In this article, a new statistical decision philosophy is developed to tackle structural damage detection problems which are defined in the context of novelty detection. In line with this philosophy, structural damage detection is achieved by deriving the posterior probability of damage presence from the Bayesian testing of two competing hypotheses, with the null and alternative hypotheses representing the undamaged and damaged states of a structure of concern, respectively. To resolve the tricky problem of prior appropriateness in Bayesian hypothesis testing, a general prior specification criterion is devised based on the notion of risk management, including the risk of false positive indication (an undamaged structure is incorrectly identified as damaged) and the risk of false negative indication (a damaged structure is incorrectly identified as undamaged). To determine an optimal risk level, two principles, namely the principle of posterior probability difference minimization (PPDM) and the principle of posterior probability product maximization (PPPM), are defined. The PPDM principle is to minimize the difference between the ability of a novelty detector to avoid a false positive and its ability to avoid a false negative, and the PPPM principle is to maximize the product of the two capabilities. Both principles essentially act as a means of achieving an optimal trade-off between the false positive and false negative risks stipulated in pursuing damage detection. To demonstrate the effectiveness of the proposed statistical decision philosophy for structural damage detection, experimental data obtained from a 5-story steel frame model and a 38-story concrete building model have been investigated.
FarrarCRWordenK.Structural health monitoring: a machine learning perspective. Chichester: John Wiley & Sons, 2013.
2.
SohnHFarrarCRHunterNF, et al. Structural health monitoring using statistical pattern recognition techniques. J Dyn Syst Meas Contr2001; 123(4): 706–711.
3.
WordenKSohnHFarrarCR.Novelty detection in a changing environment: regression and interpolation approaches. J Sound Vib2002; 258(4): 741–761.
4.
YanAMKerschenGDe BoeP, et al. Structural damage diagnosis under varying environmental conditions—part I: a linear analysis. Mech Syst Sig Process2005; 19(4): 847–864.
5.
YanAMKerschenGDe BoeP, et al. Structural damage diagnosis under varying environmental conditions—part II: local PCA for non-linear cases. Mech Syst Sig Process2005; 19(4): 865–880.
6.
NiYQHuaXGFanKQ, et al. Correlating modal properties with temperature using long-term monitoring data and support vector machine technique. Eng Struct2005; 27(12): 1762–1773.
7.
ZhouHFNiYQKoJM.Eliminating temperature effect in vibration-based structural damage detection. J Eng Mech2011; 137(12): 785–796.
8.
ZhuYNiYQJinH, et al. A temperature-driven MPCA method for structural anomaly detection. Eng Struct2019; 190: 447–458.
9.
FigueiredoEParkGFarrarCR, et al. Machine learning algorithms for damage detection under operational and environmental variability. Struct Health Monit2011; 10(6): 559–572.
10.
CrossEJWordenKChenQ.Cointegration: a novel approach for the removal of environmental trends in structural health monitoring data. Proc R Soc A: Math Phys Eng Sci2011; 467(2133): 2712–2732.
11.
CrossEJMansonGWordenK, et al. Features for damage detection with insensitivity to environmental and operational variations. Proc R Soc A: Math Phys Eng Sci2012; 468(2148): 4098–4122.
12.
GuJGulMWuX.Damage detection under varying temperature using artificial neural networks. Struct Control Health Monit2017; 24(11): e1998.
13.
LinYZNieZHMaHW.Structural damage detection with automatic feature-extraction through deep learning. Comput-Aided Civ Infrastruct Eng2017; 32(12): 1025–1046.
14.
ZhangHGülMKostićB.Eliminating temperature effects in damage detection for civil infrastructure using time series analysis and autoassociative neural networks. J Aerosp Eng2019; 32(2): 04019001.
15.
WahWSLOwenJSChenYT, et al. Removal of masking effect for damage detection of structures. Eng Struct2019; 183, 646–661.
16.
AbdeljaberOAvciOKiranyazS, et al. Real-time vibration-based structural damage detection using one-dimensional convolutional neural networks. J Sound Vib2017; 388: 154–170.
17.
BaoYTangZLiH, et al. Computer vision and deep learning–based data anomaly detection method for structural health monitoring. Struct Health Monit2019; 18(2): 401–421.
18.
