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To accurately extract the fault characteristics of vibration signals of rotating machinery is of great significance to the unit online monitoring and evaluation. However, because the current feature extraction methods are mainly for single channel, the results of feature extraction are often inaccurate. To this end, a coupling fault feature extraction method based on bivariate empirical mode decomposition (BEMD) and full spectrum is proposed for rotating machinery. Firstly, the two-dimensional orthogonal signal obtained by orthogonal sampling technique is decomposed by bivariate empirical mode decomposition to obtain the intrinsic mode function with phase information. In order to obtain the sensitive modal components, the sensitivity coefficients are constructed on the basis of mutual information. Then, the sensitivity coefficient of each intrinsic mode function is calculated, and the intrinsic mode function with the larger sensitive coefficient is selected as the sensitive component. Finally, the full spectrum of the sensitive component is obtained using the full vector envelope technique, so as to get a comprehensive and accurate characteristic component. The results of simulations experiment and an application example show that this method can extract the fault characteristic component of the rotating machinery comprehensively and accurately. It is of great significance to realize the accurate diagnosis of coupling faults of rotating machinery.

Rotating machinery is one of the key parts of large mechanical equipment, such as hydraulic turbine, steam turbine, and wind turbine, which have found wide application in various industrial fields [

At present, many scholars have done some research on the feature extraction of rotating machinery fault signal, especially in the matter of signal processing methods. The main methods are wavelet transform (WT) [

The characteristics of different fault feature extraction method.

Method | Characteristic |
---|---|

WT | The choice problem for basis functions exists and the different vibration will show the characteristics of different waveforms. |

| |

EMD | It lacks rigorous theoretical basis and there is a serious phenomenon of modal aliasing in the decomposition process. |

| |

VMD | It solves the problem of mode mixing in EMD, but there are parameter optimization problems in VMD. |

| |

BEMD | It can detect synchronous features contained in the two-dimensional signal and comprehensively extract the information of fault signal. |

However, due to the complex mechanism of the fault of rotating machinery, as well as the vibration signal being often nonlinear, the vibration signals in different directions may represent different fault characteristic information [

In 2007, bivariate empirical mode decomposition (BEMD) was firstly introduced by Rilling et al. [

Molla et al. [

The joint information between different sensors such as phase information and synchronization is of significance for rotating machinery condition to evaluate [

In this paper, we proposed a coupling fault feature extraction method based on bivariate empirical mode decomposition and full spectrum for rotating machinery. In order to suppress noise interference in the signal component, the sensitivity coefficients are constructed on the basis of mutual information and through the sensitive coefficient to extract unique IMFs of the signal. The specific arrangement of this paper is organized as follows. A review on bivariate empirical mode decomposition (BEMD) is illustrated in Section

The essence of bivariate empirical mode decomposition (BEMD) is to decompose a two-dimensional signal adaptively into intrinsic mode components with physical meaning. The modal component obtained from the decomposition is a series of single component signals from high frequency to low frequency in two directions. This paper takes Algorithm II in [

Determine the direction of projection

The two-dimensional signal

Extract the corresponding moment for the local maximum of

Calculate the mean of the maximum envelope

Similar to the EMD decomposition process, the residual component is calculated:

Determine whether the

Record the resulting IMF and remove it from the original signal. And get IMF1 as

Repeat the above steps until you get all the IMFs. The original signal can be expressed as

Mutual information can measure the degree of interdependence between the two variables, which means that the information content is shared between the two variables [

The IMFs can be obtained by bivariate empirical mode decomposition (BEMD) for the fault vibration signals. However, not all the IMFs are important to the evaluation condition of machinery rotating, so it is significant to select the sensitive IMFs [

(1) According to formula (

(2) Calculate the mutual information

(3) Calculate the sensitivity coefficient of each modal component IMFs as follows:

There are usually two vertical sensors in the same section of the rotor for rotating machinery to extract vibration information. The full spectrum can fuse the information of vibration signals in two orthogonal directions and comprehensively express the intensity and spectrum structure of the rotor vibration [

The core idea of the full spectrum is that rotating machinery shows whirling phenomena under the combination of harmonic frequencies. The whirling trajectory is a series of ellipses. The length of the long axis of the ellipse is defined as the principal vibration vector to evaluate vibration intensity. The length of the short axis of the ellipse is defined as the auxiliary vector to evaluate vibration intensity as auxiliary. And through the whirling intensity under the harmonic frequency of rotor, the rotating machinery fault is diagnosed and identified [

Set

The length of the long axis of the ellipse

The length of the short axis of the ellipse

and

Therefore, utilize Fourier transform for the vibration signals in two orthogonal directions and obtain the characteristic information of each direction, whose full spectrum is required, which can simplify the calculation between complex Fourier parameters. This method not only greatly reduces the amount of calculation, but also is very accurate and established a contact with the conventional analysis method. When the information source is a single source, the algorithm is still established, fully meeting the requirements of real-time detection and analysis.

