Abstract:

Service load spectrums of the mechanical structure throughout its life cycle are the foundation of reliability design.In theory，these spectrums are measurable via the installation of the sensors on the mechanical structure.However，in practice，due to the labour and R＆D costs，the service load spectrums are only measured for a short period in the entire life cycle of mechanical structure.To obtain the load spectrum throughout the life cycle，load spectrum extrapolation technique is usually employed in practice，which involves using the probability statistical law of the measured random load spectrum to predict the remaining operational load spectrum under the same working condition.

Currently，the load spectrum extrapolation technique is generally divided into two main categories：time-domain extrapolation method and rainflow-domain extrapolation method，according to the form of extrapolation.For the rainflow-domain extrapolation method，the from-to or range-mean rainflow matrices are generated by counting the load spectrum and are employed to estimate the two dimensional joint probability density of the rainflow matrix based on the kernel density theory.The parameters of the probability density function have been estimated using the maximum likelihood estimation method.In this type of extrapolation method，the accuracy of the extrapolated load spectrum is affected by the selection of the probability density function and the estimated parameters of the probability density function.For the time-domain extrapolation method，statistical techniques are adopted to build the measured load spectrum’s characteristic model.The extreme value theory，for example，is employed to characterize the probability distribution of the excess samples.The time domain extrapolation method extrapolates the load spectrum to a desired length with a given extrapolated factor.Moreover，it extrapolates the load spectrum directly without any conversions，such as rainflow counting and Markov time-domain reconstruction，which reduces the errors generated by too many links and maximizes the retention of load information.Therefore，the time-domain load spectrum extrapolation method based on the extreme value theory has attracted growing interest among researchers and become a popular method in load spectrum extrapolation research.

To address the main weaknesses of the existing mehtod，a time-domain extrapolation method for torsional loads with extreme value samples following the generalized Pareto distribution（GPD）function is proposed in this paper.The main process of the proposed extrapolation method is summarized in three steps：turning point extraction，extreme value sampling，and extreme sample distribution function fitting.Specifically，the extrapolation method first determines an interval range based on the mean value of the extreme value samples exceeding the function，and takes the minimum Mean squared error of the shape parameters as the goal，determines the optimal threshold value through the self sampling method，and then estimates the shape parameters and size parameters of the GPD function using the maximum likelihood estimation method.The extreme value samples obtained from the torsional random load spectrum obey the GPD distribution law.Taking the stabilizer bar in the cab of commercial vehicle as the research object，this paper introduces the method of torsional load acquisition，and then conducts extrapolation research based on the proposed torsional load time domain extrapolation method.Our results indicate the constructed load extrapolation method has good adaptability to the load extrapolation of the torsional rotation of the commercial vehicle cab stabilizer bar.