Bolted joints are widely employed as fasteners, but the loosening of them leads to severe safety risks. Prediction for Remaining Bolt Loosening Life (RBLL) allows for more proactive management of equipment and can help to optimize maintenance schedules, which hence reduces maintenance costs. Due to the complex structure and various working conditions of bolted joints, it is difficult to describe the loosening process with an intrinsic mechanism. The lack of understanding on mechanism makes it difficult to predict RBLL using conventional approaches. This paper develops a passive monitoring system based on Inertial Measurement Units (IMUs) for monitoring multi bolts in complex structures. By analyzing the vibration signals obtained by bonded sensors around joints, the changes in structural properties caused by loosening can be detected and used to evaluate RBLL. A novel prediction algorithm for RBLL is presented in this paper: with a pipeline of preprocessing, signal feature extraction, dimensionality reduction, and regression, a mapping from vibration signals to RBLL are established. The dimensionality reduction methods compress original features into fewer but informative and non-redundant ones. The compression elimination undesirable noise and prevent overfitting, resulting in improvements in both prediction accuracy and training speed. Specifically, the number of features is compressed from 972 to 200, and Rooted Mean Squared Error (RMSE) is reduced to about 19.0% with Training Time Cost (TTC) to about 22.3%.