Machine Vibration Monitoring for Diagnostics through Hypothesis Testing

Nowadays, the subject of machine diagnostics is gathering growing interest in the research field as switching from a programmed to a preventive maintenance regime based on the real health conditions (i.e., condition-based maintenance) can lead to great advantages both in terms of safety and costs. Nondestructive tests monitoring the state of health are fundamental for this purpose. An effective form of condition monitoring is that based on vibration (vibration monitoring), which exploits inexpensive accelerometers to perform machine diagnostics. In this work, statistics and hypothesis testing will be used to build a solid foundation for damage detection by recognition of patterns in a multivariate dataset which collects simple time features extracted from accelerometric measurements. In this regard, data from high-speed aeronautical bearings were analyzed. These were acquired on a test rig built by the Dynamic and Identification Research Group (DIRG) of the Department of Mechanical and Aerospace Engineering at Politecnico di Torino. The proposed strategy was to reduce the multivariate dataset to a single index which the health conditions can be determined. This dimensionality reduction was initially performed using Principal Component Analysis, which proved to be a lossy compression. Improvement was obtained via Fisher’s Linear Discriminant Analysis, which finds the direction with maximum distance between the damaged and healthy indices. This method is still ineffective in highlighting phenomena that develop in directions orthogonal to the discriminant. Finally, a lossless compression was achieved using the Mahalanobis distance-based Novelty Indices, which was also able to compensate for possible latent confounding factors. Further, considerations about the confidence, the sensitivity, the curse of dimensionality, and the minimum number of samples were also tackled for ensuring statistical significance. The results obtained here were very good not only in terms of reduced amounts of missed and false alarms, but also considering the speed of the algorithms, their simplicity, and the full independence from human interaction, which make them suitable for real time implementation and integration in condition-based maintenance (CBM) regimes.

[1]  Charles R. Farrar,et al.  Damage Detection and Evaluation II , 1999 .

[2]  Sample size determination in estimating a covariance matrix , 1987 .

[3]  Alessandro Paolo Daga,et al.  Feedback on the Surveillance 8 challenge: Vibration-based diagnosis of a Safran aircraft engine , 2017 .

[4]  D. C. Howell.  Fundamental Statistics for the Behavioral Sciences , 1985 .

[5]  Marcin Michalak,et al.  Monitoring and maintenance of a gantry based on a wireless system for measurement and analysis of the vibration level , 2019, Ekspolatacja i Niezawodnosc - Maintenance and Reliability.

[6]  Hoon Sohn,et al.  Damage detection in mechanical structures using extreme value statistics , 2002, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[7]  Ian T. Jolliffe,et al.  Principal Component Analysis , 2002, International Encyclopedia of Statistical Science.

[8]  Ying Liang,et al.  A Fault Diagnosis Model for Rotating Machinery Using VWC and MSFLA-SVM Based on Vibration Signal Analysis , 2019 .

[9]  Jianzhong Zhou,et al.  Fault Diagnosis for Rolling Element Bearings Based on Feature Space Reconstruction and Multiscale Permutation Entropy , 2019, Entropy.

[10]  Keith Worden,et al.  DAMAGE DETECTION USING OUTLIER ANALYSIS , 2000 .

[11]  Wahyu Caesarendra,et al.  A Review of Feature Extraction Methods in Vibration-Based Condition Monitoring and Its Application for Degradation Trend Estimation of Low-Speed Slew Bearing , 2017 .

[12]  Alessandro Paolo Daga,et al.  The Politecnico di Torino rolling bearing test rig: Description and analysis of open access data , 2019, Mechanical Systems and Signal Processing.

[13]  Rinya Takahashi,et al.  Normalizing constants of a distribution which belongs to the domain of attraction of the Gumbel distribution , 1987 .

[14]  Keith Worden,et al.  An Overview of Intelligent Fault Detection in Systems and Structures , 2004 .

[15]  N. Lieven,et al.  Applying Extreme Value Theory for alarm and warning levels setting under variable operating conditions , 2016 .

[16]  Keith Worden,et al.  New trends in vibration based structural health monitoring , 2011 .

[17]  Keith Worden,et al.  A comparison of linear approaches to filter out environmental effects in structural health monitoring , 2018 .

[18]  A. Wald,et al.  Probability, statistics and truth , 1939 .

[19]  Robert B. Randall,et al.  Unsupervised noise cancellation for vibration signals: part I—evaluation of adaptive algorithms , 2004 .

[20]  Daming Lin,et al.  A review on machinery diagnostics and prognostics implementing condition-based maintenance , 2006 .

[21]  J. P. Holman,et al.  Experimental methods for engineers , 1971 .

[22]  Beverly J. Volicer,et al.  Biostatistics: A Foundation for Analysis in the Health Sciences , 1979 .

[23]  Álvar Arnaiz-González,et al.  Using artificial neural networks for the prediction of dimensional error on inclined surfaces manufactured by ball-end milling , 2015, The International Journal of Advanced Manufacturing Technology.

[24]  Robert B. Randall,et al.  Rolling element bearing diagnostics—A tutorial , 2011 .

[25]  Gaëtan Kerschen,et al.  Structural damage diagnosis under varying environmental conditions - Part II: local PCA for non-linear cases , 2005 .

[26]  Rune Brincker,et al.  Vibration Based Inspection of Civil Engineering Structures , 1993 .

[27]  Gaëtan Kerschen,et al.  Structural damage diagnosis under varying environmental conditions—Part I: A linear analysis , 2005 .

[28]  K. Penny.  Appropriate Critical Values When Testing for a Single Multivariate Outlier by Using the Mahalanobis Distance , 1996 .