Robust fault detection filter using linear matrix inequalities’ approach for shaft crack diagnosis

Detecting cracks in rotating shafts is a challenging problem when using vibration-based diagnostics. This is due to the fact that a localized crack has a minimal influence on the global vibration response of the system. To increase sensitivity and reliability, the vibration response needs to be coupled with additional sources of information such as a mathematical model of the machine. Modern control theory techniques offer system-level mathematical models for both control and diagnostics. Focusing on the latter, a new and promising approach involves the use of unknown input observers. Such observers can be designed to employ robust fault detection filters (RFDFs) for isolating fault signatures while reducing the influence of real-world disturbances and noise. For the present study, a modified design procedure coupled with robust fault detection is utilized for shaft crack detection. The filter is designed using the linear matrix inequalities (LMI) technique. The LMI approach is applied to obtain the solution of the mixed H−/H∞ optimization problem, which arises during the synthesis of the RFDF. By reformulating the LMI conditions, the proposed RFDF design procedure is simplified and thus requires less iteration steps to find the optimal solution. A new feature of the present approach involves the application of the rigid finite element method for the formulation of the mathematical model of the rotor and the shaft crack. The numerical and experimental results confirm the advantages of the designed robust fault detection filter and its ability to detect shaft cracks. The filter is minimally sensitive to measurement noise while allowing for the identification of shallow cracks (2% or 5% deep). The cracks are manifested through the observance of very subtle vibration response changes. The results also confirm the effectiveness and accuracy of the rigid finite element modeling concerning the cracked rotor.

[1]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[2]  Jie Chen,et al.  Design of unknown input observers and robust fault detection filters , 1996 .

[3]  Xi Wu,et al.  Vibration-based crack diagnosis in rotating shafts during acceleration through resonance , 2003, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[4]  Jian Liu,et al.  An LMI approach to H_ index and mixed H_/Hinfinit fault detection observer design , 2007, Autom..

[5]  Jian Liu,et al.  An LMI approach to h_ index and mixed h_ /h∞ fault detection observer design , 2007 .

[6]  Donald E. Bentlhy,et al.  Detection of Rotor Cracks , 1986 .

[7]  Johan Efberg,et al.  YALMIP : A toolbox for modeling and optimization in MATLAB , 2004 .

[8]  Jie Chen,et al.  Robust Model-Based Fault Diagnosis for Dynamic Systems , 1998, The International Series on Asian Studies in Computer and Information Science.

[9]  Jerzy T. Sawicki,et al.  Detecting cracked rotors using auxiliary harmonic excitation , 2011 .

[10]  R. Gasch,et al.  A Survey Of The Dynamic Behaviour Of A Simple Rotating Shaft With A Transverse Crack , 1993 .

[11]  R. J. Patton,et al.  An LMI approach to H - /H∞ fault detection observers , 2002 .

[12]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[13]  A. S. Sekhar,et al.  Crack identification in a rotor system: a model-based approach , 2004 .

[14]  Steven X. Ding,et al.  Model-based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools , 2008 .

[15]  P. N. Saavedra,et al.  Vibration Analysis of Rotor for Crack Identification , 2002 .

[16]  Jie Chen,et al.  Observer-based fault detection and isolation: robustness and applications , 1997 .

[17]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[18]  Paolo Pennacchi,et al.  A model based identification method of transverse cracks in rotating shafts suitable for industrial machines , 2006 .

[19]  Yu Cui,et al.  Design and analysis of robust fault detection filter using LMI tools , 2009, Comput. Math. Appl..

[20]  Wei Lin,et al.  Fault detection and diagnosis of rotating machinery , 2000, IEEE Trans. Ind. Electron..

[21]  S. Seibold,et al.  a Time Domain Method for the Localization of Cracks in Rotors , 1996 .

[22]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[23]  John E. T. Penny,et al.  Crack Modeling for Structural Health Monitoring , 2002 .

[24]  R. W. Park,et al.  Noise and Fault Diagonois Using Control Theory , 1998 .

[25]  Rolf Isermann,et al.  Model-based fault-detection and diagnosis - status and applications , 2004, Annu. Rev. Control..

[26]  I. Mayes,et al.  Analysis of the Response of a Multi-Rotor-Bearing System Containing a Transverse Crack in a Rotor , 1984 .

[27]  Jerzy T. Sawicki,et al.  Auxiliary state variables for rotor crack detection , 2011 .

[28]  J. Bajkowski,et al.  Detection of Cracks in Turborotors—A New Observer Based Method , 1993 .

[29]  Zhengjia He,et al.  Crack detection in a shaft by combination of wavelet-based elements and genetic algorithm , 2008 .

[30]  Michael I. Friswell,et al.  Candidate reduced order models for structural parameter estimation , 1990 .

[31]  B. Grabowski.  The Vibrational Behaviour of a Rotating Shaft Containing a Transverse Crack , 1984 .

[32]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[33]  Paolo Pennacchi,et al.  Some remarks on breathing mechanism, on non-linear effects and on slant and helicoidal cracks , 2008 .

[34]  Dan Guo,et al.  Vibration analysis of a cracked rotor using Hilbert–Huang transform , 2007 .

[35]  M. Massoumnia.  A geometric approach to the synthesis of failure detection filters , 1986 .

[36]  Michael I. Friswell,et al.  Condition Monitoring of Rotor Using Active Magnetic Actuator , 2008 .

[37]  Fulei Chu,et al.  RETRACTED: Using genetic algorithms to detect and configure shaft crack for rotor-bearing system , 2001 .

[38]  P. Pennacchi,et al.  Identification of Transverse Crack Position and Depth in Rotor Systems , 2000 .

[39]  Zhang Ren,et al.  On the Design of Unknown Input Observers and Fault Detection Filters , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[40]  Guo-Ping Liu,et al.  Robust fault detection of dynamic systems via genetic algorithms , 1995 .

[41]  E. Wittbrodt,et al.  Dynamics of Flexible Multibody Systems: Rigid Finite Element Method , 2006 .

[42]  James Lam,et al.  An LMI approach to design robust fault detection filter for uncertain LTI systems , 2003, Autom..

[43]  Jason L. Speyer,et al.  Robust fault detection filter design , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[44]  Anoop Chawla,et al.  Coupled bending, longitudinal and torsional vibrations of a cracked rotor , 2004 .

[45]  Jerzy T. Sawicki,et al.  Rigid Finite Element Model of a Cracked Rotor , 2012 .