Energy-efficient deployment strategies in structural health monitoring using wireless sensor networks

Transcription

1 STRUCTURAL CONTROL AND HEALTH MONITORING Struct. Contro Heath Monit. 1; :1 1 Energy-efficient depoyment strategies in structura heath monitoring using ireess sensor netorks Tat S. Fu 1, Amitabha Ghosh, Erik A. Johnson and Bhaskar Krishnamachari 1 Department of Civi Engineering, University of Ne Hampshire, Durham, NH 8 Department of Eectrica Engineering, Princeton University, Princeton, NJ 85 Sonny Astani Department of Civi and Environmenta Engineering, University of Southern Caifornia, Los Angees, CA 989 Ming Hsieh Department of Eectrica Engineering, University of Southern Caifornia, Los Angees, CA 989 Tat.Fu@unh.edu, amitabhg@princeton.edu, JohnsonE@usc.edu, bkrishna@usc.edu SUMMARY Structura heath monitoring using ireess sensor netorks has dran considerabe attention in recent years. The ease of depoyment of tiny ireess devices that are couped ith sensors and actuators enhances the data coection process and makes prognostic and preventive maintenance of an infrastructure much easier. In this paper, the depoyment probem is considered for finding node ocations to reiaby diagnose the heath of a structure hie consuming minimum energy during data coection. A simpe shear structure is considered and moda anaysis is performed. The exampe verifies the expectation that pacing nodes further apart from each other reduces the mode shape errors but increases the energy consumption during data coection. A minmax, energy-baanced routing tree and optima grid separation formuation is proposed that minimizes the energy consumption as e as provide fine grain measurements. Copyright c 1 John Wiey & Sons, Ltd. KEY WORDS: Structura heath monitoring; ireess sensor netorks; sensor pacement; mode shape anaysis; Eigensystem reaization agorithm (ERA); energy-baanced routing. 1. INTRODUCTION The goa of a ireess Structura Heath Monitoring (SHM) system [1, 1,, 5, 8] is to assess structura integrity using ireess sensor netorks (WSNs). Reiabe ireess SHM systems that can hep predict faiures in structures through non-destructive diagnosis procedures can have substantia socia and economic benefits. The Coumbia space shutte tragedy and the I-5W Mississippi river bridge coapse have underined the importance and necessity of reiabe monitoring systems in anayzing structura damage and deterioration processes. Typica structura safety assessment depends on visua inspection, hich is manua, expensive, and time consuming. Moreover, damage can be hidden inside structura eements. Using sensors, SHM systems can examine the structura integrity in an automatic and efficient manner. Hoever, instaation of ired sensors is expensive, especiay in existing buidings, hereas ireess sensors are inexpensive and easiy depoyabe. By measuring and processing structura responses using damage identification techniques, a ireess SHM system can coaborativey and accuratey diagnose the structura heath. Athough use of a WSN reduces iring costs, it comes ith to major imitations in terms of energy and bandidth. Unike ired netorks, ireess sensor nodes are energy constrained as they rey on on-board batteries. Additionay, ireess channes typicay have oer bandidth compared to ired channes because of the ack of a reiabe and dedicated medium. Thus, energy efficiency in the data coection process is an important concern for a ireess SHM system. Node depoyment in a WSN is a crucia probem that depends on to reated factors: the number of sensors and their ocations. Since the sensor readings need to be exchanged and fused for further processing, a sensor nodes shoud form a connected netork. In this paper, ireess SHM is appied to a simpe n-story shear structure here each foor is equipped ith an equa number of sensors to measure structura responses. Whie many sensors (hen appropriatey depoyed) give accurate measurements and resut in higher fideity estimation, they aso incur a high Correspondence to: Tat S. Fu, Department of Civi Engineering, University of Ne Hampshire, Durham, NH 8 Copyright c 1 John Wiey & Sons, Ltd.

