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DAMAGE DETECTION OF THE Z24 BRIDGE USING CONTROL CHARTS
Mechanical Systems and Signal Processing (2003) 17(1), 163–170 doi:10.1006/mssp.2002.1555, available online at http://www.idealibrary.com on
DAMAGE DETECTION OF THE Z24 BRIDGE USING CONTROL CHARTS Jyrki Kullaa Mechanical and Production Engineering, Helsinki Polytechnic, P.O. Box 4021, FIN-00099 City of Helsinki, Finland. E-mail:jyrki.kullaa@stadia.fi (Received 28 March 2002, accepted 1 October 2002) Structural health monitoring of the Z24 Bridge in Switzerland was studied using the measurement data from three damage configurations. Changes in the modal parameters were used to detect possible damage to the structure. The identification of the modal parameters from the response data was automated using the stochastic subspace identification technique and the stabilisation diagram. Damage detection was performed using control charts, one of the primary techniques of statistical process control. An advantage of control charts is that they can be automated for on-line structural health monitoring. Univariate and multivariate Shewhart, x, CUSUM, and EWMA control charts were studied with different features including natural frequencies, mode shapes, and damping ratios. The sensitivity of the control chart to damage was substantially increased by further dimensionality reduction applying the principal component analysis. # 2003 Elsevier Science Ltd. All rights reserved.
1. INTRODUCTION
Structural health monitoring of bridges is becoming an alternative to regular visual inspection. Vibration-based monitoring is particularly attractive for the following reasons: it is a non-destructive testing method, monitoring can be performed without closing the traffic, no artificial excitation is needed, and the most promising of all, the vibration properties are global, the changes in the structure can be detected remotely from the sensor. It is assumed that the vibration characteristics of the structure change due to damage, and by identifying the appropriate features the existence of the damage can be observed. One possible set of features are the modal parameters of the structure: natural frequencies, mode shapes, and damping ratios. The use of these is justified, because the modal parameters of the structure are functions of stiffness, mass, damping, and boundary conditions, and damage can be defined as a change in these physical properties. In the damage detection process, different steps must be taken to reach the goal: (1) instrumentation, (2) data acquisition, (3) signal processing, (4) feature extraction, (5) preprocessing of the feature vector, (6) damage detection, and (7) alarms and data transfer. The feature extraction in this work is equivalent to the system identification, which is shortly described. This paper focuses mainly on parts 5 and 6 of the process, discussed in detail below. 2. SYSTEM IDENTIFICATION
The objective of the system identification was to extract damage sensitive features from the response measurements. The selected features in this study were the dynamic 0888–3270/03/+$35.00/0
# 2003 Elsevier Science Ltd. All rights reserved.
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properties of the structure: natural frequencies, mode shapes, and damping ratios. The use of dynamic properties is justified, because they can be considered as fingerprints of the structure, as described above. Also, if the structure is linear, the amplitude of the excitation has no effect on the dynamic properties. This is an important property, because the data in the monitoring system consist of output-only data without knowledge of the excitation. The stochastic subspace identification [1, 2] was used in this study, as it has proved to be reliable and relatively fast. The free parameter of the technique is the model order, which was chosen automatically using the stabilisation diagram [3]. Once the model order was chosen, the identification and extraction of the modal parameters was straightforward. The response data from the four reference sensors alone were used in this study to simulate the monitoring system. Each time record included 21 746 samples with a sampling period of 0.03 s. Because nine time histories only were available from each configuration (undamaged, and pier settlements of 40 and 95 mm), all signals were divided into 16 sequences of equal length without overlapping, resulting in 144 time histories with a record length of 40 s.
3. FEATURE PRE-PROCESSING
3.1. MODE PAIRING Each identification resulted in a vector of dynamic properties. However, the number of identified modes could differ between the measurements. Therefore, a pre-processing function, called mode pairing, had to be performed. All identified frequencies from each measurement are plotted in Fig. 1(a). The four lowest natural frequencies are clearly visible by a visual inspection, whereas the fifth natural frequency is not so distinct. In addition, several identified frequencies that were not natural frequencies of the structure were found. The mode pairing process assigned each natural mode to the nearest class using the Euclidean distance between vectors comprising the natural frequency and the corresponding mode shape. The result from the mode pairing is shown in Fig. 1(b). It can be seen that modes 1, 3, 4, and 5 identified reasonably well, whereas mode 2 could not be considered very reliable for damage detection. Also the frequency between modes 2 and 3 was not considered a structural property.
