Automated Decentralized Smart Sensor Network for Modal Analysis

Transcription

1 Autoated Decentralized Sart Sensor Network for Modal Analysis S. H. Si a, B. F. Spencer a, Jr., M. Zhang b, and H. Xie c a Dept. of Civil and Environental Engineering, University of Illinois at Urbana-Chapaign, Urbana, IL 68, USA; b Dept. of Civil Engineering, Shantou University, Shantou, Guangdong, China; c College of Civil Engineering, Shenzhen University, Shenzhen, Guangdong, China ABSTRACT Understanding the dynaic behavior of civil engineering structures is iportant to adequately resolve probles related to structural vibration. The dynaic properties of a structure are coonly obtained by conducting a odal survey that can be used for odel updating, design verification, and iproveent of serviceability. However, particularly for largescale civil structures, odal surveys using traditional wired sensor systes can be quite challenging to carry out due to difficulties in cabling, high equipent cost, and long setup tie. Sart sensor networks (SSN) offer a unique opportunity to overcoe such difficulties. Recent advances in sensor technology have realized low-cost sart sensors with on-board coputation and wireless counication capabilities, aking deployent of a dense array of sensors on large civil structures both feasible and econoical. However, as opposed to wired sensor networks in which centralized data acquisition and processing are a coon practice, the SSN requires decentralized algoriths due to the liitation associated with wireless counication; to date such algoriths are liited. This paper proposes a new decentralized hierarchical approach for odal analysis that reliably deterines the global odal properties and can be ipleented on a network of sart sensors. The efficacy of the proposed approach is deonstrated through several nuerical eaples. Keywords: decentralized odal analysis, sart sensor, sart sensor network. INTRODUCTION Research on structural vibration issues started in 93s focusing on understanding the dynaic behavior of aircraft []; since that tie, principles in structural dynaics have been widely considered in other applications. Identified dynaic characteristics are often used for odel updating, design verification, and serviceability. A typical eaple is the retrofit of the London Millenniu Footbridge to address unepected large lateral vibrations caused by pedestrians [2]. To control bridge vibrations, fluid-viscous dapers and tuned ass dapers were installed on the bridge. In designing this daping syste, understanding the dynaic characteristics of the as-built bridge was critical to ensuring efficient operation. The dynaic properties of structures are coonly obtained by conducting a odal survey that typically consists of easuring vibration signals of the structure and analyzing the easured data to estiate odal paraeters such as natural frequencies, ode shapes, odal daping factors, and odal ass. However, for large-scale civil engineering structures, the long setup tie, difficulties in cabling, and high equipent cost [3] akes conducting a odal survey using the conventional wired sensors challenging. For instance, iagine a odal survey of the Golden Gate Bridge. Miles of cables would be required to connect the central base station to the sensor nodes distributed along the towers and deck; installation would be both costly and tie-consuing. Thus, ore efficient eans for odal surveys is desired particularly for large-scale civil structures. Sart sensor networks (SSN) provides a proising alternative to traditional wired sensor networks. Recent advances in sensor technology have enabled low-cost sart sensors that have wireless counication, on-board processing, and ulti-scale sensing capabilities; even lower prices are epected once sart sensors are in ass production. A variety of coercially available sart sensors has been developed in the last decade [4], opening a new era in structural health onitoring (SHM). Although soe challenges, such as power consuption and long ter reliability, still need to be resolved for the sart sensors to be ore widely adopted, available sart sensors are already quite capable and can be epected to replace the traditional wired sensors for any applications. One particularly critical challenge relates to how the data is processed. Centralized data acquisition and processing schees (See Fig. a) that are coonly used in traditional wired sensor systes cannot be eployed in SSNs due to the liitation in wireless data counication

