Structures Journal of Intelligent Material Systems and

Journal of Intelligent Material Systems and Structures http://jim.sagepub.com

Structural Health Monitoring Using Modular Wireless Sensors Neal A. Tanner, Jeannette R. Wait, Charles R. Farrar and Hoon Sohn Journal of Intelligent Material Systems and Structures 2003; 14; 43 DOI: 10.1177/1045389X03014001005 The online version of this article can be found at: http://jim.sagepub.com/cgi/content/abstract/14/1/43

Published by: http://www.sagepublications.com

Additional services and information for Journal of Intelligent Material Systems and Structures can be found at: Email Alerts: http://jim.sagepub.com/cgi/alerts Subscriptions: http://jim.sagepub.com/subscriptions Reprints: http://www.sagepub.com/journalsReprints.nav Permissions: http://www.sagepub.com/journalsPermissions.nav

Downloaded from http://jim.sagepub.com at PENNSYLVANIA STATE UNIV on April 17, 2008 © 2003 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution.

Structural Health Monitoring Using Modular Wireless Sensors NEAL A. TANNER,1 JEANNETTE R. WAIT,2 CHARLES R. FARRAR,2

AND

HOON SOHN2,*

1

Department of Mechanical Engineering, Stanford University, Palo Alto, CA 94305, USA 2

ESA-WR, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

ABSTRACT: System integration of an online structural health monitoring module was accomplished by coupling commercially available microelectro-mechanical system sensors and a wireless telemetry unit with damage detection firmware. To showcase the capabilities of the integrated monitoring module, a bolted frame structure was constructed, and the preload in one of the bolted joints was controlled by a piezoelectric stack actuator to simulate gradual deterioration of a bolted connection. Two separate damage detection algorithms were used to classify a joint as damaged or undamaged. First, a statistical process control algorithm was used to monitor the correlation of vibration data from two accelerometers mounted across a joint. Changes in correlation were used to detect damage to the joint. For each joint, data were processed locally on a microprocessor integrated with the wireless module, and the diagnosis result was remotely transmitted to the base monitoring station. Second, a more sophisticated damage detection algorithm combining time series analysis and statistical hypothesis testing was employed using a conventional wired data acquisition system to classify a joint on the demonstration structure as damaged or undamaged. Key Words: structural health monitoring, wireless sensor module, remote sensing, real-time damage detection, statistical process control, statistical pattern recognition, and time series analysis.

INTRODUCTION TRUCTURAL health monitoring (SHM) is the implementation of a damage detection strategy to evaluate and ensure the integrity and safety of aerospace, civil and mechanical engineering infrastructure. Typical damage experienced by this infrastructure might be the development of fatigue cracks, degradation of structural connections, or bearing wear in rotating machinery. However, with the exception of applications to rotating machinery, a review of the literature (Doebling et al., 1998) indicates that there are not many examples of reliable strategies for SHM that are robust enough to be of practical use. The authors feel that this lack of success is, in part, because of the conventional practice taken where the monitoring is accomplished with a limited number of sensors dispersed over a relatively large area of the structure. Such sensing systems provide the spatial resolution that can only detect fairly significant damage, and the use of a few sparsely located sensors to determine the location and degree of damage present is not adequate to fully assess the condition of a structure. Therefore, a large number of sensors need to be instrumented to detect damage or the sensor placement should be focused on formerly identified weak points

S

*Author to whom correspondence should be addressed. E-mail: [email protected]

JOURNAL

OF INTELLIGENT

MATERIAL SYSTEMS

vulnerable to damage because damage is often a local phenomenon. Recent advances in microelectro-mechanical system (MEMS) sensor technologies are making the deployment of a dense array of sensors feasible and affordable at the cost of producing a large amount of data to be transmitted and analyzed. In addition, the initial setup and cabling of the sensors become a very time consuming process as the number of sensors increases. Wireless communication can remedy the cabling problem of the traditional monitoring system and significantly reduce the maintenance cost associated with cabling (Straser, 1998). The deployment of a large number of sensors inevitably produces an increased amount of data to be processed, and the cost and labor associated with data analysis and transmission become prohibitive. Embedded processors allow the computation power to be distributed throughout the sensor units. Then, most of the signal processing and data condensation can be locally performed at each sensor unit, transmitting only essential data to a central monitoring facility and minimizing unnecessary manual data interpretation by analysts. Because one byte of data transmission consumes the same energy as approximately 11,000 cycles of computation in the employed hardware platform, the use of embedded processors prolongs the battery life of the sensor unit

AND

STRUCTURES, Vol. 14—January 2003

1045-389X/03/01 0043–14 $10.00/0 DOI: 10.1177/104538903033641 ß 2003 Sage Publications Downloaded from http://jim.sagepub.com at PENNSYLVANIA STATE UNIV on April 17, 2008 © 2003 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution.

43

44

N. A. TANNER ET AL.

and minimizes the maintenance cost related to battery replacement (TinyOS, 2002). Therefore, the integration of MEMS sensors, wireless communication, and embedded systems creates a new opportunity to develop distributed smart sensor modules that have new configurations and characteristics for cost-effective structural health monitoring. The technical literature is replete with studies that focus on developing either new hardware for the sensing aspect of SHM or new software for the data interrogation portion of the problem. Few studies address both the hardware and software aspects of the SHM problem in an integrated manner. The ultimate goal of this research effort is to develop an online continuous health monitoring system by integrating commercially available MEMS sensors and a wireless telemetry unit with damage detection algorithms previously developed at Los Alamos National Laboratory (LANL). Because each SHM solution must be developed for a specific application, this effort focuses on monitoring bolted joints, as they are pervasive to many engineering systems. For instance, the monitoring of moment resisting welded connections in a steel frame building located in high seismic regions can benefit from the presented monitoring system. However, a significant portion of this technology development, particularly that associated with the development of damage detection algorithms, has generic application to a wide range of SHM applications.