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Figure 1. (a) Identified frequencies from each sample. (b) Mode pairing.
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3.2. DIMENSIONALITY REDUCTION The system identification from time data into few modal parameters compressed the data considerably. However, the dimensionality of the feature vector may still be too high for a statistical analysis. For example, when four natural frequencies and the corresponding mode shapes from four sensors were used for the damage detection, the dimension of the feature vector was 28, which is too high for only 80 samples from the undamaged structure. Therefore, a further dimensionality reduction was required. Principal component analysis PCA [4] was used for further dimensionality reduction, resulting in only a few new variables representing the most of the information contained in the data.
4. CONTROL CHARTS
Statistical methods were used for the damage detection. Control charts [5] are one of the primary techniques of statistical process control and are a very useful process monitoring technique. They plot the quality characteristic as a function of the sample number. The charts have lower and upper control limits, which are computed from those samples recorded when the process is assumed to be in control. When unusual sources of variability are present, sample statistics will plot outside the control limits and an alarm signal will be produced. An advantage of control charts is that they can be automated for on-line structural health monitoring. Different control charts were studied: univariate and multivariate Shewhart, x, CUSUM, and EWMA control charts. In the Shewhart chart, or x% chart [5] the subgroup mean x% of a variable is plotted. The subgroup size is typically 4, 5, or 6. The multivariate counterpart of the Shewhart chart is the Shewhart T 2, or Hotelling T 2 control chart [5]. Other control charts include the x chart, cumulative sum (CUSUM), and exponentially weighted moving average (EWMA) control charts [5]. CUSUM and EWMA charts are good alternatives when detection of small shifts is important. They incorporate all the information in the sequence of sample values. The multivariate counterparts of the x, CUSUM, and EWMA charts are the Hotelling T2 chart with the subgroup size n = 1 [5], the vector-valued CUSUM [6], or MCUSUM, and the multivariate exponentially weighted moving average (MEWMA) chart [7], respectively.
5. OFF-LINE DAMAGE DETECTION
In all control charts of this study the number of in-control samples used was 80. In the Shewhart and Shewhart T control charts the subgroup size was 4. The multivariate control charts for the natural frequencies are shown in Fig. 2. The dimension of the feature vector was 4. When the corresponding mode shapes were also included, it resulted in a dimension of 28, too high for a reliable statistical analysis. Thus, the first principal component was selected, resulting in the control charts shown in Fig. 3. The first principal component was seen to explain 78% of the variance in the features. The ranges of the samples of the three damage configurations were 1–134, 135–277, and 278–411. For the Shewhart and Shewhart T charts, the corresponding ranges were 1–33, 34–69, and 70–102. In all control charts, the higher pier settlement was clearly observed. All samples plotted outside the control limits. For the lower pier settlement and the undamaged structure the
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Figure 2. Multivariate control charts for natural frequencies 1, 3, 4, and 5.
results differed. As shown in Table 1, the multivariate control charts were more reliable than the univariate charts in the undamaged case, whereas the smaller damage was observed better by the univariate charts. The Hotelling T chart especially was seen to be quite insensitive to the 40 mm pier settlement, for which the Shewhart T showed better performance. Both the univariate and multivariate CUSUM and EWMA charts proved to be very sensitive. The false alarms in the undamaged case were produced by all univariate control charts. The comparison between the univariate and multivariate control charts is, however, difficult, because the variables in the charts are different. Generally, multivariate control charts offer more flexibility, as they can always be applied regardless of the dimensionality of the feature vector. For a higher accuracy the dimensionality should be reduced below five, preferably even lower. Multivariate control charts for damping ratios of modes 1, 3, 4, and 5 are shown in Fig. 4. It can be seen that the damping ratio is not a suitable damage indicator in this study.