2 speeds; bringing all data to a centralized location will result in severe data congestion in the SSN. This issue should be resolved for the SSN to be ore widely deployed on large-scale civil structures. A nuber of decentralized approaches have been proposed for conducting structural health onitoring and daage detection on networks of sart sensors. One of the decentralized approaches uses independent data processing, as shown in Fig. b [5][6][7][8][9]. Each sensor node processes easured data independently without counicating with other sensor nodes. The processed data, typically FFT or daage assessent results, is then sent to the base station. While the total aount of transferred data in the network is relatively sall, iportant spatial inforation (e.g. ode shape) cannot be etracted. The decentralized approach proposed by Gao et al. [] eploys a coordinated coputing strategy as shown in Fig. c, which has the ability to capture local spatial inforation. The sensor network in this schee is divided into hierarchical counities, in which sensor nodes within each counity counicate with each other in processing data; counication between counities is conducted through each counity s anager node. Data processing (a) Centralized data collection. Data acquisition (b) Independent data processing. Data acquisition & processing Outcoe forwarding Data processing In counities Data acquisition (c) Coordinated coputing strategy. Fig.. Data acquisition and processing schees. While a nuber of decentralized algoriths for structural health onitoring and daage detection have been published, relatively little effort has been devoted to developing such approaches for odal analysis. Zieran et al. [] ipleented a decentralized data processing schee on a SSN to identify the vibration characteristics of the balcony in a historic theater in etropolitan Detroit. In the SSN, natural frequencies were deterined at each node by the peak picking ethod [2][3] and sent to a central node where the final natural frequencies are decided. Based on the identified natural frequencies, phase differences between the responses of each pair of sensor nodes are deterined in a sequential anner (see Fig. 2), and collected centrally to asseble the global ode shapes. While this decentralized algorith was successfully ipleented and tested, the approach requires a linear network topology and ay result in substantial accuulation of errors in the global ode shapes. Fig. 2. Network topology by Zieran et al. [].

3 This paper proposes an autoated hierarchical decentralized approach for odal analysis that reliably deterines the global odal properties based using a decentralized hierarchical network topology. The proposed ethod estiates local features within each local counity; global odal properties are then calculated based on the collected local inforation. Herein, various sensor topologies for ore accurate estiation of the global ode shape are considered. Nuerical siulation of a plate and truss is provided to deonstrate the effectiveness of the proposed approach. 2. PROBLEM FORMULATION The proposed approach consists of two parts: (i) local feature etraction and (ii) deterination of global odal properties. In the SSN, local features are estiated in each local sensor counity independently and subsequently collected at the base station, where the global odal properties are deterined. This section describes this process. 2. Local feature etraction Consider the structure and sensor network topology depicted in Fig. 3. The structure is divided into overlapping subdoains, represented by i ( i =,, n). Data aggregation and processing are conducted independently within each subdoain. In this study, two cases regarding the input ecitation are considered. In the first, the input ecitation is assued to be easurable, allowing the transfer function to be estiated. By taking the inverse FFT of the transfer function, the ipulse response function can be obtained and used as input to the Eigensyste Realization Algorith (ERA)[4]. The second case assues that the input ecitation is unavailable, and the Natural Ecitation Technique (NET)[5] is eployed. In this approach, the cross-correlation functions between the easured responses are used as the input to ERA. In both cases, only the identified local inforation is collected centrally for deterination of the global odal properties. More inforation regarding ipleentation of these two approaches on sart sensor networks can be found in Nagayaa and Spencer [6]. i j 2.2 Deterination of global odal properties Fig. 3. Structure and overlapping subdoains (i, j = ~n). Once the local inforation is collected centrally, the first task is to delineate the true odes fro the noise odes. In this study, the true odes are selected based on the nuber of identified natural frequencies fro the subdoains []. The true odes should be identified in the ajority subdoains, while the noise odes will randoly appear in the subdoains. Thus, if a specific natural frequency is identified in a substantial nuber of the subdoains, it is considered as a true ode. If ERA fails to find the true ode in certain subdoains, the cross spectru is alternatively used to estiate the local ode shapes. Once the true odes are deterined, the corresponding ode shapes can be cobined together; the reainder of this section describes this process. Consider global ode shape φ for the th ode, along with the previously deterined local ode shapes φ, φ,, φ 2 associated with respective subdoains. The local ode shapes φ n and φ i associated with two j neighboring subdoains can be epressed as

