In orbital angular momentum(OAM)multiplexing communication systems,one of the primary technologies is the recognition of the OAM modes of vortex beams.High-order Laguerre-Gaussian(LG)beams were the subject of this investigation,and recognition approach of OAM mode high-order vortex beam superposition states based on convolutional neural networks(CNNs)was suggested.The CNNs model was trained using the intensity images of high-order LG beam superposition states propagating through the atmospheric turbulence.Accurate and effective classification and identification of the O AM modes of high-order LG beam superposition states under various situations can be achieved with training data.The present investigation focuses on how different atmospheric turbulence intensities,transmission distances,beam cross-section integrity and mode intervals affect the identification accuracy of OAM mode.Findings from investigations demonstrate that in conditions with serious atmosphere turbulence,CNNs has above 99%accuracy in classifying and recognizing fixed OAM mode sets.The conclusions of the present investigation offer fresh ideas for the intelligent demultiplexing and decoding of vortex beam superposition states in atmospheric turbulence conditions.