2 TAT FU ET AL. communication cost to exchange a arge amount of data. On the other hand, feer sensors impy a o communication cost, but estimates of structura characteristics coud be inaccurate. To understand this reationship beteen WSNs and SHM in terms of sensor pacement, this paper considers to most natura depoyment strategies, random and grid pacements, and presents simuation resuts from moda anaysis based on the Eigensystem Reaization Agorithm (ERA) and netork energy consumption. Using ERA, moda characteristics of a structure are estimated from its responses and then used for damage identification. An energy-baanced routing tree is aso constructed for the WSN to reaisticay estimate the energy consumption. The rest of the paper is organized as foos. Section discusses reated orks hie Section presents the structura, netork, and energy modes. Section provides a summary of the ERA agorithm and Section 5 presents simuation resuts. In Section 6, an energy-baanced routing tree construction agorithm is proposed, and optima determination of inter-node separation is found that minimizes both mode shape error and energy consumption. Finay, Section 7 summarizes the resuts and gives directions for future research.. RELATED WORK Recent studies [19, 1] and depoyments [15, 18, 5, ] of ireess SHM have demonstrated the feasibiity of autonomous and continuous structura data coection using a WSN, hich is inexpensive and more efficient compared to its ired counterpart [5]. Hoever, in addition to determining the optima ocations of sensor nodes for reiabe measurements, the bandidth and energy constraints on these ireess devices have aso underined the need for addressing energy efficiency in the data coection process. One of the important factors that affects data coection in ireess SHM is the underying routing mechanism. The notion of energy-baanced (or, more generay, oad-baanced) routing in the netorking community is a e researched probem and is proven to be N P -hard []. Huang et a. [1] presented to energy-aare, oad-baanced routing schemes: the maximum capacity path (MCP) and MCP combined ith path sitching, here a ayered netork is constructed and every node seects a shortest path ith maximum capacity to the sink, sometimes sitching paths to its sibing neighbors in order to share traffic. It is shon that both schemes can achieve improved oad-sharing and, thereby, increase in-netork ifetime. Gao et a. [9] presented distributed routing agorithms for ireess netorks hen a the nodes are ocated in a narro strip to minimize atency and achieve a good oad baance in terms of energy usage; Spencer and coaeagues et a. [, ] expanded on this ork, deveoping agorithms to empoy decentraized approaches in a softare frameork. Shah et a. [] argued that aays using the oest energy paths may not be optima from the point of vie of netork ifetime and ong-term connectivity, and proposed a technique to occasionay use sub-optima routing paths to provide substantia gains. A node-centric oad baancing scheme is presented by Dai and Han [8] considering the Chebyshev sum metric to evauate the quaity of the routing agorithm. Chatterjee et a. [] presented a distributed scheme in the context of data gathering, here nodes are organized into ayers and each node seects a parent from its one-hop neighborhood such that the maximum oad stays beo a certain threshod. The ork presented in this paper differs from the above in the sense that oad baancing is formuated in terms of min-max fairness ith respect to energy consumption by the nodes couped ith the accuracy of structura characteristics estimated by the nodes. In addition to energy-baanced routing, reiabe routing is another major concern for ireess SHM systems [,, 8]. Hoever, communication reiabiity is outside the scope of this paper; reiabe data transmission is assumed in this study and the authors anayze the reiabiity of the system reated to SHM purposes ony. Additionay, researchers have deveoped softare frameorks (e.g., [9]) for faciitating SHM via ireess sensors; this paper deveops a methodoogy that such a frameork coud use to incorporate imitations of the sensor hardare, and the resuting trade offs ith accuracy and other performance metrics that inevitaby arise. A number of studies examined optima node pacement for identification and contro of dynamic structures. Udadia et a. [9, ] proposed a scheme to optimay ocate sensors by maximizing the trace or determinant of the Fisher information matrix, hich is expressed as a function of seected parameters corresponding to the objective function. Heredia-Zavoni et a. [1] extended this approach to capture uncertainty in mode updating by minimizing the expected Bayesian oss function ith the Fisher information matrix. Kammer [17] evauated the sensor ocations by their contribution to the inear independence of the identified mode. Hemez et a. [1] extended this independence method in terms of strain energy contribution of the structure. Papadimitriou et a. [7] used information entropy as a unique measure to mode parameter uncertainty, and a Bayesian statistica methodoogy to find optimum sensor pacements. Recenty, genetic agorithms have aso been used for finding optimum sensor pacements (e.g., [1,11,7]). Eary studies had mosty been concerned ith observabiity and controabiity of dynamic structures, hie recent ones have started to tie sensor pacements ith the quaity of damage detection. Cobb et a. [7] studied the reationship beteen sensor pacement, measured modes, and the extent of damage ocaization on fexibe structures using moda anaysis. Shi Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

3 ENERGY-EFFICIENT DEPLOYMENT USING WIRELESS SENSOR NETWORKS. et a. [1] proposed a scheme to optimize sensor pacement according to damage detection based on the eigenvector sensitivity method. These previous studies focused on pacing sensors optimay for structura anaysis, hoever, the sensor netork as eft out. The typica objective in these orks as to determine here to pace m sensors in an n degree-of-freedom (DOF) system, here usuay m n, and at east one sensor is ocated at each DOF. This paper assumes that there are mutipe sensors on each foor of a buiding structure, since ireess sensors are designed for arge-scae systems, and considers the depoyment probem in terms of both quaity of damage detection and energy efficiency in the data coection process.. PRELIMINARIES A structura heath monitoring system using a ireess sensor netork consists of various components: (1) the structure itsef, () a carefuy depoyed set of ireess nodes equipped ith sensors (such as acceerometers) that coud measure the structura response and reay it over muti-hop ireess communication channes to a sink node, and () a set of agorithms that take as inputs the measured responses and cacuate one or more metrics that indicate the heath of the structure..1. Structura Mode A simpe civi structure, an n-story rectanguar shear structure of ength, idth and story height h, is considered, as iustrated in Figure 1. It is assumed that a foors are uniform, in that the optima ocations of the nodes on a particuar foor can be repeated on each foor so ong as there is at east one communication ink beteen nodes ocated on to adjacent foors. This i enabe measurements to be communicated across a the foors of the structure in mutipe hops and, finay, to a goba sink that can aggregate the information and make reiabe diagnosis about the heath of the structure. For the simuations herein, the dimension of the structure is taken as ength =.8 cm (1 in) by idth =. cm (8 in) by story height h = 15. cm (6 in), hich is simiar to the scaed buiding mode (see Figure ) considered by Chintaapudi et a. [5]. The equations of motion can be expressed Mẍ + Cẋ + Kx = u (1) ith bock diagona mass matrix M = diag(m 1, M,..., M n ) and stiffness matrix K 1 + K K. K K + K K = Kn 1 + K n K n, () K n K n here M i is the mass matrix of the i th foor, K i is the stiffness matrix of the i th story, x = [x 1, y 1, θ 1,..., x n, y n, θ n ] T is the dispacement/rotation vector reative to the ground, and u is the externa force/moment vector. Damping matrix C is chosen such that the damping ratio of every mode is ζ (i.e., C = MΦ(ζΛ 1/ )Φ 1 here Λ and Φ are the diagona matrix of eigenvaues and corresponding matrix of eigenvectors found from KΦ = MΦΛ). The structure in the numerica exampe herein is symmetric ith M i = diag[m, m, m θ ] and K i = diag[k x, k y, k θ ] here m θ = m( + )/1 and k θ = (k x + k y )/, ith foor mass m =.9 kg (1.8 b), story stiffnesses k x = 8 kn/m (5 bs/in) and k y = 19 kn/m (15 bs/in), and damping ratio ζ = 5% in every mode... Effect of Sensor Pacement on Measurements Let s ij denote the j th sensor (j = 1,,..., m) on the i th foor (i = 1,,..., n), and et x ij and y ij be the measurements recorded by sensor s ij in the x and y directions, respectivey. In Figure 1(c), dx ij and dy ij are the distances from the center of the i th foor to sensor s ij. The reationship beteen (x ij, y ij ) and the i th foor s movements (x i, y i, θ i ) is given by: [ ] [ ] xij 1 dyij = x i y y ij 1 dx i, () ij θ i Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