Owing to the complexity, coupling, and uncertainty of rotating machinery faults, the intrinsic dynamic characteristics of the faults are more complicated. The external manifestation is that the vibration signals in different directions may indicate different characteristic information, and the single-channel signal characteristics diagnosis for rotary machinery is prone to misjudgment and leakage judgment. And BEMD and full spectrum have advantages in the processing of two-dimensional signals and information fusion. Therefore, this paper proposes a new coupling fault feature extraction method based on BEMD and full spectrum for rotating machinery. To select the sensitive IMF, use the sensitivity coefficient based on mutual information as the screening criteria. The extraction process of this method is shown in Figure

Flow chart of the proposed method.

Collect the orthogonal vibration signal of the rotating machine in the normal and fault condition by the sensor.

The orthogonal fault vibration signal is decomposed by BEMD to obtain

Calculate the sensitivity of each IMF.

Select the modal component IMFs with the larger sensitive coefficient as sensitive modal components IMFs.

Full spectrum analysis of the selected modal components IMFs is carried out to detect the characteristic frequency of coupling fault signals.

There are two common phenomena, a change in amplitude at the typical frequency [

Components of normal and fault vibration signal.

Components of normal vibration signal

Components of fault vibration signal

The

Observation signal of normal and faulty.

The proposed method is used to extract the feature of the simulation signal in Figure

Sensitivity coefficient of each characteristic component.

IMF | IMF1 | IMF2 | IMF3 | IMF4 | IMF5 |
---|---|---|---|---|---|

Sensitivity coefficient | | 0.693 | | 0.767 | 0.654 |

Results of BEMD decomposition for fault signal.

The IMF1 and IMF3, whose sensitivity coefficient is greater than 1, are selected as sensitive IMFs. Utilize the full vector envelope technique to fuse the sensitive IMFs selected and obtain full spectrum of the sensitive IMFs as shown in Figure

Full spectrum of sensitive IMFs.

Based on the full spectrum of the sensitive IMFs in Figure

To verify the effectiveness of the proposed method in coupling fault feature extraction for rotating machinery, the experimental studies on a hydroelectric turbine in upper reaches of Yellow River are conducted. The experimental signals are acquired from the prototype of hydroelectric turbine with 5 blades and 16 guide vanes, the maximum water head is 25.7 m, the rated head is 16 m, the rated power of the turbine is about 49 MW, and the rated speed is 107.1 r/min (1.79 Hz). Figure

Specific layout of measuring point in hydroelectric turbine.

The measured data are collected turbine guide bearing by the vibration and throw monitoring sensors turbine guide bearing (As shown in Figure

Raw vibration data of normal and fault signals.

Using the method proposed in this paper to extract the coupling fault feature of turbine guide bearing, firstly, the fault signal is decomposed by BEMD, and the results of the decomposition are shown in Figure

BEMD decomposition results of measured fault signal.

EMD decomposition results of real and imaginary part of measured fault signal.

The decomposition results of real fault signal

The decomposition results of imaginary part fault signal

On the basis of BEMD decomposition, the sensitivity coefficients of each IMFs are calculated, as shown in Table

Sensitivity coefficients of BEMD modal components.

IMFs | IMF1 | IMF2 | IMF3 | IMF4 | IMF5 |
---|---|---|---|---|---|

Sensitivity coefficient | 0.661 | | | 0.564 | |

Sensitivity coefficients of EMD modal components.

IMFs | IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | IMF9 |
---|---|---|---|---|---|---|---|---|---|

Real part | 0.831 | | | 0.73 | 0.455 | | 0.495 | 0.393 | 0.543 |

Imaginary part | 0.76 | | 0.877 | | | 0.742 | 0.436 | 0.874 | 0.432 |

Full vector envelope spectrum of BEMD.

Spectrum of EMD decomposition sensitive component.

It can be seen from Figure

This paper proposed a method to extract a feature from orthogonal signals in two-direction sensors for the condition monitoring of rotating machinery based on bivariate empirical mode decomposition (BEMD) and full spectrum.

BEMD is employed to decompose signals from two orthogonal sources together; thus a complicated rotation can be represented by a set of simpler rotation components. BEMD is proved to outperform standard EMD for two orthogonal signals, because the intrinsic mode functions (IMFs) derived by BEMD preserve the signal phase information, detect synchronous features contained in the two-dimensional signal, and effectively solve the problem of misjudgment and leakage judgment in extract feature method by single-channel signal for rotary machinery. Thus the comparison of IMFs for different health conditions is made reasonable and easy.

A criterion based on mutual information is proposed for selecting the most sensitive IMF. The definition of this standard is to better represent the IMF of the original signal and penalize IMFs that cannot distinguish between different health conditions. Therefore, the IMF selected always ensures that it retains unique information about a particular health condition.

The performance of the proposed method has been evaluated for the hydroelectric turbine in upper reaches of Yellow River. Experiments results verified the effectiveness of the proposed method in two orthogonal directions, fault feature extraction and fault diagnosis for rotating machinery.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (nos. 51779206, 51279161) and the science and technology projects of Water Resources Department of Shaanxi Province (no. 2015slkj-04). Furthermore, the authors are grateful to the staff of China Electric Power Research Institute and State Grid Gansu Province Electric Power Research Institute.