Energy-Efficient and Fault-Tolerant Structural Health Monitoring in Wireless Sensor Networks

Transcription

1 3st International Symposium on Reliable Distributed Systems Energy-Efficient and Fault-Tolerant Structural Health Monitoring in Wireless Sensor Networks Md Zakirul Alam Bhuiyan, Jiannong Cao, Guojun Wang, and Xuefeng Liu School of Computer Science and Engineering, Central South University, Changsha, Hunan, P. R. China Department of Computing, Hong Kong Polytechnic University, Kowloon, Hong Kong, China Correspondence to: Abstract Wireless sensor networks (WSNs) have become an increasingly compelling platform for structural health monitoring (SHM) due to relatively low-cost, easy installation, etc. However, the challenge of effectively monitoring structural health condition (e.g., damage) under WSN constraints (e.g., limited energy, narrow bandwidth) and sensor faults has not been studied before. In this paper, we focus on tolerating sensor faults in WSN-based SHM. We design a distributed WSN framework for SHM and then examine its ability to cope with sensor faults. We bring attention to an undiscovered yet interesting fact, i.e., the real measured signals introduced by faulty sensors may cause an undamaged location to be identified as damaged (false positive) or a damaged location as undamaged (false negative) diagnosis. This can be caused by faults in sensor bonding, precision degradation, amplification gain, bias, drift, noise, and so forth. We present a distributed algorithm to detect such types of faults, and offer an online signal reconstruction algorithm to recover from the wrong diagnosis. Through simulations and a WSN prototype system, we evaluate the effectiveness of our proposed algorithms. Index Terms Wireless sensor networks; fault detection; fault tolerance; energy-efficiency; structural health monitoring. I. INTRODUCTION Wireless sensor networks (WSNs) have been widely employed for enabling various applications such as target detection and monitoring, scientific observation, safety-related []. Due to the unique advantages (e.g., low-cost, flexible, readily deployable, etc.), several recent works have explored the possibility of WSNs for structural health monitoring (SHM) [6][6]. In a typical SHM system, the interest is to monitor possible changes (e.g., damage) on structures (e.g., buildings, bridges, aircrafts, nuclear plants, etc.) and provide an alert at an early stage to reduce safety-risk, which prevails throughout the civil, structural, or mechanical engineering (CSME) communities. In such a cross-discipline application, the CSME and the computer science (CS) communities focus on and contribute their own domains. A question may arise as to who should undertake these critical issues: first, resource constraints in a WSN system; second, system reliability and dependability (i.e., to make sure that faults/failures within the system do not lead to a meaningless monitoring operation) in such domains. We think that the objective of CSME communities is the monitoring of the structures; they are less interested to study how to improve the efficiency of the WSN systems since they have their own domain-specific issues to address. On the one hand, existing SHM algorithms in wired sensor networks used by CSME are generally centralized/global []. Also, they do not consider data collection efficiency and synchronization errors, etc., because they do not need to consider issues such as energy, connectivity, and bandwidth constraints in WSNs. These algorithms work on the raw measured data, which is no longer a single value (e.g., / ) but a sequence of data with size more than hundreds of KB [][6][]. Thus, they incur huge communication overhead to the traffic sensitive WSNs. In the CS community, it is expected that resource optimization of WSNs must be tightly correlated with the respective applications, e.g., SHM. Before deploying a WSN on a real structure, an energy-efficient distributed framework is essential to address the constraints in the WSN. On the other hand, significant efforts have been made for specific fault types in WSNs [][4]. Some prominent schemes, namely, decision fusion, value fusion, heartbeat reception have been suggested for fault tolerant phenomenon (such as an event) detection problems [9][][][5], which uses simple data and few measurements to adequately detect certain faults. However, they are not able to function properly in a SHM system [6], since SHM algorithms use totally different methods to detect damage. Monitoring damage (measured from vibration, strain, etc.) is quite different, which may require a significant amount of CSME domain knowledge (e.g., finite element model updating, mode shape) [4][6][]. In this paper, we design a WSN framework for SHM that jointly considers CSME and CS requirements. We propose an algorithm to detect sensor faults efficiently under the constraints of the WSN. We are interested in different types of sensor faults, which are common but difficult to detect: ) sensor debonding faults in SHM [9]; ) faulty signals caused by precision degradation and breakage, especially in vibration capturing in SHM; 3) faults in offset, bias, or gain factors [9]; 4) noise faults. Most of the sensor data faults fall within these fault models. Since these types of faults cannot be easily identified, they directly interrupt the system from detecting damage. Under any of the fault occurrence in a practical SHM, we found an undiscovered yet interesting fact, both faulty and non-faulty sensors can generate abnormal signals or decisions. This indicates that there is a possibility of both structural damage and sensor fault occurring at the same time. Faulty sensors may cause undamaged location to be identified as damaged (false positive) or damage location as undamaged (false negative) diagnosis. As a result, removing faulty signals / $6. IEEE DOI.9/SRDS..6 3

