# A Vibration Signal-Based Method for Fault Identification and Classification in Hydraulic Axial Piston Pumps

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Analysis Procedure

- $p\left[n\right]$ predictable part of the signal (CS1) the periodic part;
- $r\left[n\right]$ is the remaining noise containing all contributions not included in $p\left[n\right]$. This term can also incorporate CS2 contributions that are related to cyclic frequencies not contained in the periodic part CS1.

## 3. Experimental Activity

^{3}/rev, equipped with a hydro-mechanical load-sensing regulator.

^{2}and a bandwidth up to 10 kHz that can measure a maximum continuous sinusoidal acceleration of 20,000 m/s

^{2}. The acquisitions were performed by means of a relative encoder for the angular sampling. The angular resolution of the encoder (0.1 deg) led to high sampling frequencies (2000 r/min, 120,000 Hz), significantly higher than the frequency necessary to exploit the accelerometer’s bandwidth.

- Fault 1: worn port plate (F1)
- Fault 2: port plate with cavitation erosion (F2)
- Fault 3: worn slippers (F3)
- Fault 4: cylinder block damaged on the contact surface with the port plate (F4).

^{3}/rev), equivalent to a swash plate angle of 12.8°, with different values of the delivery pressure and of the angular speed, as shown in Table 1.

## 4. Experimental Results

## 5. Classifier Comparison

_{ij}represents the number (frequency, if normalized by the number of samples of class i) of patterns belonging to class i classified as belonging to class j. The name comes from the fact that shows whether two classes are confused (i.e., commonly mislabeling one for another).

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BCS | Blind Component Separation |

