The functional model–based method is a unique vibration-based approach to damage localization and magnitude estimation in structures under normal operation, capable of operating on naturally arising random vibration signals without human intervention. It employs an innovative data-based stochastic functional model representing the partial dynamics under various damage scenarios, estimation techniques, and statistical hypothesis testing. Unlike alternative vibration methods employing data-based models but treat the localization and magnitude estimation approximately, as classification problems, it handles them properly as estimation problems. Among its remarkable properties is its ability to operate with a low number of vibration response sensors and low- and limited-frequency bandwidth, characteristics important in many applications. In this article, an overview of the method and its principles are presented, along with three validation case studies.
CardenEPFanningP.Vibration based condition monitoring: a review. Struct Health Monit2004; 3(4): 355–377.
3.
FritzenCP.Vibration-based techniques for structural health monitoring. In: BalageasDFritzenCPGüemesA (eds) Structural health monitoring. London: ISTE Editions, 2006, pp. 45–224.
4.
FassoisSDSakellariouJS.Time-series methods for fault detection and identification in vibrating structures. Philos Trans A Math Phys Eng Sci 2007; 365(1851): 411–448.
5.
FassoisSDSakellariouJS.Statistical time series methods for structural health monitoring. In: BollerCChangFKFujinoY (eds) Encyclopedia of structural health monitoring. Chichester: John Wiley & Sons, 2009, pp. 443–472.
6.
FarrarCRWordenK.Structural health monitoring: a machine learning perspective. Chichester: John Wiley & Sons, 2013.
7.
LiDHoSCMSongGet al. A review of damage detection methods for wind turbine blades. Smart Mater Struct2015; 24(3): 033001.
8.
BrownjohnJMWXiaPQHaoHet al. Civil structure condition assessment by FE model updating: methodology and case studies. Finite Elem Anal Des2001; 37(10): 761–775.
9.
TeughelsARoeckGD.Damage detection and parameter identification by finite element model updating. Arch Comput Method E2005; 12(2): 123–164.
10.
PereraRRuizA.A multistage FE updating procedure for damage identification in large-scale structures based on multiobjective evolutionary optimization. Mech Syst Signal Pr2008; 22(4): 970–991.
11.
ReyndersETeughelsARoeckGD.Finite element model updating and structural damage identification using OMAX data. Mech Syst Signal Pr2010; 24(5): 1306–1323.
12.
EbrahimianHAstrozaRConteJPet al. Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation. Mech Syst Signal Pr2017; 84: 194–222.
13.
MattsonSGPanditSM.Damage detection and localization based on outlying residuals. Smart Mater Struct2006; 15(6): 1801.
14.
BalmesEBassevilleMMevelLet al. Statistical model-based damage localization: a combined subspace-based and substructuring approach. Struct Control Health Monit2008; 15(6): 857–875.
15.
WordenKMansonGDenoeuxT.An evidence-based approach to damage location on an aircraft structure. Mech Syst Signal Pr2009; 23(6): 1792–1804.
16.
LautourORDOmenzetterP. Damage classification and estimation in experimental structures using time series analysis and pattern recognition. Mech Syst Signal Pr2010; 24(5): 1556–1569.
17.
LautourORDOmenzetterP. Nearest neighbor and learning vector quantization classification for damage detection using time series analysis. Struct Control Health Monit2010; 17(6): 614–631.
18.
KopsaftopoulosFPFassoisSD.Vibration based health monitoring for a lightweight truss structure: experimental assessment of several statistical time series methods. Mech Syst Signal Pr2010; 24(7): 1977–1997.
19.
TrendafilovaI.An automated procedure for detection and identification of ball bearing damage using multivariate statistics and pattern recognition. Mech Syst Signal Pr2010; 24(6): 1858–1869.
20.
KopsaftopoulosFPFassoisSD.Scalar and vector time series methods for vibration based damage diagnosis in a scale aircraft skeleton structure. J Theor Appl Mech2011; 49(3): 727–756.
21.
OkashaNMFrangopolDMSaydamDet al. Reliability analysis and damage detection in high-speed naval craft based on structural health monitoring data. Struct Health Monit2011; 10(4): 361–379.
22.
MosaviAADickeyDSeracinoRet al. Identifying damage locations under ambient vibrations utilizing vector autoregressive models and Mahalanobis distances. Mech Syst Signal Pr2012; 26: 254–267.
23.