4 TAT FU ET AL. k n cn m n m n Random Pacement m n-1 m n-1 k n-1 c n-1 m n- OR Grid Pacement y s ij m n- m 1 m 1 sensor θ dx ij dy ij x k 1 c 1 (a) (b) (c) Figure 1. (a) Shear structure (shoing one direction ony). (b) An n-story structure ith sensors paced randomy or in a grid on each foor. (c) Foor diagram ith distances dx ij and dy ij from the center of the foor to sensor s ij. assuming θ i is sma and, thus, θ i sin(θ i ). Here x i and y i are the dispacements in the x and y directions, and θ i is the rotation of the i th foor, a reative to the ground. For m sensors, () can be expanded as: T x i [x i1 y i1 x i y i... x im y im ] T = y i, () dy i1 dx i1 dy i dx i... dy im dx im θ i or, in matrix notation, by: X si = QX i. (5) With pseudo-inverse Q + = (Q T Q) 1 Q T, the foor movement can be estimated from the sensor measurements as: X i = Q + X si. (6) This is a east square estimate of foor movements, here the atera movements x i and y i are affected by the accuracy of measurements, and the rotation θ i additionay affected by the sensor ocations (dx ij, dy ij ). Large dx ij s and dy ij s are expected to improve the accuracy of the rotation estimates because sensors further aay from the rotating axis (center of the foor) can better record the effects of rotations. This is because the movements due to θ i are arger ith arge dx ij s and dy ij s as compared to that due to the same θ i ith sma dx ij s and dy ij s. Since there is noise in sensor measurements, Equation (6) is more reaisticay represented as: ˆX i = Q + (X si + W), (7) here W is a vector of measurement noise, hich is assumed to be independent and normay distributed ith zeromean and variance p ij, or N(, p ij )... Netork Mode In the netork mode, it is assumed that the nodes can adjust their poer eves up to a maximum poer eve P max giving a maximum transmission range R max. To nodes are abe to communicate ith each other if the Eucidean distance beteen them is ess than or equa to the minimum of their transmission ranges. This mode, commony knon as the disk graph mode, is ideaistic and does not capture interference and the anisotropic nature of radio propagation [6]. The center of each foor aso has a high poered node, caed the oca sink, that connects nodes in adjacent foors to exchange measurements. Thus, a nodes in a foor ony send their measurements to their oca sink. In the simuations, R max is taken as 91. cm (6 in), chosen so that, at maximum poer, a nodes can tak directy to each other... Energy Mode A ireess SHM system once depoyed is expected to be functiona for months or even years depending on ho often a diagnosis is performed. Since battery-poered nodes are imited in energy, a crucia aspect of designing Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

5 ENERGY-EFFICIENT DEPLOYMENT USING WIRELESS SENSOR NETWORKS. 5 Figure. Four-story buiding mode used in Chintaapudi et a. [5]. ireess SHM systems is to minimize the energy consumption. Athough such systems usuay have a very high samping rate and resoution and may require intense CPU usage, the poer consumption by the radio modue is orders of magnitude higher than samping and computation [, 6]. For exampe, the Tmote Sky patform, hich uses a Chipcon CC radio operating at. GHz using a IEEE MAC/PHY ayer, the currents dran for transmission and reception are 17. ma and 19.7 ma, respectivey. As these nodes use to AA batteries, suppying about.6 V, the resuting transmit and receive poers are 6 mw and 7 mw, respectivey. For the samping modue, Tmote Sky uses an utra-o poer 8 MHz Texas Instrument MSP processor, hich dras 1.8 ma hen ON,.5 ma hen IDLE, and.51 ma hen in standby; the corresponding poer consumptions are 6. mw,.19 mw, and.18 mw, respectivey. Ceary, there are a number of factors that affect the durations of samping and radio transmission/reception; in the studies herein, the durations ere of comparabe magnitude, making transmission/reception more costy than samping. Whie various radios have different characteristics, a common feature is that the seep mode generay consumes three orders of magnitude ess poer than transmission, reception, or ide modes. Thus, to cut don on the energy costs, it is best to keep the radio in the seep mode for as ong as possibe, and to transmit packets at a high data rate so as to minimize the transmission time. In this paper, the fooing energy mode is considered here the energy expenditure per bit for communication over a ink of ength d is: e(d) = α + β(d/) η, (8) here the distance-independent term α represents the energy cost of transmitter and receiver eectronics ith a typica vaue beteen 7 and 1 mw for. GHz radios; β/ η is the transmit ampifier constant, hich is normaized by the idth of the structure; and η is the path-oss exponent ith typica vaues beteen and 6 depending on the environment. Here, d η captures the ampification required to ensure constant poer reception at the receiver. In the simuations herein, α = 7 mw, β = 61 mw, and η =.. SYSTEM IDENTIFICATION USING EIGENSYSTEM REALIZATION ALGORITHM Using measurements from the sensors, the structura characteristics can be identified by first estimating the moda parameters such as frequencies and mode shapes ith the Eigensystem Reaization Agorithm (ERA). The ERA as originay deveoped by Juang and Pappa [16], and is a e-knon scheme for estimating state-space reaizations of Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

