In order to effectively identify the signs of instability in the aerodynamic system of an axial compressor, a wavelet singular spectral entropy algorithm incorporated within the wavelet transform, singular value decomposition and information entropy is proposed to describe the distribution complexity of the spatial modalities in the flow field. This kind of identification design can accurately distinguish the boundary between the stable and unstable states of the internal flow field from the view of a dynamic system. On the basis of the information entropy algorithm, the wavelet singular spectral entropy algorithm is designed to integrate with the advantages of wavelet transform analysis on the time-frequency localization and singular value decomposition for signal processing and data mining together. So that the quantitative analysis of the definition of rebuilding a system image can be achieved by the solution of wavelet singular spectral entropy. This method can automatically extract the transient information of the space mode in the time-frequency domain. It effectively avoids the shortcoming that the feature extraction on spatial information cannot be accomplished from multiple angles with the single information entropy algorithm. In the data processing of instability signals under different speeds, the wavelet singular spectral entropy algorithm shows a greater advantage in the early warning for compressor stall. The result shows that the value of the wavelet singular spectral shows an obvious mutation when the aerodynamic system approaches the instability boundary. According to the threshold set, the identification hybrid algorithm can detect the stall precursor about 23~96 r in advance. Compared to the single information entropy algorithm, the hybrid wavelet singular spectral entropy algorithm is able to shift to an earlier precursor identification by about 11~82 r. This established hybrid identification algorithm accounts for the nonlinearity of the aerodynamic system, providing a new perspective for the nonlinear system instability identification.

The prediction of a stall precursor in an axial compressor is the basic guarantee to the stable operation of an aeroengine. How to predict and intelligently identify the instability of the system in advance is of great significance to the safety performance and active control of the aeroengine. In this paper, an aerodynamic system modeling method combination with the wavelet transform and gray wolf algorithm optimized support vector regression (WT-GWO-SVR) is proposed, which breaks through the fusion technology based on the feature correlation of chaotic data. Because of the chaotic characteristic represented by the sequence, the correlation-correlation (C-C) algorithm is adopted to reconstruct the phase space of the spatial modal. On the premise of finding out the local law of the dynamic system variety, the machine learning method is applied to model the reconstructed low-frequency components and high-frequency components, respectively. As the key part, the parameters of the SVR model are optimized by the gray wolf optimization algorithm (GWO) from the biological view inspired by the predatory behavior of gray wolves. In the definition of the hunting behaviors of gray wolves by mathematical equations, it is superior to algorithms such as differential evolution and particle swarm optimization. In order to further improve the prediction accuracy of the model, the multi-resolution and equivalent frequency distribution of the wavelet transform (WT) are used to train support vector regression. It is shown that the proposed WT-GWO-SVR hybrid model has a better prediction accuracy and reliability with the wavelet reconstruction coefficients as the inputs. In order to effectively identify the sign of the instability in the modeling system, a wavelet singular information entropy algorithm is proposed to detect the stall inception. By using the three sigma criteria as the identification strategy, the instability early warning can be given about 102r in advance, which is helpful for the active control.

Many problems in practical engineering can be simplified as the cantilever beam model, which is generally studied by theoretical analysis, experiment, and numerical simulation. This paper discusses the local activity of the nonlinear nonplanar motion of a cantilever beam at the equilibrium point. Firstly, the equilibrium point of the model and the Jacobian matrix have been calculated. The stability of the characteristic root corresponding to the characteristic polynomial has been analyzed. Secondly, the corresponding complexity function of the model at the equilibrium point has been given. Then, the local activity region of the model at the equilibrium point can be obtained by using the theory of the local activity. Based on the actual engineering research background, the damping coefficient is generally taken as 0 < c < 1. The cantilever beam model is the local activity at the equilibrium point only if the parameters of the model satisfy a certain condition. In the numerical simulation, it is found that when the proper parameters are selected in the local activity region, the cantilever beam can exhibit different types of chaotic motion. The local activity theory provides a theoretical basis for the parameter selection of the chaotic motion in the cantilever beam.