the Functional Model Based Method

Transcription

1 Multi-Site Damage Localization via the Functional Model Based Method Christos S. Sakaris, John S. Sakellariou and Spilios D. Fassois Stochastic Mechanical Systems & Automation (SMSA) Laboratory Department of Mechanical & Aeronautical Engineering University of Patras, GR Patras, Greece 10th International Conference on Structural Dynamics EURODYN 2017 EURODYN, Rome, / 25

2 Talk Outline Introduction The structure & the experiments The damage localization methodology Experimental assessment Concluding remarks EURODYN, Rome, / 25

3 Introduction 1. Introduction The Problem Vibration data-based Multi-Site Damage (MSD) precise localization. State-of-the-Art Vibration based methods employing physical models (Perera et al. 2008; Fu et al. 2014; Gautier et al. 2015; Pedram et al. 2016; Zhang et al. 2017; Yin et al. 2017) Structures of high complexity (bridges, trusses, frames) large-size physical models and high number of sensors Demanding updating/tuning algorithms Uncertainty may be a problem EURODYN, Rome, / 25

4 Introduction Vibration data-based methods (Kopsaftopoulos & Fassois 2010; Lautour et al. 2010; Catbas et al. 2011; Roy et al. 2015; Yun et al. 2017) Only partial models of the dynamics typically used small in size & easy to manipulate for in-operation SHM Partial models identified via few sensors - no further tuning/updating LIMITATION: The available methods treat the problem as a classification one, assigning damage approximately to the nearest pre-selected region or to the vicinity of specific sensors : Preselected damage region : Sensor : Unknown damage EURODYN, Rome, / 25

5 Introduction The Functional Model Based Method (FMBM) (Sakellariou & Fassois 2002, 2004, , Kopsaftopoulos & Fassois 2006, 2007, 2013, Sakaris et al ) A novel method treating the problem as an estimation one, precisely estimating the damage coordinates. The method works with a minimal number of sensors. The method is based on novel Functionally Pooled (FP) models - these represent the dynamics under any Single-Site Damage (SSD) LIMITATION: In its current form it works only for Single-Site Damages (SSDs) Goal of the Study The extension and assessment of the Functional Model Based Method (FMBM) for the precise localization of Multi-Site Damages (MSDs) EURODYN, Rome, / 25

6 The structure & the experiments 2. The structure & the experiments Accelerometer Excitation point Area of interest Garteur aircraft (total mass 50 kg) The Structure Area of interest: right wing (length 80 cm) Experimental details Single accelerometer Sampling frequency 256 Hz Operational bandwidth : [ ] Hz Signal length No. of exps.: 30 (healthy state) & 469 (17 Single-Site Damages and 134 Multi-Site Damages scenarios) EURODYN, Rome, / 25

7 The structure & the experiments The Damage scenarios Single-Site Damages (SSDs): Added mass of 48 g Multi-Site Damages (MSDs): Two added masses of 48 g each Type of damage Damage location No. of damages No of experiments per damage SSDs 9 1 MSDs 36 1 SSDs 8 4 MSDs 98 4, Operational phase Baseline phase Inspection phase EURODYN, Rome, / 25

8 Mutli-Site Damage Localization Methodology 3. The damage localization methodology EURODYN, Rome, / 25

9 The damage localization methodology FP-ARX representation of the dynamics under any SSD or MSD AR X noise : vector containing the coordinates of two damages in 1D top. : excitation/response vibration signals : innovations (residual) sequence : AR and X orders : residual series variance : statistical expectation : innovations covariance : Kronecker delta : AR/X coefficients of projection : basis functions (polynomials) EURODYN, Rome, / 25

10 The damage localization methodology Baseline phase VFP-ARX model Identification procedure M 2 Data pooling signal pairs for VFP-ARX identification VFP-ARX model : i) model order selection (RSS, BIC, AIC) identification ii) functional space dimensionality determination (Genetic Alg.) iii) validation of the selected model (residuals whiteness test) EURODYN, Rome, / 25

11 The damage localization methodology Inspection phase Characterization of a currently unknown damage as SSD or MSD Current response signals are driven via each baseline FP-ARX model: The current (potential location) is estimated as: VALIDATION: Model validation via the Pena & Rodriguez Test (Pena & Rodriguez 2006): Statistic quantity: ( = partial autocorrelation function,lag) (current damage SSD at location ) Else (current damage MSD) EURODYN, Rome, / 25

12 The damage localization methodology Interval estimate (uncertainty region) of the damage locations: with the Cramer Rao lower bound EURODYN, Rome, / 25

13 Experimental Assessment 4. Experimental assessment Baseline phase FP-ARX model identification (SSD scenarios) No. of experiments Signal length/ exper. Estimated model No. of proj. coef. M1=9 (1 exper. / single damage scenario) N= samples FP-ARX (100,100) 1206 Functional subspace: 6 Shifted Legendre polynomials of one variable Sample Per Parameter (SPP): 37.3, Cond. numb.: Vector FP-ARX identification (MSD scenarios) No. of experiments Signal length/ exper. Estimated model No. of proj. coef. M2=36 (1 exper. / double damage scenario) N= samples VFP-ARX (100,100) 1809 Functional subspace: 9 Shifted Legendre polynomials of two variables Sample Per Parameter (SPP): 99.5, Cond. numb.: EURODYN, Rome, / 25

14 Experimental Assessment SSD model: FP-ARX (100,100) 6 natural frequency trajectories MSD model: VFP-ARX (100,100) 9 natural frequency surfaces EURODYN, Rome, / 25

15 Experimental Assessment Healthy vs damaged (SSD at location x=30 cm) dynamics Healthy vs damaged (MSD at x=30 cm, x=70 cm) dynamics EURODYN, Rome, / 25

16 Experimental Assessment Inspection phase: damage diagnosis Is the current damage SSD or MSD? - 32 SSD and 392 MSD experiments - Characterization results at risk level (32 experiments based on Single-Site Damages (SSDs) and 392 experiments based on Multi-Site Damages (MSDs)) EURODYN, Rome, / 25

17 Experimental Assessment Confidence Intervals (UNCERTAINTY REGIONS) for MSD locations: MSD scenario 1 MSD scenario 2 Actual damage location: Estimated damage location: Confidence intervals: at risk level α = 10-7 EURODYN, Rome, / 25

18 Overall performance assessment Experimental Assessment (mean Euclidean error histogram MSD inspection experiments) Mean localization error (392 MSD inspection experiments). Damage Scenario Model Distribution sample mean std) Single-Site Damage FP-ARX (100,100) cm Multi-Site Damage VFP-ARX (100,100) cm EURODYN, Rome, / 25

19 4. Concluding remarks Concluding remarks The vibration data-based Functional Model Based Method (FMBM) was extended to localize Multi-Site Damages (MSDs) MSDs may be identified and automatically separated from SSDs The method operates with a simple model of the partial dynamics, with few (even a single) sensors, and within a limited frequency range (presently Hz) The achievable localization accuracy is very good with mean error of approx. 1 cm (on an 80 cm wing) EURODYN, Rome, / 25

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