Structural Health Monitoring and Damage Assessment Using Measured FRFs from Multiple Sensors, Part I: The Indicator of Correlation Criteria

Transcription

1 Key Engineering Materials Vols (2003) pp online at Journal 2003 Citation Trans Tech (to Publications, be inserted by Switzerland the publisher) Copyright by Trans Tech Publications Structural ealth Monitoring and Damage Assessment Using Measured FRFs from Multiple Sensors, Part I: The Indicator of Correlation Criteria C. Zang 1, M.I. Friswell 1 and M. Imregun 2 1 Department of Aerospace Engineering, University of Bristol Queen s Building, Bristol BS8 1TR, UK, c.zang@bristol.ac.uk m.i.friswell@bristol.ac.uk 2 Department of Mechanical Engineering, Imperial College, Exhibition Road, London SW7 2BX, UK, m.imregun@imperial.ac.uk Keywords: Global shape correlation (GSC) function, global amplitude correlation (GAC) function, structural health monitoring, damage assessment Abstract. This paper presents two criteria for correlating measured frequency responses from multiple sensors and proposes to use them as indicators for structural damage detection. The first criterion is a global shape correlation (GSC) function that is sensitive to mode shape differences but not to relative scales. The second criterion, a global amplitude correlation (GAC) function, is based on actual response amplitudes. Both correlation criteria are a function of frequency and uniquely map a set of complex responses to a real scalar between zero and unity. The averaged integrations of GSC and GAC functions along the frequency points over the measurement range, also called damage indicators, are used to describe the correlation between two sets of vibration data. When a structure state remains unchanged, both correlation criteria are as close to unity simultaneously. Otherwise, the correlation with the reference data will be decreased with changes of structure states. Using GSC and GAC functions has the advantage of being able to deal with incomplete measurements. Also, all available response data are used and hence there is no critical selection of frequency points for damage detection. The above correlation criteria were applied to a bookshelf structure and various cases such as undamaged states, damage locations (single and multiple), damage levels, as well as environmental variability are discussed. As expected, it was found that indicators of correlation criteria were able to identify all various cases correctly. Introduction For successful structural health monitoring and damage assessment, at least four levels need to be considered: existence, location, extent and prediction (Rytter 1993 [1]). owever, the key issue for on-line structural health monitoring is to diagnose the state of the structure; healthy or damaged, by comparing the current dynamic response measurements with those made previously. In recent years, the discipline of novelty detection has been introduced to identify from measured data if a machine or structure has deviated from normal conditions (Worden et al [2], 2000 [3]). An approach using grey relational analysis of SVD-processed FRFs was used by Zang and Imregun (2000 [4]) to identify the structural damage. They also employed the approach of combining neural networks and reduced measured FRF data to identify structural damage (Zang and Imregun 2000 [5-7]). Messina et al. (1998 [8]) presented a sensitivity and statistically-based method called the multiple damage location assurance criterion (MDLAC), which is formulated on the same basis as modal assurance criterion (MAC) for quantifying the consistency of the correspondence between related vectors to detect and localize structural damage. Shi et al. (2000 [9]) extended this work by using incomplete mode shapes for detection and localization. In Part 1 of this paper, two criteria for correlating measured frequency responses from multiple sensors, called a global shape correlation (GSC) Licensed to University of Bristol - Bristol - UK All rights reserved. No part of the contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, (ID: /01/06,10:30:28)

