The main purpose of this work attempts to assemble a framework of a health monitoring system for smart structures based on ANN models. By investigating from analytical study to experimental study, the proposed framework for an ANN-based integrated system for structural monitoring and damage diagnosis is revealed adaptive and feasible. According to the study results shown in this research, they are summarized and discussed in the succeeding sections.
(1) The ANNSI model successfully identified the structural modal parameters of the specimen under various damage states from the measurements of the accelerometers, FBG sensors, and RSGs. The identified results show consistency between each of them.
(2) The induced damage can be reflected by the changes in structural modal parameters of the specimen. However, the modal parameters changes of the lower mode are not significant in the structure with slight damage.
(3) The FBG sensors do show their potentials in system identification and monitoring. The noise effect of the FBG sensors measurements is much smaller than that of the RSGs and accelerometers. This will make the identification easier when using the FBG sensors data. Furthermore, the distinguishing advantages of much less mass and great capacity of multiplexing a large number of sensors along a single fiber link make FBG sensors promising for health monitoring of practical structures.
(4) Compare with the CMS that based on the displacement mode shapes, the CSMS that based on the strain mode shapes is more sensitive to the structural damage. Moreover, the location of damage can be reflected by the sensing stations with larger value of CSMS. By using this approach, the damage location for the most simulated damage
cases can be identified.
(5) The damage detection strategy that based on the prediction errors from the monitoring networks is easy to implement without limitation on the number of sensors. The increasing prediction error from the global monitoring network in the simulation of degradation development signifies deterioration of the structural integrity. Moreover, the larger prediction errors from the decentralized neural networks indicate the locality of the structural damage.
(6) Although the damage detection method that based on the DLF and the UFN model failed to be applied to the experimental measurements due to the problem of without a suitable analytical model, the damage diagnosis of the structure can still be carried out by other proposed strategies. If a suitable analytical model is available, the damage diagnosis of the structure will be improved and enhanced.
(7) Since the methods and approaches involved in the system are mainly based on ANNs, the system is adaptive because ANNs are expected to improve their performance as they experience more episodes form the reality.
(8) The damage detection mechanism of the system was designed to integrate different diagnosis strategies to implement the similar tasks. In this way, even one of the diagnosis strategies fails to perform its duty, the system can still work properly.
(9) The system is independent of the methods used in each mechanism and is expandable.
Any effective or improved method can be added to the corresponding mechanism to enhance the performance of the whole system.
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Table 4.1 Specifications of the shaking table in NCTU
Item Value
Table size (m ) 2 3×3
Weight of table (kg) 5000 Max. specimen weight (kg) 10,000 Max. displacement (cm) ± 12.5
Max. velocity (cm/sec) ± 60 Max. acceleration (g) ± 1
Table 4.2 The characterizations of the experimental specimen
Item Value
Plane size (m2) 2× 2
Story height (m) 1.6
Weight (kg) ≈ 5000
Cross section of the column (mm) 125×60×6×8 Cross section of the beam (mm) 125×60×6×8 Cross section of the girder (mm) 100×50×5×7 Size of the mass block (mm) 1360×1360×32 Mass at 4th floor (kg−s2/m) 117.06 Mass at 3rd floor (kg−s2/m) 121.21 Mass at 2nd floor (kg−s2/m) 121.21 Mass at 1st floor (kg−s2/m) 121.54
Table 4.3 Analytical modal parameters of the test model in the transverse direction
Mode 1 2 3 4
Frequency (Hz) 1.18 3.48 5.45 6.80
Damping ratio (%) 5 5 5 5
4F 1.000 1.000 0.664 0.380
3F 0.879 0.011 -0.846 -0.903
2F 0.648 -0.998 -0.348 1.000
Mode shape
1F 0.332 -0.976 1.000 -0.659
Table 4.4 Specifications of the accelerometers
TYPE Axes Span (g)
A4 CrossBow CXL02LF1 X ± 2 A3 CrossBow CXL02LF1 X ± 2 A2 CrossBow CXL01LF1 X ± 1 A1 CrossBow CXL01LF1 X ± 1 Abase CrossBow CXL01LF1 X ± 1
Table 4.5 Specifications of the FBG-SLI
Optical
Number of Optical Channels 4
Maximum Number of FBG Sensors/Channel 64 (256 total across 4 channels)
Wavelength Range 1525 - 1565 nm
Absolute Accuracy +/- 5 pm (~4.2 µ) typ, +/- 10 pm max Repeatability +/- 2 pm (~1.7 µ) typ, +/- 5 pm max
Optical Power/Channel -10 dBm approx.
