Discrete element model simulation and verification of fertilizer blending uniformity of variable rate fertilization based on relevance vector machine

Abstract: With the development of computer simulation technology, the model establishment of variable rate fertilization with EDEM, demonstrates effectively the microcosmic dynamics behavior of fertilizer particles which can't be analyzed by experiments. The calibration of discrete element model parameters mainly includes experimental determination and indirect calibration. When method of particle board is used to measure the static friction coefficient between particles, particle bounce and collision are inevitable and accuracy is difficult to pursue. The method of indirect calibration, using try-and-error method or quadratic polynomial regression, isn't appropriate for the discrete element model of variable rate fertilization with nonlinear as well as multiple parameter values to be calibrated. Aiming at the problem above, a calibration method based on relevance vector machine is proposed. The discrete element simulation process of variable rate fertilization is a nonlinear system regarding model parameters as input and uniformity of fertilizer blending as output (when a group of parameters are given, certain uniformity value of fertilizer blending can be gotten by fertilization simulation). Firstly, the model parameter influencing the fertilization outcome of the discrete element simulation most can be defined as the main parameters by sensitivity analysis. The value domain of each main parameters are found and then the sample of parameters are got. The sample of parameters and the corresponding uniformity of fertilizer blending are regarded as training and test sample. The relevance vector machine is used to reveal mapping relationship between model parameters and the uniformity, and the regression model is established. The uniformity based on the optimal model parameters should be consistent with the that in experiment, the model parameters fitness function is constructed combined the established models with experimental statistical results. Based on the mathematical thought of the constraint optimization, the mathematical model of optimal parameters calculating is established, and the optimal parameters are generated by the genetic algorithm. For A-type mixing cavity whose the collision edge is the outer convex curve, the mean relative error of uniformity between test values and simulation values from model calibrated: for nitrogen fertilizer is 6.4%, phosphate fertilizer of 4.1%, and potash fertilizer of 5.9%. While nitrogen fertilizer is 26.8%, phosphate fertilizer is 28.9% and potash fertilizer is 36.1% for the model before calibration. For B-type mixing cavity whose the collision edge is the straight-line, the mean relative error of uniformity from model calibrated: nitrogen fertilizer is 5.8%, phosphate fertilizer of 5.6% and potash fertilizer of 4.9%. While nitrogen fertilizer is 21.9%, phosphate fertilizer is 32.5% and potash fertilizer is 28.9% for the model before calibration. For C-type mixing cavity whose the collision edge is the concave curve, the mean relative error of uniformity from model calibrated: for nitrogen fertilizer is 5.0%, phosphate fertilizer of 3.7%, potash fertilizer of 8.7%. While nitrogen fertilizer is 36.2%, phosphate fertilizer is 31.6% and potash fertilizer is 24.4% for the model before calibration. The above results show that the method can be used to realize accurate calibration of discrete element model parameters of variable rate fertilization.