2 from the measured signals and identifying what happens exactly in a structure is a challenging task. We use a new general measurement mutual information independence (MII) between two signals u and v from two different sensors for evaluating results in the absence of the ground truth. We think that mutual statistical information can be used as an indicator to decide on a sensor fault detection in conjunction with damage detection. We attempt to reconstruct faulty sensor signals using Kalman filter techniques so that if there is damage, it can be recovered after the reconstruction. This does not require cost-ineffective actions, i.e., sensor grouping, masking, isolating, or replacing. This recovery is applicable to any kind of faulty signals caused by numerous sensor faults. We make three major contributions. ) We are the first to study a problem in an overlapping area, namely damage detection under sensor faults. We design a distributed WSN framework for SHM. ) We propose an automated online faulty sensor detection algorithm and a recovery algorithm to reconstruct faulty sensor signals. 3) We evaluate our scheme via simulations using real data sets adopted from an existing SHM system. We implement a prototype system developed by the TinyOS [7] running on the Imote [8] and verify it on a test infrastructure. The results validate that the use of recovery from faulty signals is effective and can lead to a fully automated fault tolerant monitoring system. This paper is organized as follows. Section II reviews related work. Section III formulates our problem. Section IV explains the distributed framework for SHM. The algorithm for faulty sensor detection is in Section V. Recovery from the sensor fault is explained in Section VI. Performance evaluation is outlined in Section VII. We conclude this paper in Section VIII. II. RELATED WORK Wireless sensor networks (WSNs) have been widely suggested for SHM by the both CSME and CS communities in recent years [4][6][6][][]. The existing schemes mainly focus on data acquisition, compression, aggregation, damage detection, etc. In order to ensure the quality of health monitoring it is necessary for the WSN to be able to detect the faults and take actions to avoid meaningless monitoring operations. Fault tolerance in WSNs has been studied extensively by researchers in computer science (CS) [5][9][][4][5]. The application background is mainly event/target detection, environment monitoring, etc. Some detection methods are based on correlation analysis between neighboring sensors readings. A widely adopted fault tolerant scheme is decision fusion [9][] where binary / decision is made for fault status. This scheme is further improved in [] by allowing only part of neighbors in fusion to further decrease the energy cost. Although the problem of making decision on a sensor status in SHM looks similar to the problem of making binary / detection decision [9][][], our problem is fundamentally different from them. Instead of binary / decision predicates, we need the actual sensor reading factors that are captured by structural response: (i) structural characteristics for damage detection, which may need further processing Identified peak frequency Sensor Sensor Frequency (Hz.) Frequency (Hz.) Fig.. Measured natural frequencies captured by sensor and sensor under manual input excitation on the structure, respectively. A specific vibration pattern of a structure at a specific frequency is called a mode shape. Each sensor decision on mode shape corresponds to the sensor location status, where each such mode contains several elements information (a) (b) (c) (d) (e) around the location. (Original) frequency = 3.7 Hz frequency = 4. Hz frequency =.Hz Fig.. (a) The finite element model (FEM) [6] of our designed physical infrastructure; (b) its original mode shape; (c)-(d) its three mode shapes. at upper stream sensors; (ii) the characteristics should include spatial information. The vibration characteristics of a structure should be identified from measured signals, and damage is then detected by examining the characteristics. An important property of SHM is that the accurate identification always requires data-level collaboration of multiple sensors [3], i.e., the raw data from multiple sensors is processed simultaneously, generally via various matrix computations, e.g., eigen decomposition, singular value decomposition [] etc. A damage information cannot be reliably analyzed by the individual sensor s / decision, even when the sensor itself is not faulty. Thus, such decision and value fusion are not able to function in SHM. It is also justified in [6]. Sensor fault detection algorithm for SHM is recently proposed in [6] that works on Natural Frequency extraction and Matching in Cluster (NFMC for short) and then tackles faulty sensor readings. However, it has several shortcomings. Detection task is carried out by using knowledge of natural frequency of vibration. Frequency sets, which include only the pick frequencies (see Fig. ) collected from different sensors in a cluster, are matched. However, the same pick frequency sets are not possible to achieve since the real measurement can vary from structure to structure, sensor to sensor, and time to time. The normal assumption is that unmatched frequencies are as a result of faulty sensor signals and is then deleted from the frequency set. We think that the probability of the actual damage detection is seriously affected by such assumption (for more details, see Section IVC). Besides, the faulty sensors are isolated from the network in NFMC. Both transmitting all sets of natural frequencies and sensor isolating/masking require significant energy cost, which are not verified in NFMC. Conversely, in this proposed scheme, in order to remove faulty sensor data form structural damage data, we find a fault indicator based on MII, which is sensitive to sensor fault but insensitive to damage, and then implement damage detection algorithm. These are based on structural mode information (shape) computation (see Fig. ) rather than natural frequency considering WSN constraints. Because mode shape is more sensitive to damage detection and is computationally-efficient, it includes fewer amounts of noises and data transmission. 3

