Zur Beschreibung fahrbahnunebenheitsinduzierter Radkraftschwankungen von Straßenfahrzeugen auf der Basis stochastischer Differentialgleichungen

Statistical analysis of vehicle vibrations due to random road roughness using stochastic differential equations.

The pavement roughness as the main source of low frequent vehicle oscillations leads to a significant variation in the vertical wheel forces. Describing the pavement roughness as a normally distributed stochastic process, an efficient method to quantify these variations in the vertical wheel forces based on simplified vehicle models is shown. As can be seen from experiments, a proper consideration of the correlation between the roughness amplitudes acting at the several wheels is essential. Applying the spectral factorization theorem the transformation matrix of a shaping filter, a synthetic system describing the stochastic characteristics of the roughness amplitudes, can be obtained. By establishing a state space model of the shaping filter and combining it with that of the vehicle to an augmented state space model, stochastic differential equations can be used to describe the vibrations of vehicles due to random surface roughness. The covariance matrix, which for zero mean and normally distributed system input contains the total information about the system's response, can be calculated very efficiently based on the Lyapunov matrix equation.