Title: Energy-efficient SHM in wireless sensor networks by damage detection from short time series
Authors: Jyrki Kullaa, Maurizio Bocca, Lasse M. Eriksson
ABSTRACT A new structural health monitoring (SHM) approach for wireless sensor networks (WSN) is proposed, in which damage detection is performed from short time series applying central data fusion architecture. Damage detection is done using minimum mean square error (MMSE) estimation of each sensor in time domain. The main advantages of the proposed method are: (1) energy consumption is decreased; (2) no data processing or feature extraction is needed in the node; (3) data storage in the node is decreased; and (4) data are not exchanged between nodes. The data must be time synchronized and the amount of training data should be relatively high. The proposed approach is experimentally verified by monitoring a wooden bridge with increasing damage. The required length of the time series for damage detection and the resulting energy saving are discussed. INTRODUCTION Structural health monitoring (SHM) with wireless sensor networks (WSN) is attractive, because no cables are needed. The number of sensors installed to the structure can therefore be high, resulting in a better spatial coverage and consequently more accurate damage identification capability. However, new challenges emerge when applying SHM with WSN: 1. The wireless nodes must be relatively inexpensive. They typically do not have high computing or data storage capabilities. However, in SHM applications, features are often extracted from long time series. Many feature extraction _____________
Jyrki Kullaa, Department of Applied Mechanics, Aalto University, P.O. Box 14300, 00076 Aalto, Finland. Alternative address: Helsinki Metropolia University of Applied Sciences, P.O. Box 4021, 00079 Metropolia, Finland (email@example.com). Maurizio Bocca, Lasse M. Eriksson, Department of Automation and Systems Technology, Aalto University, P.O.Box 15500, 00076 Aalto, Finland (firstname.lastname@example.org, email@example.com).
procedures require data storage and complex and powerful computational algorithms. 2. Simultaneous sensing, transmission or reception, and data storage may not be possible. With long time series, some samples may be missed during recording. 3. Several features, e.g. mode shapes and cross-spectra, require simultaneous data from other nodes. Consequently, data exchange and accurate time synchronization (even in the order of microseconds) between nodes are needed. 4. Power consumption is often a critical issue. Data transmission typically consumes most energy. Also, if the node is equipped with a powerful processor, the energy needed for data processing in the node is not negligible . The research is active on distributed feature extraction in the node or in a cluster of nodes. The objective is to minimize the data transmission to save energy. Decentralized data fusion and independent sensor architectures  are therefore very promising and have gained a lot of interest in the SHM community. The approach proposed in this paper which addresses most of the aforementioned issues is alternatively based on centralized data fusion architecture . Damage detection is performed from short time series. These short time series are transmitted to the central computer, in which data storage and processing take place. In order to extract damage-sensitive features, such as natural frequencies or power spectra from the time series, a relatively long measurement period and consequently a large amount of data are needed. If, however, short time series are only available for the test data, an alternative is to utilize a one model approach , in which a model of the undamaged structure is only identified using the training data. In this paper, each sensor in the sensor network is modelled using minimum mean square error (MMSE) estimation . Once the MMSE model is identified, generation of the residuals for the short time series is straightforward. Changes in the residuals are assumed to reveal structural damage. An advantage of this approach is that no model identification for the test data is needed . It should, however, be noted that the residuals are less sensitive to damage than the likelihood ratio test (LRT) [6, 7]. However, LRT also requires a large amount of data in order to accurately identify the MMSE model. The main advantage of the proposed method is a decrease in energy consumption due to reduced data transmissions from the nodes to the sink, thus extending the lifetime of the network. Another advantage is that no feature extraction or other computationally demanding data processing in the node is needed. The restrictions are that the system needs synchronized data from several sensor nodes and the amount of training data must be relatively high. The paper is organized as follows. The minimum mean square error (MMSE) estimation model is shortly reviewed. The residual-based damage detection and localization techniques are then introduced. The design of the wireless sensor network is presented, which would be used for the tests. The proposed approach is experimentally verified by monitoring a wooden bridge with gradual damage. Finally, concluding remarks are presented. DAMAGE DETECTION AND LOCALIZATION WITH MMSE ESTIMATOR In the minimum mean square error (MMSE) estimation, each sensor in the network is estimated in turn directly in the sensor space. Simultaneous sampling of each sensor is assumed, which requires the availability of an accurate time
synchronization method for the WSN, such as . The sensors are divided into observed sensors v and missing sensors u: ?u ? x=? ? ?v ? with a partitioned covariance matrix Σ of the training data
? =? ?
uu vu uv
? ? ?=? vv ? ?
? ? vv ?
where the precision matrix Γ is defined as the inverse of the covariance matrix Σ and is also written in the partitioned form. A linear MMSE estimate is :
where ?u and ?v are the mean of u and v, respectively. The error covariance matrix is
cov(u v ) =
The feature used for damage detection is the subgroup mean x or the sample ?. standard deviation S  of the first principal component of the residuals = u ? u The subgroup consists of 100 subsequent observations. x is used to monitor the change of the mean, while S is used to monitor the variability. For damage localization, each residual is standardized with the estimated error covariance matrix (4), and it is proposed that the largest rms of these scaled residuals identifies the sensor closest to damage. The standardized variable z used in a multivariable case becomes the Mahalanobis distance:
? ? z 2 = [u ? u ] [cov(u v)] [u ? u ]
WIRELESS SHM SYSTEM The WSN design considered in this study takes advantage of a time synchronization (TS) protocol  that limits the synchronization error between nodes below 2 ?s per hop. Accuracy in TS is challenging due to the low-power and lowquality oscillators present in sensor nodes, which introduce a significant drift of the clocks. Moreover, the drift is different in each node and varies depending on the external temperature and age of the node. Therefore, in SHM applications it is very important to frequently synchronize the clocks of the nodes to minimize the error while collecting the acceleration samples. In , the effect of the TS error between the nodes on the estimation of the mode shapes of the monitored structure is analyzed. In the proposed WSN, the nodes store data in an external flash memory. Because of the high applied sampling frequency (1 kHz), each node misses 3 samples while
writing 36 samples in the memory. Before data analysis, these missing samples are first estimated using MMSE. Temporal correlation model  is used, because the missing samples occur at the same time instant in all nodes. Time synchronization between the nodes is obtained as follows: prior to sampling the sink node broadcasts a series of n time synchronization beacons, one in every ?ts ms, which are received by the other nodes to adjust their clocks. In the time interval between the transmissions of two consecutive TS beacons, each node drifts d node ?s from the clock of the sink node. The nodes estimate their own clock drifts, and at the end of the TS phase, they compute the median value of these estimates. During sampling, each node autonomously gets re-synchronized in every ?ts ms by adjusting its own clock by the computed median value of the drift estimates. In this way, each node is capable of limiting the synchronization error below 2 ?s per hop for an extended period of time even with a high sampling frequency. In this study, the acceleration data collected with the wireless sensor nodes are not included in the analysis. This is due to the fact that the plastic casing of the nodes and accelerometers , together with the used strong magnetic attachment to the monitored structure, increased consistently the floor noise level of the recorded data. Because of the casing redesign, the data were not available for this paper, but the data and the results obtained with the WSN will be available in the results section at http://mide.tkk.fi/en/ISMO later in the spring of 2010. EXPERIMENTAL RESEARCH The proposed approach was investigated with a monitoring system built in the laboratory. The structure was a 4.2 meters long, 36 kg wooden model bridge shown in Figure 1. Random excitation was applied to the structure to excite the lowest modes. As mentioned before, the WSN nodes were not available for this paper, but the wired measurement system was used instead. The response of the structure was measured with 15 accelerometers located at three different longitudinal positions. The sampling frequency was 2560 Hz. The data were low-pass filtered below 51.2 Hz and resampled. Damage was a change in the cross-section in one of the braces (Figure 1). The damage cases and the corresponding measurements are listed in Table I. The first three measurements with a 60 s measurement period were used as training data. Spatiotemporal correlation with model order 5 was used to identify the MMSE model . The measurement period for the test data was only 6 s. The S control chart for the first principal component of the residual was designed using the first four measurements and is shown in Figure 2 left. Each damage level is clearly visible. Notice also the different measurement periods and the logarithmic scale. Damage localization was done by plotting the standardized rms residual (Equation 5) for each sensor and each measurement. The result is shown in Figure 2 right, where sensor 7 has the highest value once damage was introduced. Indeed, sensor 7 was located on the top flange closest to the damaged brace measuring lateral acceleration.
Figure 1. Left: Wooden bridge test setup. Right: A detail of the damaged member.