6. ON-LINE DAMAGE DETECTION
If the objective is to detect the damage once it has occurred, the control charts must be applied on-line after each measurement. Using the principal component analysis as the
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Figure 3. Univariate control charts for natural frequencies 1, 3, 4, and 5 and corresponding mode shapes using the first principal component.
Table 1 Number of outliers in different control charts. The first four charts are for the four natural frequencies, and the last four charts are the first principal component of the four natural frequencies and the corresponding mode shapes Control chart
Shewhart T Hotelling T MCUSUM MEWMA Shewhart x chart CUSUM EWMA
Pier settlement Undamaged
40 mm
95 mm
0/33 1/134 0/134 0/134 3/33 2/134 12/134 8/134
20/36 8/143 141/143 138/143 36/36 133/143 143/143 142/143
33/33 134/134 134/134 134/134 33/33 134/134 134/134 134/134
data reduction technique in the on-line damage detection, the control charts may change after each measurement and must be reconstructed. In this study it was stated that at least 50% of the variation in the data had to be accounted for by the principal components.
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J. KULLAA Hotelling T Control Chart
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Figure 4. Multivariate control charts for damping ratios of modes 1, 3, 4, and 5.
Therefore, the number of principal components could vary between samples and multivariate control charts were applied as shown in Fig. 5, where the statistics of the most recent measurement only and the corresponding control limits are plotted. The in-control samples are not shown. The ranges of samples of the three damage configurations in Fig. 5 are 1–54, 55–197, and 198–331. It should be noted that the control charts in Fig. 2 are identical whether used in the on-line or off-line mode, as no principal component analysis was made. The control limits decrease with increasing damage, because they are proportional to the variance in the in-control data. Principal component analysis is performed using all data. In the undamaged case the principal components account for the maximum variance in the in-control data. After damage has occurred, the direction of the maximum variance changes and the principal component axes rotate to a new position, which accounts for less variance in the in-control data. The same conclusion as in the previous section holds also for the on-line damage detection. Both damage cases could be clearly detected with all control charts, but the false indications occurred as in the off-line damage detection. Similar results can be explained from the fact that the principal axis directions did not change much between the two damage scenarios that differed only by their magnitude. If two different types of damage were introduced, the results from the on-line and off-line control charts would probably have been different.
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DAMAGE DETECTION OF Z24 Shewhart T
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Figure 5. Multivariate on-line control charts for natural frequencies 1, 3, 4, and 5 and corresponding mode shapes using principal components. The charts represent the most recent sample and the corresponding instantaneous limits.
7. CONCLUSION
Damage detection of the Z24 Bridge was studied using different univariate and multivariate control charts. All control charts worked well for the damage detection. The natural frequencies and mode shapes were seen to be reliable indicators of damage, whereas damping ratios were too inaccurate or insensitive for damage detection. Because it is usually not known in advance, which features change due to damage, it is suggested to use a high-dimensional feature vector. The subsequent dimensionality reduction can be performed using principal component analysis, which effectively finds the directions of largest variation. The damage detection can be performed either on-line or off-line. In the off-line damage detection one can experiment with different control charts, which facilitates damage detection considerably, because the decision can be made by a human, not by the computer. The ultimate goal, however, is a monitoring system with on-line damage detection. False alarms or too insensitive control charts should be avoided. This study showed that Shewhart charts are probably the most reliable tools. Hotelling T for individual variables is a good choice if false alarms should be avoided, because it is insensitive to small shifts. CUSUM and EWMA charts are sensitive to small shifts and may cause frequent false alarms in an automated monitoring system. Techniques to eliminate false alarms are a topic for future research.
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ACKNOWLEDGEMENTS
The funding for this work was provided by the Academy of Finland.