3 III. PROBLEM FORMULATION AND MODELS A. Network Model Consider a set P of m sensors is deployed on a structure by finding locations from a set of candidate locations of the structure; L = {l,l,l,,l m }, where sensor i is placed at location l i, and l is a suitable location of the sink. This deployment is performed through methods proposed by CSME [6]. Sensor i collects structural response data, processes locally, and makes decisions on sensor faults and mode shape. Let R max and R min be the maximum and minimum communication ranges of a sensor, respectively. R min is used to maintain local topology, where a number of sensors is allowed to share their signals with their neighbors for damage detection, also used for fault detection. The intention of adopting adjustable communication range is to reduce energy cost for transmission. Note that Imote sensor platform supports discrete power levels [7]. Two local topologies can be seen in Fig. 3, where each sensor can be overlapped by one or more sensors. When a sensor communicates to the sink directly, R max is used. Each sensor corresponds to a vertex in a network G and two vertices are connected in G iff their corresponding sensors can communicate directly. B. Energy cost Model (cost(e i )) One important objective is to minimize the energy cost of the network. Let cost(e i ) denote the total energy cost, including measurement, computation, transmission, and overhead on sensor i. Consider a shortest path routing model [7][]; there is a path from a sensor i to a neighbor u or to the sink. Sensor i propagates the data to them. We can find the ith hop sensor on each path and calculate the amount of traffic that passes along on the paths within each round of monitoring data collection (T d, d=,,..., n). Then, the cost(e i ) is calculated by: cost(e i )=e T + e comp + e samp + e oh () Here, (i) e T is the maximum energy cost per bit for transmission over a link between a transmitter and a receiver, where a sensor i uses its power level to a maximum, but not beyond the maximum power. We use an standard energy cost model for packet transmission [3]. (ii) e comp is the energy cost for data processing locally, e.g., computing equation (6). If a sensor is allowed to transmit the raw data to the sink directly, e comp would be zero. (iii) e samp is the energy required for sampling cost of M data points; when sensors capture vibration signals, assuming maximum 5% overlapping, M =(n a /+/) c r, where n a and c r are the number of averages mainly for denoising purpose that practically ranges from to and cross-correlation factor, respectively [6][]. We assume that n a and c r are set by fixed values on a sensor. (iv) e oh is any additional overhead for some causes, such as sensor fault detection and signal reconstruction, copying data to a local buffer, and other possible sources, e.g., network latency. C. Sensor Faults ) Fault Model: We focus on a set of sensor faults that may occur in a real WSN-based SHM deployment: () debonding (a) overlapping sensors and 3 neighbors Fig. 3. (b) overlapping sensors and 4 neighbors Topologies with different numbers of overlapping sensors. fault sensor may slightly detach from the host structure, which affects in vibration capturing; () signal fault this is caused by precision degradation, breakage, etc., especially in vibration capturing, e.g., a sensor reports a constant value for a large number of successive samples where the constant value is either very high or very low compared to the normal or reference value; (3) faults in offset, bias, or amplification gain factors [9]; (4) noise fault. We intend to tackle these faults in this work. ) Fault Detection Model: We assume that a sensor i can exchange its signals with its neighbors in each sampling instant t. The signal yi t measured by a faulty sensor at t is subject to noise effect σ. Then, the measured output of i is given by: y = yi t + σ () The measurement noise, σ, for non-faulty sensors may be a small random noise in practice. However, it also can affect damage detection a lot. Consider a subset N of sensors is non-faulty at time t. In SHM, when all of the sensors are non-faulty, it is easily possible to estimate the mode shape from the signals. However, if a sensor is faulty, it is possible to produce predicted signals for the mode shape by using neighbors signals, correlation statistics, and the extent of σ. Suppose that damage may occur at anytime t anywhere in the structure. A subset D P of sensors around the damage area possibly be able to detect the damage. Some of the sensors from D may provide faulty signals. Thus, to detect the faulty sensors, the sensors in D split into two further subsets: N= sensors assumed to be non-faulty F = sensors assumed to be faulty Note that these two sets are disjoint so that N F = {} and N F = D, where D P Generally, in other WSN applications, sensors anywhere in the network are assumed to be faulty/failed. However, in SHM, we assume that only the sensors that are around a damage area may fail during operation. Nevertheless, there may be multiple damage occurrences in the structure. Definition [MII: Mutual Information Independence]. A function denoted by () is defined by the quantify how much the measurement correlation between the sensor nodes in N and the sensor nodes in F deviate from the correlation model. We state the MII function as an indirect vibration signal measurement. Assume that a prior correlation model C of x t P presents []. C can be given as a reference set by each immediately data stored in the sensor local memory after system initialization. MII function between two signals of sensors i and j at time t in D is as follows. (y i,y j,c) (3) Consider the sensors in N and F capture vibration signals and broadcast their measured signal sets y N and y F, respectively. Thus, MII between the two sets of signals is given by: 33

