Damage Identification from Power Spectrum Density Transmissibility

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6th Euroean Worksho on Structural Health Monitoring - h.3.d.3 More info about this article: htt://www.ndt.net/?id=14083 Damage Identification from Power Sectrum Density ransmissibility Y. ZHOU, R.

SEVILLANO ABSRAC Damage identification under real oerating conditions of the structure during its daily use would be suitable and attractive to civil engineers due to the difficulty and roblems of

In this case, outut-only resonse measurements would be available, and an outut-only damage identification rocedure should be imlemented.

1 6th Euroean Worksho on Structural Health Monitoring - h.3.d.3 More info about this article: htt:// Damage Identification from Power Sectrum Density ransmissibility Y. ZHOU, R. PERERA and E. SEVILLANO ABSRAC Damage identification under real oerating conditions of the structure during its daily use would be suitable and attractive to civil engineers due to the difficulty and roblems of carrying out controlled forced excitation tests on this kind of structures. In this case, outut-only resonse measurements would be available, and an outut-only damage identification rocedure should be imlemented. ransmissibility, defined on an outut-to-outut relationshi, is getting increased attention in damage detection alications because of its deendence with outut-only data and its sensitivity to local structural changes. In this aer, a method based on the ower sectrum density transmissibility (PSD) is roosed to detect structural damage. INRODUCION Periodic insection and maintenance of structures are essentials for the urose of ensuring their healthy oerational condition. Many methods have been roosed in the last years for the detection and location of damage in structural systems [1, ]. hese methods include time and frequency domain techniques and emirical and model-based aroaches. he key oint for most of the available techniques is the comarison between features obtained from exerimental resonse measurements and features evaluated under normal working conditions. Modal testing and modal arameter identification have been one core issue in dynamics-based structural health monitoring. From inut and outut measurement data, modal arameters can be obtained through the frequency resonse functions address: yunlai.zhou@alumnos.um.es erera@etsii.um.es Enrique.sevillano@um.es Adress: E..S. de Ingenieros Industriales Dto. Mecánica Estructural y Construcciones Industriales C/José Gutiérrez, Abascal,, 8006,Madrid License: htt://creativecommons.org/licenses/by/3.0/ 1

2 (FRF). However, damage identification under real oerating conditions of the structure during its daily use would be suitable and attractive to civil engineers due to the difficulty and roblems of carrying out controlled forced excitation tests on this kind of structures. In this case, outut-only resonse measurements would be available, and an outut-only damage identification rocedure should be imlemented. Classical outut-only techniques often require the oerational forces to be white noise. his is not necessary for the roosed transmissibility-based aroach [3, 4, 5]. he unknown oerational forces can be arbitrary as long as they are ersistently exciting in the frequency band of interest. he transmissibility function, defined as the frequency-domain ratio between two oututs, describes the relative admittance between the two measurements and makes ossible the damage detection without any assumtion about the nature of the excitations although different loading conditions have to be obtained during the exeriments. he scalar transmissibility is deterministic in case of one single oerational force. However, when several (uncorrelated) oerational forces are exciting the structure, the scalar transmissibility is in general not deterministic anymore and the concet of multivariable transmissibility [6] is introduced increasing the comlexity of the roblem. In ractice, a transmissibility measurement can be estimated in several ways although the most common choice is using an estimator involving cross-and auto-ower sectral density functions of the outut resonses. Furthermore, any measurable outut, such as strain, dislacement, acceleration, might be used to evaluate the sectral density functions. In this aer the ower sectrum density transmissibility (PSD) has been used for the damage detection rocedure [7]. PSDs are indeendent of the alied excitations and transferring oututs at the system oles. he oututs from only one load condition are needed to define the transmissibility and therefore to detect damage circumventing the roblems of multile excitations in large civil engineering structures. POWER SPECRUM DENSIY RANSMISSIBILIY (PSD) ransmissibility measurement is a outut-only technique, very suitable therefore for oerational dynamic analysis. ransmissibility functions are defined by taking the ratio of two resonse sectra by assuming a single force alied in an inut degree of freedom. When several oerational forces are exciting the structure, the calculation of the transmissibility becomes much more comlex. he use of the ower sectrum density transmissibility, estimated by using a reference resonse signal instead of an excitation signal, allows avoiding this roblem. he ower sectrum density transmissibility between the oututs yi ( t ) and yj () t with reference to the outut y () t is defined as the ratio between the ower sectral densities resonses X ( ) and X ( ): i j X i ( ) ( ) (1) X ( ) where is the frequency. ransmissibility can be measured in several ways, being one of the most common the use of cross- and auto-ower functions G : j