BSE | Blind Signal Extraction |

BSS | Blind Source Separation |

CS1 | First-Order Cyclostationary |

CS2 | Second-Order Cyclostationary |

CSC | Cyclic Spectral Coherence |

FDI | Fault Detection and Identification |

KNN | K Nearest Neighbors |

PCA | Principal Component Analysis |

PHM | Prognostics and Health Management |

PSD | Power Spectral Density |

RUL | Remaining Useful Life |

SA | Synchronous Average |

SCD | Spectral Correlation Density |

STD | Standard |

SVM | Support Vector Machine |

## References

- Ma, Z.; Wang, S.; Shi, J.; Li, T.; Wang, X. Fault diagnosis of an intelligent hydraulic pump based on a nonlinear unknown input observer. Chin. J. Aeronaut.
**2018**, 31, 385–394. [Google Scholar] [CrossRef] - Lu, C.; Wang, S.; Wang, X. A multi-source information fusion fault diagnosis for aviation hydraulic pump based on the new evidence similarity distance. Aerosp. Sci. Technol.
**2017**, 71, 392–401. [Google Scholar] [CrossRef] - Tidriri, K.; Chatti, N.; Verron, S.; Tiplica, T. Bridging data-driven and model-based approaches for process fault diagnosis and health monitoring: A review of researches and future challenges. Annu. Rev. Control
**2016**, 42, 63–81. [Google Scholar] [CrossRef] - Gao, Y.; Zhang, Q. A Wavelet Packet and Residual Analysis Based Method for Hydraulic Pump Health Diagnosis. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2006**, 220, 735–745. [Google Scholar] [CrossRef] - Gao, Y.; Zhang, Q.; Kong, X. Wavelet-based pressure analysis for hydraulic pump health diagnosis. Trans. ASAE
**2003**, 46, 969–976. [Google Scholar] - Lu, C.; Wang, S.; Zhang, C. Fault diagnosis of hydraulic piston pumps based on a two-step MD method and fuzzy C-means clustering. Proc Inst. Mech. Eng. Part C J Mech. Eng. Sci.
**2016**, 230, 2913–2928. [Google Scholar] [CrossRef] - Du, J.; Wang, S.; Zhang, H. Layered clustering multi-fault diagnosis for hydraulic piston pump. Mech. Syst. Signal Process.
**2013**, 36, 487–504. [Google Scholar] [CrossRef] - Mancò, S.; Nervegna, N. Theoretical and experimental studies on the thermodynamic efficiency of a hydraulic pump. In Proceedings of the ASME International Mechanical Engineering Congress and Exposition, San Francisco, CA, USA, 12–17 November 1995. [Google Scholar]
- Lana, E.D.; de Negri, V.J. A New Evaluation Method for Hydraulic Gear Pump Efficiency through Temperature Measurements. In Proceedings of the SAE 2006 Commercial Vehicle Engineering Congress & Exhibition, Rosemont, Chicago, IL, USA, 31 October–2 November 2006. [Google Scholar] [CrossRef]
- Casoli, P.; Campanini, F.; Bedotti, A.; Pastori, M.; Lettini, A. Overall Efficiency Evaluation of a Hydraulic Pump with External Drainage Through Temperature Measurements. J. Dyn. Syst. Meas. Control
**2018**, 140, 081005. [Google Scholar] [CrossRef] - Antoni, J.; Danière, J.; Guillet, F. Effective vibration analysis of IC engines using cyclostationarity. Part I: A methodology for condition monitoring. J. Sound Vib.
**2002**, 257, 815–837. [Google Scholar] [CrossRef] - Antoni, J.; Danière, J.; Guillet, F.; Randall, R.B. Effective vibration analysis of IC engines using cyclostationarity. Part II: New results on the reconstruction of the cylinder pressure. J. Sound Vib.
**2002**, 257, 839–856. [Google Scholar] [CrossRef] - Yu, J. Machine health prognostics using the Bayesian-inference-based probabilistic indication and high-order particle filtering framework. J. Sound Vib.
**2015**, 358, 97–110. [Google Scholar] [CrossRef] - Fan, Z.; Li, H. A hybrid approach for fault diagnosis of planetary bearings using an internal vibration sensor. Measurement
**2015**, 64, 71–80. [Google Scholar] [CrossRef] - Cernetic, J. The use of noise and vibration signals for detecting cavitation in kinetic pumps. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
**2009**, 223, 1645–1655. [Google Scholar] [CrossRef] - Alfayez, L.; Mba, D. Detection of incipient cavitation and determination of the best efficiency point for centrifugal pumps using acoustic emission. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng.
**2005**, 219, 327–344. [Google Scholar] [CrossRef] - Altare, G.; Rundo, M. CFD analysis of gerotor lubricating pumps at high speed: Geometric features influencing the filling capability. In Proceedings of the ASME/BATH Symposium on Fluid Power and Motion Control, Chicago, IL, USA, 12–14 October 2015. [Google Scholar] [CrossRef]
- Rundo, M.; Altare, G.; Casoli, P. Simulation of the Filling Capability in Vane Pumps. Energies
