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LiDAR is widely used in Simultaneous Localization and Mapping (SLAM) and autonomous driving. The LiDAR odometry is of great importance in multi-sensor fusion. However, in some unstructured environments, the point cloud registration cannot constrain the poses of the LiDAR due to its sparse geometric features, which leads to the degeneracy of multi-sensor fusion accuracy. To address this problem, we propose a novel real-time approach to sense and compensate for the degeneracy of LiDAR. Firstly, this paper introduces the degeneracy factor with clear meaning, which can measure the degeneracy of LiDAR. Then, the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering method adaptively perceives the degeneracy with better environmental generalization. Finally, the degeneracy perception results are utilized to fuse LiDAR and IMU, thus effectively resisting degeneracy effects. Experiments on our dataset show the method's high accuracy and robustness and validate our algorithm's adaptability to different environments and LiDAR scanning modalities., Comment: 13 pages