Abstract

Based on entropy characteristics, some complex nonlinear dynamics of the dynamic pressure at the outlet of a centrifugal compressor are analyzed, as the centrifugal compressor operates in a stable and unstable state. First, the 800-kW centrifugal compressor is tested to gather the time sequence of dynamic pressure at the outlet by controlling the opening of the anti-surge valve at the outlet, and both the stable and unstable states are tested. Then, multi-scale fuzzy entropy and an improved method are introduced to analyze the gathered time sequence of dynamic pressure. Furthermore, the decomposed signals of dynamic pressure are obtained using ensemble empirical mode decomposition (EEMD), and are decomposed into six intrinsic mode functions and one residual signal, and the intrinsic mode functions with large correlation coefficients in the frequency domain are used to calculate the improved multi-scale fuzzy entropy (IMFE). Finally, the statistical reliability of the method is studied by modifying the original data. After analysis of the relationships between the dynamic pressure and entropy characteristics, some important intrinsic dynamics are captured. The entropy becomes the largest in the stable state, but decreases rapidly with the deepening of the unstable state, and it becomes the smallest in the surge. Compared with multi-scale fuzzy entropy, the curve of the improved method is smoother and could show the change of entropy exactly under different scale factors. For the decomposed signals, the unstable state is captured clearly for higher order intrinsic mode functions and residual signals, while the unstable state is not apparent for lower order intrinsic mode functions. In conclusion, it can be observed that the proposed method can be used to accurately identify the unstable states of a centrifugal compressor in real-time fault diagnosis.

Highlights

  • In recent years, centrifugal compressors have been used widely in industry

  • Multi-scale fuzzy entropy, as a special kind of fuzzy entropy, gives a measurement of the complexity of a sequence under different scale factors [15]. Both multi-scale fuzzy entropy (MFE) and improved multi-scale fuzzy entropy (IMFE) are used in the paper to investigate the complex nonlinear dynamic characteristics of dynamic pressure at the outlet of a centrifugal compressor, and identify the unstable state of the system

  • The multi-scale fuzzy entropy curves based on the dynamic pressure with different scales are are

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Summary

Introduction

Centrifugal compressors have been used widely in industry. As an intrinsic characteristic of the centrifugal compressor, surge can cause flow-induced vibration and lower aerodynamic performance. Based on the scale feature of the signal itself, EEMD could decompose a signal into several intrinsic mode functions, in order to achieve better analysis performance [18] It is suitable for analyzing nonlinear and non-stationary signal sequences because of its high signal-to-noise ratio. Some fundamental theories related to MFE, improved multi-scale fuzzy entropy (IMFE), and EEMD, are used and developed to describe the dynamic pressure of flow at the outlet of a centrifugal compressor. A method combining IMFE with EEMD is proposed to measure the complexity of the intrinsic mode function of dynamic pressure under different scale factors and the probability of new information with the changes of dimension. Some conclusions are obtained, and the feasibility of the method is verified to identify surge

Multi-Scale Fuzzy Entropy and Improved Multi-Scale Fuzzy Entropy
Define the distance d jl between and as the maximum value
Fuzzy entropy is defined as the negative natural logarithm
Coarse-grained fuzzyentropy entropy
Ensemble Empirical Mode Decomposition
Data Acquisition of Dynamic Pressure
Multi-Scale
Improved
EEMD Decomposition of Dynamic Pressure
Correlation between IMF Components and Dynamic Pressure
IMFE of IMF Components for Dynamic Pressure
11. Spectrograms time series series and better IMF components in 68
Statistical Reliability of IMFE of IMF Components for Dynamic Pressure
7.Conclusions
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