**2019**, 12, 283. [Google Scholar] [CrossRef] - Buono, D.; Siano, D.; Frosina, E.; Senatore, A. Gerotor pump cavitation monitoring and fault diagnosis using vibration analysis through the employment of auto-regressive-moving-average technique. Simul. Model. Pract. Theory
**2017**, 71, 61–82. [Google Scholar] [CrossRef] - Du, W.; Yang, C.; Li, A.; Wang, L. Wavelet leaders based vibration signals multifractal features of plunger pump in truck crane. Adv. Mech. Eng.
**2013**, 2013, 676404. [Google Scholar] [CrossRef] - Wang, J.; Hu, H. Vibration-based fault diagnosis of pump using fuzzy technique. Measurement
**2006**, 39, 176–185. [Google Scholar] [CrossRef] - MHodkiewicz, R.; Norton, M.P. The effect of change in flow rate on the vibration of double-suction centrifugal pumps. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng.
**2002**, 216, 47–58. [Google Scholar] [CrossRef] - Sinha, J.K.; Rao, A.R. Vibration Based Diagnosis of a Centrifugal Pump. Struct. Health Monit.
**2006**, 5, 325–332. [Google Scholar] [CrossRef] - Sakthivel, N.R.; Sugumaran, V.; Babudevasenapati, S. Vibration based fault diagnosis of monoblock centrifugal pump using decision tree. Expert Syst. Appl.
**2010**, 37, 4040–4049. [Google Scholar] [CrossRef] - Casoli, P.; Bedotti, A.; Campanini, F.; Pastori, M. A methodology based on cyclostationary analysis for fault detection of hydraulic axial piston pumps. Energies
**2018**, 11, 1874. [Google Scholar] [CrossRef] - Paliwal, M.; Kumar, U.A. Neural networks and statistical techniques: A review of applications. Expert Syst. Appl.
**2009**, 36, 2–17. [Google Scholar] [CrossRef] - Ramdén, T. Condition Monitoring and Fault Diagnosis of Fluid Power Systems—An Approaches with Neural Networks and Parameter Identification. Ph.D. Thesis, Linköping University, Linköping, Sweden, 1998. [Google Scholar]
- Ramdén, T.; Krus, P.; Palmberg, J. Fault diagnosis of complex fluid power systems using neural networks. In Proceedings of the Fourth Scandinavian International Conference on Fluid Power, Tampere, Finland, 26–29 September 1995. [Google Scholar]
- Ramdén, T.; Krus, P.; Palmberg, J. Reliability and sensitivity analysis of a condition monitoring technique. Proc. JFPS Int. Symp. Fluid Power
**1996**, 1996, 567–572. [Google Scholar] [CrossRef] - Campanini, F.; Bianchi, R.; Vacca, A.; Casoli, P. Optimized control for an independent metering valve with integrated diagnostic features. In Proceedings of the ASME/BATH 2017 Symposium on Fluid Power & Motion Control, Sarasota, FL, USA, 16–19 October 2017. [Google Scholar] [CrossRef]
- Kong, F.; Chen, R. A combined method for triplex pump fault diagnosis based on wavelet transform, fuzzy logic and neuro-networks. Mech. Syst. Signal Process.
**2004**, 18, 161–168. [Google Scholar] [CrossRef] - Backas, J.; Huhtala, K. Modelling the efficiencies of hydraulic pumps with neural networks. In Proceedings of the Twelfth Scandinavian International Conference on Fluid Power, Tampere, Finland, 18–20 May 2011. [Google Scholar]
- Torikka, T. Evaluation of Analysis Methods for Fault Diagnosis on axial-piston pumps. In Proceedings of the Twelfth Scandinavian International Conference on Fluid Power, Tampere, Finland, 18–20 May 2011. [Google Scholar]
- Muralidharan, V.; Sugumaran, V.; Indira, V. Fault diagnosis of monoblock centrifugal pump using SVM. Eng. Sci. Technol. Int. J.
**2014**, 17, 152–157. [Google Scholar] [CrossRef] - Bartram, G.; Mahadevan, S. Integration of heterogeneous information in SHM models. Struct. Control Health Monit.
**2014**, 21, 403–422. [Google Scholar] [CrossRef] - Helwig, N.; Pignanelli, E.; Schutze, A. Condition Monitoring of a Complex Hydraulic System using Multivariate Statistics. In Proceedings of the Instrumentation and Measurement Technology Conference (I2MTC), Pisa, Italy, 11–14 May 2015. [Google Scholar]
- Helwig, N.; Pignanelli, E.; Schutze, A. Detecting and compensating sensor faults in a hydraulic condition monitoring system. In Proceedings of the AMA Conferences 2015—SENSOR 2015 and IRS 2015, Nuremberg, Germany, 19–21 May 2015. [Google Scholar]
- Helwig, N.; Schutze, A. Data-based condition monitoring of a fluid power system with varying oil parameters. In Proceedings of the 10th International Fluid Power Conference, Dresden, Germany, 8–10 March 2016. [Google Scholar]
- Azadeh, A.; Ebrahimipour, V.; Bavar, P. A fuzzy inference system for pump failure diagnosis to improve maintenance process: The case of a petrochemical industry. Expert Syst. Appl.
**2010**, 37, 627–639. [Google Scholar] [CrossRef] - Gupta, M.M.; Rao, D.H. On the principle of fuzzy neural networks. Fuzzy Sets Syst.
**1994**, 61, 1–18. [Google Scholar] [CrossRef] - Antoni, J.; Randall, R.B. Differential diagnosis of gear and bearing faults. ASME J. Vib. Acoust.
**2002**, 124, 165–171. [Google Scholar] [CrossRef] - Antoni, J.; Bonnardot, F.; Raad, A.; el Badaoui, M. Cyclostationary modelling of rotating machine vibration signals. Mech. Syst. Signal Process.
**2004**, 18, 1285–1314. [Google Scholar] [CrossRef] - Antoni, J. Blind separation of vibration components: Principles and demonstrations. Mech. Syst. Signal Process.
**2005**, 19, 1166–1180. [Google Scholar] [CrossRef] - Capdessus, C.; Sidahmed, M.; Lacoume, J.L. Cyclostationary processes: Application in gear faults early diagnosis. Mech. Syst. Signal Process.
**2000**, 14, 371–385. [Google Scholar] [CrossRef] - Bonnardot, F.; Randall, R.B.; Antoni, J.; Guillet, F. Enhanced unsupervised noise cancellation (E-SANC) using angular resampling. In Proceedings of the Application for Planetary Bearing Fault Diagnosis, Surveillance 5 CETIM, Senlis, France, 11–13 October 2004. [Google Scholar]
- Salo, F.; Nassif, A.; Essex, A. Dimensionality reduction with IG-PCA and ensemble classifier for network intrusion detection. Comput. Netw.
**2019**, 148, 164–175. [Google Scholar] [CrossRef]

