Statistical Models for Nonstationary and Non-Gaussian Road Vehicle Vibrations

This paper presents some of the outcomes of a research project concerned with the development of a method for synthesizing, under controlled conditions in the laboratory, the random vibrations generated by road transport vehicles. Firstly, the paper deals with the development of a technique for decomposing non-stationary random vibration signals into constituent Gaussian elements. The hypothesis that random non-stationary vehicle vibrations are essentially composed of a sequence of zero-mean random Gaussian processes of varying standard deviations is tested and the paper reveals that the variations in the magnitude of the vibrations are the cause of the leptokurtic, non-Gaussian nature of the process. It is shown how non-stationary vibration signals can be systematically decomposed into these independent random Gaussian elements by means of a numerical curve-fitting procedure. The paper describes the development of the algorithm which is designed to automatically extract the parameters of each constituent Gaussian process namely the RMS level and the Vibration Dose. The validity of the Random Gaussian Sequence Decomposition (RGSD) method was tested using a set of road vehicle vibration records and was found to be capable of successfully extract the Gaussian estimates as well as the corresponding Vibration Doses. Validation was achieved by comparing the sum of these Gaussian estimates against the PDF of the original vibration record. All validation cases studied show that the RGSD algorithm is very successful in breaking-down non-stationary random vibration records into their constituent Gaussian processes. Secondly, the paper describes the development of a statistical model for characterising the nonstationarity of road vehicle vibrations. It shows that the Rayleigh and two-parameter Weibull distributions cannot be used to model the magnitude distribution. An alternative model, which is a modified form based on the Rayleigh and Weibull distributions, is introduced and is shown to offer good agreement with the statistical distribution of a broad range of experimental data.