6 6 TAT FU ET AL. a system from impuse responses. It uses a singuar vaue decomposition of the fooing Hanke matrix: Y(k) Y(k + 1)... Y(k + p) Y(k + 1) Y(k + )... Y(k + p + 1) H(k 1) =......, (9) Y(k + r) Y(k + r + 1)... Y(k + p + r) here Y(k) is the m b puse matrix such that Y ij (k) is the impuse response at the k th time instant coected at the i th ocation due to an impusive excitation at the j th ocation in the structure. The singuar vaue decomposition of H() is given by: H() = PDQ T, (1) here P and Q T are unitary matrices formed by eft and right singuar vectors, respectivey, and D is the diagona matrix formed by the singuar vaues. Singuar vectors corresponding to sma singuar vaues are attributed to noise, and the reduced order matrices P n, Q n and D n are generated by using ony the singuar vectors corresponding to the arge singuar vaues. The inear system parameters corresponding to the reduced order system can no be estimated using the equations: A = D 1/ n P T n H(1)Q n D 1/ n (11) B = D 1/ n Q T n E b (1) C = E T mp n D 1/ n (1) here E T i = [I i ] ith I i being the identity matrix of order i. The mode shapes of the structure correspond to the coumns in the matrix V = C Φ, here Φ contains the eigenvectors of A; the moda frequencies of the structure correspond to the magnitude of the eigenvaues of A. To check the accuracy of the system identification using various sensor pacements, comparisons are made beteen mode shapes estimated using the ERA from measured responses ith and ithout noises. The noise-free estimated mode shapes are used as the baseine case ith hich other estimated mode shapes (ith different noise eves) are compared. Since mode shapes, simiar to eigenvectors, are scaabe vectors for specific frequencies, the Moda Ampitude Coherence (MAC) is used to differentiate beteen different sets of mode shapes [16]. The MAC beteen to vectors a and b is defined as: a b MAC(a, b) = (1) (a a)(b b) ith vaues ranging from to 1, here a denotes compex conjugate of a. When to vectors are parae, their MAC vaue is 1, hereas to orthogona vectors have a MAC vaue of. Thus, by finding the MAC vaues of the mode shapes from the base case and from cases ith different sensor pacements and noise eves, accuracy can be measured. For square matrices A = [a 1, a,..., a k ] and B = [b 1, b,..., b k ], the MAC is defined as: MAC(a 1, b 1 ) MAC(a 1, b )... MAC(a 1, b k ) MAC(a, b 1 ) MAC(a, b )... MAC(a, b k ) MAC(A, B) =......, (15) MAC(a k, b 1 ) MAC(a k, b )... MAC(a k, b k ) ( ) Error is measured as the Frobenius norm of MAC( ˆΦ, Φ) I or ( [ ] T [ error = trace MAC( ˆΦ, Φ) I MAC( ˆΦ, Φ) I] ), (16) here ˆΦ is the estimated mode shape from the measured responses of the structure and I is the identity matrix. When ˆΦ = Φ, MAC( ˆΦ, Φ) = I and error =. 5. MODE SHAPE ERRORS FROM SIMULATIONS To types of node depoyments are studied: random and grid. In random depoyment, nodes are paced randomy on each foor ith uniform distributions in both x and y directions. The number of sensors per foor m, and the noise eve p are varied to study their effects on the mode shape error. For a given foor, 1 reaizations of random sensor pacement are simuated and anayzed for different noise eves. In grid depoyment, nodes are paced on a foors ith Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

7 7 ENERGY-EFFICIENT DEPLOYMENT USING WIRELESS SENSOR NETWORKS. Mode Frequency (Hz) Tabe I. Tota of 1 modes out of hich ony 5 are reiabe (shon in bod). 1% noise 8% noise 6% noise % noise % noise error error error error error Number of sensors Reaizations Figure. Mode shape errors of 1 reaizations ith different numbers of sensors and noise eves. The errors in some cases converge into a singe band and in other cases into to bands. different inter-node separations. As before, the number of sensors per foor and the noise eves are varied to study their effects. Using a structura mode ith four foors described in Figure, there are 1 modes ( foors each ith degrees of freedom x, y and θ) in this structure. Mode parameters are estimated using ERA ith the structure being simuated ith impuses (i.e., singuar vaues or 1 modes are found ith ERA anaysis). Hoever, not a 1 rea modes can be successfuy identified. There are usuay a fe unidentifiabe modes because of noise in the data, hich have unpredictabe effect on the mode shape error. To dea ith the noise modes, the authors choose to incude ony 5 modes for the rest of the study (shon in the Tabe 5), hich are aays identified from a the simuation cases. The authors acknoedge that reying ony on the 5 modes can sometimes favor sensor pacements ith poor performance. For exampe, a pacement that can successfuy identify 8 modes shoud be vieed more superior than another pacement that ony identifies 5 modes. In other ords, the number of successfuy identified modes shoud aso be factored in measuring the SHM performance. Hoever, for simpicity ony these 5 reiabe modes are considered Random Depoyment In random depoyment, the sensors are uniformy distributed on each foor. In other ords, dxij and dyij have uniform and independent distributions of U ( /, /) and U ( /, /), respectivey. A random depoyment might not be the best pacement strategy ith respect to the accuracy of measurements and netork connectivity, but it faciitates ooking at a ide range of different depoyment configurations. Figure shos the mode shape errors of 1 reaizations simuated for different combinations of the number of sensors per foor (m =,,..., 1) and noise eves (p = %, %,..., 1%) reative to the maximum response. Ceary, as p increases, so do the errors. Meanhie, increasing m oers the overa errors since more sensors can improve measurements averaging out the assumed hite sensor noise. Typicay, the mode shape errors converge to a singe band as m increases, but for some noise eves (p = 8%, 1%) the errors converge into to bands. To understand the reationship beteen sensor depoyment and mode shape errors, the reaizations ith the best Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

