基于KANN-DBSCAN带宽优化的核密度估计载荷谱外推

Extrapolation of Load Spectrum Based on KANN-DBSCAN Bandwidth Optimization Kernel Density Estimation

针对核密度估计载荷外推全局固定带宽的局限性,提出一种基于KANN-DBSCAN(K-average nearest neighbor density-based spatial clustering of applications with noise)改进带宽取值的核密度估计(kernel density estimation, KDE)载荷外推方法。通过KANN-DBSCAN聚类算法对载荷数据进行分组聚类,采用拇指法求得不同簇间的最优带宽,然后进行核密度估计,再采用蒙特卡洛模拟进行外推。以某电动汽车在用户道路的实测载荷数据为应用对象,对外推方法的合理性进行检验。从统计参数检验量、拟合度检验和伪损伤检验3个指标对外推效果进行评估。结果表明:相比固定带宽的核密度估计外推方法,基于KANN-DBSCSN核密度估计的外推方法获得的外推载荷在统计参数上与实测载荷更为接近,均值、标准差和最大值的误差分别仅为1.9%、 4.3%和1.9%;幅值累计频次曲线拟合度R2均大于0.99,伪损伤均接近1。结果验证了该聚类方法在核密度估计载荷外推的有效性,有助于编制汽车在用户道路上的载荷谱,为具有相似载荷分布特点的机械零部件载荷外推提供了参考。

Considering the limitation of global fixed bandwidth of load extrapolation for kernel density esti⁃mation,a load extrapolation method based on K-Average Nearest Neighbor Density-Based Spatial Clustering of Ap⁃plications with Noise(KANN-DBSCAN)kernel density estimation(KDE)is proposed.The load data is grouped and clustered using the KANN-DBSCAN clustering algorithm,and the Rule-of-thumb(ROT)method is used to ob⁃tain the optimal bandwidth between different clusters.Then the kernel density estimation is conducted,and finally extrapolation is carried out using Monte Carlo simulation.The extrapolation rationality is verified using the measured load data of a certain electric vehicle on user road as the application object.The extrapolation effect is assessed by the three indicators of statistical parameter quantity,goodness of fit,and pseudo-damage.The results show that com⁃pared with the traditional fixed bandwidth kernel density estimation extrapolation method,the extrapolation load ob⁃tained by the DBSCSN kernel density estimation extrapolation method is closer to the actual load in statistical param⁃eters,and the error of the mean,standard deviation,and maximum value is only 1.9%,4.3%,and 1.9%,respec⁃tively.The magnitude cumulative frequency curve fits R2 are all greater than 0.99,and the pseudo-damage is close to 1.The results show the effectiveness of the clustering method in kernel density estimation load extrapolation,which is helpful for compiling the load spectrum of electric vehicles on customer service road,and can provide refer⁃ence for the load extrapolation of mechanical parts with similar load distribution characteristics.