# Impact Load Sparse Recognition Method Based on Mc Penalty Function
## 1 Introduction  
The rotor system is the most important part of large rotating machinery, and its reliability and safety have been paid increasing attention. When the rotor system operates under complex and non-stationary conditions, the internal structure of the rotor system is prone to collision, causing periodic vibration load impact of the bearing, causing the bearing to deviate from the ideal trajectory, and causing great harm [1; 2; 3]. The impact load signal is easy to be dampened by the background noise under complex working conditions. In addition, the vibration sensor is usually installed on the outer wall of the rotor system. Due to the complex transmission path, the signal will inevitably encounter signal weakening and noise interference in the process from the impact bearing to the sensor [4; 5; 6]; therefore, finding a suitable bearing impact load identification method for gas turbine rotor systems is of great help for its optimal design and stability analysis. After decades of continuous development, identification methods of impact loads have made great progress, which can be roughly divided into frequency domain method and time domain method [7; 8; 9]. The former has a long development time, mainly through the inversion of the frequency response function matrix of the system in the concerned frequency band to realize the identification of impact load. For example, [PERSON] [10] and othersdefined the coherence factor of transfer function, based on the coherence analysis of transfer function, and proposed the dynamic load identification with the minimum coherence factor of transfer function as the target. On the contrary, the time domain method uses step force integral to identify the dynamic load in time domain. For example, [PERSON] [11] proposed a method of multi-source dynamic impact load identification, based on optimal output tracking in time domain. By designing an optimal output tracker, the load identification problem is transformed into an optimal output tracking problem. [PERSON] [12] proposed a conjugate gradient iterative identification method by combining singular entropy denoising correction and regularization pre-optimization, which not only improves the ill-posed inverse problem, but also improves the solution of the inverse problem of impact load identification. [PERSON] et al. [13] proposed an L1 norm sparse recognition regularization model to break through the bottleneck of low accuracy of impact recognition based on traditional regularization. [PERSON] et al. [14] proposed an iterative weighted L1-regularized sparse decomposition method to process noisy hyperspectral information. In addition, many scholars try to add new theories and techniques to impact load identification methods, and have also made many achievements, such as optimal quality factor [15; 16], envelope demodulation [17; 18], wavelet basis [19; 20], correlation kurtosis deconvolution [21], Bayesian theory [22; 23; 24], etc. However, the above regularization method based on the L1 norm is widely used in the impact load identification, but there are still some problems in the impact of high-speed rotating machinery, such as low recognition accuracy of response noise and high amplitude components. It can be seen that the efficiency of the traditional regularization method is limited, and cannot meet the real-time requirements. Because the regularized sparse decomposition method is very sensitive to extremum, and the penalty term is a more extensive choice to produce sparse approximate solution [25; 26], in convex optimization mathematical models, the selection of penalty term will have a greater impact on the final result. On the basis of L1 norm, MC penalty function can further improve the sparsity of the solution, greatly improve the noise reduction effect, and avoid the local minimum, which makes it easier to achieve the global optimal solution [27; 28].