergence behavior for higher order response moments or small response probabilities.
Therefore, after multiplicative decomposition in a deterministic and a random part, local polynomial expansions of the solution are introduced by partitioning the domain of random variables and the physical domain. By carefully choosing the local basis, the problem decouples in the random domain. The expansion coefficients can then be determined independently by parallel processing. Moreover, local expansions allow to construct new hybrid simulation schemes, that is, combinations of analytical and simulation based techniques.
For reliability estimation, the expansion can be interpreted as a local response surface. Starting from the global approximation, a local response surface can be constructed by computing the design point and sensitivities. After that, suitable local approximations can be introduced by decomposing the region of most probable failure.

For failure probability estimates of large structural systems, the numerical expensive evaluations of the limit state function have to be replaced by suitable approximations. Most of the methods proposed in the literature so far construct global approximations of the failure hypersurface. The global approximation of the failure hypersurface does not correspond to the local character of the most likely failure, which is often concentrated in one or several regions in the design space, and may therefore introduce a high approximation error for the probability of failure. Moreover, it is noted that global approximations are often constructed for parameter spaces that ignore constraints imposed by the physical nature of the problem.In this study, a robust and efficient local approximation scheme of the limit state function for the estimation of failure probabilities is proposed. The major advantages of the proposed local approximation are that the limit state function is evaluated close to the region of most likely failure only and that it is not necessary to compute zeros of the limit state function. Moreover, an interaction between the importance sampling scheme and the limit state approximation scheme becomes possible.