Multiscale fluctuation dispersion entropy (MFDE) has been proposed to measure the dynamic features of complex signals recently. Compared with multiscale sample entropy (MSE) and multiscale fuzzy entropy (MFE), MFDE has higher calculation efficiency and better performance to extract fault features. However, when conducting multiscale analysis, as the scale factor increases, MFDE will become unstable. To solve this problem, refined composite multiscale fluctuation dispersion entropy (RCMFDE) is proposed and used to improve the stability of MFDE. And a new fault diagnosis method for hydraulic pumps using particle swarm optimization variational mode decomposition (PSO-VMD) and RCMFDE is proposed in this paper. Firstly, PSO-VMD is adopted to process the original vibration signals of hydraulic pumps, and the appropriate components are selected and reconstructed to get the denoised vibration signals. Then, RCMFDE is adopted to extract fault information. Finally, particle swarm optimization support vector machine (PSO-SVM) is adopted to distinguish different work states of hydraulic pumps. The experiments prove that the proposed method has higher fault recognition accuracy in comparison with MSE, MFE, and MFDE.

Hydraulic pumps are the core components of the entire hydraulic system, which are known as the “heart” of the hydraulic system. They are typical high-speed rotating machines which are often in a state of high speed and high load, so they are more to be out of order than other construction machines. The faults of hydraulic pumps will affect the work of the entire hydraulic system and even cause huge economic losses and casualties. Therefore, the research of hydraulic pumps fault diagnosis has very important practical significance [

Analyzing vibration signals of mechanical equipment is a common method for fault diagnosis [

Variational mode decomposition (VMD) [

Entropy is a good method to detect the stability of complex signals. The commonly used entropy includes sample entropy (SE) [

However, the traditional coarse-graining method does not consider the relationship between each coarse-grained time series, and as the scale factor increases, the entropy values will become unstable [

Combining PSO-VMD and RCMFDE, a novel fault diagnosis method of hydraulic pumps based on PSO-VMD, RCMFDE, and PSO-SVM is proposed. First, PSO-VMD is adopted to process the original vibration signals of hydraulic pumps, and the sensitive IMFs are filtered out through the correlation coefficient method for reconstruction to obtain the denoised vibration signals, then the fault features are extracted by RCMFDE, and finally the fault feature vectors are input into PSO-SVM to complete the fault diagnosis of hydraulic pumps. PSO-VMD can effectively remove the impact of noise and highlight the fault features. RCMFDE is more stable and has a stronger ability to extract fault features in comparison with MFDE, MSE, and MFE. And SVM is a powerful supervised machine learning method with good generalization ability, which possesses obvious advantages in dealing with small sample classification problems [

In conclusion, the core innovation of this paper is the application of entropy theory in the field of fault diagnosis. RCMFDE is proposed and applied to hydraulic pump fault diagnosis; meanwhile, optimized VMD is proposed to preprocess vibration signals so as to highlight fault features. The rest structure of this paper is as follows. Sections

VMD is a novel signal processing method, which is adopted to decompose the original signal into several IMFs. In this section, we briefly summarize the steps of VMD algorithm. The detailed principle of VMD is shown in [

The core idea of VMD is to address the following constrained optimization problem:

In order to solve the constraint problem, a quadratic penalty term

The optimal solution is

The effect of VMD is greatly affected by

PSO-VMD algorithm needs to determine a fitness function, calculate the corresponding fitness value when the particle position is updated, and update it by comparing the fitness value of old and new particles. It can be seen from the above that entropy can well reflect the dynamic features of complex time series. PE is sensitive to noise, and the higher the PE value, the higher the noise content of the component, while the smaller it indicates that the component contains more fault information. Therefore, the mean permutation entropy (MPE) is taken as the fitness function in this paper. Each particle represents a combination of

Set the initial parameters of PSO algorithm and take

Calculate the MPE corresponding to the particle positions of the initial population and obtain the MMPE as the fitness value

Update particles and calculate the MPE corresponding to each particle after update

Compare and update the fitness value

Iterative loop and output the best

Flow chart of PSO-VMD.