OzdagliAIKoutsoukosX.Machine learning based novelty detection using modal analysis. Comput-Aided Civ Infrastruct Eng2019; 34(12): 1119–1140.
19.
TangZChenZBaoY, et al. Convolutional neural network-based data anomaly detection method using multiple information for structural health monitoring. Struct Control Health Monit2019; 26(1): e2296.
JiangKHanQDuX, et al. A decentralized unsupervised structural condition diagnosis approach using deep auto-encoders. Comput-Aided Civ Infrastruct Eng2021; 36(6): 711–732.
22.
SarmadiHYuenKV.Early damage detection by an innovative unsupervised learning method based on kernel null space and peak-over-threshold. Comput-Aided Civ Infrastruct Eng2021; 36(9): 1150–1167.
23.
WangZChaYJ.Unsupervised deep learning approach using a deep auto-encoder with a one-class support vector machine to detect damage. Struct Health Monit2021; 20(1): 406–425.
24.
WordenKMansonGFiellerNR.Damage detection using outlier analysis. J Sound Vib2000; 229(3): 647–667.
25.
SarmadiHKaramodinA.A novel anomaly detection method based on adaptive Mahalanobis-squared distance and one-class kNN rule for structural health monitoring under environmental effects. Mech Syst Sig Process2020; 140: 106495.
26.
FurukawaAOtsukaHKiyonoJ.Structural damage detection method using uncertain frequency response functions. Comput-Aided Civ Infrastruct Eng2006; 21(4): 292–305.
27.
CheungACabreraCSarabandiP, et al. The application of statistical pattern recognition methods for damage detection to field data. Smart Mater Struct2008; 17(6): 065023.
28.
JiangXMahadevanSAdeliH.Bayesian wavelet packet denoising for structural system identification. Struc Control Health Monit2007; 14(2): 333–356.
29.
KullaaJ.Distinguishing between sensor fault, structural damage, and environmental or operational effects in structural health monitoring. Mech Syst Sig Process2011; 25(8): 2976–2989.
30.
ShahsavariVChouinardLBastienJ.Wavelet-based analysis of mode shapes for statistical detection and localization of damage in beams using likelihood ratio test. Eng Struct2017; 132: 494–507.
31.
MarianiSCawleyP.Change detection using the generalized likelihood ratio method to improve the sensitivity of guided wave structural health monitoring systems. Struct Health Monit2020; 20(6): 1475921720981831.
32.
EntezamiAShariatmadarHKaramodinA.Data-driven damage diagnosis under environmental and operational variability by novel statistical pattern recognition methods. Struct Health Monit2019; 18(5–6), 1416–1443.
33.
EntezamiAShariatmadarHMarianiS.Fast unsupervised learning methods for structural health monitoring with large vibration data from dense sensor networks. Struct Health Monit2020; 19(6): 1685–1710.
34.
YanWJChronopoulosDYuenKV, et al. Structural anomaly detection based on probabilistic distance measures of transmissibility function and statistical threshold selection scheme. Mech Syst Sig Process2022; 162: 108009.
35.
JiangXMahadevanS.Bayesian wavelet methodology for structural damage detection. Struct Control Health Monit2008; 15(7): 974–991.
36.
JiangXMahadevanS.Bayesian probabilistic inference for nonparametric damage detection of structures. J Eng Mech2008; 134(10): 820–831.
37.
SankararamanSMahadevanS.Bayesian methodology for diagnosis uncertainty quantification and health monitoring. Struct Control Health Monit2013; 20(1): 88–106.
LipowskyHStaudacherSBauerM, et al. Application of Bayesian forecasting to change detection and prognosis of gas turbine performance. J Eng Gas Turbines Power2010; 132(3): 031602.
40.
WangYWNiYQWangX.Real-time defect detection of high-speed train wheels by using Bayesian forecasting and dynamic model. Mech Syst Sig Process2020; 139: 106654.
41.
NiYQZhangQH.A Bayesian machine learning approach for online detection of railway wheel defects using track-side monitoring. Struct Health Monit2021; 20(4): 1536–1550.
42.
GoiYKimCW.Bayesian outlier detection for health monitoring of bridges. Procedia Eng2017; 199: 2120–2125.
43.