8 8 TAT FU ET AL. mode shape error 1 1 sensors: 1 grid sensors: grid 6 sensors: grid 9 sensors: grid 1 sensors: grid 16 sensors: grid sensors: 5 grid sensors: 6 grid sensors: 5 6 grid normaized grid separation, d / (a) (b) Figure. (a) 19 different configurations in grid depoyment. (b) Effect of the number of sensors and distances on mode shape error ith % noise eve. and orst errors are further examined. For m = sensors and p = 8% noise eve, comparing five different cases ith highest and oest errors, it is observed that the sensors in the o error cases are ess custered than those in the high error cases. This observation fas in ine ith the mathematica interpretation that the accuracy of rotation estimate increases as the distance beteen the sensors increases. For reaizations ith a arger number of sensors per foor (m = 7) and the same noise eve (p = 8%), there is no significant difference in custering beteen the high and o error cases; as a resut, no concusive inference coud be dran from the observations for these cases. 5.. Grid Depoyment In grid depoyment, for a given number m of sensors per foor, m = m 1 m grids are formed ith different internode separations, and one sensor is paced at each grid point. To maintain connectivity on each foor, the maximum inter-node separation is assumed to be smaer than the communication range of a node. The objective here is to study the reationship among the number of sensors depoyed, their inter-node separations and the mode shape error for a given foor dimension. Figure (b) iustrates the corresponding mode shape error for each of the configurations shon in Figure (a), hich decreases sharpy as the nodes are paced further apart from each other. Hoever, after a certain point, hen the separation reaches around.15 (here is the idth of the foor), the rate of decrease fattens out. A simiar trend is observed hen the number of sensors per foor is increased keeping the noise eve fixed at %. These resuts indicate the expected observation that a arge number of sensors hen paced further apart reduces the mode shape errors, athough, ith diminishing returns. 6. ACCURACY AND ENERGY EFFICIENCY The resuts presented in the previous section sho that the mode shape error decreases ith increasing inter-node separation and the number of sensors per foor, athough ith diminishing returns. Hoever, as the separation increases, a node must transmit at a higher poer eve to reach its neighbors, hich requires more energy. Simiary, a arge number of sensors aso resuts in high energy consumption. The goa in this section is to study this trade-off and find an optima grid separation and number of sensors per foor to baance minimizing the amount of energy consumed in communicating the measurements ith minima error in mode shape estimation. Based on the netork mode described in Section., an energy efficient routing tree is first constructed assuming that a the nodes on a given foor can send their measurements to a oca sink ocated at the center of that foor. Then, from the energy mode described in Section., the tota energy spent for gathering a the measurements over the routing tree to the oca sink is estimated for a given inter-node separation. Finay, simuations sho the trends in energy consumption ith varying inter-node separation and the number of nodes. Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