This paper is organized as follows. First, the description of a test structure and test configurations is provided in ‘‘Description of Experiment’’. Next, a hardware aspect of the modular wireless sensor unit is presented in ‘‘Wireless Sensor Module’’. Then, the damage detection algorithms used for this study and applications to the test frame structure are presented in ‘‘Damage Detection Algorithms’’ and ‘‘Diagnosis Results’’, respectively. ‘‘Hardware and Software Issues’’ summarizes issues that must be addressed from the hardware and firmware perspectives of the senor module system if it is to be deployed on real-world structures, and ‘‘Summary’’ concludes this paper with the findings of this study.

DESCRIPTION OF EXPERIMENT A demonstration structure was constructed for use as a laboratory test bed for studying damage in bolted joints and for demonstrating wireless and traditional SHM systems. As shown in Figure 1(a), the demonstration structure was a 56.0 cm 30.5 cm bolted frame structure. The top aluminum plate (56.0 cm 5.0 cm 0.6 cm) was bolted together with aluminum columns (30.5 cm 5.0 cm 0.6 cm) by steel angles (6.35 cm 6.35 cm 0.635 cm). Each plate to angle joint used a single 3.81-cm diameter steel bolt. All mating surfaces were sanded to provide a smoother contact area.

Figure 1. Schematic of the wireless online monitoring system.


Structural Health Monitoring

The columns were mounted to a 1.3-cm-thick aluminum base plate, which was clamped to a table. It should be noted that two different configurations of the experiment were used. The first test configuration (Experiment 1) is set up for the demonstration of the online automated monitoring system using the modular wireless sensor unit, and the second test (Experiment 2) was conducted using the conventional wired data acquisition system to fully demonstrate the capabilities of more sophisticated damage detection algorithms. A piezoelectric (PZT) actuator is a solid state (ceramic) actuator that converts electrical energy directly into mechanical energy (motion) of extremely high resolution. This study used a PZT ring actuator shown in Figure 1 (b) to change the bolt preload of a joint without disturbing the structure. The PZT actuator had a 25-mm outer diameter, a 15-mm inner diameter, a 23-mm length, a maximum force of 10 kN, and a maximum stroke of 15 mm. By placing the actuator underneath the head of one of the bolts and varying the input voltage to the actuator from 200 to þ1000 V, a 4 kN change in the bolt preload was achieved. This design could simulate gradual deterioration of the bolt preload rather than simple discrete damaged or undamaged events. In Experiment 1, the bolt was hand tightened with the actuator in the fully contracted position. The actuator was then set to its fully expanded position providing a nominal tension in the bolt. All other bolts were tightened to 13.6 N m. During the test, the voltage supply to the PZT actuator was manually run through the entire range (þ1000 to 200 V) as fast as possible by hand. This took approximately 2–3 s. For Experiment 2, a function generator was used to control the voltage input to the actuator with a low frequency half sine wave. The PZT actuator was fully expanded at the peak of the half sine wave, and the preload was fully released at the trough of the wave. The same pulse controlling the PZT actuator triggered the start of the data acquisition. For the demonstration of the integrated sensor, RF transmitter and microprocessor system, two Analog Devices MEMS accelerometers were placed across the actuated joint as shown in Figure 1 (b). Both accelerometers, one on the top beam and the other on the side of the column, were positioned to record the horizontal motion near the joint. For the conventional wired test, four commercially available piezoelectric accelerometers with a sensitivity of 10 mv/g were mounted on both joints. One pair of accelerometers were mounted across each joint. The accelerometer on the top plate recorded the vertical motion of the beam while the other accelerometer recorded the horizontal motion of the column. An electromagnetic shaker was used to excite the structure for both experiments. For Experiment 1 the structure was excited horizontally near the base of

45

the right column with a 100 Hz sine wave as shown in Figure 1 (a). The shaker was connected to the right column using a 9.5-mm diameter rod. To avoid the use of large amplifiers and signal generators with the structure, a random signal was generated using MATLABÕ on the PC that output the random signal to a standard set of computer speakers. One speaker was replaced with the shaker that was powered by the small stereo amplifier built into the other speaker. For Experiment 2, the shaker was suspended by elastic cords from a small frame built next to the left side of the test structure to remove undesired feedback forces from the test structure. In addition, an amplified random signal was generated using a commercial signal generator to excite the structure. The random signal had a bandwidth approximately equal 0–4 kHz and was 0.28 V in amplitude.

WIRELESS SENSOR MODULE This paper emphasizes on adapting the SHM system to the limitations of off-the-shelf wireless sensing and data processing hardware because of the focus towards a proof-of-concept rather than designing a field installable product. A wireless sensing system called ‘‘Motes’’ developed at University of California, Berkeley (BSAC, 2002) and commercially available from Crossbow Inc. (Crossbow, 2002) was chosen for this study because of their ready-made wireless communication capabilities. A mote consists of two circuit boards. The first one integrates a microprocessor, analog-todigital converter (ADC), and wireless transmitter. The second one is the sensor board. Each component of the sensor unit is described in this section. Accelerometers Two sensor boards were obtained from UC Berkeley that contained ADXL202 accelerometers. The ADXL202 is a dual axis, þ/ 2 g MEMS accelerometer commercially available from Analog Devices (Analog Devices, 1995). The sensor board’s original configuration only allowed for a bandwidth of 50 Hz, but it was modified by changing capacitors to increase the bandwidth of the accelerometer to 1 kHz. Custom cables were made to connect two accelerometer boards to a single processing board to isolate the accelerometers from the dynamics of the original cantilever connection between the main processing and sensor boards (Figure 3). In Figure 3, only one accelerometer board was connected to the main processing board. The processing board had an identical sensor I/O interface slot on the other side of the board that was not shown in the picture, and the other accelerometer was connected through this additional slot to the processing board. A simple crossover in one of the cables allowed the two


