基于自适应带宽核密度估计的载荷外推方法研究  

Load Extrapolation Method Based on Adaptive Bandwidth Kernel Density Estimation

作　　者：牛文铁[1] 才福友 付景静 NIU Wentie;CAI Fuyou;FU Jingjing(Key Laboratory of Mechanism Theory and Equipment Design, Ministry of Education, Tianjin University, Tianjin 300350, China)

机构地区：[1]天津大学机构理论与装备设计教育部重点实验室,天津300350

出　　处：《农业机械学报》2021年第1期375-384,共10页Transactions of the Chinese Society for Agricultural Machinery

基　　金：国家重点研发计划项目(2017YFD0700300)。

摘　　要：为了快速准确地得到玉米收获机车架的载荷谱,针对载荷谱编制过程中传统的载荷外推方法的局限性,提出一种基于四叉树算法的自适应带宽核密度估计(Kernel density estimation)算法,用来进行载荷外推。将经过预处理的实测原始载荷数据进行雨流计数统计,得到载荷循环均幅值矩阵,将小于载荷循环最大幅值10%的载荷滤除,其余的载荷循环均幅值数据根据四叉树分割算法进行不同区域的分割,选择高斯核函数,根据拇指法则计算各个区域的局部最优带宽,并根据数据区域内数据点的密集程度对核密度估计的输入进行优化,减少了核密度估计的计算量,最后结合蒙特卡洛模拟算法进行载荷外推。采用玉米收获机车架实测载荷数据进行实例验证,结果表明,与传统的固定带宽、自适应带宽核密度估计的载荷外推方法相比,本文提出的方法大大提高了计算效率,其概率密度函数图与实际载荷分布更为接近;载荷循环均幅值频次分布相关系数更接近于1,均方根误差更小;载荷循环幅值累积频次曲线的决定系数均大于0.99。For the limitation of the traditional load extrapolation methods in the process of load spectrum compilation,an adaptive bandwidth kernel density estimation algorithm was proposed based on the quad-tree algorithm to obtain the load spectrum,which can obtain the corn harvester frame more accurately and quickly.Firstly,the rain flow counting method was applied to count the pretreated measured load data.The load cycles whose amplitudes were less than 10%of the maximum load cycle amplitude value were filtered.The remaining load data were segmented into different regions according to the quad-tree segmentation algorithm.The Gaussian kernel function was selected as the kernel function,and the local optimal bandwidth of the data in each region was calculated according to the rule of thumb.In addition,the input of the kernel density estimation was optimized according to the density of data points in the data area,which reduced the calculation consumption of kernel density estimation.The measured load data from the frame of the corn harvester were used for verifying the effectiveness of proposed method.Compared with the traditional load extrapolation methods of fixed and adaptive bandwidth kernel density estimation,the proposed method greatly improved the computational efficiency,the probability density calculated by the proposed method was closer to the actual load distribution.The correlation coefficient of frequency distribution of load cycle mean and amplitude was closer to 1,and the root mean square error was smaller.The determining coefficient of the amplitude cumulative frequency curve was greater than 0.99.The results showed that the research result can provide reference for load extrapolation and load spectrum compilation.

关 键 词：玉米收获机 车架 载荷谱 载荷外推 自适应带宽核密度估计 蒙特卡洛模拟 

分 类 号：S225.5[农业科学—农业机械化工程] TU413.4[农业科学—农业工程]