4 φi,2 φ φ = i i, p o φ i, o φ ir, and φ j φ j,2 = φ jq, o φ j, o φ jr, where the superscript o denotes the overlapping node in the i th and j th subdoains, r is the nuber of the overlapping nodes, and p and q are the nuber of non-overlapping nodes in the i th and j th subdoains, respectively. To allow assebly, the ode shapes in Equation () should be rescaled to have the sae values at the overlapping nodes, i.e., o o φ i, φ j, Ri = Rj (2) o o φ ir, φ jr, where R i and R j are the noralization factors for the ode shapes φ and i is the union of the local ode shapes as n i= i i φ j (), respectively. The global ode shape φ = Rφ (3) In the presence of noise, the solution to Equation (2) for any r > does not eist in general. Therefore, the noralization factor Ri ( i =, 2,, n) ust be approiately deterined, for eaple as a solution in the leastsquare sense. Because the subdoains are interconnected, Equation (2) can be epanded up to n( n ) 2 equations for all pairs of the overlapping local ode shapes as follows. φ = R φ φ = R φ φ = R φ + n 2 n n Rφ = Rφ R φ = Rφ n 3 n 2 2n (4) R φ = R φ + n n n n nn ( n ) n where φ is the th local ode shape in the i th doain at the nodes that overlap the j th doain, and i j ij is the error between the ode shapes. Note that the noralization factor for the first subdoain R is selected to be. In atri for, Equation (4) becoes y = XR+ (5) where

5 φ φ 2 2 φ φ 3 3 R φ 2 φ n n R 3 y =, X = φ φ, = 2 3 R, R φ φ 2 n n 2 φ φ n n nn and 2 3 n = 23 2n ( n ) n The estiator ˆR that iniizes the square of errors T is given by [7] ( ) ˆ T T R = X X X y (6) Using the noralization factor R, the local ode shapes are scaled and assebled to obtain the global ode shape. At the overlapping nodes, the local ode shapes are averaged to obtain the associated values of the global ode shape. The accuracy of the cobined global ode shapes can be evaluated by the error between the cobined and reference global ode shapes, φ and φ, ref, respectively: e φ φ, ref = (7) The reference global ode shapes are estiated using all easured accelerations siultaneously. Note that the reference global ode shapes correspond to the centralized data acquisition and processing schee coonly used in the wired sensor networks, while the proposed decentralized approach is for the SSN. For the error e to be eaningful, the two global ode shapes should be appropriately noralized. Thus, φ, ref is noralized so that the largest eleent in φ, ref is equal to, and φ is then scaled to iniize the square error between φ and φ, ref : in T ( φ φ, ref ) ( φ φ, ref ) Once noralized, the error e of the cobined global ode shapes can be calculated. (8) 3. NUMERICAL EXAMPLE A nuerical eaple of a plate is provided to validate the proposed approach. In this eaple, the effects of the sensor topologies on the accuracy of the cobined global ode shapes are investigated. 3. Nuerical odel Consider the unifor plate shown in Fig. 4. The top and left edges of the plate are considered as fied, and the botto and right edges are siply supported. The plate is assued to be.7 by and ade of steel having an elastic odulus of 2 GPa, a Poisson ratio of.3, ass density of kg/3, and thickness of. The nuerical odel of the plate is ipleented in MATLAB using the 2 DOF (3DOF at each node) rectangular Kirchhoff plate eleent known as the ACM eleent [8]. The shape functions are selected to be incoplete, 4 th -order polynoials in the - and y-directions with 2 ters. The first seven out-of-plane ode shapes of the plate odel are presented in Fig. 5, and the transfer functions between the input ecitation applied vertically at the nodes arked by an X and the accelerations at nodes N and N2 (see Fig. 4) are shown in Fig. 6. A total of 63 evenly spaced sensor nodes are selected as shown in Fig. 4 to obtain vertical accelerations under the input ecitation. As suarized in Table 2, four different siulation cases are considered: an ipulse loading (cases and 2) or a band-liited white noise up to 5 Hz (cases 3 and 4). 5% RMS noise is added to all easureents. ERA is used to identify the ode shapes and frequencies in cases, 2, and 3, whereas NET/ERA is used in case 4. As the input

6 ecitation to large-scale civil engineering structures is not generally available, output-only odal analysis for rando ecitations is often eployed; thus, case 4 ay be considered as the ost iportant for structural health onitoring. Fig. 4. Plate odel. f n =.554 Hz f n = Hz f n = Hz y.2 y.2 y f n =3.759 Hz f n = Hz f n = Hz y.2 y.2 y f n = Hz y Fig. 5. Global ode shapes fro the Finite Eleent odel.

