Modeling of loads on a vehicle through Laplace moving averages is extended to the multivariate setting and efficient methods of computing the damage indexes are discussed. Multivariate Laplace moving averages are used as statistical models of multi-axial loads represented by forces and moments measured at some locations of a cultivator. As opposed to models based on the Gaussian distribution, these models account explicitly for transients that have a common origin—vibrations that can be caused by large obstacles encountered by a cultivator or a vehicle driving into potholes.
The model is characterized by a low number of parameters accounting for fundamental characteristics of multivariate signals: the covariance matrix representing size of loads and their mutual dependence, the excess kurtosis that in the model is related to relative size of transients, and the time scale that accounts for the vehicle speed. These parameters can be used to capture diversity of environmental conditions in which the vehicle operates. Distributions of parameter values that are specific to a given market or encountered by specific customers can be then used to describe the long term loading. The model is validated by analysis of the resulting damage index. It is shown that the parameters enter this index in a multiplicative and explicit manner and, for a given damage exponent, only the factor representing dependence on the kurtosis has to be obtained through regression approximation based on Monte Carlo simulations. An example of actual cultivator data is used to illustrate the accuracy of damage and fatigue life prediction.
Keywords Damage variability; Multi-axial rainflow; Laplace moving averages; Multi-axial loads
Authors and Affiliations
- Mats Kvarnström, Fraunhofer-Chalmers Centre
- Krzysztof Podgorski, Lund University (Statistics)
- Igor Rychlik, Mathematical Sciences, Chalmers University of Technology