2 132 Damage Assessment of Structures V 2 Title of Publication (to be inserted by the publisher) function and a global amplitude correlation (GAC) function, were employed for structural damage detection. The averaged integrations of GSC and GAC functions along the frequency points over the measurement range were used as damage indicators to establish the ground rules for a successful correlation of measured responses for damage identification. This approach is not only able to deal with incomplete measurements, but also circumvents the difficulty of the selection of the best frequency points. The application of the methodology to a bookshelf structure demonstrated that these damage indicators using correlation criteria were sensitive to changes in structural states and capable of recognizing all tested cases correctly. Development of Correlation Criteria The purpose of performing a systematic comparison and correlation between two sets of vibration data is mostly for model updating and model validation. Over the last 30 years, many correlation and updating methods have been proposed and review articles can be found in [10~13]. Broadly speaking, correlation techniques can be considered as two groups: modal based and response based. Correlation methods using modal properties, for instance, include the Correlated Mode Pairs (CMPs), the Modal Assurance Criterion (MAC), the automac, and the Coordinate MAC (COMAC), etc., and have the advantage of predicting modal parameters individually. owever, additional demands on modal analysis from measurement tests are required. In some cases, the modal analysis of measured responses is difficult and the excitation force may not always be measured. Therefore, it is generally accepted to choose response-based methods. In reference [14], a Response Vector Assurance Criterion (RVAC) is introduced and SVD-based method (Tengzelius et al [15]) is used to combine shape and frequency information in one single value. As we know, frequency response functions can be described in terms of a three axes: frequency, spatial position and amplitude. For instance, the response function at co-ordinate i due to an excitation at co-ordinate j can be considered to be a function of frequency and amplitude at a specific spatial location. Any response function can be projected onto a pair of orthogonal planes such as the amplitude-co-ordinate plane and the amplitude-frequency plane. The amplitude-coordinate plane includes the amplitude vs. frequency information for the entire range for each spatial location. Such a correlation criterion, Frequency Response Assurance Criterion (FRAC), is proposed by eylen and Lammens (1996) [16]. 2 { Xij ( ω)} { Aij ( ω)} FRAC = (1) ({ ( ω)} { ( ω)})({ ( ω)} { ( ω)}) Xij Xij Aij where i and j are the response and excitation co-ordinates, { ( ω)} is a vector the predicted FRFs over a frequency range of interest and { ( ω)} Xij Aij Aij is the corresponding measured FRF. { } is a column vector of complex conjugate (ermitian) transpose. The FRAC exists for all ij-pairs and the vector sum is over the frequencies. Therefore, it can be considered to be a frequency-domain MAC. It returns a real constant between zero and unity, indicating no match at all or a complete match. On the other hand, the projection of the entire measured FRF set onto the amplitude-frequency plane contains information about every single measurement location in the set. Any such correlation can be called global correlation. Zang et al. (2001 [17]) compared several correlation functions in the frequency domain and advanced a global shape criterion and a global amplitude criterion for model updating. ere, we extend the application of both correlation functions to structural health monitoring and damage assessment.

3 Key Engineering Materials Vols Two Global Correlation Functions Similar to the definitions in [17], the first global shape correlation function (GAC) for structural health monitoring can be defined as: χ ( ω ) = { x1( ω )} { ( ω )} ({ x1( ω )} { x1( ω }) { ( ω )} { ( ω )} 2 ( ) s (2) Where { x1 (ω)} is a column of FRF data measured initially at frequency ω as a reference and { x2 (ω)} is the current measured FRF data. From equation (2), it can easily be seen that χ s (ω ) is a real-valued function of frequency between zero and unity. Unlike FRAC, the function here exists for all frequencies and the sum is over all locations. The second global amplitude correlation function (GSC) can be defined as: χ ( ω ) = 2 { x1( ω )} { ( ω )} ({ x1( ω )} { x1( ω )}) + { ( ω )} { ( ω )} ( ) a (3) From equation (3), it can easily be seen that χ a (ω ) is also a real-valued function of frequency between zero and unity. Both correlation criteria map complex-valued response function vectors into real-valued scalars between zero and unity. It is easily seen that the shape correlation coefficient is sensitive to mode shape differences but not to relative scales. On the other hand, the amplitude correlation coefficient uses actual response amplitudes. A simultaneous use of both correlation criteria should be able to quantify the closeness of two sets of vibration data. The Averaged Integration of GSC and GAC Functions As can be seen that GSC and GAC functions reveal the closeness of two sets of vibration response in the frequency domain. The averaged integration over the actual response values at each frequency can be defined as: AIGSC = 1 N 1 AIGAC = N f f N f i= 1 N f i= 1 GSC( ω ) GAC( ω ) i i The AIGSC and AIGAC will be a real constant between zero and unity to indicate total/zero change of structural responses. Therefore, they can be used as damage indicators for structural health monitoring. (4) Case Study: Bookshelf Structure Experimental Test Consider the three-story bookshelf structure of Figure 1. The experimental testing was proformed at the Los Alamos National Laboratory and the time histories data are provided on the Los Alamos website [18]. The structure consisted of Unistrut columns and aluminium floor plates with two-bolt