7 2 2 Magnitude - -2 Magnitude Frequency (Hz) Frequency (Hz) (a) N (b) N2 Fig. 6. Transfer functions (Circles represent natural frequencies). Table. Global and local ode shapes. Ecitation type Input easured Input not easured Ipulse Case (ERA) Case 2 (ERA) Band-liited white noise Case 3 (ERA) Case 4 (NET/ERA) 3.2 Sensor topology To investigate the effect of the sensor topologies on the cobined global ode shapes, the nodes are grouped in four different ways, as shown in Fig. 7: (a) Topology : two nodes in each group with one overlapping node, (b) : four nodes in each group with two overlapping nodes, and (c) : nine nodes in each group with three overlapping nodes. Note that Topology corresponds to the approach adopted by Zieran et al. []. (a) Topology : 2 nodes in each group. (b) : 4 nodes in each group. (c) : 9 nodes in each group. Fig. 7. Scheatic view of subdoains (dashed line). Fro the data counication perspective, having fewer local groups is advantageous due to less aount of data being transitted over the radio. In a local group, the reference sensor sends sensor data that is generally long, while all other sensors transits the condensed data such as the correlation function of the cross spectru. Thus, the aount of transitted data can be reduced by adopting a topology with less nuber of local groups. Assuing the tie history record of length N and n d ties averaging without any overlap between spectral windows, the total nuber of transitted data points [6] is at ost N Ndata = ng N nd + ( ns ) 2 (9) where n g and n s are the nubers of local groups and sensor nodes, respectively. Fro Equation (9) with N = 24, N data are about.3,.6, and.29 for topology, 2, and 3, respectively. Thus, has the least data counication requireent.

8 3.3 Deterination of true odes As previously described, the nuber of groups in which a natural frequency is locally identified is utilized to delineate between true odes and noise odes. The natural frequencies estiated in each group are collected, and if the nuber of collected natural frequencies in a specific frequency range is greater than a predeterined threshold value, it is assued to be a true ode. The threshold is selected to be 7% of the nuber of local groups. The frequency range in which identified frequencies are counted is ( fc Δ f fc +Δ f ) where f c is the central frequency of the range and 2Δ f is the width. In this study, f c and Δ f are selected as follows. fs fc = r r =, 2, NFFT () fs Δ f = 2 N FFT where f s is the sapling rate, N FFT is the nuber of FFT points, and r is any positive integer such that f c is less than the bandwidth of the input ecitation. Note that the adjacent ranges are ade to overlap with each other to prevent the case that the identified frequencies are evenly distributed over two adjacent non-overlapping ranges. Fig. 8 shows the typical nuber of groups in which a natural frequency is found in case 4 (rando ecitation, input not easured). The identified frequencies in the local groups are concentrated at several frequencies such as about Hz, 8 Hz, 27 Hz, 3 Hz, 34 Hz, 47 Hz, and 49 Hz that are finally considered as corresponding to true odes. In soe frequency ranges, the nuber of local groups is greater than the total nuber of local groups due to noise odes that are closely located to the true odes. In this case, the frequency that is closest to f c is considered as the natural frequency of the local group. 6 5 Nuber of Local Groups Nuber of Local Groups Nuber of Local Groups Frequency (Hz) Frequency (Hz) Frequency (Hz) (a) Topology (b) (c) Fig. 8. Nuber of identified natural frequencies (case 4: rando ecitation and input not easured). 3.4 Global ode shapes The global ode shapes can be assebled with the local ode shapes using the proposed ethod described in section 2.2. If a true ode is not identified in a certain local group, cross spectra of the accelerations in the group are alternatively utilized to estiate the local ode shapes. The cross spectru values at the spectral line nearest to the natural frequency of the ajority groups are assued as the ode shape. Note that ode shapes obtained only fro the cross spectra ay not be as accurate as those fro the ERA because the cross spectra have values only at the spectral lines. The error e j defined in Equation (7) is calculated to assess the accuracy of the cobined global ode shape. Typical plots of the error e 2 for each topology in case 4 are shown in Fig. 9. Iproveent in accuracy is clearly shown for Topologies 2 and 3, where a larger size of local groups and ore overlapping nodes are eployed. Two error easures are considered to quantitatively evaluate the accuracy of the cobined global ode shapes. The first is the aiu error for the j th ode: ( ) E = a e, e,, e () a, j j, j,2 j, n