REFERENCES 1. P. Van Overschee and B. De Moor 1996 Subspace Identification for Linear Systems: Theory– Implementation–Applications, 272pp. Dordrecht, Netherlands: Kluwer Academic Publishers. 2. B. Peeters 2000 Ph.D. thesis, KU Leuven, Department of Civil Engineering. System identification and damage detection in civil engineering. 3. J. Kullaa 2000 European COST F3 Conference on System Identification & Structural Health Monitoring. Proceedings of the Conference held in E.T.S.I. Aerona!uticos, Madrid, June 7–9, 2000, 353–362. Monitoring simulation and damage detection of the Z24 Bridge. 4. S. Sharma 1996 Applied Multivariate Techniques, 493pp. New York: John Wiley & Sons. 5. D. C. Montgomery 1997 Introduction to statistical quality control, 3rd edn, 728pp. New York: John Wiley & Sons. 6. R. B. Crosier 1988 Technometrics, 30, 291–303. Multivariate generalizations of cumulative sum quality-control schemes. 7. C. A. Lowry, W. H. Woodall, C. W. Champ and S. E. Rigdon 1992 Technometrics, 34, 46–53. A multivariate exponentially weighted moving average control chart.
DAMAGE DETECTION OF THE Z24 BRIDGE USING CONTROL CHARTS Jyrki Kullaa Mechanical and Production Engineering, Helsinki Polytechnic, P.O. Box 4021, FIN-00099 City of Helsinki, Finland. E-mail:jyrki.kullaa@stadia.fi (Received 28 March 2002, accepted 1 October 2002) Structural health monitoring of the Z24 Bridge in Switzerland was studied using the measurement data from three damage configurations. Changes in the modal parameters were used to detect possible damage to the structure. The identification of the modal parameters from the response data was automated using the stochastic subspace identification technique and the stabilisation diagram. Damage detection was performed using control charts, one of the primary techniques of statistical process control. An advantage of control charts is that they can be automated for on-line structural health monitoring. Univariate and multivariate Shewhart, x, CUSUM, and EWMA control charts were studied with different features including natural frequencies, mode shapes, and damping ratios. The sensitivity of the control chart to damage was substantially increased by further dimensionality reduction applying the principal component analysis. # 2003 Elsevier Science Ltd. All rights reserved.
1. INTRODUCTION
Structural health monitoring of bridges is becoming an alternative to regular visual inspection. Vibration-based monitoring is particularly attractive for the following reasons: it is a non-destructive testing method, monitoring can be performed without closing the traffic, no artificial excitation is needed, and the most promising of all, the vibration properties are global, the changes in the structure can be detected remotely from the sensor. It is assumed that the vibration characteristics of the structure change due to damage, and by identifying the appropriate features the existence of the damage can be observed. One possible set of features are the modal parameters of the structure: natural frequencies, mode shapes, and damping ratios. The use of these is justified, because the modal parameters of the structure are functions of stiffness, mass, damping, and boundary conditions, and damage can be defined as a change in these physical properties. In the damage detection process, different steps must be taken to reach the goal: (1) instrumentation, (2) data acquisition, (3) signal processing, (4) feature extraction, (5) preprocessing of the feature vector, (6) damage detection, and (7) alarms and data transfer. The feature extraction in this work is equivalent to the system identification, which is shortly described. This paper focuses mainly on parts 5 and 6 of the process, discussed in detail below. 2. SYSTEM IDENTIFICATION
The objective of the system identification was to extract damage sensitive features from the response measurements. The selected features in this study were the dynamic 0888–3270/03/+$35.00/0
# 2003 Elsevier Science Ltd. All rights reserved.
164
J. KULLAA
properties of the structure: natural frequencies, mode shapes, and damping ratios. The use of dynamic properties is justified, because they can be considered as fingerprints of the structure, as described above. Also, if the structure is linear, the amplitude of the excitation has no effect on the dynamic properties. This is an important property, because the data in the monitoring system consist of output-only data without knowledge of the excitation. The stochastic subspace identification [1, 2] was used in this study, as it has proved to be reliable and relatively fast. The free parameter of the technique is the model order, which was chosen automatically using the stabilisation diagram [3]. Once the model order was chosen, the identification and extraction of the modal parameters was straightforward. The response data from the four reference sensors alone were used in this study to simulate the monitoring system. Each time record included 21 746 samples with a sampling period of 0.03 s. Because nine time histories only were available from each configuration (undamaged, and pier settlements of 40 and 95 mm), all signals were divided into 16 sequences of equal length without overlapping, resulting in 144 time histories with a record length of 40 s.
3. FEATURE PRE-PROCESSING
3.1. MODE PAIRING Each identification resulted in a vector of dynamic properties. However, the number of identified modes could differ between the measurements. Therefore, a pre-processing function, called mode pairing, had to be performed. All identified frequencies from each measurement are plotted in Fig. 1(a). The four lowest natural frequencies are clearly visible by a visual inspection, whereas the fifth natural frequency is not so distinct. In addition, several identified frequencies that were not natural frequencies of the structure were found. The mode pairing process assigned each natural mode to the nearest class using the Euclidean distance between vectors comprising the natural frequency and the corresponding mode shape. The result from the mode pairing is shown in Fig. 1(b). It can be seen that modes 1, 3, 4, and 5 identified reasonably well, whereas mode 2 could not be considered very reliable for damage detection. Also the frequency between modes 2 and 3 was not considered a structural property.
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Figure 1. (a) Identified frequencies from each sample. (b) Mode pairing.
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3.2. DIMENSIONALITY REDUCTION The system identification from time data into few modal parameters compressed the data considerably. However, the dimensionality of the feature vector may still be too high for a statistical analysis. For example, when four natural frequencies and the corresponding mode shapes from four sensors were used for the damage detection, the dimension of the feature vector was 28, which is too high for only 80 samples from the undamaged structure. Therefore, a further dimensionality reduction was required. Principal component analysis PCA [4] was used for further dimensionality reduction, resulting in only a few new variables representing the most of the information contained in the data.
4. CONTROL CHARTS
Statistical methods were used for the damage detection. Control charts [5] are one of the primary techniques of statistical process control and are a very useful process monitoring technique. They plot the quality characteristic as a function of the sample number. The charts have lower and upper control limits, which are computed from those samples recorded when the process is assumed to be in control. When unusual sources of variability are present, sample statistics will plot outside the control limits and an alarm signal will be produced. An advantage of control charts is that they can be automated for on-line structural health monitoring. Different control charts were studied: univariate and multivariate Shewhart, x, CUSUM, and EWMA control charts. In the Shewhart chart, or x% chart [5] the subgroup mean x% of a variable is plotted. The subgroup size is typically 4, 5, or 6. The multivariate counterpart of the Shewhart chart is the Shewhart T 2, or Hotelling T 2 control chart [5]. Other control charts include the x chart, cumulative sum (CUSUM), and exponentially weighted moving average (EWMA) control charts [5]. CUSUM and EWMA charts are good alternatives when detection of small shifts is important. They incorporate all the information in the sequence of sample values. The multivariate counterparts of the x, CUSUM, and EWMA charts are the Hotelling T2 chart with the subgroup size n = 1 [5], the vector-valued CUSUM [6], or MCUSUM, and the multivariate exponentially weighted moving average (MEWMA) chart [7], respectively.
5. OFF-LINE DAMAGE DETECTION
In all control charts of this study the number of in-control samples used was 80. In the Shewhart and Shewhart T control charts the subgroup size was 4. The multivariate control charts for the natural frequencies are shown in Fig. 2. The dimension of the feature vector was 4. When the corresponding mode shapes were also included, it resulted in a dimension of 28, too high for a reliable statistical analysis. Thus, the first principal component was selected, resulting in the control charts shown in Fig. 3. The first principal component was seen to explain 78% of the variance in the features. The ranges of the samples of the three damage configurations were 1–134, 135–277, and 278–411. For the Shewhart and Shewhart T charts, the corresponding ranges were 1–33, 34–69, and 70–102. In all control charts, the higher pier settlement was clearly observed. All samples plotted outside the control limits. For the lower pier settlement and the undamaged structure the
166
J. KULLAA Hotelling T Control Chart
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Figure 2. Multivariate control charts for natural frequencies 1, 3, 4, and 5.
results differed. As shown in Table 1, the multivariate control charts were more reliable than the univariate charts in the undamaged case, whereas the smaller damage was observed better by the univariate charts. The Hotelling T chart especially was seen to be quite insensitive to the 40 mm pier settlement, for which the Shewhart T showed better performance. Both the univariate and multivariate CUSUM and EWMA charts proved to be very sensitive. The false alarms in the undamaged case were produced by all univariate control charts. The comparison between the univariate and multivariate control charts is, however, difficult, because the variables in the charts are different. Generally, multivariate control charts offer more flexibility, as they can always be applied regardless of the dimensionality of the feature vector. For a higher accuracy the dimensionality should be reduced below five, preferably even lower. Multivariate control charts for damping ratios of modes 1, 3, 4, and 5 are shown in Fig. 4. It can be seen that the damping ratio is not a suitable damage indicator in this study.