For the nonlinear time series

where

where

The time series

where

Transform

Each time series

where

FDE is calculated by

For

where

By calculating the FDE value of time series

The above coarse-graining method is currently the most commonly used data processing method for multiscale entropy. As shown in Figure

For

where

RCMDE is calculated by

Two different coarse-graining methods. (a) The traditional coarse-graining method when

The sliding coarse-graining processing method comprehensively considers all elements in original time series, avoids information omission in traditional coarse-graining processing method, and thus has better performance. Therefore, this paper adopts RCMFDE to extract fault feature information of hydraulic pumps.

The main parameters of RCMFDE are the embedding dimension

In order to compare the performance of RCMFDE, CMFDE, and MFDE, simulation noise signals are adopted for experiments, in which CMFDE, MFDE, and RCMFDE have the same parameters, where

Comparison of RCMFDE, CMFDE, and MFDE. (a) Mean value and SD of WGN and l/f noise using different methods. (b)CV of WGN and l/f noise using different methods.

It is observed from Figure

In order to accurately distinguish different fault states of hydraulic pumps, this paper proposes a fault diagnosis method of hydraulic pumps using PSO-VMD and RCMFDE. Figure

Step 1: PSO-VMD is adopted to decompose collected vibration signals of hydraulic pumps, and sensitive IMF components are reconstructed according to correlation coefficient method to enhance the fault features and obtain vibration signals after noise reduction.

Step 2: take

Step 3: all training samples are input into PSO-SVM for training.

Step 4: all testing samples are input into the fault classifier after training to identify, and complete hydraulic pumps fault identification.

Flow chart of the proposed method.

The hydraulic pump vibration signals were collected by the hydraulic pump experiment platform. The model type of hydraulic pump in the experiment was SY-10MCY14-1EL. Figure

The experiment device. (a) The experiment platform of hydraulic pump. (b) Hydraulic pump and test device.

The fault types of plungers. (a) Plunger loose slipper. (b) Piston shoe wear.

Time domain waveforms of original vibration signals. (a) Normal working state. (b) Single plunger loose slipper. (c) Double plungers loose slipper. (d) Piston shoe wear.

Using PSO-VMD and correlation coefficient method to remove the impact of noise, the specific steps are as follows:

Use PSO to optimize VMD to get the best

Calculate the correlation coefficients between the original signal and each IMF components, and calculate the mean value as the threshold values

Filter out and reconstruct the IMF components whose correlation coefficient is greater than the threshold to obtain the vibration signal after noise reduction

This paper takes the vibration signal of piston shoe wear (S) as an example. First, PSO is used to optimize VMD to get the best

Parameters of PSO-VMD.

G | ||||||
---|---|---|---|---|---|---|

10 | 10 | 1.5 | 1.5 | 0.5 | [3 12] | [50 5000] |

Fitness value curve.

PSO-VMD decomposition.

Correlation coefficients.

IMF | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Average |
---|---|---|---|---|---|---|---|---|---|

Correlation coefficient | 0.1232 | 0.1873 | 0.4628 | 0.3893 | 0.3167 | 0.4626 | 0.3734 | 0.3742 | 0.3362 |

Optimum combination of parameters.

Fault types | |
---|---|

N | |

S | |

D | |

P |

Time domain waveforms of denoised vibration signals. (a) Normal working state. (b) Single plunger loose slipper. (c) Double plungers loose slipper. (d) Piston shoe wear.

After obtaining the denoised vibration signals, 50 samples are selected for each state, and the sample length is 2048 points. There are total 200 samples (50 samples × 4 fault types). RCMFDE, CMFDE, and MFDE of 20 scale factors for each sample are calculated, and the corresponding results are shown in Figure

RCMFDE, CMFDE, and MFDE of four kinds states of the hydraulic pump.