9 where n is the nuber of eleents in e j, and e ji, are the i th eleent of the error e j. The second error easure is the average error for the j th ode: ( ) E = ean e, e,, e (2) avg, j j, j,2 j, n When a ode is not identified, the error of the ode is set to %. Error Error Error y y y (a) Topology. (b). (c). Fig. 9. Absolute value of the errors between the cobined and reference global ode shapes (case 4, 2nd ode). Repeating the siulation ties for each case, the averages of each error easure are calculated for the first seven odes as shown in Fig. and Fig.. Zooed figures fro % to 5% are also provided in Fig. to clearly show E avg, j. In Fig. and Fig., topology 3 consistently has the sallest errors in ost cases. It can be concluded that sufficiently large local groups and ultiple overlapping nodes as in contribute to reliable and accurate estiation of global odal properties. Topology Topology 8 8 Ma Error (%) 6 4 Ma Error (%) (a) Case : Ipulse loading, input easured (b) Case 2: Ipulse loading, input not easured. Topology Topology 8 8 Ma Error (%) 6 4 Ma Error (%) (c) Case 3: rando ecitation, input easured. (d) Case 4: rando ecitation, input not easured. Fig.. Maiu error.

10 8 Topology 8 Topology 6 6 Average Error (%) Average Error (%) (a) Case : Ipulse loading, input easured. (b) Case 2: Ipulse loading, input not easured. 8 Topology 8 Topology 6 6 Average Error (%) Average Error (%) (c) Case 3: rando ecitation, input easured. (d) Case 4: rando ecitation, input not easured. Fig.. Average error. 4. CONCLUSION An autoated hierarchical decentralized approach for odal analysis using sart sensors has been proposed to obtain the global odal properties using a decentralized network topology. The proposed approach consists of two ain parts: () local feature etraction and (2) deterination of global odal properties. The odal analysis is conducted independently in each sensor group to estiate local inforation using ERA or NET/ERA. Global odal properties are then obtained using the collected local properties in the base station. The nuber of local groups in which natural frequencies are locally identified is utilized to delineate between the true and noise odes. Then, local ode shapes are assebled using the least squares approiation to estiate the global ode shape. The proposed approach was nuerically validated. Fro the eaple of the plate, appropriately selected sensor topologies with the sufficiently large size of local groups and the ultiple overlapping nodes were found to reduce errors in the assebled global ode shape. The nuerical results show that the proposed approach for decentralized odal analysis is proising for the SSN. While ERA and NET/ERA are used in this study to characterize the local odal

