基于核密度估计的拖拉机传动轴载荷外推方法

An extrapolation method of tractor propeller shaft load based on kernel density estimation

关键词:  拖拉机  传动轴  载荷外推  非参数法  核密度估计  拇指法

Key words:  tractor  propeller shaft  load extrapolation  non-parameter method  kernel density estimation  rule-of-thumb

摘要:

为编制拖拉机传动轴在实际作业工况下的载荷谱，针对拖拉机传动轴载荷具有单峰和多峰的特点及参数外推的局限性，运用拇指法(Rule-of-thumb，ROT)确实带宽，提出一种改进的基于核密度估计(Kernel density estimation，KDE)的载荷外推方法。通过搭建拖拉机传动轴无线扭矩测试系统并进行田间试验，获得了传动轴犁耕工况下的载荷数据，采用拇指法求得From-To雨流矩阵的最优带宽，并由雨流矩阵计算出核密度估计阈值，对大于阈值的载荷采用基于核密度估计的非参数法进行外推，小于阈值的载荷则按比例外推，最后对外推载荷的合理性进行验证。结果表明:与传统非参数法相比，采用基于核密度估计的外推方法时，运算时间缩短了54.16%；与实测载荷相比，外推后的均值、标准差和最大值的误差分别为2.2%、0.87%和6.3%，拟合度R²和伪损伤比均大于0.99。用此方法对传动轴的其他工况载荷进行外推，同样得到了良好的效果。基于核密度估计的外推方法有助于编制反映拖拉机传动轴实际受载工况的载荷谱，同时为具有相似载荷分布特点的机械零部件载荷外推提供参考。

Abstract:

In order to compile the load spectrum of the tractor propeller shaft under actual working conditions for the characteristics of single peak and multi-peak of tractor propeller shaft load and the limitation of parameter extrapolation, the rule-of-thumb(ROT)method was used to calculate the bandwidth. An improved load extrapolation method based on kernel density estimation(KDE)was proposed in this study. By building a set of wireless torque test system for tractor propeller shaft and conducting field tests, the propeller shaft load data under ploughing conditions were obtained, the optimal bandwidth of the From-To rain flow matrix was obtained based on ROT, and the kernel density estimation threshold was calculated from the rain flow matrix. The non-parametric method based on KDE was used to extrapolate the loads larger than the threshold, and the loads smaller than the threshold were extrapolated proportionally. Finally, the rationality of the extrapolated loads was verified. The results showed that: Compared with the traditional non-parametric method, when using the extrapolation method based on KDE, the calculation time was shortened by 54. 16%; Compared with the measured load, the extrapolated mean, standard deviation, and maximum error were respectively 2. 2%, 0. 87% and 6. 3%, which were within the allowable error range of engineering application. The cumulative frequency curves of extrapolated load and test load were drawn, respectively, Both the goodness of fit R² and the pseudo-damage ratio were greater than 0. 99. This method was used to extrapolate the load of other working conditions of the propeller shaft, and good results were also obtained. In conclusion, the extrapolation method based on KDE is helpful to compile the load spectrum reflecting the actual loading condition of the tractor propeller shaft. This study provides references for the extrapolation of mechanical parts with similar load distribution characteristics.