4 (y N,y F,C) (4) Given R consecutive signals, the MII function estimates how much correlation between y N and y F at time t as: R R Δ(N,F) = (y N,y N,C) (y F,y N,C) (5) t= t= Δ(N,F) is achieved by minimizing the deviation between non-faulty sensors in N, and by maximizing the deviation between non-faulty sensors in N and faulty sensors in F. D can be controlled by the system user considering R min, neighborhood size, or network density. D. Problem Statement Given: a network of a set P of m sensors with limited energy and an external sink. Find: a subset D ( P ) of sensors that involves in detecting structural damage such that the sensors in N( D) are nonfaulty and the sensors in F = D N are faulty subjecting to the following constraints: () data delivery q = z...z k used for data delivery, where q[j ]q[j] R max, j =...k; () connectivity i =...m, q = z...z k, q[] = l i, q[k] =l ; (3) structural modeling. Objectives: minimize Δ(N,F), and minimize cost(e i ). IV. DISTRIBUTED WSN FRAMEWORK FOR SHM In this section, we discuss our fault-tolerant WSN framework for SHM, including local damage detection. A. Structural Damage Detection Algorithm The central focus of SHM is the detection and localization of damage in a variety type of structures. A variety of sensors, e.g., accelerometers, strain gauges, can be used to measure structural responses. SHM techniques infer the existence and location of damage by detecting differences in local or global structural response before/after damage. Increasingly, the CSME communities are becoming interested in active sensing techniques [4], which measures structural response to forced excitations. To identify the damage, two necessary structural characteristics are important: mode shape (Φ) and natural frequency (f). B. Structural Response and Mode Shape Computation Each type of structure (aircraft, building, bridge, etc.) has a tendency to vibrate with much larger amplitude at some frequencies than others. A specific vibration pattern at a specific frequency is called mode shape. f and Φ rely on structural material properties, geometry, and assembly of its constituent members. We use state space model, which is widely accepted by CSME communities for capturing structural dynamics to compute Φ [4][]. We mention that the process we use for Φ computation, the same process is used for designing faulty signal reconstruction. The state space matrices for a finitedimensional linear structural dynamic system can be succinctly obtained by the linear differential equation: Mẍ + Kx + σ = F (x, t) (6) Here, function F (x, t) is the response of the structure over a period of interest at certain sensor locations, where x is the structural response at time instant t. M and K are the matrices of mass and stiffness coefficients of the various elements of the structure, respectively. σ is the signal to noise. In traditional SHM algorithms, the state space model is computed in a centralized/global fashion. We argue that it could be quite costly for the resource-limited WSN. To make use of the WSN for SHM, we mitigate this problem by allowing each sensor working only with local structural response rather than the global. For this purpose, we consider implementing the model for each sensor location. To reduce the system order, a transformation of the state space into mode coordinates is necessary. This transformation is derived by determining a diagonal matrix, which contains a certain number of Eigen frequencies covering the natural frequency ranges of interest. By applying the mode transformation, based on the mass normalization {φ i }, the refined Φ is given by: x =Φh (7) where h is the mode participation factor. We have, ḧ i + δ i h i = H i (8) (7) implies the refined response of the structure that is a sum of the responses in each mode. We can express it more explicitly: n x = h i φ i (9) i= where δ i is the ith eigenvalue, and H i = φ T i f is the ith mode of responses under force or ambient excitation input. The summation is given over all of the n modes of the structure that are measured by the individual sensor. Typically, only the lower modes are important because the force excitation is concentrated in these modes. C. Local Mode Shape Analysis Suppose that a total of m sensors are deployed on a structure and extract a total of p mode shapes from the measurement of m sensors. The corresponding natural frequencies and mode shapes are represented, respectively, as follows: f =[f,f,...,f p ] () Φ= [ φ... φ p Φ... Φ m] =..... () φ m φ mp where f k (k =,...,p) is the k th natural frequency, Φ k is the mode shape corresponding to f k φk i (i =,...,m) is the value of Φ k at the i th sensor. For example, Fig. and Fig illustrate the first two sensors natural frequencies and corresponding mode shapes of a physical structure, receptively, which are extracted from measurements in our prototype system. The difference between f and Φ can be observed by comparing () with () and Fig. with Fig.. According to the CSME theory, f is not suitable characteristic for damage detection due to several reasons: ) f is not a sensitive indicator to damage, where only severe damage causes noticeable change on the set of f; ) due to the global property, f does not contain any spatial information and thus localizing damage is difficult, while damage detection using f is computationally 34

5 Structural damage detection Start sampling Vibration Signal Measured Signal Data aggregation Final Mode Shape Global Mode shape assembly Damage identification results Form a WSN Sensor fault detection (No) decision (Yes) Signal reconstruction Start Fault Tolerance Fig. 4. Fault-tolerant WSN Framework for SHM showing step by step process of damage detection and sensor fault tolerance. inefficient; 3) f is susceptible to additional noise [6]; 4) importantly, a large set of f is required to be sent to the sink (e.g., SPEM [6] NFMC [6]), damage detection is greatly affected if a portion of it is lost during transmission. On the other hand, it can be seen from () that Φ has elements corresponding to each sensor thus containing spatial information. Φ and its derivatives have been proven to be very sensitive features to detect damage. It takes into account out-of-frequency-bandwidth modes of the structure and is also applicable to a complex linear structure. This is why we target on Φ computation and observe the impact of sensor fault on Φ. In this paper, we utilized mode shape curvature method proposed by civil engineering to identify significant change (i.e., damage) in the mode shape [8]. Is it Possible to Compute Φ under Sensor Fault: In practice, Φ is greatly affected by a faulty sensor signals, especially when a sensor is placed at a optimal location [6]. If a signal is detected as faulty, the measured signal is reconstructed directly for the actual mode shape, by collecting the signals from the sensor location or reference signals. We use neighboring sensor nodes s signals for detecting a faulty sensor and reconstruct its signal. In this work, not all the sensors signals using (6) will be measured. The measured output of a sensor i at time t, yi t, can be obtained by: yi t = Qx () where Q is the the measurement matrix. D. General Overview of the WSN Framework for SHM Fig. 4 summarizes the whole WSN framework for SHM. Once the WSN starts operating, in each monitoring round (T d ), a number of signals is measured at each sensor. Based on the measured signals, each sensor identifies faulty sensors by using MII. If any faulty sensor is detected, the neighboring sensors reconstruct the signals, while a faulty sensor itself can do the same task if it still works. It is highly possible that a sensor exhibit faulty behavior temporarily in many cases. However, if a sensor fails or it is missing, we still guarantee Damping is neglected in the model (6) considering individual measurement estimation. In any case, (a) faults in the sensors will only be identified if they cause changes in the response of a greater magnitude than the errors in the estimated mode shape, and (b) the modes with low damping, having approximately real modes, will be excited strongly. Thus, undamped mode shapes can be estimated accurately by (6). the signal reconstruction for the sensor. We do not assume to isolate or deploy a new sensor as it is a costly task doing so. For the high quality SHM, we must provide monitoring information of each sensor location since CSME communities mostly deploy sensors at optimal locations [6]. Each sensor locally computes the final Φ and transmits to the sink directly, which is relatively small amount of data. The sink assembles all the received final Φs and identifies the structural damage. There is a high possibility that the sink does not receives any of Φ caused by data packet-loss or others. If a sensor forwarding fails, the sink still has the final results received through the neighboring sensor nodes. In addition, we allow each sensor to keep the final results in the local memory until a sensor receives an acknowledgment from the sink. Each set of raw Φ is of a number of KBs while each final result or Φ computed by a sensor is a number of bytes. In this framework, each final Φ received from the neighbors is not processed. V. FAULTY SENSOR DETECTION This section describes non-faulty sensor data collection and faulty sensor detection algorithms. A. Data Collection and Faulty Sensor Indication We assume that sensors are likely to generate abnormal signals. The signals are measured by the vibration, which may be incorrect compared to the neighbors, previous signals or reference signals. We first show data collection at every sensor in the network. A subset of sensors, say D of sensors that are in a sensor s R min, share their data each other, and participate faulty sensor detection. Algorithm simply presents the data collection method. While theoretically this procedure involves multi-hop communication, given the fact that for SHM application the radio communication range of current sensor nodes exceeds the area in which sensors gather signals. The nodes that are one-hop away from the sink will directly send the data, otherwise data is sent through one or more intermediate nodes. In Step of the Algorithm, every sensor transmits and receives measured signals captured from the vibration response. They check if there are any faulty sensors via Step. Step executes Algorithm. Let us consider the statistical dependency between the two sensors signals quantified by MII. measures the information about one sensor that is shared by another sensor in the set of signals in D. It is seen that changes as soon as a sensor fault occurs, because the faulty signal is not present in the reference or other sensor signals. A joint Gaussian distribution based correlation model is used in this work. Multivariate Gaussian distribution has been used to accurately model the correlation of many types of signals in literature [3][5]. Each signal is broadcast to the sensors in D, where ith sensor signal yi t yt D and jth sensor signal yj t yt D, i, j D and D P. For simplicity, yt i as u and yj t as v are denoted hereafter. Hence, it would be worth to consider finding joint probability density between two signals. The statistical dependency/independency between the two Gaussian distributed 35

6 Algorithm. Non-faulty Data Collection for Damage Detection Input: a neighborhood with a bounded degree, t transmission at a time slot Step: every node i transmits its data to its neighboring nodes j for t= to n do: for each node i do: if node i has data not forwarded to the neighbors then i transmits a new data to its neighboring nodes in each t end if end for end for Step: call Algorithm //faulty sensor detection and recovery k Step3: data aggregation (extracting frequency sets, compute Φ ) compute final mode shape Φ// make final decision Step4: transmit the Φ toward the sink // Φ contain damage/undamaged information return health status of every sensor location time signals u and v can be expressed in form of the joint probability density p(u, v) of the signals as follows: p(u, v) = πτ uτ v ρuv e ( ρ ) uv [ ( u μu τ u ) ρuv (u μ u)(v μ v ) τ uτ v + ( ) ] v μ v (3) τv are the means and the standard where μ u, μ v, τ u, and τ v deviations of the signals u and v, respectively. ρ uv is the correlation coefficient between the two signals. It is given by: ρ uv = E {(u μ x)(v μ y )} (4) τ u τ v The correlation coefficient can also sometimes be used to determine if two signals are statistically independent. On one hand, if ρ uv =, there is a strong correlation between the two signals. On the other hand, if ρ uv =, the two signals are not correlated. The correlation can be interpreted as a weak form of statistical dependency. In [9], it is shown that two random variables, which are not correlated can even so be statistically dependent. This is why, we consider the statistical dependency or independency. The product of the marginal densities ρ u and ρ v of the signals u and v, respectively, is stated as follows: p(u, v) =p(u)p(v) (5) If the expression in (3) is equal to the product of the marginal densities in (5), the signals are completely independent. One possibility to quantify the statistical dependency between two signals is to calculate the MII of them as follows: p(u, v) (u, v, C) = p(u, v)log du dv (6) p(u)p(v) The base of the logarithm determines the units in which information is measured. (6) shows that if u and v are