46

N. A. TANNER ET AL.

accelerometers to be accessed through separate channels on the ADC. In this manner, a single processing board could collect data from a pair of accelerometers (for up to a total of 4 channels). In the experimental study presented in Figure 1 (a), the two accelerometers were attached near one of the bolted connections of the test structure as shown in Figure 1 (b), and the time history data from the accelerometers were collected and processed at the processing board (Figure 1 (c)) connected by the aforementioned custom-made cables. In Figure 1 (d), a second processing board situated in the programming bay remotely received broadcast data from the instrumented joint and relayed it to the PC acting as the base monitoring station. Finally, the damage diagnosis results were displayed on the screen of the PC (Figure 1 (f )). Processing Board The core of the processor board is a 4 MHz ATMEL AVR 90LS8535 microprocessor with 8 kB of flash programmable memory and 512 B of RAM (ATEML Corporation, 1984). A 10-bit ADC is included in the microprocessor. The ADC is capable of sampling 8 channels but only by sequentially multiplexing them. The processor board also contains three light emitting diode (LED) lights (red, green, and yellow) and a short range 916 MHz radio transmitter. The processor board mounted on a programming bay is shown in Figure 2. The physical size of this main processing board is approximately 2.5 cm 4.0 cm, and this board mates directly with the sensor board, which is a similar size to the processing board, using the I/O interface slot shown in the figure. The ADC itself can handle sampling rates of up to 4 kHz, but the actual sampling rate was dictated by

either the radio bandwidth of transmitting raw data or the processing power of the microprocessor. It turned out that the achievable sampling rate typically ranged between 256 Hz and 1 kHz. Because the ADC multiplexes multiple channels onto a single actual converter, two channels could not be sampled simultaneously. The minimum time offset between samples from two channels was on the order of 100 ms. In addition, the system had a full-scale range of þ/ 2 g with a resolution of 17 mg and a sensitivity of 312 mv/g. Both the accelerometers and the ADC showed considerable DC bias and required calibration for each combination of particular accelerometers and a ADC. Programming Bay Damage detection algorithms, which will be discussed later on, were coded in the C programming language on a PC and then compiled into a binary image file that was downloaded into the flash program memory on the processing board using a parallel port connection. After the completion of the damage detection algorithm encoding, the PC was used only for displaying the damage diagnosis results. All computation necessary for damage diagnosis was accomplished on the main processing board. The firmware download was accomplished by placing the processing board in a programming bay connected to a PC parallel port (Figure 2). The programming bay also has a serial port to transfer processed data from the processing board back to the PC. Operation System TinyOS (2002) is an operating system developed at UC Berkeley for small wireless devices like the one used in

Figure 2. Processing board mounted on programming bay.



this study. As the name of this operating system indicates, this operation system is specifically designed to provide support for deeply embedded systems that require concurrency intensive operations while constrained by minimal memory and power resources. For instance, a 4 MHz 8 bit microcontroller with 512 B RAM and 8 kB ROM is used in the mote system and TinyOS occupies only 256 B RAM and 4 kB ROM. This operating system is built on top of the C programming language and provides the programmer with prepackaged functionality for interfacing with hardware components such as the ADC. TinyOS also allows for configuring a group of sensors into a network for peer-to-peer communication and message relaying back to a base station. The data processing can be written in C with minor modifications to incorporate it within TinyOS. All sensor programming for this study was done within the confines of TinyOS. System Power In this study, two standard AA batteries are used to power the wireless sensor module (Figure 3). If a portable power source such as a battery is selected, an effective power usage strategy is critical to maximize the unit’s operational life before replacing the batteries. In fact, power consumption is one of the most difficult resource constraints to meet in the context of wireless embedded sensors. To minimize power consumption, the main microprocessor and the wireless transmitter operates in two modes: active and sleep. Each component is capable of being placed in sleep mode where power usage is significantly reduced. The low power ATMEL microcontroller, responsible for overall unit operation, is always kept in its active mode. Once data are collected and processed locally, the wireless telemetry component is awakened from its sleep mode to transmit only the diagnosis results (red, green and yellow LEDs) to the base station. This wireless transmitter represents the most power demanding component of the wireless sensing unit design. As a

47

result, the importance of locally processing the collected data with the on-board microprocessor before transmission is underscored again. For instance, one byte of data transmission in the Mote system uses the same energy as approximately 11000 cycles of computation. Wireless Transmitter The vast majority of wireless devices such as IEEE 802.11 cards, Bluetooth chipsets, the BWRC PicoRadio and cellular phone include a dedicated radio controller that handles all communication protocol processing (Hill, 2000). However, the Mote takes an alternative approach to the protocol processor based approach by time-sharing a single execution engine across application and protocol processing. In this virtual parallelism, the interface between wireless protocol and application processing is purely in software, and this parallelism allows for rich interfaces to be constructed that can give the application tight control over the communication protocol. RF Monolithic TR 1000 transceiver (RF Monolithics, 1999) is used to operate the radio, and the transmission radius is externally specified to range from centimeters to meters. Many sensor applications also require time correlated data and therefore need an underlying time synchronization mechanism, which is another major design constraint for wireless sensors. However, an advantage of the damage detection algorithms presented in ‘‘Damage Detection Algorithms’’ is that they perform data interrogation locally within an individual sensor and the sensor reading from one sensor unit does not need to be time synchronized with other sensors.

DAMAGE DETECTION ALGORITHMS The primary goal of SHM is to ascertain the existence of damage within a system being monitored. Particularly, vibration-based damage detection techniques

Figure 3. Custom cable connection between the accelerometer and processing boards.