**Figure 2.**(

**a**) Position on the pump of the two accelerometers. (

**b**) Hydraulic scheme of the experimental layout.

**Figure 3.**Raw signal for fault 1 (

**a**), fault 2 (

**b**), the flawless pump (

**c**), fault 3 (

**d**), and fault 4 (

**e**) for the signal acquired with sensor 1 (1500 r/min, 150 bar).

**Figure 4.**(

**a**) Raw signal, (

**b**) synchronous average, and (

**c**) residual signal of the signal measured by sensor 1 for the standard pump (1500 r/min, 150 bar).

**Figure 5.**FFT of (

**a**) acceleration signal, (

**b**) synchronous average, and (

**c**) residual signal for the signal acquired with sensor 1 in the case of flawless pump (1500 r/min, 150 bar).

**Figure 6.**FFT of the raw signal for (

**a**) the standard pump, (

**b**) fault 1, and (

**c**) fault 2 pump for the signal acquired with sensor 1 (1500 r/min, 150 bar).

**Figure 7.**FFT of the raw signal for (

**a**) the standard pump, (

**b**) fault 3, and (

**c**) fault 4 pump for the signal acquired with sensor 1 (1500 r/min, 150 bar).

**Figure 8.**FFT of the synchronous average for (

**a**) the standard pump, (

**b**) fault 1, and (

**c**) fault 2 pump for the signal acquired with sensor 1 (1500 r/min, 150 bar).

**Figure 9.**FFT of the synchronous average for (

**a**) the standard pump, (

**b**) fault 3, and (

**c**) fault 4 pump for the signal acquired with sensor 1 (1500 r/min, 150 bar).

**Figure 10.**Classifier accuracy (

**A**) and training time (

**B**) with 13,000 features (raw signal, sensor 1).

**Figure 15.**Classifier accuracy of raw signal, synchronous average, and residual signal with sensor 1 (50 features).

**Table 1.**Operating points considered for the acceleration acquisitions in healthy and faulty conditions.

Angular Velocity | Swash Angle | Delivery Pressure | ||
---|---|---|---|---|

50 bar | 150 bar | 250 bar | ||

500 r/min | 12.8 deg | ✓ | ✓ | ✓ |

1500 r/min | 12.8 deg | ✓ | ✓ | ✓ |

2000 r/min | 12.8 deg | ✓ | ✓ | ✓ |

Classifier Category | Classifier |
---|---|

Decision Trees | Coarse tree |

Discriminant Analysis | Linear discriminant |

Ensemble Classifier | Bagged trees |

K Nearest Neighbor Classifier | Weighted KNN Medium KNN |

Support Vector Machine | Fine Gaussian SVM Linear SVM |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Casoli, P.; Pastori, M.; Scolari, F.; Rundo, M.
A Vibration Signal-Based Method for Fault Identification and Classification in Hydraulic Axial Piston Pumps. *Energies* **2019**, *12*, 953.
https://doi.org/10.3390/en12050953

**AMA Style**

Casoli P, Pastori M, Scolari F, Rundo M.
A Vibration Signal-Based Method for Fault Identification and Classification in Hydraulic Axial Piston Pumps. *Energies*. 2019; 12(5):953.
https://doi.org/10.3390/en12050953

**Chicago/Turabian Style**

Casoli, Paolo, Mirko Pastori, Fabio Scolari, and Massimo Rundo.
2019. "A Vibration Signal-Based Method for Fault Identification and Classification in Hydraulic Axial Piston Pumps" *Energies* 12, no. 5: 953.
https://doi.org/10.3390/en12050953