Structural Health Monitoring in Wireless Sensor Networks ... - CiteSeerX

Structural Health Monitoring in Wireless Sensor Networks by the Embedded Goertzel Algorithm Maurizio Bocca1, Janne Toivola2, Lasse M. Eriksson1, Jaakko Hollmén2, and Heikki Koivo1 1

Department of Automation and Systems Technology, School of Electrical Engineering 2 Department of Information and Computer Science, School of Science Aalto University Helsinki, Finland {maurizio.bocca, jannetoivola, lasse.eriksson, jaakko.hollmen, heikki.koivo}@tkk.fi

Abstract— Structural health monitoring aims to provide an accurate diagnosis of the condition of civil infrastructures during their life-span by analyzing data collected by sensors. To this purpose, detection and localization of damages are fundamental tasks. This paper introduces a wireless sensor network for structural damage detection and localization in which the sensor nodes, in order to estimate the energies of specific frequency bands, process the acceleration data locally in real-time using the Goertzel algorithm. The nodes then share their results inside the network and exploit them to compute transmissibility functions, which can be exploited as damage indicators and for correctly localizing damages within the monitored structure. The use of the embedded Goertzel algorithm prevents the nodes from transmitting large volumes of acceleration data to the sink node for off-line analysis, reducing the latency and increasing the life time of the cyber-physical system by 80 % and 52 %, respectively. The tests performed on a truss structure confirm the capability of the distributed approach in correctly detecting and localizing structural damages. Keywords: Goertzel algorithm, structural health monitoring, wireless sensor networks, transmissibility functions.

I.

INTRODUCTION

Wireless sensor networks (WSNs) have the capability to efficiently reach the main goals of structural health monitoring (SHM), which consists of accurately diagnosing the health of civil infrastructures such as bridges, dams, road tunnels, etc. from data collected by sensors. Specifically, SHM targets a correct detection, localization, and quantification of structural damages, and the assessment of the remaining life time of the monitored structure [1]. Compared to the traditional wired systems, the advantages of applying WSNs to SHM are many: firstly, by eliminating the cabling, they allow consistent savings in installation time and costs. Moreover, the low cost of the nodes composing the wireless network allows the deployment of a large number (potentially hundreds) of measurement units on the structure, thus increasing the total amount of data available for off-line analysis and improving the screening resolution of the system. However, the design and implementation of a reliable and efficient low-power WSN for SHM is made challenging by the limitations of the sensor nodes in terms of available power, micro-controller unit (MCU) computational power, RAM memory space, and, in the case of low-power IEEE 802.15.4 radios, communication bandwidth and range. Some of the requirements of SHM, such as high time synchronization accuracy and storage and transmission of large data sets, are

not straightforward to be implemented in a multihop network. Among all the operations that a sensor node can perform, transmissions and receptions of packets have by far the heaviest impact on power consumption. Due to this fact, it becomes particularly important to minimize the amount of data that need to be transmitted in the network, especially when the number of hops from the data source to the sink node is high. One feasible approach to achieve this goal is to process the collected measurements locally in the sensor nodes, and then transmit only significant results to the sink node. In order to do this, the exploited processing algorithm must consider the hardware limitations of the MCU of the sensor nodes. This distributed approach would considerably extend the life time of the network and reduce the total time required by the system to complete a structural test of the monitored structure, i.e. the latency. This paper presents a WSN in which the nodes, equipped with a 3-axis accelerometer, process the collected vibration measurements by the Goertzel algorithm [1] in real-time. The nodes then share the results of the computations inside the network in order to derive transmissibility functions, which are finally exploited to correctly detect and localize structural damages. By applying the Goertzel algorithm, the nodes perform a frequency-domain analysis of the acceleration signals in an efficient way: the key parameters of the algorithm are dynamically adjusted by the end-user operating at the sink node to e.g. perform a low resolution scan of the entire frequency spectrum, or accurately monitor those specific ranges of frequencies known to show significant changes in presence of damages. This procedure could also be (partly or totally) automated, and interrupted by the operator only if needed. To validate the proposed distributed approach, several tests were performed on a wooden truss structure, shown in Fig. 1, by introducing damages at different locations. The results show that by processing the acceleration data using the embedded Goertzel algorithm in real-time, the nodes are able to correctly detect structural damages. Through the computation of transmissibility functions, the system is also able to correctly localize the damages. The use of these embedded computations prevents the sensor nodes from transmitting long series of acceleration signals (usually up to 60 kB of data for each sensor node) to the sink node for off-line analysis. The remainder of the paper is organized as follows. Related work is presented in Section II. The Goertzel algorithm and transmissibility functions are introduced in Section III and IV. Section V briefly describes the sensor node hardware and truss

structure used in the tests. In Section VI, the application flow is given. Damages detection and localization results are presented in Section VII, while Section VIII quantifies the power consumption and latency savings of the proposed distributed approach. II.

RELATED WORK

In recent years, several real-world deployments of WSNs for SHM have been completed. In [3], 64 sensor nodes were distributed over the main span and tower of the Golden Gate Bridge, forming a 46-hop network. Normally, nodes deployed on civil structures collect and store acceleration measurements at regular intervals (e.g. once every hour), when requested by the end-user operating at the sink node, or when anomalous events (e.g. vibrations exceeding a pre-defined threshold) are detected. The vibration data are then transmitted wirelessly to the sink node, which is in turn connected to an external PC in which they are permanently stored and processed [4]. The data can eventually be uploaded in real-time on the Internet together with other features of the network (e.g. routing paths, battery levels of the nodes, etc.) [5]. A different approach is described in [6], where a WSN is organized in a star topology in which 20 nodes sampling at 128 Hz continuously transmit data in real-time to the sink node for operational modal analysis. WSNs are exploited also for structural control: in [7], the sensing nodes periodically transmit measurements to the controlling nodes, which process the data and calculate the proper control forces to be applied at the dampers. In order to minimize wireless data transfer and accordingly power consumption, the nodes can process the collected vibration measurements locally and then transmit only some extracted damage-sensitive features to the sink node. An additional advantage of such embedded processing methods is that, differently than in other centralized off-line processing methods such as modal analysis [8], an accurate synchronization of all the nodes composing the network at the beginning of the sampling is not required, thus reducing the communication overhead of the application. However, clock skew compensation is still required in order to guarantee that all the nodes will monitor precisely the same frequency bins. Several embedded and distributed data processing methods have been proposed. In [9], the nodes fit an AR(p) model to the collected acceleration measurements first and then transmit its coefficients to the sink, where they are compared by means of Euclidean distance to a database of AR-ARX models calculated for the undamaged structure. The sink then transmits back the coefficients of the matching ARX model. After this, the nodes signal the presence of the damage if the residual error of the measured data is larger than a pre-defined threshold. In [10], the acceleration signals are locally processed to generate a signature vector of filtered wavelet coefficients. By using this method, the volume of transmitted data is reduced to less than 5 % of the raw amount. However, the method fails in detecting damages corresponding to one third stiffness reduction in one beam of the analyzed benchmark structure. A WSN for distributed damage localization is partially implemented in [10]. In it, the nodes deployed on the structure initially perform only a portion of the damage localization procedure. The partial results are then transmitted to the sink node, which completes the procedure. This method requires an

accurate numerical model of the changes of the natural frequencies of vibration of the structure in response to damage placed at different locations. Time synchronization inaccuracy introduced by the nodes hardware affects the correspondence between the measured and analytical natural frequencies of the steel beam and truss structure used in the tests. Moreover, the simulated damages, i.e. a 1.5 kg weight on a 10 kg steel beam, and a simultaneous 50 % area reduction of four elements of the truss structure, represent major structural damages not allowing an evaluation of the sensitivity of the proposed approach. A flexibility-based damage localization method is presented in [11]. In the proposed architecture, the cluster head nodes first aggregate the power spectrums (obtained by FFT) of the cluster members beneath them in the hierarchy, then extract the mode shapes of the structure which are finally transmitted to the central sink node where the actual flexibility calculation is executed. The latency at the cluster heads (approximately 110 s) can be attributed to time synchronization of the sensor nodes and data transmission from the cluster members to their cluster heads. In this paper, the sensor nodes process the acceleration data locally in real-time by the embedded Goertzel algorithm. This algorithm, originally proposed in [1], is able to identify the different frequency components of a signal. Because of this, over the years, it has been most commonly used in dual-tone multi-frequency (DTMF) recognition to recognize the tones produced by pushing the buttons on a telephone keypad [13], and in low-power underwater acoustic communication [14]. Compared to the fast Fourier transform (FFT) algorithm which computes the spectrum evenly across the bandwidth of the signal, the Goertzel algorithm can be efficiently tuned to analyze only specific frequencies or intervals of frequencies. This feature makes it particularly suitable for SHM, since each sensor node can be tuned to monitor only those frequencies of interest which ultimately can indicate the presence of damages. In addition, the Goertzel algorithm works iteratively, updating the partial results after every new sample. Because of this, the nodes do not need to store the acceleration data in their RAM, saving memory space, or in an external flash memory, saving power, and can transmit the final results of the computations at the end of the sampling phase, thus reducing the latency. In [15], transmissibility functions, which only depend on the zeros of the system, are shown to be more sensitive to localized damages than other methods, such as modal analysis, which only monitor the poles (global properties) of the system. The use and the performance of transmissibility functions for damage localization have been investigated also in [16] for chain-like mass-spring systems. In [17], the transmissibility functions analysis is embedded in autonomous mobile sensing nodes that process the collected acceleration data by a 4096point Cooley-Tukey algorithm. III.

EMBEDDED GOERTZEL ALGORITHM IMPLEMENTATION

The FFT allows calculating the frequency spectrum of a Nsample signal in O(N log(N)) steps. Since in the Goertzel algorithm calculating a single bin of the frequency spectrum requires O(N) steps, if fewer bins than O(log(N)) are needed, it becomes more efficient to calculate only specific bins instead of the entire frequency spectrum [18]. This can be efficiently achieved through the Goertzel algorithm, which can be thought

of as a second order infinite impulse response (IIR) filter for each DFT coefficient. The transfer function, H(Z), of the filter is: 1 1

2

,

(1)

2

where fi is the frequency of interest (or vector of frequencies of interest), and fs is the applied sampling frequency. The key parameters of the Goertzel algorithm embedded in the sensor nodes are the sampling frequency fs, the distance between two consecutive bins on the frequency axis db, and the vector of frequencies of interest fi, i.e. the range of monitored frequencies. In the proposed WSN, these three parameters are defined by the end-user operating at the sink node and then broadcasted to all the sensor nodes. The sensor nodes calculate the number of samples N that must be collected to obtain the resolution r=1/db as: .

(2)

N does not need to be a number power of two in the Goertzel algorithm, unlike in the FFT case. The bins k corresponding to the selected frequencies of interest are computed as: ·

0.5

.

(3)

Due to the approximation in (3), the actual monitored frequencies could differ from the ones originally selected. This is not the case of the proposed WSN, since the frequencies of interest are chosen as integer multiple of the bins distance db. During the sampling, the sensor nodes iteratively execute the following three equations: · (4) , where si is the last collected accelerometer measurement, and q1 and q2 store the results of the two previous iterations. The coefficients c used in the iterations are computed as: 2

2

(5)

.

After the N-th iteration, the nodes calculate the squared magnitude of the spectrum at the frequencies of interest as: |

| IV.

·

·

.

(6)

TRANSMISSIBILITY FUNCTIONS

In civil infrastructures, changes in the frequency spectrums of the acceleration signals collected by sensors deployed at different locations can be caused not only by the onset of damages, but also by changes of the environmental conditions (e.g. temperature and humidity [19]) and in the magnitude and position of the excitation to which the structure is subjected. Therefore, in order to detect the presence of structural damages and reduce the risk of false alarms, the frequency spectrums of the acceleration signals collected by the sensor nodes under

different experimental conditions need to be normalized to achieve environmental invariability. Transmissibility functions are suitable structural features to monitor for this purpose. Transmissibility refers to resonance, and represents the result of the interference of the vibrations propagating and reflecting along the structure. A change of one of the transmissibility functions indicates the onset of a damage in the monitored structure. Additionally, the input excitation measurements are not required for the computation of these functions. By considering a pair of sensor nodes, si and sj, where i,j = 1…N, and i ≠ j, deployed at different locations, and the range of frequencies of interest [f1, f2], the transmissibility function T is defined as: ∑ ,

(7)

,

∑

in which X is the frequency spectrum, computed by applying the Goertzel algorithm, of the acceleration signal collected by the sensor node. In (7), the power spectrums of the signals are considered. In [20] it was shown that a satisfying damage detection performance is achieved by monitoring only a subset of the possible combinations of sensor pairs and ranges of target frequencies. This fact further motivates the use of the Goertzel algorithm as data processing method embedded in the nodes. The relative difference Dr between the transmissibility functions calculated by pairs of sensor nodes placed on the structure in reference and current conditions was selected as damage indicator. This is calculated as: ,

,

, ,

,

(8)

where the indices Ref and Test correspond to the reference and current condition of the monitored structure. V.

SENSOR NODE HARDWARE AND TEST BED SETUP

The sensor node used in the tests, the ISMO-2 node [21], is based on Sensinode U100 Micro.2420 sensor networking platform. Its core is a TI MSP430F1611 MCU with 48 kB of program and 256 B of data flash memory, and 10 kB of RAM. The platform has also an external 500 kB serial data flash memory (M25P40 by STMicroelectronics). The radio module is an IEEE 802.15.4 compatible Chipcon CC2420 transceiver, operating in the 2.4 GHz band, having 250 kbps bandwidth The platform runs the FreeRTOS real-time operating system kernel. A dedicated PCB contains the 3-axis digital accelerometer LIS3LV02DQ by STMicroelectronics, having a selectable full scale of ±2g or ±6g and a selectable 12 or 16 bit representation. Its sensitivity, when ±2g scale and 16 bit representation are selected (as in the tests carried out), is 76.4 mV/m/s2. The maximum accelerometer bandwidth is 640 Hz for all axes. The integrated ΣΔ ADCs, which translate the produced signal into a digital bit stream, are coupled with dedicated reconstruction filters that remove the high frequency components of the quantization noise. The PCB containing the accelerometer and the Micro.2420 platform are connected in a stack through a 50-

(b) (a) Figure 1. Test bed setup: eight ISMO-2 nodes (numbered boxes), four damages (D1, D2, D3, and D4), damaged cross bar (D5 and D6). To validate the results obtained with the wireless platforms, 16 high-quality wired accelerometers are installed on the wooden truss structure.

pin connector. The data provided by the sensor are accessed through a SPI interface. The Micro.2420 platform, accelerometer PCB, and two AA batteries are contained in an aluminum case, of size 22 x 6 x 3.5 cm. In order to increase the transmitting range, the ISMO-2 node is equipped with an external WLAN antenna (5.0 dBi gain). The sensor PCB and the wireless platform are tightly screwed to an aluminum bar which provides the required rigidity to the entire node in order to minimize noise and damping. The total weight of the ISMO-2 node is 850 grams. The tests were carried out on a wooden truss structure, 420 cm long, 65 cm wide, and 34 cm high. The wooden bridge is connected to a programmable electro-dynamic shaker. In order to simulate the varying environmental conditions to which civil structures are typically subjected, random noise excitation was applied. In the tests, the eight ISMO-2 nodes were magnetically attached to the truss structure. The magnets are located at the two ends of the aluminum bar of the nodes, far from the accelerometer, since in previous tests it was observed that the proximity of the magnets to the sensor was increasing the floor noise level of the acceleration signals. The two magnets are placed on the top of two tiny iron plates, which are in turn tightly fixed to the top bar of the truss structure. This way of attaching the nodes provides the required rigidity to the entire platform. The total weight of the wooden truss structure together with the eight sensor nodes is 44 kg. First, a 500 g mass (1.1 % of the total mass of the truss structure) was used to simulate the presence of structural damages. The mass was placed in four different positions, i.e. D1, D2, D3, and D4. Later, a portion of a cross bar was removed, reducing its stiffness first by 27.6 % (D5) and subsequently by 55.2 % (D6). In the tests, the applied sampling frequency was set to 125 Hz in order to provide the MCU with sufficient time between one sample acquisition and the following one to execute the equations in (4). The test bed setup is shown in Fig. 1. VI.