48

N. A. TANNER ET AL.

assume that changes of the structure’s integrity affect characteristics of the measured vibration signals that can be detected with the developed sensing system. Many current approaches to this problem, however, involve methods that leave much to the interpretation of analysts. These methods may enable a trained eye to discern and locate damage, but are not easily automated or objective. Therefore, as part of the online intelligent sensor module development, damage detection algorithms were developed to automate a decision-making procedure for SHM applications. Two specific damage detection algorithms were developed to classify a joint of the test structure as damaged or undamaged. For the first algorithm tested, a simple statistical process control was implemented and embedded into the main processing board of the wireless sensor module. This online damage detection algorithm was then used to continuously monitor the loss of preload in the bolted connection. The second damage detection algorithm was based on a combination of time series analysis and statistical hypothesis testing. Because of the complexity of the second algorithm, this approach was demonstrated using a conventional data acquisition system rather than the wireless sensor module. Statistical Process Control Statistical process control is a commonly used tool for achieving the stability and repetition of manufacturing processing by monitoring its variations such as changes of the process mean or variance (Montgomery, 1997). In this study, statistical process control is adopted to detect anomalies from vibration signals for SHM applications. First, the upper and lower control limits of the statistical process control are set based upon data measured during the normal conditions of the process. Then, these limits are used to continuously monitor variation of the process. Once the measured data or features extracted from the raw data cross the control limits, the monitoring system is triggered to send out a warning signal. In the present experimental example, the statistical process control was implemented to monitor variation of the bolt preload. The specific feature used for the statistical process control was the cross-correlation coefficient between the time responses measured from the two accelerometers mounted across a joint; Pm n ¼

i¼1

xi yi m

ð1Þ

where xi and yi are the acceleration responses at the ith time point from the two accelerometers, and m is the packet size, which is set to 32 in this example. n is the cross-correlation coefficient obtained from the nth packet. The lack of sufficient memory to save all of

the cross-correlation values for an entire time history forced the use of ‘‘on-the-fly’’ algorithms to compute the mean and variance. This recursive computation of the mean and variance presented at Equations (2) and (3) reduced the required memory size at the price of significantly decreasing the attainable sampling rate. Because of this use of recursive algorithms and the inherent limitation of the available processor power, the sampling rate was limited to 256 Hz. TRAINING PHASE Once n had been calculated for the nth packet of data, it was passed on to a training algorithm that continuously updated the sample mean n and variance n2 of n as follows:

nþ1

2 nþ1 ¼ n2

n nþ1 ¼ n þ nþ1 nþ1

ð2Þ

2 n1 nþ1 þ 2n þ nþ1 2nþ1 n n n ð3Þ

The training was performed when the structure was in a known ‘‘healthy’’ condition, and data from the healthy condition were used to establish the upper and lower bounds of the statistical process control (Montgomery, 1997). The control limits were set at 1:5 in this example. The computation of the control bounds was originally performed on the main processing board. However, because of time, memory and processing constraints in calculating the variance, the computation of the control bounds was temporarily off-loaded onto the PC. The processing shift was accomplished by broadcasting the values of the cross-correlation coefficient to the base station physically connected to the PC. After the bounds were calculated on the PC, they were hard-coded back onto the main processing chip using the serial connection. It should be possible to refine the calculation of the mean and variance such that setting the bounds for the cross-correlation coefficient can be moved back onto the processing board, allowing for the consolidation of separate training and monitoring programs into a single autonomous monitoring system. MONITORING PHASE In the monitoring phase, the cross-correlation coefficients were calculated from newly measured acceleration time signals in exactly the same manner as in the training phase. However, instead of computing the control limits, the cross-correlation coefficients from each packet were simply checked against the previously determined control limits to determine if any of the cross-correlation values was an outlier. Here, an outlier in a data set is an observation that is surprisingly different from the rest



of the data and therefore is believed to be generated by an alternative mechanism (Barnett and Lewis, 1994). When an outlier was detected, its occurrence was signaled by a blinking yellow LED. In addition, the outlier was registered in a binary variable Tn . Tn took a value of one when there was an outlier and was set to zero when the current cross-correlation value was within the control limits. However, it should be noted that the occurrence of a single outlier does not necessarily indicate damage. For instance, if the control bounds were set in accordance with a 99% confidence interval of the data distribution obtained from the normal condition, 1% of data from the healthy condition would still be outside the control limits. Therefore, another step of damage classification is necessary to relate the frequency of outliers to the actual occurrence of damage. For this purpose, a damage measure Sn was defined as: Sn ¼ Sn1 W1 þ Tn W2 ( 0 if n is not an outlier: Tn ¼ 1 if n is an outlier:

ð4Þ ð5Þ

where Tn is a binary variable representing if n is an outlier or not. W1 and W2 are the weighting factors for Sn1 and Tn , respectively. Equation (4) shows that the value of the current damage measure Sn is a weighted summation of the one step previous damage measure Sn1 and the current outlier indicator Tn . The values of W1 and W2 were determined empirically in simulation to achieve the proper response of the monitoring system to damage while balancing the range and precision limits of fixed-point integer arithmetic. Taking into account these constraints, W1 and W2 were set to 0.96 and 40 in this example. To illustrate how the damage measure Sn is related to the outlier indicator Tn , two different scenarios for outlier occurrence are investigated. First, an evenly

49

spaced occurrence of outliers is considered. Figure 4(a) shows the occurrence of one outlier out of every 12 measured correlation coefficients n , and Figure 4(b) displays the characteristics of the associated damage measure Sn . Because of the scaling required by the integer fixed-point arithmetic, Sn oscillated about a value 10 times the percentage of evenly spaced outliers. That is, the frequency of the outlier occurrence was about 8.3% (1/12) of the measured n values, and Sn fluctuated around the value of 83, which is 10 times of this percentage (¼ 8.3% 10). In the current monitoring system, joint damage was declared by lighting the red LED and transmitting a warning message back to the base station when Sn exceeded 100. In this setting, evenly spaced outliers less frequent than every 12 crosscorrelation coefficients did not trigger the red LED light. Figure 5(a) shows the other scenario of outlier occurrence. Three successive outliers in Figure 5(a) would cause Sn in Figure 5(b) to exceed 100, signaling the red LED. The green LED came on only when there was no outlier indicating the test structure was in a healthy state. Sequential Probability Ratio Test In the previous section, many design aspects of the statistical process control were constrained by the computation power and memory limitations of the processing board. Because of these limitations, the damage detection algorithm presented in the previous section was implemented in a somewhat ad hoc manner without being able to fully highlight the data interrogation aspect of SHM. In this section, a more statistically rigorous damage detection algorithm, which is based on combination of time series analysis and statistical hypothesis testing, is presented. First, damage-sensitive features are extracted from the measured acceleration response using a time series analysis

Figure 4. An outlier indicator for an outlier detected every 12th window and resulting plot of a damage measure.


50

N. A. TANNER ET AL.

Figure 5. An outlier indicator for three outliers in succession and resulting plot of a damage measure.

technique called autoregressive (AR) and autoregressive with exogenous inputs (ARX) (AR-ARX) model. Then, one branch of statistical hypothesis tests called sequential probability ratio test (SPRT) is applied to the aforementioned features to classify the current state of the structure to either a damaged or undamaged state. A brief summary of the combined AR-ARX and SPRT algorithm is presented in this section for the completeness of the paper. The details of AR-ARX and SPRT techniques can be found in Sohn and Farrar (2001) and Sohn et al. (2002a), respectively. Because of the complexity of this damage detection algorithm, the applicability of the algorithm to damage detection is demonstrated using a conventional wired data acquisition system rather than the wireless sensor module. FEATURE EXTRACTION USING AR-ARX TIME PREDICTION MODEL A linear prediction model combining AR and ARX models is employed to extract features for the subsequent SPRT analysis. First, all time signals are normalized prior to fitting an AR model by subtracting its mean and dividing by the standard deviation. Then, an AR(r) model with r AR terms is constructed for a given time signal xðtÞ (Sohn and Farrar, 2001): xðtÞ ¼

r X

xj xðt jÞ þ ex ðtÞ

ð6Þ

j¼1

In this example, r is set to 30. Assuming that the error between the measurement and the prediction obtained by the AR model [ex ðtÞ in Equation (6)] is mainly caused by not incorporating the unknown external input into the model, an ARX model is employed to reconstruct the input/output relationship between ex ðtÞ and xðtÞ; xðtÞ ¼

p X i¼1

i xðt i Þ þ

q X j¼1

j ex ðt j Þ þ "x ðtÞ

ð7Þ

where "x ðtÞ is the residual error after fitting the ARX( p,q) model to ex ðtÞ and xðtÞ pair. Ljung (1999) suggests keeping the sum of p and q smaller than r (p þ q r). Although the p and q values of the ARX model are set rather arbitrarily, similar results are obtained for different combinations of p and q values as long as the sum of p and q is kept smaller than r. In this example, both p and q are set to 5. DAMAGE CLASSIFICATION USING A SEQUENTIAL PROBABILITY RATIO TEST In the previous section, the AR-ARX model is constructed using the time signal from the baseline structure. When a new time series yðtÞ is obtained from an unknown condition of the structure, the prediction or residual error becomes: "y ðtÞ ¼ yðtÞ

p X

i yðt iÞ

i¼1

q X

j ey ðt jÞ

ð8Þ

j¼1

where "y ðtÞ is the residual error of yðtÞ obtained using the previously estimated AR-ARX model. ey ðtÞ is computed in a similar way to ex ðtÞ in Equation (6). When a new time signal is obtained from a damaged structure and fed to the AR-ARX model, the time prediction model trained with the undamaged cases will not properly predict the new time series. Therefore, the standard deviation of the residual error "y ðtÞ is expected to increase compared to that of the baseline residual error "x ðtÞ. Based on this premise, a simple hypothesis test discriminating two hypotheses is constructed using the standard deviation of the residual errors as the parameter in question (Sohn et al., 2002a): Ho : ð"y Þ o ,

H1 : ð"y Þ 1 ,

0 < o < 1 < 1 ð9Þ

When the standard deviation of the residual error ð"y Þ is less than a user specified lower bound o , the system in


51


question is considered undamaged. On the other hand, when ð"y Þ becomes larger than the other user specified upper bound 1 , the system is suspected to be damaged. Note that the selection of o and 1 is structuredependent and it might be necessary to use signals from both undamaged and damage cases to accurately establish these two decision boundaries. A SPRT starts with observing a sequence of the residual errors, f"y ðiÞg ði ¼ 1, 2, . . .Þ. Define this accumulated data set at stage n as En ¼ ½"y ð1Þ, . . . , "y ðnÞ. The goal of a statistical inference is to reveal the probability model of En , which is assumed to be at least partially unknown. When the statistical inference is cast as a parametric problem, the functional form of En is assumed known and the statistical inference poses some questions regarding the parameters of the probability model. For instance, if f"y ðiÞg are independent and identically distributed normal variables, one may pose some statistical test about the mean and/or the variance of this normal distribution. A sequential test is one of the simplest tests for such a statistical inference where the number of samples required before reaching a decision is not determined in advance. An advantage of the sequential test is that, on average, a smaller number of observations are needed to make a decision compared to the conventional fixed-sample size test. For the well-established fixedsampling test, the sample size n is fixed, and an upper bound on the Type I error is prespecified. Then, an optimal fixed-sample test is selected by minimizing the probability of Type II error. Here, Type I error arises if Ho is rejected when in fact it is true. Type II error arises if Ho is accepted when it is false. On the other hand, a sequential test specifies upper bounds on the probabilities of Types I and II errors, and minimizes the sample number required to make a decision. Among various valid sequential tests, it can be proved that the SPRT minimizes on average the sample size required to obtain a correction making it an optimal sequential test (Ghosh, 1970). Because of the sensitivity of the SPRT to signal disturbance, the SPRT has been applied for the surveillance of nuclear power plant components (Humenik and Gross, 1990). For the hypothesis test in Equation (9), a SPRT, S(b,a), makes three distinctive decision at stage n (Ghosh, 1970); Accept Ho if Zn b Reject Ho if Zn a

ð10Þ

Continue observing data if b Zn a where the transformed random variable Zn is the natural logarithm of the probability ratio at stage n; Zn ¼ ln

f ðEn jH1 Þ f ðEn j1 Þ ¼ ln ¼ f ðEn jHo Þ f ðEn jo Þ

for n 1

ð11Þ

where f ðEn jHo Þ or f ðEn jo Þ is the conditional probability of observing the accumulated data set En given the assumption that the null hypotheses is true. f ðEn jH1 Þ or f ðEn j1 Þ is defined in a similar fashion. Without any loss of generality, Zn is defined zero when f ðEn j 1 Þ¼ f ðEn j o Þ ¼ 0. b and a are the two stopping bounds for accepting and rejecting Ho , respectively, and they can be estimated by the following Wald approximations (Wald, 1947); b ﬃ ln

1

and

a ﬃ ln

1

ð12Þ

where and the predetermined upper limits for Types I and II errors, respectively. When implementing the SPRT, a trade-off must be considered before assigning values for and . When there is a large penalty associated with false positive alarms (for example, alarms that shut down traffic over a bridge), it is desirable to keep smaller than . On the other hand, for safety critical systems such as nuclear power plants, one might be more willing to tolerate a false positive alarm to have a higher degree of safety assurance. In this case, is often P specified larger than . If Zn ¼ ni¼1 zi , the modified observations fzi gði ¼ 1, 2, . . .Þ are defined as follows: Zn ¼

n X

zi ,

i¼1

z1 ¼ ln

f ðE1 j1 Þ f ðE1 jo Þ

and ð13Þ

f ðEi j1 Þf ðEi1 jo Þ zi ¼ ln f ðEi jo Þf ðEi1 j1 Þ Assuming that En has a normal distribution with mean and standard deviation , zi can be related to "y ðiÞ: 1 1 zi ¼ ðo2 12 Þð"y ðiÞ Þ2 ln o 2

ð14Þ

In a graphical representation of the SPRT S(b,a), Zn , which is the cumulative sum of the transformed variable zi , is continuously plotted against the two stopping bounds b and a. A Zi value less than a is indicative of acceptance of the Ho hypothesis, while a Zi value greater than b indicates an acceptance of the H1 hypothesis. This original form of the SPRT assumes that the extracted feature has a Gaussian distribution. The normality assumption, however, may place misleading constrain on the tails of the distribution. As the problem of damage detection specifically focused attention on the tails, the assumption of normality is likely to lead the analysis astray. To overcome this difficulty, the performance of the SPRT can be improved by integrating the extreme value statistics EVS, which specifically models behavior in the tails of the distribution of interest, into the SPRT (Sohn et al., 2002a). However, the EVS is not applied in


52

N. A. TANNER ET AL.

this study because the feature distribution in this experiment turned out to be close to a normal distribution.

DIAGNOSIS RESULTS Application of Statistical Process Control Using the cross-correlation coefficient approach, remote SHM was successfully demonstrated on the laboratory demonstration structure. With the bolt in the fully tight condition, baseline data were collected to establish the control limits of the statistical process control. In this configuration, the training phase of the program indicated that the cross-correlation coefficient across the actuated joint had a sample mean of 2.37 and a standard deviation of 9.11 resulting in lower and upper bounds of 16.03 and þ11.29, respectively. The monitoring program was started with the actuator at full voltage, representing the healthy structure. When the voltage to the actuator was decreased to 200 V, the monitoring program detected the newly introduced damage and signaled it accordingly. The yellow LED on the processing board flashed repeatedly as outliers were detected, and after a few seconds the red LED came on, indicating that the on-board statistical process control had successfully detected the simulated failure of the joint. Upon reapplication of the voltage to the actuator, the monitoring program displayed the return to the healthy condition of the joint by flashing the green LED. A sample statistical process control chart showing both healthy and damaged conditions as well as the threshold values used for damage detection is shown in Figure 6.

Application of Sequential Probability Ratio Test The combined AR-ARX/SPRT algorithm was demonstrated using data measured from the conventional wired data acquisition system. Four accelerometers were numbered from the accelerometer on the left column of the test structure to the one on the right column as Channels 1–4. The left and right joints of the test structure were labeled as Joints 1 and 2, respectively. During the training phase, the actuator voltage was set to þ1000 V to simulate the tight condition of the bolt, and the gradual loss of preload in Joint 1 was simulated during the monitoring phase. The acceleration time histories from the two joints were compared for this analysis. First, the raw time responses are visually inspected. Figure 7(a) shows the acceleration time histories from Joint 1 and the half sine wave that controls the PZT actuator and triggers the start of the data acquisition. The change in the acceleration time histories of Channels 1 and 2 caused by the loss of preload in Joint 1 is clearly shown in the figure. As the bolt preload decreased, the mean of the acceleration response moved up on the plot, signifying loosening of Joint 1. On the other hand, there were no noticeable changes in the response of Channels 3 and 4 near Joint 2 as seen in Figure 7(b). It should be noted that, although the damage occurrence in this example was identifiable by visual observation of the raw time histories, there are other cases where changes caused by damage are subtle. Furthermore, the transition of subjective visual interpretation to an objective automated damage classification procedure is often not a trivial matter. This

Figure 6. Statistical process control for monitoring variation of the preload in a bolted connection.



53

Figure 7. Waveform input to the ring actuator and acceleration time response at damaged/undamaged joints.

Figure 8. Sequential probability ratio test applied to acceleration time series measured from damaged/undamaged joints.

automation of the decision-making procedure for online continuous monitoring is attempted using the SPRT procedure described in ‘‘Sequential Probability Ratio Test’’. Figure 8 reports the results of applying the SPRT to the previously shown acceleration time signals. Instead of analyzing individual signals, the point-bypoint differences between the two accelerometers near each joint are used as inputs to the AR-ARX model. For instance, if x1 ðtÞ and x2 ðtÞ denote the responses from Channels 1 and 2, xðtÞ ¼ x1 ðtÞ x2 ðtÞ is used as an input to the AR-ARX model. In Figure 8, the Zn statistics defined in Equation (13) is plotted against the two decision limits, a and b in Equation (10). The monitoring system indicates damage when Zn moves across the upper decision boundary, or it concludes that there is no damage if Zn crosses the lower decision boundary.

