利用优选状态数的MCMC模拟农机装备负载

传统马尔科夫链蒙特卡洛（Markov chain Monte Carlo，MCMC）方法中状态数的选取常依赖于主观经验，用于农机装备负载模拟时，状态数取值不当将导致负载模拟精度降低或算法运行时间冗长。针对此问题，该研究提出一种基于伪损伤一致性的状态数优选方法。首先确定MCMC算法中状态数的初选范围，然后分别计算范围内不同状态数所对应的负载模拟结果，最后以生成的模拟负载与原始载荷之间的损伤一致性为评价准则确定优选状态数。利用拖拉机关键零部件的实测载荷数据对该方法进行验证。结果表明，随着状态数的提高，模拟负载与原始载荷之间的损伤一致性变化趋于平稳，算法运算时长增速不断提高，相比于传统方法，基于优选状态数的MCMC算法能够得到伪损伤差异在1%以内的负载模拟结果，与载荷谱编制的目标需求更加匹配，在保证模拟结果精度的同时有效减少运算成本。该研究能够为农机装备关键零部件的动态仿真分析及可靠性试验提供更加可靠的数据支撑。

Simulation of agricultural equipment load using MCMC with optimal state number

Abstract: The selection of state number depends highly on the subjective experience in the traditional Markov Chain Monte Carlo (MCMC). However, an inappropriate value of state number can lead to a great reduction in the accuracy of load simulation, even an increase in the running time during the simulation of agricultural equipment loads. This study aims to clarify the effect of state number on the simulation when the MCMC was applied to agricultural equipment load. Specifically, the mean error, standard deviation error, and deviation of rain flow matrix between the simulated and original load decreased rapidly to stabilize, as the state number increased. Moreover, the indicators were not generalizable, if there was no significance between them. An optimization of state number was also proposed using pseudo damage consistency. As such, the damage consistency between the simulated and original load gradually improved and smoothed out, as the state number increased, whereas, the rate of increase in the operation time continued to increase. The optimal state number was calculated to satisfy the damage consistency and minimum operation time, where a threshold value was set for the pseudo damage factor. Furthermore, the field tests were carried out for both tractor ploughing and soil preparation. The specific parameters were measured to validate, including the front axle vibration, front axle stress, and driveshaft torque load. The vibration loads were also utilized to apply for the tractor front drive axle during ploughing operations. It was found that the MCMC using optimal state number can be expected torealize the load simulation with pseudo damage differences within 1%. Furthermore, there were more significant differences between the load segments in the adjustment stage, where the optimal state numbers for each load segment were more dispersed than that in the operation stage. A cyclic simulation was also developed for the loads of key components, according to the operational characteristics of a tractor. Subsequently, the MCMC cycle simulations were also performed on the front axle vibration loads for ploughing. The results show that the simulated load retained the alternating switching between the operating and adjustment stages under tractor ploughing. The same procedure was used to simulate the stress load on the front axle under ploughing, where the torque was separately loaded on the driveshaft under soil preparation. The statistical characteristic indicators were selected, including the mean, standard deviation, and the maximum load cycle amplitude for each load segment. The deviation range of each statistical eigen value was also obtained, compared with the original. The eigen values simulation for each load segment was in a higher agreement with the original eigen values. The generality was further validated when applied to the load simulation of agricultural equipment with the objective of load spectrum preparation. Consequently, the MCMC using optimal state number was better matched to the target requirements of load spectrum preparation, compared with the conventional. The finding can also effectively reduce the computational cost for the higher accuracy during load simulation of agricultural machinery.