independent, becomes zero. A forward approach is to divide the range of u and v into finite bins and to count the number of sampled pairs of z k = (u k,v k ),k =,,,n, falling into these finite bins. This count allows to approximately determining the probabilities, replacing (7) by the finite sum: bin (u, v, C) = (7) a,b where p u (a) n u (a)/n and p u (b) n u (b)/n are the probabilities based on the number of points n u (a) and n v (b) p uv (a, b)log p u,v(a, b) p u (a)p v (b) Algorithm. Distributed Faulty Sensor Detection. (decision: λn.5): non-faulty, λ >.5: faulty r nr for each sensor i N, N D do: //set initial decision as a uniform distribution ( λn ) ; //each r i sensor i is non-faulty loop for each sensor i do: ( λn ) ( ) receive neighbor th decision; r j neighbor j samples N samples from ( λn ) ( ); r j neighbor for each sample h do: // h is an index for each sample Rh non -faulty sensors; Fh faulty sensors; f h ( Rh, Fh); //Eq. 3 for each sensor i do: if λn >.5 r i marks/reports itself as a faulty sensor node; end if if i does not transmit the decision // to be described j marks/report about i as faulty sensor node // j is a neighbor sensor end if call Algorithm 3 // ith sensor signal reconstruction end falling into the ath bin of u and the bth bin of v, respectively. The joint probability is p uv (a, b) n(a, b)/n based on the number n(a, b) of points falling into box no. a, b. MII is nonnegative and symmetric: (u, v, C) =(v, u, C) (8) The MII for all possible combinations of sensor outputs y r and y s (except r = s, i =,,,r,j =,,,s) is computed, which leads to an -matrix for all combinations of r and s. The basic idea is that the MII changes when a sensor fault f r is present. Suppose that it is in the rth channel or index: ỹ r = y r + f r (9) This fault appears only in the rth channel. Thus, we should expect that all combinations with index r should show a reduction of. This allows us to localize the faulty sensor. One or more faulty sensors can be simultaneously detected in the same way. One possibility to visualize the faulty sensor is to use the relative change as a sensor fault indicator λ y r : λ y r = y r ref () yr where y r is an actual data set and the lower index ref represents one reference data set. The method based on MII is able to detect sensor faults in different combinations of them. B. Algorithm Under centralized detection, the sink handles the damage and faulty sensor detection process. In each decision cycle, the sink makes decision about the faulty sensors solely based on the k most recent signals received from each sensor. The sink computes the MII for each signal and chooses the signal with the maximal independence for fault detection. The centralized detection is not suitable for resource-constraint WSNs. For example, if each sensor needs to send their all signals to the sink, the centralized WSN may not be able to operate for a given period of time, especially in a large-scale WSN, the situation becomes serious. After capturing data at high frequency, sensors should reduce data before transmission. 36

7 On the other hand, the faulty sensor detection (see Algorithm ) can execute in a distributed manner where each sensor makes decision on the collected signals locally as described earlier. In the algorithm, if the local decision on a sensor s signals, λ y r >.5, the sensor is faulty. This means that MII is high on the sensor s measured signals. The distributed method only requires neighbors to be synchronized. In addition, the detection is almost immediate and online since a sensor does not need to wait for the signals from sensor nodes at more than one hop away. Moreover, the detected faulty signal set is not forwarded toward the sink; thus, the communication cost is relative low. The energy cost becomes lower. VI. SENSOR SIGNAL RECONSTRUCTION In this section, we propose a Kalman Filter technique (KF) for faulty wireless sensor signal reconstruction. A. Kalman Filter in State Space Representation The description of KF is made with the help of the state space representation of the system as described in Section IVB. Using (6), the equation of motion for time discrete and time invariant case are given as follows: l t = M t z t + K t u t + σ t () m t = M t z t + K t u t + σ t u t is the excitation at a specific frequency at time t. The signals σ t and σ t represent the measurement noises, respectively. They are assumed to be independent and normally distributed with covariance matrices, c v =[σσ T ]. The underlying information KF is that KF is a recursive algorithm consisting of a loop, which is passed through for each time instant t. The estimation of the system state for t is determined from the weighted average of the actual measured value at time instant t and the prediction of the system states for this time instant. The weight factors of this average are determined from the estimated uncertainties in each loop, which are also connected to the predicted system state and to the new measured value. The lower the uncertainty the higher is the weight factor, i.e., Kalman gain (K t ). The uncertainty is determined with the help of the covariance matrices [5]. We shortly describe the faulty signal reconstruction process. At first a priori state estimate P k for the state vector l pr t of the system are estimated [5]: l pr t = M t z t + K t u t P k = M t z t M T + c () t v After getting the measured value l pr t,aposteriori state can be estimated in the correction step, see (3). For the posteriori estimation, the difference between the measured and estimated signals are weighted by the Kalman gain factor K k. l post t = l prio t +K t [m t M t l prio t K t u t ]=l prio t +K k [m t m prio t ] (3) K k = P k Mt T [M t P k Mt T + c v ] (4) The priori estimated error covariance P k in the prediction step is used to update the Kalman gain factor in (3) whereas P k itself is updated by the a posteriori estimated error covariance. The KF is used here based on the Matlab implementation, Algorithm 3: Sensor Signal Reconstruction MI Step. Detect the faulty sensor by changes of the λ n m indicator (Algorithm ). Step. Recreate the state space model of the structure w.r.t. the sensor location (including faulty or nonexistent sensor) on the structure (see M and K matrices in Eq. (6)) Step 3. Determine