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.