9 ENERGY-EFFICIENT DEPLOYMENT USING WIRELESS SENSOR NETWORKS. 9 m 1 m (a) (b) (c) Figure 5. Min-max fair, energy-baanced routing trees on grid depoyment: (a) Numbers indicate eves; arros correspond to routing paths from nodes at different eves; sink is on a grid point. (b) Four eve one nodes ith the sink at the center of a grid ce. (c) To eve one nodes ith the sink at the center of a grid ine Energy-Baanced Routing Tree Consider the scenario in hich data measured by a set of m nodes on each foor must be deivered to the oca sink ocated at the center of that foor. According to the energy mode herein, the energy dissipation at a sensor node is proportiona to the tota number of bits the node receives and transmits. To increase the ongevity of the netork, a fair utiization of energy resources is needed so that no node suffers from an eary energy depetion. Thus, it is important to construct an energy-baanced routing tree that i ensure uniform energy dissipation among a nodes. Assuming there is no data aggregation en route to the sink, the number of bits received by a node, and hence the energy required to transmit them, is proportiona to the size of its subtree. Let e(t, i) be the energy spent by node i to send its measurements to the oca sink over a routing tree T that is rooted at the sink. Assume that each node generates k bits of data. The goa is to construct an energy-baanced routing tree such that the fooing condition hods: (i) tota energy spent by a the m nodes is minimized, (ii) maximum energy spent by any node is minimized. It is assumed that the nodes can organize themseves into eves based on their hop distance from the sink, ith oer eves corresponding to nodes that are coser to the sink, as iustrated through an exampe in Figure 5(a). For a distance dependent energy mode, the first condition corresponds to a shortest path routing tree in terms of hop distance, here each node other than the sink seects one of its nearest neighbors from the previous eve as its parent. Note that in a grid depoyment, a nodes except those at the first eve have to choices as their nearest neighbors from their previous eves. The best choice is made in such a ay that the resuting sizes of the subtrees rooted at the nearest neighbors are as cose to each other as possibe. This i ensure that the size of a subtree rooted at a oer eve node is at east equa to or greater than that at a higher eve node. At each eve, this parent assignment strategy coud be achieved either in a centraized or distributed ay by exchanging messages beteen the neighboring nodes. Note this particuar parent assignment strategy may not aays guarantee a min-max fair, energy-baanced routing tree on an arbitrary depoyment of nodes here each node generates possiby a different amount of data (e.g., if one node has a singe acceerometer and another has a triaxia acceerometer). Hoever, for a grid depoyment here each node generates the same amount of data (k bits), choosing the best nearest neighbor from the previous eve i resut in a min-max fair, energy-baanced tree. This is because choosing a neighbor from the previous eve that is not one of the nearest ones i require more energy and, therefore, vioate the first condition. Moreover, this i not hep in better energy baancing because the amount of data generated by a the nodes is the same and the sink is ocated at the center of the foor. It shoud be noted that instead of constructing a tree in hich every node has a singe parent, one coud empoy a non-tree based or graph-based routing strategy, herein a singe node can have more than one parent. In such cases, for exampe, the uppermost node on the right at eve in Figure 5(a) can use both of the nodes at eve, one to its eft and one beo, for sending its data in order to oad baance energy consumption. Hoever, typicay in a sensor netork, the nodes are organized as a tree, hich makes routing simper and easier to maintain; this assumption is made herein. Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

10 1 TAT FU ET AL. 6.. Energy Consumption Per Foor Having constructed a min-max fair, energy-baanced routing tree for a grid depoyment, an expression is derived in this section for the tota amount of energy required to route a data on a foor to a oca sink, ocated at the center of the foor, as a function of grid separation. As before, the grid depoyment for each foor has m 1 m sensors ith grid separation d. The routing tree constructed on such a configuration is symmetric around the sink node, i.e., the subtrees rooted at the eve one nodes are identica. The number γ of eve one nodes depends on the vaues of m 1 and m. For m 1 and m both odd (Figure 5(a)) or both even (Figure 5(b)), there are four eve one nodes (i.e., γ = ), and the sink is ocated either on a grid point or at the center of a grid ce. When one of m 1 and m is odd and the other is even, there are ony to eve one nodes (γ = ), and the sink is ocated at the center of a grid ine (Figure 5(c)). Since the subtrees rooted at the eve one nodes are identica, their energy consumption to route a data to their respective eve one nodes are the same. In the fooing, expressions are derived for the tota energy consumption per foor to deiver a the bits generated by the sensors to the oca sink ocated at the center of the foor. Without oss of generaity, consider the subtree rooted at the eve one node just above the sink, as shon in dotted eipse in Figure 5(a). The number of ros and coumns in this subtree is m 1 / and m /, respectivey, here and denote the foor and the ceiing integer of their argument. Since a node transmits its on data aong ith a data received from its on subtree, the tota number of bits transmitted over a one hop distance by a nodes in a given ro to reach the eftmost node is: m / 1 N 1 = k i = k m / ( m / 1). (17) i=1 By symmetry, a ros transmit the same amount of data to reach their respective eftmost nodes. Therefore, the tota number of bits transmitted over one hop to the eftmost nodes is N 1 m 1 /. Finay, a data from the eftmost nodes at each ro are transmitted to the eve one node. Thus, tota bits transmitted by these eftmost nodes over a one hop distance is: m 1/ 1 N = k m / i = k m 1/ m / ( m 1 / 1). (18) i=1 Finay, the eve one node transmits a these data to the sink. Therefore, the tota energy spent by a the nodes to get their data to the sink is given by: Substituting (17) and (18) into (19) and simpifying yieds, E(d) = γ (N 1 m 1 / + N + m 1 / m / k) e(d). (19) E(d) = γk m 1/ m / ( m 1 / + m / ) e(d), γ =. () Fooing a simiar procedure, the tota energy spent to deiver a of the bits to the oca sink hen m 1 and m are both even is: E(d) = γk ( m 1/ m / m 1 / + m / + ) e(d), γ =, (1) and, hen m 1 is odd and m is even, is: E(d) = γk m / ( m 1 m / + m 1 / + m 1 / ) e(d), γ =. () Note that hen m 1 is even and m is odd, one can aays rotate the vie point and take m 1 as odd and m as even, and () i appy. 6.. Location and Number of Sensors The simuation resuts presented so far indicate that the mode shape error decreases ith increasing inter-node separation and the number of nodes. Hoever, an increase in the number of nodes eads to the generation of more data, and an increase in inter-node separation requires higher transmission poer. The combination of these to effects, consequenty, resuts in an increase in energy consumption. Thus, these to opposing factors ead to a joint optimization probem of finding the right grid separation and the number of nodes that i optimay baance the mode shape errors ith energy consumption. For ease of presentation and understanding, the optimization is first iustrated Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