4 134 Damage Assessment of Structures V 4 Title of Publication (to be inserted by the publisher) connections to brackets on the Unistrut. 24 piezoelectric single axis accelerometers, two per joint, were mounted on the aluminium blocks, eight in each plate. The shaker was attached at corner D using a stinger connected to a tapped hole at the mid-height of the base plate. In each test case, excitation signals from the shaker to the base were random. Each time signal gathered consisted of 8192 points and were sampled at 1600 z. The frequency response functions (FRFs) were calculated from both the measured force and response signals. The number of averaging individual time records was selected to be eight in order to reduce the random fluctuation in the estimation of the FRFs. The final FRF was produced with 512 spectrum lines. Fig. 1 A three-story Frame structure for damage detection Correlation Criteria for Various Damage States The first interest was to compare the correlations between various structure states and the reference state. Four different states were considered: ealthy State (S): the original state of the bookshelf structure. Damaged State One (DS1): the bracket was completely removed from the 1C location. Damaged State Two (DS2): the bracket was completely removed from the 3A location. Damaged State Three (DS3): the bracket was completely removed from the 1C and 3A locations in order to represent the multiple damage cases. 24 FRFs were obtained for each test from the twenty-four acceleration sensors and one force transducer. A FRF comparison for all four states, together with the reference FRF at point 1 is shown in Fig. 2. Clearly, large natural frequency differences exist between the reference state and the various damaged states while the reference (Ref.) and the healthy state FRF (S1) are almost coincident throughout the frequency range. The correlation criteria, which contain contributions from all 24 FRFs, are overlaid in Fig. 3. The good agreement between the reference and the healthy states can clearly be seen from the two global correlation functions. On the other hand, poor agreement between the reference and damaged states can also be seen. Values of damage indicators (AIGSC, AIGAC) are listed in Table 1. As expected, values of AIGSC and AIGAC are near unity for the healthy state while those for the damaged states are sharply reduced. The poorest correlation with the reference state is the multiple

5 Key Engineering Materials Vols damage state (DS3) for which AIGSC and AIGAC are 0.38 and 0.46 respectively. Clearly, damage indicators are sensitive to damaged states and they can be used for damage identification purposes. Fig. 2 Comparison of measured FRFs for various states Fig. 3 Overlay of correlation criteria (GSC, GAC) for various states Table 1 Damage indicators for various structure state Damage Structure States Indicators S DS1 DS2 DS3 AIGSC AIGAC

6 136 Damage Assessment of Structures V 6 Title of Publication (to be inserted by the publisher) Correlation Criteria for Various Damage Levels The second study aims at investigating the applicability of the correlation criteria for detecting increasing damage levels. Three types of torque damage were considered as follows: Damage Level 1 (DL1): a torque value of 5ft.lbs was applied to the bolts Damage Level 2 (DL2): a torque value of 10ft.lbs was applied to the bolts Damage Level 3 (DL3): a hand tight torque was applied to the bolts Four sets of 24 measured FRFs, corresponding to states S, DL1, DL2, and DL3, were used for the correlation analysis. FRFs for all 4 states are shown in Fig. 4. The FRF-based shape and amplitude correlations between the reference and 3 damage levels were calculated respectively and are overlaid in Fig. 5. The best agreement is for the 0 ~ 220 z frequency range for DL1 and DL2 since the correlation values are close to unity. It follows that damages DL1 and DL2 are likely to affect the higher frequency range 250 ~ 800 z. There is poor correlation for state DL3 throughout the frequency range, suggesting that the damage affects all measured modes. The damage indicators are listed in Table 2. Three damage states can be identified and state DL3 has the worst correlation with the healthy state. Table 2. Damage indicator for various damage levels Damage Structure States Indicators Damage Level1 Damage Level2 Damage Level3 AIGSC AIGAC Fig. 4 Comparison of measured FRFs for various damage levels

7 Key Engineering Materials Vols Fig.5 Overlay of correlation criteria (GSC, GAC) for various damage levels Correlation Criteria for Environmental Variability To represent environmental variability, three excitation levels, corresponding to 2, 5, 8 volts, were used in the measurements. Considering that the structure was in its original healthy state, the tests were labelled as EV1, EV2 and EV3 respectively. Fig. 6 shows the corresponding FRFs, together with the reference FRF. It is seen that the FRF for the EV1 is identical to the reference FRF since both have the same excitation levels. Due to excitation variations, there are differences between EV2 and EV3 FRFS. Using all 24 FRFs in each set, the correlation criteria are plotted in Fig. 7. It is shown that the three global shape correlation (GSC) functions are in good agreement. owever, the three global magnitude correlation (GAC) functions exhibit large differences. Table 3 lists actual values of the damage indicators. As expected, the three environmental states are identified in the correct order. Table 3. Damage indicator for environmental variability Damage Structure States: Environmental variability Indicators EV1 EV2 EV3 AIGSC AIGAC