11 properties, other syste identification ethods such as Stochastic Subspace Identification [9] [2] or Frequency Doain Decoposition [2] can be alternatively used. Ipleenting the proposed approach on the SSN is currently underway. ACKNOWLEDGEMENT The authors gratefully acknowledge the support of this research by the National Science Foundation, under grant 6433 (Dr. S. C. Liu, progra anager) and Vodafone. The support is gratefully acknowledged. REFERENCES [] [2] [3] [4] [5] [6] [7] [8] [9] [] [] [2] [3] [4] [5] [6] [7] [8] Maia, N. M. M. and Silva, J. M. M., Modal Analysis Identification Techniques, Philosophical Transactions: Matheatical, Physical and Engineering Sciences 359(778), 29-4 (2). Dallard, P., Fitzpatrick, A. J., Flint, A., Le Bourva, S., Low, A., Ridsdill Sith, R. M., and Willford, M., The London Millenniu Footbridge, The Structural Engineer 79(22), 7-33 (2). Lynch, J. P., Sundararajan, A., Law, K. H., Kireidjian, A. S., Carryer, E., Sohn, H., and Farrar, C., Field Validation of a Wireless Structural Monitoring Syste on the Alaosa Canyon Bridge, Proc. SPIE th Annual Int. Syposiu on Sart Structures and Materials, San Diego, CA, USA, March 2-6 (23). Lynch, J. P., and Loh, K., A suary review of wireless sensors and sensor networks for structural health onitoring, Shock and Vibration Digest 38(2), 9 28 (26). Tanner, N. A., Wait, J. R., Farrar, C. R., and Sohn, H., Structural Health Monitoring Using Modular Wireless Sensors, Journal of Intelligent Material Systes and Structures 4(), (23). Caffrey, J., Govindan, R., Johnson, E., Krishnaachari, B., Masri, S., Sukhate, G., Chintalapudi, K., Dantu, K., Rangwala, S., Sridharan, A., Xu, N., and Zuniga, M., Networked Sensing for Structural Health Monitoring, Proc. 4 th Int. Workshop on Structural Control, New York, NY, June, (24). Lynch, J. P., Sundararajan, A., Law, K. H., Kireidjian, A. S., and Carryer,E., Ebedding Daage Detection Algoriths in a Wireless Sensing Unit for Operational Power Efficiency, Sart Materials and Structures 3(4), 8 8 (24). Lynch, J. P., Parra-Montesinos, G., Canbolat, B. A., and Hou, T-C., Real-tie Daage Prognosis of Highperforance Fiber Reinforced Ceentitious Coposite Structures, Proc. Advances in Structural Engineering and Mechanics (ASEM 4), Seoul, Korea, Septeber 2 4 (24). Nitta, Y., Nagayaa, T., Spencer Jr., B. F., and Nishitani, A., Rapid daage assessent for the structures utilizing sart sensor MICA2 MOTE, Proc 5 th Int. Workshop on Structural Health Monitoring, Stanford, CA., (25). Gao, Y., Spencer Jr., B. F. and Ruiz-Sandoval, M., "Distributed coputing strategy for structural health onitoring," Journal of Structural Control and Health Monitoring 3(), (26). Zieran, A. T., Shiraishi, M., Swartz, R. A., and Lynch, J. P., Autoated Modal Paraeter Estiation by Parallel Processing within Wireless Monitoring Systes, Journal of Infrastructure Systes 4(), 2-3 (28). Ewins, D. J., Modal testing: Theory and practice, Research Studies Press, Ltd., Staunton, Soerset, U.K. (986). Alleang, R. J., Vibrations: Eperiental odal analysis, Course Notes (UC-SDRL-CN /664), Structural Dynaics Research Laboratory, University of Cincinnati, Cincinnati ( Juang, J. N. and Pappa, R. S., An Eigensyste realization algorith for odal paraeter identification and odel reduction, Journal of Guidance Control and Dynaics 8, (985). Jaes, G. H., Carne, T. G., Lauffer, J. P. and Nord, A. R., Modal testing using natural ecitation, Proc. th Int. Modal Analysis Conference, San Diego, CA (992). Nagayaa, T. and Spencer Jr., B. F., Structural Health Monitoring Using Sart Sensors, Newark Structural Engineering Laboratory (NSEL) Report Series, No., University of Illinois at Urbana-Chapaign, Urbana, Illinois ( (27). Montgoery, D. C. and Runger, G. C., Applied Statistics and Probability for Engineers, John Wiley & Sons, Inc. (994). Zienkiewicz, O. C. and Cheung, Y. K., The finite eleent ethod for analysis of elastic isotropic and orthotropic slabs, Proc. Inst. Civ. Eng. 28, (964).

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