11 ENERGY-EFFICIENT DEPLOYMENT USING WIRELESS SENSOR NETWORKS. 11 mode shape error ( 1 ) mode shape error energy consumption 5 energy consumption (mw) cost α M (normaized mode shape error) M α E (normaized energy consumption) E J = α M + M α E (objective function) E d * (optima inter node separation) normaized grid separation, d / normaized grid separation, d / (a) (b) Figure 6. Comparison of mode shape error and energy consumption for different grid separations. through an exampe ith fixed number of nodes for finding the optima grid separation and energy consumption, and then extended to incorporate optimaity on the number of nodes. In Figure 6(a), the mode shape errors and the energy consumption per foor ith increasing grid separations are potted for 16-node configurations. The mode shape errors are high at sma grid separations hereas the energy consumption is high at arge grid separations. Denoting the mode shape error by M(d) and the energy consumption per foor by E(d) at separation d, the optima separation d can be found by minimizing the fooing objective function: J = α M M(d) + α E E(d), d min d d max () here α M and α E are eighting constants. The choice of α M and α E heaviy depends on the reative cost of the mode shape error and the energy consumption. The optima d is bounded by the minimum and maximum aoabe separations, d min and d max, respectivey, hich are infuenced by the sensor configurations. Figure 6(b) iustrates the objective function of () using the fooing vaues for α M and α E : α M = 1/ min d M(d) and α E = 1/ min d E(d). () Here, athough min d M(d) and min d E(d) are the minimum vaues over d [d min, d max ], they approximate the absoute minimum vaues ithout constraining d since the range [d min, d max ] is sufficienty ide. For the 16-node configuration, M(d) and E(d) asymptoticay approach their absoute minimum vaues. The numerica soution for d, as shon in Figure 6(b), is approximatey.165. The constants α M and α E in () are used to normaize M(d) and E(d) such that they are equay eighted in optimizing d. Extending to jointy optimize the grid separation and the number of nodes, the cost () becomes J = α M M(d, m) + α E E(d, m). (5) here M(d, m) and E(d, m) are the mode shape error and energy consumption, respectivey, for m sensors per foor at grid separation d. As before, the eighting constants can be expressed as: α M = 1/ min M(d, m) and α E = 1/ min E(d, m). (6) d,m d,m Minimizing (5) over d and m gives d and m such that moving aay from (d, m ) i resut in no improvement in the mode shape error or energy consumption that i not be outeighed by the decrease in the other measure. Figure 7(a) and 7(b) sho ho M(d, m) and E(d, m) change ith respect to both the grid separation and the number of sensors per foor (among the set of 9 possibe grid depoyments given in Figure (b)), respectivey. Figure 7(c) iustrates the objective function (5) ith α M and α E from (6). The optima pair of vaues are (d =.15, m = ) in this particuar exampe. The eights in () and (5) are used to accommodate ith different units and scaes of the mode shape error and the energy consumption. The reative importance of the mode shape error and the energy consumption can be varied by adjusting the eights α M and α E, hich in turn i affect the optima soutions for d and/or m, favoring Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

12 1 TAT FU ET AL. normaized mode shape error α M M number of sensors, m..1 normaized grid separation, d / (a) normaized energy consumption α E M 1 1 number of sensors, m..1 normaized grid separation, d / (b) objective function J = α M + M α E E 1 1 number of sensors, m..1 normaized grid separation, d / (c) Figure 7. (a) Normaized mode shape error α M M, (b) normaized energy consumption α EE, and (c) objective function J = α M M + α EE, a as functions of the number of sensors and grid separation. Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

13 ENERGY-EFFICIENT DEPLOYMENT USING WIRELESS SENSOR NETWORKS. 1 mode shape error ( 1 ) /α M mode shape error energy consumption 1/α E 5 energy consumption (mw) cost α M (normaized mode shape error) M α E E (normaized energy consumption) J = α M M + α E E (objective function) d * (optima inter node separation) normaized grid separation, d / normaized grid separation, d / (a) (b) mode shape error ( 1 ) 1 1/α E 1 8 1/α M normaized grid separation, d / (c) 5 energy consumption (mw) cost normaized grid separation, d / (d) Figure 8. (a) Mode shape error and energy consumption ith more eight given to energy efficiency. (b) The corresponding objective function vaue for (a). (c). Mode shape error and energy consumption ith more eight given to mode shape estimation. (d) The corresponding objective function for (c). either the accuracy in mode shape estimation or the energy efficiency. For exampe, decreasing α M hie keeping α E unchanged i essen the eight on the mode shape estimation reative to the energy efficiency in the optimization, and vice versa. Figure 8 demonstrates the effect of different vaues of α M and α E on the optima soutions for d in minimizing (). In Figure 8(a) and 8(b), instead of using (), α M and α E are set to different vaues such that more eight is given to energy efficiency. The optima grid separation d is no.1198 instead of.165. The decreased d improves energy usage by reducing the radio transmission range. In contrast, more eight is given to the mode shape estimation in Figure 8(c) and 8(d); the optima separation increases to.199. Depending on the reative cost of the mode shape estimation and the energy consumption, different vaues of α M and α E shoud be given to the objective functions in () and (5). The resuts shon herein are, of course, based on a shear structure ith simpe rectanguar foor ayouts, and a particuar method for estimating mode shapes. Different foors ayouts and types of structures (e.g., bridges, trusses) may ead to different preferred pacements of sensors and sinks (data receivers). For exampe, bridges may have the argest dispacement in the midde of spans but may have sinks at the ends of the bridges or at toer ocations. This is quite a different topoogy than the probem studied herein. Hoever, the tradeoffs beteen energy efficiency and SHM accuracy are simiar, and the proposed methodoogy coud be easiy appied to other types of structures. Simiary, the ERA for mode shape estimation coud be repaced ith other identification approaches in the time or frequency domains. The particuar resuts may change, such as the exact optima separation distances, but there i aays remain a trade off beteen accuracy and energy consumption; sensors ocated here the effective signa-to-noise ratio Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

