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The planetary boundary layer height (PBLH) has a significant impact on the energy and material exchange in the atmosphere. The traditional gradient method (GM) determines the PBLH based on the gradient change of the aerosol profile. It is susceptible to the effect of complex atmospheric conditions, which leads to uncertainties in the estimation of PBLH. Here, a random forest (RF) algorithm that considers the vertical distribution of aerosols is proposed to find the PBLH under complex atmospheric conditions. The height of the three minimum local peaks of the range correction signal (RCS) profile and seven other variables, such as aerosol layer number (ALN), relative humidity (RH), solar radiation, and other meteorological parameters, from January 2017 to December 2021 is used as an RF model input. The radiosonde estimated PBLH (PBLHRS) is used as a reference value. The sensitivity analysis indicates that the relative error of RF-estimated PBLH (PBLHRF) is smaller than that of GM-estimated PBLH (PBLHGM), and it decreases with an increase in aerosol optical depth (AOD). Moreover, RF achieves good performance under different atmospheric conditions. It can effectively overcome the effects of complex atmospheric conditions in PBLH estimation. Based on the correlation analysis, it is found that the estimation accuracy of the RF algorithm is greatly improved compared with the GM. The correlation coefficient between the PBLHRF and the PBLHRS reaches 0.8, which is much larger than that of the PBLHGM (0.47). Finally, long-term PBLHRF analysis shows that there are obvious diurnal and seasonal variations of PBLH. It increases and then decreases from early morning to late evening. It is highest in summer and lowest in winter. Overall, RF can effectively overcome the shortcomings of traditional GM and has high accuracy and robustness for various atmospheric conditions. The findings obtained here have great potential for lidar application in obtaining reliable PBLH estimations.

Electric rotary kiln is one of the key equipment in the chemical industry, which is mainly used for heating materials. In the current research, the heat calculation method of the electric rotary alumina kiln is constructed, and the heat transfer processes in the furnace, the furnace tube, and the furnace tube wall are systematically analyzed. The theoretical model of the electric rotary alumina kiln is established and solved by the fourth-order Runge–Kutta method, and the temperature rise curves in the kiln are obtained. The numerical simulation is carried out to investigate the temperature distribution of materials and gases in the furnace tube. It is revealed in the results that the temperature distribution of the electric rotary alumina kiln is more uniform than that of the internal rotary kiln, and the stable operation state can be reached in a very short time, which means that reduced furnace tube length and reduced production cost can be achieved under the same roasting requirements.