8 138 Damage Assessment of Structures V 8 Title of Publication (to be inserted by the publisher) Fig. 6 Comparison of measured FRFs in the case of environmental variability Concluding Remarks Fig. 7 Overlay of correlation criteria (GSC, GAC) for environmental variability Both global correlation criteria (GSC, GAC) are based on measured response functions and are functions of frequency, uniquely mapping the response into a real scalar between zero and unity. The closeness between the two sets of measured vibration data is adequately quantified by these correlation functions. The averaged integrations of the GSC and GAC (AIGSC, AIGAC) have the capability of recognizing various structure states and, therefore, can be used as damage indicators. Various damage states of a bookshelf structure, including damage location and level, have been investigated in detail using the proposed correlation criteria. The study shows the possibility of

9 Key Engineering Materials Vols devising health monitoring and damage assessment rules using the correlation criteria simultaneously. Further studies are needed to develop approaches that can accurately recognize and assess structural states and damage. An intelligent decision making method based on radial basis function (RBF) neural network will be introduced in Part 2 of the paper. References [1] T. Rytter: Vibration based inspection of civil engineering structure, PhD dissertation, Department of building technology and structure engineering, Aalborg University, Denmark, [2] K. Worden: Damage detection using a novelty measure, Proceedings of the 15th international modal analysis conference, Florida, (1997). [3] K. Worden, G. Manson, and N. R. J. Fieller: Damage detection using outlier analysis, Journal of Sound and Vibration, Vol. 229(3), (2000), p [4] C. Zang, and M. Imregun: Structural damage identification via grey relational analysis of SVDprocessed FRFs, ISMA25, Sept [5] C. Zang, and M. Imregun: Structural damage detection using artificial neural networks and measured FRF data reduced via principal component projection, Journal of Sound and Vibration, Vol. 242, No. 5, (2001), p [6] C. Zang, and M. Imregun: FRF-based structural damage detection using Kohonen selforganizing maps, International Journal of Acoustics & Vibration, Vol. 5, No. 4, (2000). [7] C. Zang, and M. Imregun: Combined neural network and reduced FRF techniques for slight damage detection, Journal of the Archive of Applied Mechanics, Vol. 71, No. 8, (2001), p [8] A. Messina, E. J. Williams and T. Contursi: Structural damage detection by a sensitivity and statistical-based method, Journal of Sound and Vibration, Vol. 216(5), (1998), p [9] Z. Y. Shi, S. S. Law and L. M. Zhang: Damage localization by directly using incomplete mode shapes, Journal of Engineering Mechanics, Vol. 126(6), (2000), p [10] J. E. Mottershead and M. I. Friswell: Model updating in structural dynamics: a survey. Journal of Sound and Vibration, Vol. 167(2), (1993), p [11] P. Avitable: Correlation Considerations Parts th International Modal Analysis Conference, Santa Barbara, California, (1998) [12] M. Baker: Review of test/analysis correlation methods and criteria for validation of finite element models for dynamic analysis, 14 th International Modal Analysis Conference (1996), p [13] R. J. Allemang and D. J. Brown: A correlation Coefficient for Modal Vector Analysis, 1st International Modal Analysis Conference, (1982), p [14] W. eylen, S. Lammens, P. Sas: Combining numerical and experimental analysis models. Modal Analysis Theory and Testing, Section A.6, K.U. Leuven-PMA, Belgium, 1998 [15] U. Tengzelius, N. orlin, U. Emborg, M. Gustavsson,. Van der Auweraer, M. Iadevaia: Correlation of medium frequency test and FE models for a trimmed aircraft section, Proc. 4 th CEAS/AIAA Aeroacoustics conference, June 2-4, (1998) pp [16] W. eylen and S. Lammens: FRAC: a consistent way of comparing frequency response functions. Proceedings of conference on identification in engineering systems, (1996) [17] C. Zang,. Grafe, and M. Imergun: Frequency-domain criteria for correlating and updating dynamic finite element models, Mechanical System and Signal Processing, Vol. 15(1), (2001), p [18] Los Alamos National Laboratory Website: