Citation: Zhang, M.; Zhang, J.;
Hou, A.; Xia, A.; Tuo, W. Dynamic
System Modeling of a Hybrid Neural
Network with Phase Space
Reconstruction and a Stability
Identification Strategy. Machines 2022,
10, 122. https://doi.org/10.3390/
machines10020122
Academic Editor: Hui Ma
Received: 22 December 2021
Accepted: 6 February 2022
Published: 9 February 2022
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Article
Dynamic System Modeling of a Hybrid Neural
Network with Phase Space Reconstruction and a Stability
Identification Strategy
Mingming Zhang
1,2
, Jia Zhang
1
, Anping Hou
3,
*, Aiguo Xia
4
and Wei Tuo
4
1
Faculty of Science, Beijing University of Technology, Beijing 100124, China; mmzhang@bjut.edu.cn (M.Z.);
j15090483406@163.com (J.Z.)
2
Zhengzhou Aerotropolis Institute of Artificial Intelligence, Zhengzhou 451162, China
3
School of Energy and Power, Beihang University, Beijing 100191, China
4
Beijing Aeronautical Technology Research Center, Beijing 100076, China; xag14l@tsinghua.org.cn (A.X.);
tirwit@163.com (W.T.)
* Correspondence: houap@buaa.edu.cn; Tel.: +86-010-8231-6624
Abstract:
Focusing on the identification of dynamic system stability, a hybrid neural network model
is proposed in this research for the rotating stall phenomenon in an axial compressor. Based on the
data fusion of the amplitude of the spatial mode, the nonlinear property is well characterized in
the feature extraction of the rotating stall. This method of data processing can effectively avoid the
inaccurate recognition of single or multiple measuring sensors only depending on pressure. With the
analysis on the spatial mode, a chaotic characteristic was shown in the development of the amplitude
with the first-order spatial mode. With the prerequisite of revealing the essence of this dynamic
system, a hybrid radial basis function (RBF) neural network was adopted to represent the properties
of the system by artificial intelligence learning. Combining the advantages of the methods of K-means
and Gradient Descent (GD), the Chaos–K-means–GD–RBF fusion model was established based on
the phase space reconstruction of the chaotic sequence. Compared with the two methods mentioned
above, the calculation accuracy was significantly improved in the hybrid neural network model.
By taking the strategy of global sample entropy and difference quotient criterion identification, a
warning of inception can be suggested in advance of 12.3 revolutions (296 ms) with a multi-step
prediction before the stall arrival.
Keywords:
dynamic system stability; hybrid neural network; spatial modal amplitude; chaotic phase
space reconstruction; global sample entropy; identification strategy
1. Introduction
As one of the most difficult problems in dynamic system stability, the rotating stall
phenomenon seriously restricts the performance and operation safety of the compressor.
After the idea of active control for the stall in compressors proposed by Epstein [
1
], two
recognized stall types were reported by researchers. McDougall [
2
] and Day [
3
] first
discovered the pre-stall inception as the modal wave and the spike wave. Paduano [
4
]
divided the development of the rotating stall in the compressor into four stages in detail,
namely as the pre-stall, the initial disturbance stage of the rotating stall, the complete stall
stage and the surge stage. Considering the importance of identifying stall precursors in
advance, a lot of effort has been made in terms of signal recognition.
The cross-correlation analysis on the measured pressure signals was performed by
Tahara [
5
]. It was found that as the stall approached, the correlation decreased significantly.
A variance method was used by Liu [
6
] to detect the precursor signal of instability in the
compressor. Then, an embedded early warning system was developed for rotating stall
recognition. An alarm can be given about 20 ms and 80 ms before the stall arrival, for the
Machines 2022, 10, 122. https://doi.org/10.3390/machines10020122 https://www.mdpi.com/journal/machines