ZhangFLKimCWGoiY.Efficient Bayesian FFT method for damage detection using ambient vibration data with consideration of uncertainty. Struct Control Health Monit2021; 28(2): e2659.
44.
JeffreysH.The theory of probability. 3rd ed.Oxford, UK: Oxford University Press, 1961.
BartlettAMS.A comment on D. V. Lindley’s statistical paradox. Biometrika1957; 44: 533–534.
47.
BergerJOSellkeT.Testing a point null hypothesis: the irreconcilability of p values and evidence. J Am Stat Assoc1987; 82(397): 112–122.
48.
LiangFPauloRMolinaG, et al. Mixtures of g priors for Bayesian variable selection. J Am Stat Assoc2008; 103(481): 410–423.
49.
RouderJNSpeckmanPLSunD, et al. Bayesian t tests for accepting and rejecting the null hypothesis. Psychon Bull Rev2009; 16(2): 225–237.
50.
RobertCP.On the Jeffreys-Lindley paradox. Philos Sci2014; 81(2): 216–232.
51.
CousinsRD.The Jeffreys–Lindley paradox and discovery criteria in high energy physics. Synthese2017; 194: 395–432.
52.
IsukapalliSS.Uncertainty analysis of transport-transformation models. PhD Thesis, The State University of New Jersey, US, 1999.
53.
TatangMA.Direct incorporation of uncertainty in chemical and environmental engineering systems. PhD Thesis, Massachusetts Institute of Technology, US, 1995.
54.
BenjaminJRCornellCA.Probability, statistics and decision for civil engineers. New York: McGraw-Hill, Inc., 2014.
55.
HoggRMcKeanJCraigA.Introduction to mathematical statistics. 6th ed.Upper Saddle River, NJ: Pearson/Prentice Hall, 2005.
56.
MaesKLombaertG.Monitoring railway bridge KW51 before, during, and after retrofitting. J Bridge Eng2021; 26(3): 04721001.
57.
Vamvoudakis-StefanouKJSakellariouJSFassoisSD.Vibration-based damage detection for a population of nominally identical structures: unsupervised Multiple Model (MM) statistical time series type methods. Mech Syst Sig Process2018; 111: 149–171.
58.
ZhangQHNiYQZhouL.A Bayesian probabilistic approach for damage detection of a population of nominally identical structures: application to railway wheel condition assessment. In: 12th International workshop on structural health monitoring: enabling intelligent life-cycle health management for Industry Internet of Things (IIOT), IWSHM 2019, Stanford, US, 2019, pp.3508–3515.
59.
BullLAGardnerPAGosligaJ, et al. Foundations of population-based SHM, Part I: homogeneous populations and forms. Mech Syst Sig Process2021; 148: 107141.
WassersteinRLLazarNA.The ASA statement on p-values: context, process, and purpose. Am Stat2016; 70(2): 129–133.
62.
McShaneBBGalDGelmanA, et al. Abandon statistical significance. Am Stat2019; 73(sup1): 235–245.
63.
AmrheinVGreenlandSMcShaneB.Scientists rise up against statistical significance. Nature2019; 567(7748): 305–307.
64.
HungSLHuangCSWenCM, et al. Nonparametric identification of a building structure from experimental data using wavelet neural network. Comput-Aided Civ Infrastruct Eng2003; 18(5): 356–368.
65.
AdeliHJiangX.Dynamic fuzzy wavelet neural network model for structural system identification. J Struct Eng2006; 132(1): 102–111.
66.
NiYQZhouXTKoJM.Experimental investigation of seismic damage identification using PCA-compressed frequency response functions and neural networks. J Sound Vib2006; 290(1–2): 242–263.
67.
LjungLAnderssonCTielsK, et al. Deep learning and system identification. IFAC-PapersOnLine, 2020; 53(2): 1175–1181.
68.
ErazoKNagarajaiahS.An offline approach for output-only Bayesian identification of stochastic nonlinear systems using unscented Kalman filtering. J Sound Vib2017; 397: 222–240.
69.
PapakonstantinouKGAmirMWarnGP.A Scaled Spherical Simplex Filter (S3F) with a decreased n+2 sigma points set size and equivalent 2n+1 Unscented Kalman Filter (UKF) accuracy. Mech Syst Sig Process2022; 163: 107433.
