Time-domain load extrapolation method for combine harvesters based on MEF-LSM threshold optimization

Combined harvesters often work under alternating random loads in complex field environments. Fatigue failure can be caused in critical components, such as the front and rear axles and chassis frames. Therefore, the performance and harvesting efficiency of the combine harvester is also required to accurately analyze the time-domain load features of key components during field harvesting. Load spectra can be used to accurately assess fatigue life, specifically for the fatigue endurance and reliability of agricultural machinery, like harvesters. Among them, load spectra can be derived from the actual field working conditions. Due to the high cost of compiling load spectra, it is often feasible only to measure load data over a limited period, followed by load extrapolation to obtain the full-life load spectrum. Current load extrapolation can be classified into time-domain and rainflow extrapolation. Among them, rainflow extrapolation can include the fitting approaches into parametric rainflow with single or mixed distributions, and nonparametric rainflow with kernel density estimation and extremal theory. However, rain-flow extrapolation can lose the load time history during extrapolation, thus limiting its application in load extrapolation. Time-domain extrapolation is used as the peak over threshold (POT) for extrapolation. However, empirical approaches can suffer from significant variability in extrapolation due to an unreasonable threshold. An accurate threshold is often required for the accurate computation under an overly complex scenario. This study aims to obtain high accuracy of load extrapolation using imaging techniques. The optimal thresholds were then selected for the POT models in time-domain extrapolation. A threshold optimization was proposed in empirical mode decomposition (EMD) using the mean excess function-least squares method (MEF-LSM) approach. An example was taken to measure the strain signals from a tracked combine harvester. Time-domain load extrapolation was conducted to validate the approach. Initially, the EMD was employed to decompose the non-stationary load signals of combine harvesters during the field operation. These signals were separated into the primary load and trend components suitable for the POT extrapolation using non-stationary time-domain load signals. The amplitude load was then selected for optimal extrapolation. Furthermore, the MEF was applied to the dominant load after decomposition to determine candidate threshold intervals. The optimal threshold was obtained to investigate the relationship between the LSM feature parameters of different candidate thresholds and the validation metrics of the extrapolation. It was found that the overshoot threshold samples exhibited the best fitting performance, with the maximum validation metric R² for the extrapolation, when the feature parameters were minimal (the residual sum of squares was minimal). Therefore, the threshold was selected as the optimal parameter. The super-threshold load was extracted from the super-threshold sample. The generalized pareto distribution (GPD) was used to fit the distribution of extreme points in the super-threshold sample. The shape and scale parameters were calculated to obtain the GPD distribution function. The GPD distribution function was then used to simulate the extrapolation for the extrapolated main load. The main and trend loads were linearly combined to obtain the time-domain extrapolated load for the combine harvester. Finally, the original and the extrapolated load were compared with the relative errors of 1.62%, 1.04%, and 3.89%, for the standard deviation, root mean square, and kurtosis coefficient, respectively. Rainfall count analysis showed that both original and extrapolated loads shared an amplitude correlation coefficient of 0.9953 and a mean correlation coefficient of 0.9936 between them. The smaller characteristic parameters corresponded to higher accuracy in threshold extrapolation. Specifically, the MEF-LSM was achieved in a 1.23% improvement in the R² verification metric for threshold extrapolation, compared with the mean excess function image. The MEF-LSM was verified after comparison. The findings can provide a strong reference to compile the load spectra for combined harvesters. The fatigue life can also be accurately predictand after reliability analysis of agricultural machinery equipment.