14 1 TAT FU ET AL. is strong are often not the ocations for minima poer. 7. CONCLUSIONS AND FUTURE WORK Wireess SHM systems are promising due to their ease of instaation, inexpensive costs, and scaabiity. Hoever a WSN comes ith its poer and bandidth constraints. This paper provides a study on optimizing sensors pacements for SHM in terms of the quaity of system identification and energy cost. These to opposing metrics prefer a tight pacement of a fe sensors to decrease the energy cost and a separated pacement of many sensors to increase the accuracy in estimating structura moda parameters. A compromise is suggested by defining an objective function ith eighting factors on energy needs and estimation accuracy. The number of sensors and the distances beteen them are anayzed using the mutivariate objective function and an optima sensor separation is found. The effect of an optima pacement due to different eights is aso anayzed. Future ork i invove optima depoyment for more compex structures in terms of foor ayouts, non-shear structures, sensor faiures, reaistic ireess interference modes, data transfer time efficiency, etc. Experiments in a aboratory setting are needed to further vaidate the resut of this study. Furthermore, an existing buiding is suitabe for future investigation here practica difficuties in depoying sensors, rea ord noise, movements in the buiding and factors affecting the quaity of system identification cannot be foreseen in simuation. 8. ACKNOWLEDGMENTS The first and third authors gratefuy acknoedge the partia support by the Nationa Science Foundation under CAREER aard CMS -9 and through grants ANI and CMMI The second and fourth authors gratefuy acknoedge the partia support by the Nationa Science Foundation under grant CNS Any opinions, findings, and concusion or recommendations expressed herein are those of the authors and do not necessariy refect the vies of the Nationa Science Foundation. REFERENCES 1. Abduah, M.M., Richardson, A., and Hanif, J. (1). Pacement of Sensor/Actuators on Civi Structures using Genetic Agorithms. Earthquake Engineering Structura Dynamics, (8): Casciati, S., and Chen, Z.C. (1). A Muti-Channe Wireess Connection System for Structura Heath Monitoring Appications. Structura Contro and Heath Monitoring, 18(5): CC Radios: Chatterjee, P. and Das, N. (8). A Distributed Agorithm for Load-Baanced Routing in Mutihop Wireess Sensor Netorks. ICDCN, pp. 8, Kokata, India. 5. Chintaapudi, K., Fu, T., Paek, J., Kothari, N., Rangaa, S., Caffrey, J., Govindan, R., Johnson, E., and Masri, S. (6). Monitoring Civi Structures ith a Wireess Sensor Netork. IEEE Internet Computing, 1():6. 6. Cark, B.N., Cobourn, C.J., and Johnson, D.S. (199). Unit Disk Graphs. Discrete Mathematics, 86(1 ): Cobb, R.G. and Liebst, B.S. (1997). Sensor Pacement and Structura Damage Identification from Minima Sensor Information. AIAA Journa, 5(): Dai, H. and Han, R. (). A Node-Centric Load Baancing Agorithm for Wireess Sensor Netorks. IEEE Gobecom, pp , San Francisco, CA. 9. Gao, J. and Zhang, L. (6). Load-Baanced Short-Path Routing in Wireess Netorks. IEEE Transactions on Parae and Distributed Systems, 17(): Gao, Y., Spencer Jr., B.F., and Ruiz-Sandova, M. (6). Distributed Computing Strategy for Structura Heath Monitoring. Structura Contro and Heath Monitoring, 1(1): Guo, H.Y., Zhang, L., Zhang, L.L., and Zhou, J.X. (). Optima Pacement of Sensors for Structura Heath Monitoring using Improved Genetic Agorithms. Smart Materias and Structures, 1(): Hemez, F.M. and Farhat, C. (199). An Energy Based Optimum Sensor Pacement Criterion and its Appication to Structure Damage Detection. IMAC, pp , Honouu, HI. 1. Heredia-Zavoni, E. and Esteva, L. (1998). Optima Instrumentation of Uncertain Structura Systems Subject to Earthquake Ground Motions. Earthquake Engineering and Structura Dynamics 7(): Huang, S.C. and Jan, R.H. (). Energy-Aare, Load Baanced Routing Schemes for Sensor Netorks. 1th Internationa Conference on the Parae and Distributed Systems, pp. 19 5, CA. 15. Jang, S., Jo, H., Cho, S., Mechitov, K.A, Rice, J.A., Sim, S.H., Jung, H.J., Yun, C.B., Spencer, B.F., Jr., and Agha, G.A. (1). Structura Heath Monitoring of a Cabe-Stayed Bridge using Smart Sensor Technoogy: Depoyment and Evauation. Smart Structures and Systems, 6(5 6): Juang, J.N. and Pappa, R.S. (1985). An Eigen-system Reaization Agorithm for Moda Parameter Identification and Mode Reduction. Journa of Guidance, Contro, and Dynamics, 8(5): Kammer, D.C. (1991). Sensor Pacement for On-Orbit Moda Identification and Correation of Large Space Structures. AIAA Journa of Guidance, Contro, and Dynamics, 1(): Copyright c 1 John Wiey & Sons, Ltd. Struct. Contro Heath Monit. 1; :1 1

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