the process and measurements noise covariance matrices. //(see Eq. (3)) Step 4. Set the covariance value(s) of the assumed faulty sensor(s) to be high. Step 5. Solve the state space equation of motion through Post KF with the estimated state vector lt (in signal correction step). The KF is driven by the input i u = and the measured signals y. t which delivers the optimum Kalman gain (K k ) together with the steady state error covariance matrix (P k ). For the system state estimation using the KF, the process and the measurement noise covariance are determined. Since the system input is assumed to be unknown and the model uncertainty is high, the process noise covariance is set to high values. The values for measurement noise covariance matrix will be determined a priori by a first estimation of the measurement error m t l post t, as given in (3). B. Sensor Signal Reconstruction Algorithm If there is a sensor detected as faulty using Algorithm, the sensor signal reconstruction algorithm (see Algorithm 3) is used by the neighbor sensors. The basic idea of the signal reconstruction is as follows. When a sensor signal does not correspond to the modeled system (monitoring its location) and it was erroneously assumed that this signal has a low measurements noise covariance, then the signals from the other sensors cannot be correctly reconstructed and the difference between the measured and estimated signals will be high. If the value of the covariance for the faulty sensor signals is set as high, then the KF will reconstruct all the signals including the incorrect signal with the help of the other signals and the model. In this manner, it is possible to reconstruct more than one signal simultaneously. The number of signals that can be reconstructed relying on the number of neighbors in case of the distributed system, all of the sensors in the network in case of the centralized system, and on the quality of the model. For a better understanding of the Algorithm 3, the procedure is broken into several steps. By means of Algorithm, when just one sensor does not work properly it is possible to identify and reconstruct it only with the help of KF. For this purpose, Step to Step 5 are applied. Here, Step 3 to Step 5 have to be calculated for several times. The number of loops over these steps corresponds to the number of neighboring sensors in the case of the distributed WSN or all of the sensors in the case the centralized WSN. In each loop, the measurement variance of one sensor is set to be high. VII. EVALUATION A. Simulation ) Methodology: We conduct simulations using MATLAB to evaluate our framework, faulty sensor detection methods and signal reconstruction. We use real data sets [4] collected t 37

8 MII #-th sensors NFMC CFD-LP DFD-LP SPEM Fault detection accuracy #-th sensors Mode shape (Fault detection + NO recovery) Mode shape (Fault detection + recovery) Tower height Mode shape ( Φ ) Fault detection ability SPEM CFD-LP DFD-LP NFMC The number of sensors (d) Fig. 5. Performance of fault detection and tolerance: (a) achieved MII under sensor faults; (b) detection accuracy; (c) observation on the actual mode shape curvature vs. mode shape curvature in cases of faulty sensor and recovery (signal reconstruction); (d) fault detection ability vs. the number of sensors. Energy consumption (mah) In case of normal monitoring Computation Transmission Overhead.8 (+ fault detection, + recovery).6 Computation Transmission.4 Overhead DFD-LP CFD-LP SPEM Fig. 6. Energy cost in five rounds of monitoring by a real SHM system on high-rise GNTVT and a toolsuite []. We use the data sets for -sensor case in our simulations where the sensors are deployed through a optimal deployment method [6] in a 45 5 sensing field regarding structural environment, e.g., bridge, building, aircraft, etc. A random Gaussian noise is added to all data. The mean of the noises is zero and the standard deviation is % of the real signals. From the data sets, a set of data is used as reference data to train the joint distribution and another set of similar data is used for testing. The noise is present in the both sets. Thus, the trained correlation model reflects the noises. After a sensor receives a decision, it recomputes its MII and chooses to change its decision accordingly. The energy cost and routing models described in Section IIIB are used for evaluation. For comparison, we implement other two schemes, SPEM [6] and NFMC [6]. Using simulation results, currently we only compare our scheme with them in two aspects: fault detection accuracy and detection ability. Here, the detection ability is the rate that is calculated by the percentage of successful faulty sensor detection to the percentage of the amount of the sensor fault injection. ) Results: In the first set of simulations, we implement our scheme considering three detection methods under the sensor fault injection (through modifying a number of sensors signals randomly in the data sets [4]): ) distributed fault detection under localized data processing (DFD-LP); ) centralized fault detection under localized processing (CFD-LP); 3) SPEM centralized data collection method for SHM, where we carry out SPEM under fault detection and tolerance. A fraction of the sensors is randomly selected and the modified faulty signals are fed into their acquisition modules. We vary the number of faulty sensors from 5% to 5%. Such a fault model is selected since it yields uncorrelated data in the same magnitude as the collected signals in practice. Fig. 5(a) shows MII achieved by four methods. Out of them, DFD-LP achieves the smallest value, followed by CFD- LP method. SPEM method performs poorly since it requires centralized data collection and shows a significant amount of data packet loss. Nevertheless, NFMC still outperforms SPEM in many sensor fault detection cases. Fig. 5(b) shows the fault detection accuracy computed as accuracy = (true positive + true negative)/all. The detection accuracy in DFD-LP is about 98% that outperforms others. In SPEM, the detection accuracy is poorer (less than 8%) than others, while it is from 75% to 85% in NFMC. One of the major cause is that peak natural frequency signals in NFMC achieve higher MII. We next recover the first Φ (see Fig. 5(c)) of the simulated structure with