6. ON-LINE DAMAGE DETECTION
If the objective is to detect the damage once it has occurred, the control charts must be applied on-line after each measurement. Using the principal component analysis as the
167
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Figure 3. Univariate control charts for natural frequencies 1, 3, 4, and 5 and corresponding mode shapes using the first principal component.
Table 1 Number of outliers in different control charts. The first four charts are for the four natural frequencies, and the last four charts are the first principal component of the four natural frequencies and the corresponding mode shapes Control chart
Shewhart T Hotelling T MCUSUM MEWMA Shewhart x chart CUSUM EWMA
Pier settlement Undamaged
40 mm
95 mm
0/33 1/134 0/134 0/134 3/33 2/134 12/134 8/134
20/36 8/143 141/143 138/143 36/36 133/143 143/143 142/143
33/33 134/134 134/134 134/134 33/33 134/134 134/134 134/134
data reduction technique in the on-line damage detection, the control charts may change after each measurement and must be reconstructed. In this study it was stated that at least 50% of the variation in the data had to be accounted for by the principal components.
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Figure 4. Multivariate control charts for damping ratios of modes 1, 3, 4, and 5.
Therefore, the number of principal components could vary between samples and multivariate control charts were applied as shown in Fig. 5, where the statistics of the most recent measurement only and the corresponding control limits are plotted. The in-control samples are not shown. The ranges of samples of the three damage configurations in Fig. 5 are 1–54, 55–197, and 198–331. It should be noted that the control charts in Fig. 2 are identical whether used in the on-line or off-line mode, as no principal component analysis was made. The control limits decrease with increasing damage, because they are proportional to the variance in the in-control data. Principal component analysis is performed using all data. In the undamaged case the principal components account for the maximum variance in the in-control data. After damage has occurred, the direction of the maximum variance changes and the principal component axes rotate to a new position, which accounts for less variance in the in-control data. The same conclusion as in the previous section holds also for the on-line damage detection. Both damage cases could be clearly detected with all control charts, but the false indications occurred as in the off-line damage detection. Similar results can be explained from the fact that the principal axis directions did not change much between the two damage scenarios that differed only by their magnitude. If two different types of damage were introduced, the results from the on-line and off-line control charts would probably have been different.
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Figure 5. Multivariate on-line control charts for natural frequencies 1, 3, 4, and 5 and corresponding mode shapes using principal components. The charts represent the most recent sample and the corresponding instantaneous limits.
7. CONCLUSION
Damage detection of the Z24 Bridge was studied using different univariate and multivariate control charts. All control charts worked well for the damage detection. The natural frequencies and mode shapes were seen to be reliable indicators of damage, whereas damping ratios were too inaccurate or insensitive for damage detection. Because it is usually not known in advance, which features change due to damage, it is suggested to use a high-dimensional feature vector. The subsequent dimensionality reduction can be performed using principal component analysis, which effectively finds the directions of largest variation. The damage detection can be performed either on-line or off-line. In the off-line damage detection one can experiment with different control charts, which facilitates damage detection considerably, because the decision can be made by a human, not by the computer. The ultimate goal, however, is a monitoring system with on-line damage detection. False alarms or too insensitive control charts should be avoided. This study showed that Shewhart charts are probably the most reliable tools. Hotelling T for individual variables is a good choice if false alarms should be avoided, because it is insensitive to small shifts. CUSUM and EWMA charts are sensitive to small shifts and may cause frequent false alarms in an automated monitoring system. Techniques to eliminate false alarms are a topic for future research.
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ACKNOWLEDGEMENTS
The funding for this work was provided by the Academy of Finland.
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