To accurately distinguish different work states, the RCMFDE of all samples are calculated. For each state, 30 groups of samples are randomly selected for training and another 20 groups are as testing samples. Input the fault feature vectors of 120 training samples into the PSO-SVM classifier for training. The labels corresponding to the four states of N, S, D, and P are 1, 2, 3, and 4, respectively. The parameter settings of PSO-SVM are shown in Table

Parameters of PSO-SVM.

G | ||||||
---|---|---|---|---|---|---|

200 | 20 | 1.5 | 1.5 | 0.5 | [0 100] | [0 1000] |

Outputs of testing samples.

To compare the performance of different methods, CMFDE, MFDE, MDE, MFE, and MSE are adopted to replace the RCMFDE for the hydraulic pump fault diagnosis. Each method has been run 50 times. Table

Parameters of different methods.

RCMFDE | CMFDE | MFDE | MDE | MFE | MSE | |
---|---|---|---|---|---|---|

Embedding dimension | 2 | 2 | 2 | 2 | 2 | 2 |

Time delay | 1 | 1 | 1 | 1 | 1 | 1 |

Classes | 6 | 6 | 6 | 6 | ||

Threshold | 0.15 | 0.15 | ||||

Fuzzy parameter | 2 | |||||

Largest scale factor | 20 | 20 | 20 | 20 | 20 | 20 |

Classification accuracy of different methods.

The accuracy of different methods.

Different methods | Classification accuracy (%) | CPU time (s) | ||
---|---|---|---|---|

Max | Min | Mean | ||

PSO-VMD and RCMFDE | 100 | 100 | 100 | 204.01 |

PSO-VMD and CMFDE | 100 | 98.75 | 99.78 | 205.88 |

PSO-VMD and MFDE | 100 | 91.25 | 96.75 | 39.12 |

PSO-VMD and MDE | 98.75 | 92.50 | 96.58 | 39.29 |

PSO-VMD and MFE | 98.75 | 92.50 | 95.73 | 843.11 |

PSO-VMD and MSE | 97.5 | 87.5 | 93.63 | 453.50 |

To compare the effect of fault identification before and after noise reduction, without PSO-VMD, multiscale entropy methods are adopted to directly extract fault information of the hydraulic pump. The sample processing method is the same as previous. Figure

Classification accuracy of different methods without PSO-VMD.

The accuracy of different methods without PSO-VMD.

Different methods | Classification accuracy (%) | ||
---|---|---|---|

Max | Min | Mean | |

RCMFDE | 98.75 | 91.25 | 95.33 |

CMFDE | 97.5 | 90 | 95.25 |

MFDE | 97.5 | 90 | 92.90 |

MDE | 95 | 90 | 92.53 |

MFE | 93.75 | 86.25 | 90.03 |

MSE | 93.75 | 83.75 | 89.25 |

In order to accurately and efficiently identify different fault states of hydraulic pumps to prevent the occurrence of safety accidents. This paper proposes a new method for hydraulic pumps fault diagnosis based on PSO-VMD and RCMFDE. Experimental analysis proves the great performance of the proposed method. The main work and innovations of this article are as follows:

The coarse-graining method of MFDE is improved and RCMFDE is proposed, which has better fault features extraction ability and stability.

PSO is used to optimize VMD, which solves the defect that the parameters need to be set manually.

Combining PSO-VMD and RCMFDE, a new hydraulic pump fault diagnosis method is proposed. Experimental analysis shows that this method has the best fault diagnosis capability compared with other methods.

In the future, we will further study the entropy theory and try to apply similar methods to fault diagnosis of other mechanical equipment such as planetary gearboxes and rolling bearings, so as to expand the application scope of similar methods.

The experimental data are provided by the Mechanical Engineering College and cannot be disclosed.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Thanks are due to the Mechanical Engineering College for supplying the hydraulic pump data.