Section III in a Matlab program running on an external laptop connected via serial port to the sink node. These values are then broadcasted to all the sensor nodes placed on the truss structure, which in turn start collecting accelerometer data while iteratively executing the Goertzel algorithm as in (4) and, at the end of the sampling phase, (6). Each node then shares its results with all the other sensor nodes by following a TDMA schedule in which the order of the broadcasts is defined by the unique ID number of the nodes. When a node receives the Goertzel algorithm results coming from another node it computes the transmissibility function as in (7). If the end-user wanted to set the current transmissibility function value as the reference one for subsequent tests, this result is also stored in the external serial flash memory of the node. Otherwise, the current result is matched against the one already stored in the external serial flash memory. At the end of the results sharing phase, the same TDMA schedule is exploited when each node transmits its damage indicators values computed as in (8) to the sink node. Fig. 2 summarizes the application flow.

APPLICATION FLOW

Before starting a test, the end-user defines the values of the three key parameters of the Goertzel algorithm defined in

Figure 2. The application flow.

(a)

(b)

(c) (d) Figure 3. Damage indicators between transmissibility functions of pairs of sensor nodes deployed on the same bar of the truss structure where the damages D1 (a), D2 (b), D3 (c), and D4 (d) were introduced.

VII. EXPERIMENTAL VALIDATION Since the most dominant natural frequencies are normally found in the lower part of the spectrum [21], only the frequency range [0, 40] Hz was considered during the tests in the computation of the transmissibility functions. Fig. 3 shows the values of the damage indicators Dr between the transmissibility functions of pairs of sensor nodes deployed on the same bar of the truss structure where the damages D1, D2, D3 and D4 were introduced. From the results it can be observed that, depending on the position of the damage, some pairs of nodes are more sensitive to the change of conditions of the structure caused by the presence of the damage. Besides, some intervals of frequencies (e.g. [30, 35] Hz for D1, [23, 26] Hz for D2) show significant changes in the transmissibility functions between several pairs of nodes, while other intervals of frequencies (e.g. [0, 3] Hz for D3, [33, 37] Hz for D4) show consistent changes only in those

pairs of nodes which are close to the real position of the damage. The changes occurring inside these identified intervals of frequencies represent a signature for the position of the damage, and are efficiently monitored by optimally tuning the parameters of the embedded Goertzel algorithm running in the sensor nodes in order to maximize the probability of both correct detection and localization. The localization of damages D1, D2, D3, and D4 is represented in Fig. 4. From these results it is clear that the position in which the electro-dynamic shaker is connected to the truss structure plays a big role in defining the values of the damage indicators, i.e. the closer the damage to the connection point, the higher the values. However, also D1 is correctly detected and localized. In the case of D4, which was placed right above the point of connection of the electro-dynamic shaker to the structure, the transmissibility functions which show the highest changes are the ones between node 5, which is placed in the proximity of

(a)

(b)

(c)

(d)

Figure 4. Damage indicators values between transmissibility functions of pairs of sensor nodes deployed on the truss structure: damages D1 (a), D2 (b), D3 (c), and D4 (d).

the damage, and the nodes placed on the other side of the truss structure. By introducing a 500 g mass in the proximity of the source of the excitation, the global mode shapes of the bridge are drastically modified, making the localization of the damage less accurate than with the other damages. However, when only the transmissibility functions between the pairs of nodes placed on the same side of the damage are considered, the localization is again correct. This phenomenon is shown in Fig. 5. Similar conclusions can be drawn from the two cases in which the damage was introduced by progressively reducing the stiffness of one cross bar of the truss structure (i.e. D5 and D6). Also in these cases, when the transmissibility functions of all the pairs of sensor nodes are considered, the highest changes are the ones between node 4, placed in the proximity of the damaged cross bar, and nodes 5, 6, and 7, placed on the other side of the bridge, already providing an approximated estimate of the position of the damage. When only the transmissibility functions between pairs of nodes placed on the same side of the damaged cross bar are considered, the localization is correct, as Fig. 6 shows.

Figure 5. Damage indicators values between transmissibility functions of pairs of sensor nodes deployed on the same bar of D4.

(a)

(b)

Figure 6. Damage indicatorsvalues between transmissibility functions of pairs of sensor nodes deployed on the same side of the damaged bar: D5, 27.6 % stiffness reduction (a) and D6, 55.2 % stiffness reduction (b).

