基于FDR阈值自动选取的拖拉机PTO转矩载荷谱外推

Extrapolation of Tractor PTO Torque Load Spectrum Based on Automated Threshold Selection with FDR

摘要:

针对时域外推过程中常用的阈值选取计算复杂、精度低等问题，基于错误发现率（False discovery rate, FDR）提出了一种阈值自动选取方法，并基于该方法进行了拖拉机动力输出轴（Power takeoff, PTO）转矩载荷谱外推研究。首先，利用开发的拖拉机PTO转矩无线监测系统采集拖拉机作业工况下的载荷数据，并进行数据预处理；将顺序拟合检验与多重检验相结合，采用FDR自动阈值选取法选取了最优阈值，确定了时域外推数据的上限阈值为342N·m，下限阈值为100N·m；基于极大似然估计对超阈值数据进行了广义帕累托分布（Generalized Pareto distribution, GPD）尺度参数和形状参数的拟合，建立了PTO转矩载荷的超阈值模型，并与传统图像法的拟合结果进行了比较，结果表明，两种方法的拟合结果与载荷样本的决定系数均大于0.995；从拟合优度来看，对于上限阈值，自动阈值选取法的拟合优度比图像法的拟合优度降低8.7%，而对于下限阈值，自动阈值选取法比图像法降低31.21%。利用时域外推方法对PTO转矩载荷数据进行外推，对外推1倍后的载荷时间历程与原载荷时间历程进行对比分析；当时域外推因子为131、PTO转矩累积频次达到106次时，得到了PTO转矩载荷谱；基于统计学特征与雨流计数分析对外推载荷谱进行了验证，结果表明，外推后的载荷谱与样本载荷谱分布规律一致，能够在保留载荷特征的前提下实现均值、幅值的双向外推。

Abstract:

The compilation of the load spectrum of tractor power output components is the main method to study the relationship between tractor working load and fatigue life. Based on the peak over threshold (POT) model, the time-domain extrapolation method of the tractor power take-off (PTO) operation load spectrum was studied. Aiming at the problems of complex calculation and low accuracy of the commonly used threshold selection methods for timedomain extrapolation, an automatic threshold selection method based on false discovery rate (FDR) was proposed. Based on this method, extrapolation of the tractor PTO torque load spectrum was realized. Firstly, a tractor PTO torque wireless acquisition system was developed to collect tractor PTO operating load data and perform data preprocessing;then, the FDR automatic threshold selection method was used to select the optimal threshold, and the upper threshold of the time-domain extrapolation data was determined to be 342N·m and the lower threshold was 100N·m. The maximum likelihood estimation was used to fit the scale parameters and shape parameters of the generalized Pareto distribution of excess threshold data, and the peak over threshold (POT) model of PTO torque load was built and compared with the fitting results of traditional image methods: the determination coefficients between the fitting results of the two methods and the load samples were greater than 0.995;from the perspective of goodness of fit, for the upper threshold, the goodness of fit of the automatic threshold selection method was 8.7% smaller than that of the image method, and for the lower threshold, the goodness of fit of the automatic threshold selection method was 31.21% smaller than that of the image method. Finally, the PTO load data was extrapolated based on the POT model, and 1 time extrapolated load data was compared with the original load time history;when the time domain extrapolation factor was 131 and the cumulative frequency of PTO torque reached 106 times, the PTO torque load spectrum was obtained. The extrapolated load spectrum was verified based on statistical characteristics and rainflow counting method. The results showed that the extrapolated load spectrum had the same distribution law as the original load spectrum, which can realize the twoway extrapolation of the average amplitude on the basis of retaining the load characteristics, providing a theoretical basis for the compilation of the tractor PTO torque load spectrum.