1.Energy and Power Engineering Institute, University of Shanghai for Science and Technology, Shanghai 200093, China 2.Shanghai Key Laboratory of Multiphase Flow and Heat Transfer for Power Engineering, Shanghai 200093, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 51976131, 51676131) and the Shanghai Committee of Science and Technology, China (Grant No. 19060502200)
Received Date:27 April 2020
Accepted Date:06 August 2020
Available Online:22 December 2020
Published Online:20 December 2020
Abstract:A novel signal processing method named adaptive variational mode decomposition with the fractal (AFVMD), which is based on variational mode decomposition and fractal theory, is proposed in this paper for solving a problem that it is easy to misjudge the working conditions of the centrifugal compressor. The measured signal of a compressor is unstable, so a traditional method is used to analyze the nonlinear phenomenon of the stall flutter. Owing to the fact that the robustness of VMD method is strong and its combination with the fractal dimension can accurately describe self-similarity and fractal characteristics of a measured signal, the proposed AFVMD method can not only achieve noise reduction, but also extract nonlinear feature from a complex signal. Taking the dynamic pressure data of the impeller during the instability of a centrifugal compressor as an object to verify the effectiveness and superiority of the proposed AFVMD method, the results are obtained as follows. Firstly, compared with the wavelet noise reduction method, the proposed AFVMD method has both noise reduction and feature extraction functions, and the compressor pressure pulsation spectrum has more significant stall characteristics. Secondly, none of the traditional nonlinear analysis methods can reflect the stall process, so the chaotic phase space attractor is used to visualize the flow field changes. Due to the reasonable choice of the delay time and the embedding dimension, the physical information originally mixed in the signal is separated, so that the attractor phase diagram method has a better process of judging the flow stall than the frequency spectrum method. The results show that the proposed AFVMD method can judge the compressor about to enter into the deep surge earlier. Thirdly, In order to quantify the superiority of the proposed method, if the process of surging and the occurrence of deep wheezing can be predicted in advance, the largest Lyapunov exponent is used as an evaluation index. The above results show that the largest Lyapunov exponent of the proposed AFVMD is smallest for illustrating that the signal has more accurate flow field nonlinear information, which improves the predictability of the signal. Keywords:chaotic/ Lyapunov exponent/ variational mode decomposition/ fractal
如图4所示, 为同时实现流场信号降噪与非线性特征提取. 引入粒子群优化算法(particle swarm optimization, PSO), 交替更新由惩罚因子α及模态分解数K构成的PSO种群参数, 提取具有最小分形维数的模态分量, 以实现降噪和特征提取. 其中AFVMD的迭代停止条件与PSO进化停止条件一致, 由(11)式给出: 图 4 FGN序列处理前后对比 Figure4. Comparison of FGN before or after the filtering.
表2最佳延迟时间及嵌入维数 Table2.Optimal parameters including delay time and embedded dimension.
图 5 流场降噪效果对比 (a) 最小流量工况1; (b) 最小流量工况2; (c) 浅喘工况1; (d) 浅喘工况2 Figure5. De-noise effectiveness comparisons of the flow field information: (a) The minimum flow condition 1; (b) the minimum flow condition 2; (c) the shallow breath condition 1; (d) the shallow breath condition 2.
由图5可知, 从“最小流量工况”与“浅喘工况”中的流场转频(约584 Hz)在AFVMD处理后比小波降噪更加明显, 体现所提出方法的优越性. 在“最小流量工况2”中, 140 Hz为最大主频, 表明此系统处于失速状态(约为主频的24%); “浅喘工况1”中, 出现主频为19 Hz的峰值, 因接近亥姆霍兹共振频率18.1 Hz[32], 故为系统的浅喘频率, 体现所提出方法的可靠性. 基于最佳延迟时间与嵌入维数, 分别对原序列、小波处理及AFVMD处理后的信号进行相空间重构. 重构10种不同工况结果如图6所示. 图 6 不同工况相空间 (a) 原始序列; (b) 小波降噪处理序列; (c) AFVMD处理序列 Figure6. Reconstructed phase space of different conditions: (a) The original signals; (b) the signals proceed by the wavelet; (c) the signals processed by the AFVMD.