VIII. POWER CONSUMPTION AND LATENCY ANALYSIS Table 1 lists the current consumption of the ISMO-2 nodes used in the SHM system. Turning off the radio when it is not needed is the key factor for reduced power consumption. Based on these values, the expected life time and latency of the proposed distributed approach is compared to the one of a monitoring system in which the sensor nodes transmit all the raw acceleration data to the sink node for off-line modal analysis. In this centralized system, each activation consists of accurate MAC-layer time synchronization, sampling, data transmission to the sink node, and sleep till the next activation. Fig. 7 shows the results of the comparison. The expected life time of the two systems was calculated by assuming a network composed of eight sensor nodes organized in a singlehop star topology (as in the real experiments). The proposed distributed approach increases the expected life time by approximately 80 %. The latency of the two systems was calculated by varying the number of sensor nodes in the network. In this case, the proposed distributed approach reduces the latency by approximately 52 %. These results are due to the fact that by processing the acceleration data locally in the sensor nodes, the amount of data that need to be transmitted wirelessly is dramatically reduced compared to the case of offline modal analysis. TABLE I.

CURRENT CONSUMPTION OF THE ISMO-2 NODE (3V SUPPLY VOLTAGE)

Operation Sleep mode (radio off, MCU off, Timer-A on) Idle mode (radio off, MCU on, Timer-A on) External flash memory page reading External flash memory page writing Temperature and humidity acquisition Accelerometer sampling Radio packet transmission Radio listening / packet reception

[mA] 0.002 10.8 11.4 13.4 12.5 12.2 38.4 39.3

IX.

DISCUSSION

The results listed in Section VII were obtained by setting the bins distance db to 0.05 Hz (r = 20 bins/Hz). By setting the sampling frequency to 125 Hz (as in the tests carried out), the duration of the sampling and Goertzel algorithm computation phase is 20 s (N = 2500). The latency of the distributed SHM system could be further reduced by setting the resolution r to smaller values. However, in the tests, this adjustment showed to decrease the accuracy of the damage localization because of the very sparse sampling along the frequency axis, and substantially reduced the reliability of the damage detection procedure. Similarly, the latency of the distributed SHM system could be further reduced by increasing the sampling frequency. The drawback of this approach is that, by reducing the length of the time interval between two consecutive sample acquisitions, the MCU would be able to execute the equations in (4) for a smaller number of bins, thus reducing the width of the range of monitored frequencies. However, this MCU-specific limitation could be easily overcome, but at the expense of a higher power consumption, by using a different wireless platform, i.e. the IMote2 [22], with a larger RAM memory (256 kB) and capability to execute the equations in (4) at a much higher speed (up to 416 MHz). In addition, the duration of the TDMA results sharing phase could be reduced by dividing the sensor nodes into clusters based on the usefulness of the informative content of their transmissibility functions, so that only those pairs of nodes that are actually sensitive to damages in specific locations would share their results. X.

CONCLUSIONS AND FUTURE WORK

WSNs provide flexible and low cost means to accurately diagnose the structural health of civil infrastructures. For this purpose, damage detection and localization represent critical tasks to be performed. Transmitting hundreds of kB of data to the sink node for off-line data analysis would quickly drain the power source of the nodes, reducing the life time of the entire system, and would consistently increase the latency. In this

(b)

(a)

Figure 7. Comparison between the expected life time (a) and latency (b) of the systems (for both systems: measurement period = 30 s, sampling frequency = 125 Hz).

paper, the sensor nodes equipped with a 3-axis accelerometer perform a real-time frequency-domain analysis of the collected data by the embedded Goertzel algorithm. Each node then shares its results inside the network and exploits them to compute transmissibility functions, which ultimately indicate the presence and location of damages. When compared to traditional centralized architectures, the proposed distributed approach reduces the latency by 80 % and increases the system life time by 52 %. One of the feasible solutions to increase the life time of the sensor network is represented by energy scavenging systems such as piezoelectric energy harvesters. This technology is particularly suitable for SHM applications, since vibrations are always present across structures. However, the production of energy by these systems is usually low and is optimal only at specific frequencies of vibrations. In future work, the results of the embedded Goertzel algorithm are going to be used to maximize the production of energy in each node by locally tuning the energy scavenging system to operate at the predominant frequency of vibration. XI.

ACKNOWLEDGEMENTS

This work was funded by the Multidisciplinary Institute of Digitalisation and Energy (MIDE) at Aalto University, Helsinki, Finland. The authors wish to thank Ville Lämsä for his contribution to the realization of the tests.

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