3 ( ) X ( ) ( ) ( ) ( ) i Xi X GYY i () X ( ) X ( ) X ( ) G ( ) j j YjY Furthermore, as has been roved [3, 4], when the Lalace variable s aroaches system s rth ole, denoted by r, the following equation is verified ir lim ( s) (5) sr herefore, if two different reference oints, k and l, are considered the subtraction of the two PSDs satisfies k l ir ir lim( () s ()) s 0 (6) sr his means that the system s oles are zeros of the rational function: kl k l () s () s () s (7) And oles of its inverse, 1 kl 1 1 () s kl k l () s () s () s jr jr he above theoretical results conclude that transmissibility is feasible to establish a 1 rational function () s, with oles equal to the system s oles. kl DAMAGE DEECION BY USING PSD As shown in the revious section, the natural frequencies can be simly determined from the observation of the eaks in the grahs of the inverse transmissibility 1 subtraction function ISF, () s. Furthermore, these eaks are related with values of the mode shae ratios, i.e. the values of kl jr (8) 1 kl () s at the system oles are related to the scalar oerational mode-shae values iv and. jv herefore, once the resonant frequencies are identified, it is also ossible to identify vectors from different ISFs. By choosing a fixed reference DOF j the full unscaled vector for the th frequency 1 1,,, 1,, 1 (K is the number of measured outut DOFs) can 1j j jj Kj be constructed from ISF. he different comonents of the vector might be defined in the following way: f 1 1 ( f) df (9) f v1 where f f 1 is the integrated frequency bandwidth for the th ISF. he same rocedure should be reeated for each by choosing the aroriate bandwidth affecting each system s ole. In articular, the modal assurance criterion (MAC) [8], usually emloyed to indicate the correlation between two sets of mode shaes, might be used to estimate the correlation between the undamaged ISFs (ISF u ) and damaged ISFs (ISF d ) 1 3

4 for each mode at the measurement degrees of freedom. he new criterion, denoted as MACISF, is for each mode as follows: MACISF ISFu ISFd ISFu ISFu ISFd ISFd (10) his index, alied to each th aired mode, has the advantage that each term is between 0 and 1. An index equal to zero means no correlation between the two sets, while a value equal to one means no change in ISF, and therefore, no structural damage. he criterion above has been defined for only one vibration mode. o consider the N m vibrating modes, a total modal assurance criterion has been defined in the following way: Nm MACISF MACISF (11) 1 and an average value might be exressed as follows: AMACISF MACISF / Nm (1) NUMERICAL EXAMPLE Numerical simulation is carried out with a cantilever beam which was adoted to examine the erformance of the roosed damage detection index. A schematic diagram of this beam with its geometric dimensions and material roerties is shown in Fig. 1. wo different simulations were carried out by considering a mesh of 50 beam elements. he beam was assumed to be lightly damed with a constant daming ratio of 0.5%. he damage was numerically simulated by introducing a stiffness reduction into the elements chosen to be damaged. o excite the undamaged and damaged beams, a simulated imulse force sectrum with constant amlitude of 1000 was alied to the midsan node (node 6) (Fig. 1). hen, the vertical acceleration resonse PSD of each node was catured and analyzed to construct the cross ower sectrum and ower sectrum density transmissibility (PSD) of the first five flexural modes. Figure 1. Numerical simulation with 50 elements. Fig. shows the inverse transmissibility subtraction function defined for two nodes randomly selected. 4

severity. Predictions using the AMACISF index are shown in Fig.3.

5 Figure. Inverse transmissibility subtraction function. Firstly, a single damage scenario was considered. Element between nodes 5 and 6 was considered to be damaged and different levels of damage were introduced to study the sensitivity of the roosed method to the damage severity. Predictions using the AMACISF index are shown in Fig.3. In general, higher levels of damage (lower flexural stiffness) give an AMACISF value further from one. Fig.4 shows the AMACISF value in a multile damage scenario (three damaged elements). he same scenario is studied by introducing a % noise and results are shown in Fig.5. Figure 3. AMACISF value in a single damage scenario. 5

he ability of detecting minor damage qualifies the roosed method for a ossible alication on real structures under random excitation.

6 Figure 4. AMACISF values in a multile damage scenario. CONCLUSIONS Figure 5. AMACISF values in a multile damage scenario with % noise. One damage detection rocedure based on the ower sectral density transmissibility has been roosed in this aer. he ability of detecting minor damage qualifies the roosed method for a ossible alication on real structures under random excitation. New imrovements of the method, such as the ability of locating damage, should be erformed in the future. ACKNOWLEDGEMENS he writers acknowledge the suort for the work reorted in this aer from the Sanish Ministry of Science and Innovation (roject BIA C03-01). Finantial suort for the FPI research fellowshi given to Enrique Sevillano and the CSC research fellowshi given to Yunlai Zhou is also acknowledged. 6

7 REFERENCES 1. Friswell, M.I. (007) Damage identification using inverse methods, Philosohical ransactions of the Royal Society, 365, Perera, R., Ruiz, A., Manzano, C. (007) An evolutionary multiobjective framework for structural damage localization and quantification, Engineering Structures, 9, Devriendt, C. & Guillaume, P. (007), he use of transmissibility measurements in outut-only modal analysis, Mechanical Systems and Signal Processing, 1(7), Devriendt, C., Guillaume, P. (008), Identification of modal arameters from transmissibility measurements, Journal of Sound and Vibration, 314, Urgueira, A.P.V., Almeida, R.A.B., Maia, N.M.M. (011), On the use of the transmissibility concet for the evaluation of frequency resonse functions, Mechanical Systems and Signal Processing, 5, Devriendt, C., De Sitter, G., Guillaume, P. (010), An oerational modal analysis aroach based on arametrically identified multivariable transmissibilities, Mechanical Systems and Signal Processing, 4(5), Yang, W.J., Ren, W.X. (01), Oerational Modal Parameter Identification from Power Sectrum Density ransmissibility, Comuter-Aided Civil and Infrastructure Engineering, 7(3), Allemang, R.J., Brown, D.L. (198) A correlation for modal vector analysis, Proceedings of 1st International Modal Analysis Conference,

POWER DENSITY OPTIMIZATION OF AN ARRAY OF PIEZOELECTRIC HARVESTERS USING A GENETIC ALGORITHM

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