the locations, which cover up to 45 meters. We see the impact on the health status that the actual mode is distorted under the sensor fault, which is successfully recovered by the corresponding sensor signal reconstruction. Fig. 5(d) shows the fault detection ability of DFD-LP is much better than NFMC and SPEM. NFMC shows higher detection error than DFD-LP. This is because the set of the same pick frequencies cannot be achieved in many neighborhoods or clusters. Under the random fault injection, we found that, (i) one or more clusters are disconnected as one or more faulty sensors are isolated based on natural frequency comparison, although it shows good ability rate of fault detection in some clusters; (ii) the scheme is limited to the frequency matching based fault detection; it fails to detect other types of faults. The energy cost in the first five rounds of monitoring can be seen in Fig. 6 for all the methods. We calculate energy cost for computation, transmission, and overhead. The CFD- LP consumes around 6% energy more than DFD-LP. B. WSN Prototype System Implementation ) Methodology and Wireless Sensor Platform: We validate our scheme by implementing a proof-of-concept system using the TinyOS [7] on Imote platforms [8]. Our objective is to observe ) accuracy of Φ identification in the presence of sensor faults and ) energy-efficiency. We employ integrated Imotes called SHM motes on the infrastructure as shown in Fig. 7, an additional Imote located at 5 meters away as the sink mote, and a PC as a command center for the sink mote and data visualization. The test infrastructure has floors; at each floor, a mote is deployed to monitor the structures horizontal accelerations. Each mote runs a program (implemented in the nesc language) to process the acceleration data acquired from 38

9 The SHM Mote 5th Td (Mode (3. Hz) 5th Td (Mode (6. Hz) th Td (Mode ( 7.3 Hz) th Td Mode ( 9. Hz) 3th Td (Mode (3. Hz) 33th Td (Mode (6. Hz) radio-triggered wakeup & synchronization module ith Sensor (a) (b) ith Sensor sensor board module Imote (a) An integrated SHM mote (b) Test building structure (c) Fig. 7. (a) The SHM mote integrated by Imote; (b) twelve-story test structure and the placement of SHM motes on it; (c) their deployment. MII ith sensor ith sensor MII NFMC DFD-LP SPEM ith sensor (a) (b) -3 5th Sensor Measured signal Estimated signal (c) Time [ms] Acceleration [m/s] Fig. 8. (a) Distributed sensor fault detection (5th sensor and th sensor are faulty); (b) MII achieved by the two detection methods under the sensor faults; (c) signal reconstruction of the 5th sensor. on-board accelerometers. The sink receives the data packets from the sensors through wireless communication and relay the data to the PC over a USB cable. Java and Matlab used to calculate and visualize the whole structural health condition. In the experiment, R min is adjusted by the diameter of the structure. Imote s discrete levels of range are set to use R min and R max [8]. Fault Injection. To produce a sizable vibration response of the test structure, we collected the original data by vertically exciting the test structure using a magnetic shaker. We inject the sensor faults in two cases: () debonding fault between the 5th sensor and the structure; () precision degradation fault during acceleration signal capturing by at the th sensor. The sensors are expected to work properly but exhibit faulty acceleration measurements or decisions. ) Experiment Results: Fig. 8(a) shows the results about fault detection. Remarkable changes in the signals of the 5th and th sensors and some of their neighbors are detected. The MII changes in the both sensor fault cases that can be seen in Fig. 8(b). The corrupted signals at 5th sensor is reconstructed as shown in Fig. 8(c). SPEM achieves some amount of MII 36th Td 3 (Mode (3. Hz) 36th Td (Mode (6. Hz) Fig. 9. (c) ith Sensor 4th Td (Mode (3. Hz) 3 4th Td (Mode (6. Hz) (d) ith Sensor The Φ s curvature under sensor faults and recovery from the faults. almost at all of the sensor locations, even when the sensors are not faulty; the amount of MII is largest in NFMC method. In the DFD-LP, when sensors process data locally, the small value in the MII is achieved, ranging from % to 4%, and they are not faulty. MII provides the best value when a remarkable change in the signals. Now, we identify exactly what happen in the structure. Recall that if there is a change in the signals with a single sensor only, the sensor may be faulty. If the change is with multiple sensors, there is possibly damage. In Fig. 9(a), at T d =5, the 5th sensor detected faulty, and at T d =, the th sensor is detected faulty. The changes in Φ are computed at those time interval. We inject structural physical damage through removing the plates on the 5th and th floors, since sensors located at these floors are faulty. We can see in Fig. 9(b) that the neighbors (4th, 6th, and 9th ) are able detect an extent of changes, where the slightly affected Φs are clearly appeared. We further take experiments that a faulty sensor signal is reconstructed using our algorithm. Φ s curvature is recovered significantly at the th sensor location as shown in Fig. 9(c), which means that there is possibly a damage, since the Φ is still slightly affected. However, the changes in Φ at the 5th sensor is still remained and slightly recovered at the neighbors. Further proof of the damage detection can be seen in Fig. 9(d). Here, we replace the plate on the same floors. When the sensors wakeup and start monitoring, that time T d =4. In Fig. 9(d), there is no remarkable change appeared at the th sensor location. Distorted Φ s information at the neighbor locations is completely recovered. We can say there is no MII appeared. In contrast, at the 5th location, Φ is still not recovered but there is no remarkably Φ s curvatures at the neighbor sensors location. It proves that the 5th sensor is surely faulty while there was damage at the th sensor. Through analysis, the quality of the faulty sensor signal reconstruction is about 9% compared to the results under fault-free condition. We conclude that in the present of sensor faults, the damage can be detected. Energy cost (cost(e i )). We allow all of the sensors to sleep after each monitoring period to perform power management. 39