As long as Zn stays within these two boundaries, the monitoring system continues observing new measurements. For this experiment, o and 1 in Equation (9) were set to 2.8ð"x Þ and 3.0ð"x Þ, respectively, based on time series from both undamaged and damaged cases. Here, ð"x Þ is the standard deviation of the baseline prediction errors. When the SPRT were applied to the acceleration response from the damaged Joint 1, the SPRT indicated the loosening of the bolted joint only after monitoring 19 time points as shown in Figure 8(a). When the SPRT was applied to the time signals from the other undamaged joint in Figure 8(b), the Z-statistic also crossed the lower bound very quickly inferring that the joint was intact. The main advantage of using the SPRT is that it continuously performs the hypothesis test


54

N. A. TANNER ET AL.

point-by-point whereas a conventional hypothesis test conducts the hypothesis testing after the completion of the entire time history measurement. This sequential nature of the SPRT greatly reduces the amount of data that has to be processed and results in much faster decision-making.

HARDWARE AND SOFTWARE ISSUES Ideally, an integrated approach to the development of a SHM solution would incorporate a significant numerical modeling effort. This effort would be used to simulate anticipated damage in the system and to simulate the response of the undamaged and damaged structures to their postulated dynamic inputs. Such modeling would be used to define the required properties of the sensing system (e.g. bandwidth, resolution, sensor numbers and location) and properties of the data processing hardware (e.g. power, memory and processor speed requirements). Data from these simulations would be used to demonstrate that the postulated damage produces changes in the dynamic response that can be detected by the sensing system and identified by the data interrogation software. The assumption being made here is that, for most ‘‘real-world’’ SHM applications, data will not be available from the damaged system during the design phase of the SHM hardware and software. Because of the approach of using off-the-shelf hardware, several very serious issues arose that greatly complicated or impeded the development of the remote SHM system. These limitations are summarized below. The first of these limitations was related to the limited range and resolution of the sensing system itself. The range was limited by the accelerometer while the resolution was limited by only having a 10-bit ADC. The full resolution of the ADC was not used because the voltage range of the sensors and the ADC did not match exactly. This mismatch resulted in a narrower effective dynamic range and lower resolutions of the sensors. In addition, the excitation level of the shaker was adjusted so that relative motions from a loosened joint could be fit into the effective dynamic range without overloading the sensors. Another limitation of the actual sensing system was the inability to simultaneously sample multiple channels for calculating the cross-correlation coefficient. Sampling the two sensors sequentially caused the correlation to break down if there was any high frequency content in the signals. Most of these issues could be easily remedied by selecting sensors and an ADC that were better suited to this application. Because of the small size of the programmable flash memory, any programs that contained floating-point calculations would not fit into the flash memory. Having to perform all processing in integer fixed-point arithmetic led to trade-offs between range and precision

of calculations. This problem was the source of difficulty in calculating the mean and variance of the features on the processing board. Similar but less drastic complications and inaccuracies were found throughout the programs. The extremely small amount of RAM available on the processing board prevented the storage of accumulated data. This memory limitation was dealt with by implementing the damage detection algorithm in a recursive manner at the cost of consuming additional processing time, and a lower sampling rate. Processing power was another major limiting factor in improving the sampling rate and the transmission rate of the acquired data. For the present experiment, the frequency content of the signal was kept very low through the design of the structure and its excitation. However, most of the structural damage is expected to manifest itself at much higher frequencies than this system can currently resolve. The employment of a microprocessor with much higher sampling rates would make the proposed modular wireless sensor more applicable to generalized structures and excitations. Additional processing power would also enable the incorporation of more sophisticated damage detection algorithms such as the SPRT into the sensor module. The processing limitations encountered are specific to the current hardware and are not inherent for other commercially available hardware. In fact, Crossbow Inc. (2002) is currently fabricating an updated version of the Mote system, and the development of a wireless sensor unit with more advanced computational core such as Motorola MPC555 PowerPC can be also found in Lynch (2002). From the perspective of damage identification software, one of the main issues is to develop a robust damage detection algorithm to minimize false-positive and false-negative indications of damage. Features used to identify damage in a structure are often also sensitive to sources of variability other than damage such as operational and environmental variations of the system. The statistical process control employed in the first experiment is not immune to such false alarms, which might be triggered by simply varying the type and location of excitation inputs to the structure. A process to discern signal changes caused by damage from those caused by other natural variations of the system is called data normalization. Although the applicability of the second SPRT algorithm to data normalization is demonstrated in (Sohn et al., 2002b) this data normalization feature of the SPRT was not fully illustrated in this study. To facilitate data normalization, the authors are further investigating the employment of a local excitation capability to avoid the reliance on ambient vibration excitation sources that typically have considerable variability associated with them. Although the combination of the AR-ARX and SPRT algorithms was consistent with the correct



classification of the joint damage, the algorithm is too large to be embedded into the current wireless sensor module. This limitation was the reason why a traditional data acquisition system was used to demonstrate the AR-ARX/SPRT algorithm. This constraint can be fixed by implementing a new chip that has greater processor power and a much larger memory capacity. It is also worthwhile to discuss the establishment issue of the o and 1 values in the SPRT. Obviously the more data are available for establishing o and 1 , the better diagnosis results are obtained. However there is no minimum training size requirement for the SPRT. One can even assign initial values of o and 1 based on engineering judgments and experiences, and subsequently adjust these values as more data become available. Alternatively, the probability density function of the extracted feature can be approximated using either parameter or nonparametric approximation techniques (Silverman, 1998). Then, the o and 1 values associated with a certain confidence interval can be assigned. This density estimation based method seems most attractive for the development of an automated monitoring system. Further research is in order to automate the establishment of these bounds.

SUMMARY The main goal of this study was to develop and demonstrate an integrated wireless structural health monitoring system for structural joints whereby the damage detection algorithms were seamlessly integrated with commercially available sensors, microprocessors and wireless transmitters. The monitoring system was applied to a bolted frame structure specifically designed such that preload in a bolted connection could be gradually changed by using a piezoelectric ring actuator. Within the hardware limitations of the off-the-shelf components, the monitoring system was shown to successfully identify changes in the preload of a bolted connection. This damage was detected by implementing a simplified statistical pattern recognition algorithm onto the local processor of the wireless sensor module and by applying the algorithm to acceleration time histories measured from the structure. In addition, a conventional data acquisition system was used to implement a more statistically rigorous damage detection algorithm. Both damage detection algorithms were successful in detecting and locating a damaged bolted joint. Now that it has been shown that structural health monitoring can be implemented using on-board processing of data from wireless sensors, the next logical step is to develop a set of hardware tailored to fit the needs of ‘‘real-world’’ structural health monitoring applications

55

such as the moment-resisting connections in steel frame structures. The technology is readily available to design such a monitoring system with significantly greater capabilities in data acquisition, processing, and storage. Removing the barriers created by the current hardware components will open up tremendous opportunities for further development of wireless structural health monitoring systems.

NOMENCLATURE The following symbols are used in this paper: Ho ¼ null hypothesis H1 ¼ alternative hypothesis Sn ¼ damage measure at stage n Tn ¼ binary variable signaling occurrence of an outlier at stage n Zn ¼ Z-statistic, natural logarithm of probability ratio at stage n ex ðtÞ ¼ error between the training phase acceleration measurement and AR prediction ey ðtÞ ¼ error between the testing phase acceleration measurement and AR prediction i and j ¼ positive integer indices m ¼ packet size n ¼ sample number p ¼ number of AR terms in an ARX model q ¼ number of moving-average terms in an ARX model r ¼ number of AR terms in an AR model t ¼ time variable xðtÞ ¼ training phase time history at time t xi ¼ the ith time history point from acceleration 1 yðtÞ ¼ monitoring phase time history at time t yi ¼ the ith time history point from acceleration 2 ¼ type I error i ¼ the ith AR coefficient in an ARX model ¼ type II error i ¼ the ith moving-average coefficient in an ARX model "x ðtÞ ¼ residual error corresponding to the training phase signal xðtÞ "y ðtÞ ¼ residual error corresponding to the monitoring phase signal yðtÞ xj ¼ the jth AR coefficient in an AR model corresponding to xðtÞ ¼ sample mean in statistical process control n ¼ sample mean at the nth packet computed in a recursive manner ¼ standard deviation in statistical process control n ¼ standard deviation at the nth packet computed in a recursive manner o ¼ user defined SPRT lower bound 1 ¼ user defined SPRT upper bound


56

N. A. TANNER ET AL.

ð"x Þ ¼ standard deviation of "x ðtÞ ð"y Þ ¼ standard deviation of "y ðtÞ n ¼ cross-correlation coefficient obtained from the nth packet

ACKNOWLEDGMENTS Funding for this project was provided by the Department of Energy through the internal funding program at Los Alamos National Laboratory known as Laboratory Directed Research and Development. The first author, Neal A. Tanner, was supported by a fellowship from the Fannie and John Hertz Foundation. The authors would also like to acknowledge Jason Hill in the Computer Science Department at the University of California, Berkeley for his consultation regarding programming of the motes. Finally, the authors acknowledge the contribution of Crossbow, Inc. in San Jose, CA for providing the Mote hardware.

REFERENCES ‘‘Analog Devices: World Leader in High Performance Signal Processing Solutions,’’ 1995. . (Oct. 16, 2002). ‘‘ATEML Corporation,’’ 1984. . (Oct. 16, 2002). Barnett, V. and Lewis, T. 1994. Outliers in Statistical Data, Third Edition, John Wiley and Sons, Inc., Chichester, UK. ‘‘BSAC: Berkeley Sensor and Actuator Center,’’ 2002. . (Oct. 16, 2002). ‘‘Crossbow: Smarter Sensors in Silicon,’’ 2002. . (Oct. 16, 2002).

Doebling, S. W., Farrar, C. R., Prime, M. B. and Shevitz, D. W. 1998. ‘‘A Summary Review of Vibration-Based Damage Identification Methods,’’ Shock and Vibration Digest, 30(2):91–105. Ghosh, B. K. 1970. Sequential Tests of Statistical Hypotheses, Addison-Wesley, Menlo Park, CA. Hill, J. 2000. A Software Architecture Supporting Networked Sensors, Master Thesis, Department of Electrical Engineering & Computer Sciences, University of California, Berkeley, CA. Humenik, K. and Gross, K. C. 1990. Sequential Probability Ratio Tests for Reactor Signal Validation and Sensor Surveillance Applications,’’ Nuclear Science and Engineering, 105:383–390. Ljung, L. 1999. System Identifications: Theory for the User, Prentice Hall, Englewood Cliffs, NJ. Lynch, J. P., Sundararajan, A., Law, K. H., Kiremidjian, A. S., Kenny, T. and Carryer, E. 2002. ‘‘Computational Core Design of a Wireless Structural Health Moniotirng System,’’ The Second International Conference on Advances in Structural Engineering and Mechanics, Pusan, South Korea, August 21–23. Montgomery, D. C. 1997. Introduction to Statistical Quality Control, John Wiley & Sons, Inc., New York, NY. ‘‘RF Monolithics:,’’ 1999. . (Oct. 21, 2002). Silverman, B. W. 1998. Density Estimation for Statistics and Data Analysis, Chapman & Hall/CRC, New York, NY. Straser, E. G. 1998. A Modular, Wireless Damage Monitoring System for Structures, Ph.D. Thesis, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA. Sohn, H. and Farrar, C. R. 2001. ‘‘Damage Diagnosis Using Time Series Analysis of Vibration Signals,’’ Journal of Smart Materials and Structures, 10:446–451. Sohn, H., Allen, D. W., Worden, K. and Farrar, C. R. 2002a. ‘‘Statistical Damage Classification Using Sequential Probability Ratio Tests,’’ An International Journal of Structural Health Monitoring (in print). Sohn, H., Worden, K. and Farrar, C. R. 2002b.‘‘Statistical Damage Classification Under Changing Environmental and Operational Conditions,’’ Journal of Intelligent Materials Systems and Structures (in print). ‘‘TinyOS: A Component-based OS for the Networked Sensor Regime,’’ 2002. . (Oct. 15, 2002). Wald, A. 1947. Sequential Analysis, John Wiley and Sons, New York, NY.


Structures Journal of Intelligent Material Systems and - CiteSeerX

Structures Journal of Intelligent Material Systems and - CiteSeerX

Suggest Documents