# Intelligent Diagnosis of Compound Faults of Gearboxes Based on Periodical Group Sparse Model
## 5 Conclusions and Future Work  
This paper proposes an intelligent diagnosis method for gearbox compound faults based on a periodic group sparse model and verifies its effectiveness through experiments. First, a group sparse model with overlapping characteristics is constructed by combining the respective advantages of different models. Then, a binary periodic sequence is constructed as prior knowledge of fault components, and the penalty term of the group sparse model is improved to achieve inter-group sparsity among different faults and intra-group sparsity of a single fault. Finally, combining the label-consistent sparse dictionary achieves fault classification and identification under different states. In the experimental verification, simulation signals containing two different fault components and the PHM Data Challenge gearbox fault dataset were used. The experimental results show that the proposed method exhibits high accuracy and robustness under various conditions. Specifically:  
1. Simulation Signal Experiment: In the simulation signal containing 55 Hz and 30 Hz fault components, the proposed method successfully extracted their respective fault features without underestimating the amplitude, maintaining high signal reconstruction accuracy. 2. PHM Dataset Experiment: Using the PHM Data Challenge gearbox fault dataset under different rotational speeds and load conditions, the proposed method achieved an overall accuracy of 97% in identifying compound faults. In the dataset containing six fault types, the overall recognition accuracy was 91%. Compared to traditional methods such as Sparse Representation Classification (SRC) and K-SVD, the proposed method improved fault recognition accuracy by 6% and 4%, respectively. Additionally, tests conducted in actual industrial environments demonstrated that the method can stably and effectively identify gearbox compound faults under various working conditions, further proving its feasibility in engineering applications. Future research can further explore the following directions:  
1. Model Optimization: Improving the penalty term and algorithms in the periodic group sparse model to enhance the accuracy and computational efficiency of fault feature extraction. 2. Multi-fault Type Recognition: Extending the method to handle more types of compound faults, especially those involving complex mechanical systems with multiple fault scenarios. 3. Real-time Application: Applying the proposed diagnostic method in actual industrial environments to verify its real-time performance and stability under different working conditions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Fault Categories**} & \multicolumn{2}{c}{**Rotational Speed:**} & \multicolumn{2}{c}{**Rotational Speed:**} & \multicolumn{2}{c}{**Rotational Speed:**} \\  & \multicolumn{2}{c}{**2100 rpm/min**} & \multicolumn{2}{c}{**2400 rpm/min**} & \multicolumn{2}{c}{**3000 rpm/min**} \\ \cline{2-7}  & **High Load** & **Low Load** & **High Load** & **Low Load** & **High Load** & **Low Load** \\ \hline Normal & 97.0 & 97.0 & 97.0 & 98.0 & 96.0 & 98.0 \\ \hline Rolling & \multirow{2}{*}{91.0} & \multirow{2}{*}{84.0} & \multirow{2}{*}{89.0} & \multirow{2}{*}{87.0} & \multirow{2}{*}{93.0} & \multirow{2}{*}{85.0} \\ element fault & & & & & & \\ \hline Outer & \multirow{2}{*}{94.0} & \multirow{2}{*}{93.0} & \multirow{2}{*}{90.0} & \multirow{2}{*}{93.0} & \multirow{2}{*}{97.0} & \multirow{2}{*}{88.0} \\ ring fault & & & & & & \\ \hline Shaft imbalance & 92.0 & 90.0 & 91.0 & 90.0 & 95.0 & 91.0 \\ \hline Overall & \multirow{2}{*}{93.5} & \multirow{2}{*}{91.0} & \multirow{2}{*}{91.8} & \multirow{2}{*}{92.0} & \multirow{2}{*}{95.3} & \multirow{2}{*}{90.5} \\ Accuracy & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fault classification identification performances under different working conditions. Data-driven Optimization: Utilizing big data and machine learning techniques to further optimize the fault diagnosis model, enhancing its adaptability and accuracy.