YaoRPakzadSN.Autoregressive statistical pattern recognition algorithms for damage detection in civil structures. Mech Syst Signal Pr2012; 31: 355–368.
24.
BaoCHaoHLiZX.Vibration-based structural health monitoring of offshore pipelines: numerical and experimental study. Struct Control Health Monit2013; 20(5): 769–788.
25.
PapatheouEMansonGBarthorpeRJet al. The use of pseudo-faults for damage location in SHM: an experimental investigation on a Piper Tomahawk aircraft wing. J Sound Vib2014; 333(3): 971–990.
26.
Vamvoudakis-StefanouKJSakellariouJSFassoisSD.Output-only statistical time series methods for structural health monitoring: a comparative study. In: Proceedings of the 7th European workshop on structural health monitoring (EWSHM), Nantes, 8–11 July 2014, pp. 978–985. INRIA Rennes - Bretagne Atlantique.
27.
KopsaftopoulosFPFassoisSD.A vibration model residual-based sequential probability ratio test framework for structural health monitoring. Struct Health Monit2015; 14(4): 359–381.
28.
SpanosNISakellariouJSFassoisSD.Vibration-response-only statistical time series SHM methods: a critical assessment via a lab-scale wind turbine jacket foundation structure and two sensor types. In: Proceedings of the international conference on noise and vibration engineering (ISMA), Leuven, 19–21 September 2016.
29.
SpanosNISakellariouJSFassoisSD. Exploring the limits of the Truncated SPRT method for vibration-response-only damage diagnosis in a lab-scale wind turbine jacket foundation structure. In: Proceedings of the X International Conference on Structural Dynamics, Rome, Italy, 2017, vol. 199, pp. 2066–2071. Elsevier.
30.
SakellariouJSRizosDDFassoisSD. Fault detection and magnitude estimation for an aircraft skeleton structure via a Functional Model Based Method. In: Proceedings of the 1st European workshop on structural health monitoring (EWSHM), Paris, 2002, pp. 253–260. DEStech Publications, Inc.
31.
SakellariouJSPetsounisKAFassoisSD. On board fault detection and identification in railway vehicle suspensions via a Functional Model Based Method. In: Proceedings of the international conference on noise and vibration engineering (ISMA), Leuven, 16–18 September 2002.
32.
SakellariouJSFassoisSD.Nonlinear ARX (NARX) based identification and fault detection in a 2 DOF system with cubic stiffness. In: Proceedings of the international conference on noise and vibration engineering (ISMA), Leuven, 16–18 September 2002.
33.
SakellariouJSFassoisSD.Vibration based fault detection and identification in an aircraft skeleton structure via a stochastic Functional Model Based Method. Mech Syst Signal Pr2008; 22(3): 557–573.
34.
KopsaftopoulosFPFassoisSD.A functional model based statistical time series method for vibration based damage detection, localization, and magnitude estimation. Mech Syst Signal Pr2013; 39(1–2): 143–161.
35.
SakellariouJSFassoisSD.Functionally pooled models for the global identification of stochastic systems under diferent pseudo-static operating conditions. Mech Syst Signal Pr2016; 72–73: 785–807.
36.
SakellariouJSFassoisSD.Global identification of stochastic dynamical systems under diferent pseudo-static operating conditions: the functionally pooled ARMAX case. Mech Syst Signal Pr2017; 82: 32–55.
37.
SakarisCSSakellariouJSFassoisSD.Vibration-based damage precise localization in three-dimensional structures: single versus multiple response measurements. Struct Health Monit2015; 14(3): 300–314.
38.
SakarisCSSakellariouJSFassoisSD.A time series generalized Functional Model Based Method for vibration-based damage precise localization in structures consisting of 1D, 2D and 3D elements. Mech Syst Signal Pr2016; 74: 199–213.
39.
SakarisCSSakellariouJSFassoisSD.Random-vibration-based damage detection and precise localization on a lab-scale aircraft stabilizer structure via the generalized Functional Model Based Method. Struct Health Monit2017; 16(5): 594–610.
40.
SakarisCSSakellariouJSFassoisSD. Vibration-Based Multi-Site Damage Precise Localization via the Functional Model Based Method. In: Proceedings of the X International Conference on Structural Dynamics, Rome, Italy, 2017, Vol. 199, pp. 2072–2077. Elsevier.
41.
LjungL.System identification: theory for the user. 2nd ed.Upper Saddle River, NJ: Prentice Hall, 1999, p. 123.
