Solid-state LiDARs have become an important perceptual device for simultaneous localization and mapping (SLAM) due to its low-cost and high-reliability compared to mechanical LiDARs. Nevertheless, existing solid-state LiDARs-based SLAM methods face challenges, including drift and mapping inconsistency, when operating in dynamic environments over extended periods and long distances. To this end, this paper proposes a robust, high-precision, real-time LiDAR-inertial SLAM method for solid-state LiDARs. At the front-end, the raw point cloud is segmented to filter dynamic points in preprocessing process. Subsequently, features are extracted using a combination of Principal Component Analysis (PCA) and Mean Clustering to reduce redundant points and improve data processing efficiency. At the back-end, a hierarchical fusion method is proposed to improve the accuracy of the system by fusing the feature information to iteratively optimize the LiDAR frames, and then adaptively selecting the LiDAR keyframes to be fused with the IMU. The proposed method is extensively evaluated using a Livox Avia solid-state LiDAR collecting datasets on two different platforms. In experiments, the end-to-end error is reduced by 35% and the single-frame operational efficiency is improved by 12% compared to LiLi-OM.