TABLE I. DIFFERENT DAMAGE CASES AND MEASUREMENTS. Damage case Undamaged Undamaged D1 D2 D3 Meas. number 1– 3 4– 6 7–13 14– 20 21– 27 Meas. period T [s] 60 6 6 6 6 No. samples/ sensor 6124 594 594 594 594 Beam Width b [mm] 30 30 22 14 6
S Chart, n = 100
2 4 6 Sensor 8 10
3 4 7 Measurement
10 15 Measurement
Figure 2: Left: S control chart for the first principal component of the residuals. Right: Damage localization. Sensor 7 has the highest residual.
CONCLUSION Current research of SHM using wireless sensor networks is mainly concentrated on distributed feature extraction. In this study, a different approach is proposed, which utilizes short time series directly without a feature extraction process in the nodes. The proposed approach has the following advantages: 1) The amount of data transmitted is small; 2) no feature extraction is needed in the nodes; and 3) no excessive local computing or data storage is necessary. The main disadvantage is that the residuals are
not optimal features for damage detection. In addition, the method requires simultaneous sampling of all sensors, which in the case of WSN is not trivial to achieve, although the sample-and-transmit application itself is not complicated. The energy consumption in the node is strongly related to data storage and transmission. Compared to a scenario, in which test data with a long measurement period are transmitted to the sink for model estimation, the proposed residual-based approach is able to double the lifetime of the nodes. It should be noted that in a real application, the amount of training data should be much higher in order to include a full range of environmental or operational conditions. However, for the test data this restriction does not apply . Also damage detection and localization performance of other features based on short time series in centralized data fusion architecture should be studied and compared. ACKNOWLEDGEMENT This research was performed in the Intelligent Structural Health Monitoring System (ISMO) project, funded by the Multidisciplinary Institute of Digitalisation and Energy (MIDE) research programme at the Aalto University, Finland. REFERENCES
1. Lynch, J.P., Sundararajan, A., Law, K.H., Kiremidjian, A.S. and Carryer, E. 2004. Embedding damage detection algorithms in a wireless sensing unit for operational power efficiency. Smart materials and structures, Vol. 13, No. 4, 800– 810. 2. Su, Z., Wang, X., and Ye, L. 2009. Data fusion of multiple signals from the sensor network. In the Encyclopedia of Structural Health Monitoring, Boller, C., Chang, F. and Fujino, Y. (eds.), John Wiley & Sons, Chichester, UK, 697– 708. 3. Gustafsson, F. 2000. Adaptive filtering and change detection. Chichester, UK, John Wiley & Sons. 500 p. 4. Kullaa, J. 2010. Sensor validation using minimum mean square error estimation. Mechanical Systems and Signal Processing, doi:10.1016/j.ymssp.2009.12.001 5. Fassois, S.D. and Sakellariou, J.S. 2009. Statistical Time Series Methods for SHM. In Encyclopedia of Structural Health Monitoring, Boller, C., Chang, F. and Fujino, Y. (eds.), John Wiley and Sons, Chichester, UK, 443– 472. 6. Basseville, M. and Nikiforov, I.V. 1993. Detection of abrupt changes - Theory and application. Englewood Cliffs, NJ, Prentice-Hall. 447 p. 7. Kay, S.M. 1998. Fundamentals of statistical signal processing. Detection theory. Upper Saddle River, NJ, Prentice-Hall. 560 p. 8. Basseville, M. 2009. Model-based statistical signal processing for change and damage detection. In the Encyclopedia of Structural Health Monitoring, Boller, C., Chang, F. and Fujino, Y. (eds.), John Wiley & Sons, Chichester, UK, 677– 696. 9. Mahmood, A. and J?ntti, R. 2009. Time synchronization accuracy in real-time sensor networks. In Proceedings of the 9th IEEE Malaysia International Conference on Communications 2009 (MICC 2009), Kuala Lumpur, Malaysia, December 17-19. 10. Montgomery, D.C. 1997. Introduction to statistical quality control. 3rd ed. New York. John Wiley & Sons. 728 p. 11. Krishnamurthy, V., Fowler, K., and Sazonov, E. 2008. The effect of time synchronization of wireless sensors on the modal analysis of structures. Smart Materials and Structures, Vol. 17, No. 5. 12. Bocca, M., Cosar, E. I., Salminen, J., and Eriksson, L. M. 2009. A reconfigurable wireless sensor network for structural health monitoring. In Proceedings of the 4th International Conference on Structural Health Monitoring of Intelligent Infrastructure, U. Meier, B. Havranek, and M. Motavalli (eds.), Zurich, Switzerland. International Society for Structural Health Monitoring of Intelligent Infrastructure.