Dynamic Range (4 software-controlled gain settings) 30 dB
Resolution <1 pm (~0.8µ )
Scan Frequency 108 Hz max
Minimum FBG Spacing 0.5 nm
Optical Connector FC/APC
Hardware and Software
Computer Interface Card PCI or PC CARD (PCMCIA)
Interface Cable Included
FBG-IS Software for Windows
95, 98, 2000, NT and XP Included Electrical
Power Supply 95-135 VAC or 190-265 VAC, 15W Uncalibrated Analog Output - BNC Connectors Test, sync and scan
Mechanical
Operating Temperature 10o – 40oC
Dimensions 69 x 277 x 267 mm
Weight 4.1 kg
Options
Test Processor Laptop computer/data management system Custom Optical Connectors FC/SPC
Custom Computer Interface Cards ISA
Table 4.6 Center wavelength of the FBG sensors along Channel 1
FBG1 FBG2 FBG3 FBG4 FBG5 FBG6 FBG7 FBG8 Wavelength
(nm) 1542 1545 1548 1551 1554 1557 1560 1563
Table 4.7 Center wavelength of the FBG sensors along Channel 2 FBG9 FBG10 FBG11 FBG12 Wavelength
(nm) 1530 1533 1539 1536
Table 4.8 Dimension of the SC Cross section
(mm)
Area (cm2)
Mass (kg/m)
Ix (cm4)
SC-A 100×50×20×2.3 5.14 4.06 80.7 SC-B 75×45×15×2.3 4.14 3.25 37.1
Table 4.9 Characterizations of the simulated damage cases
No. Notation of the damage case
SC arrangement (1F-2F-3F)
Notation of the damage class
1 AAA A-A-A Intact
2 Dcase_BAA B-A-A Dclass_k1
3 Dcase_NAA N-A-A Dclass_k1
4 Dcase_ABA A-B-A Dclass_k2
5 Dcase_ANA A-N-A Dclass_k2
6 Dcase_AAB A-A-B Dclass_k3
7 Dcase_AAN A-A-N Dclass_k3
8 Dcase_BBA B-B-A Dclass_k1&k2
9 Dcase_BNA B-N-A Dclass_k1&k2
10 Dcase_NBA N-B-A Dclass_k1&k2
11 Dcase_NNA N-N-A Dclass_k1&k2 12 Dcase_BAB B-A-B Dclass_k1&k3
13 Dcase_BAN B-A-N Dclass_k1&k3
14 Dcase_NAB N-A-B Dclass_k1&k3
15 Dcase_NAN N-A-N Dclass_k1&k3 16 Dcase_ABB A-B-B Dclass_k2&k3 17 Dcase_ABN A-B-N Dclass_k2&k3
18 Dcase_ANB A-N-B Dclass_k2&k3
19 Dcase_ANN A-N-N Dclass_k2&k3 20 Dcase_BBB B-B-B Dclass_k1&k2&k3 21 Dcase_BBN B-B-N Dclass_k1&k2&k3
22 Dcase_NBB N-B-B Dclass_k1&k2&k3
23 Dcase_BNN B-N-N Dclass_k1&k2&k3
24 Dcase_NNB N-N-B Dclass_k1&k2&k3 25 Dcase_NNN N-N-N Dclass_k1&k2&k3
Table 4.10 Operation sequence of the shaking table tests
Case Save acc. data as Save RSG data as Save FBG data as
AAA AAA_acc AAA_RSG AAA_FBG
Dcase_BAA BAA_acc BAA_RSG BAA_FBG
Dcase_NAA NAA_acc NAA_RSG NAA_FBG
Dcase_ABA ABA_acc ABA_RSG ABA_FBG
Dcase_ANA ANA_acc ANA_RSG ANA_FBG
Dcase_AAB AAB_acc AAB_RSG AAB_FBG
Dcase_AAN AAN_acc AAN_RSG AAN_FBG
Dcase_BBA BBA_acc BBA_RSG BBA_FBG
Dcase_BNA BNA_acc BNA_RSG BNA_FBG
Dcase_NBA NBA_acc NBA_RSG NBA_FBG
Dcase_NNA NNA_acc NNA_RSG NNA_FBG
Dcase_BAB BAB_acc BAB_RSG BAB_FBG
Dcase_BAN BAN_acc BAN_RSG BAN_FBG
Dcase_NAB NAB_acc NAB_RSG NAB_FBG
Dcase_NAN NAN_acc NAN_RSG NAN_FBG
Dcase_ABB ABB_acc ABB_RSG ABB_FBG
Dcase_ABN ABN_acc ABN_RSG ABN_FBG
Dcase_ANB ANB_acc ANB_RSG ANB_FBG
Dcase_ANN ANN_acc ANN_RSG ANN_FBG
Dcase_BBB BBB_acc BBB_RSG BBB_FBG
Dcase_BBN BBN_acc BBN_RSG BBN_FBG
Dcase_NBB NBB_acc NBB_RSG NBB_FBG
Dcase_BNN BNN_acc BNN_RSG BNN_FBG
Dcase_NNB NNB_acc NNB_RSG NNB_FBG
Dcase_NNN NNN_acc NNN_RSG NNN_FBG
Table 4.11 Statistical summaries of the acceleration records I. Max. response (g)
.) max(acc
II. Standard deviation (g) .)
( std acc Case
1F 2F 3F 4F 1F 2F 3F 4F AAA 0.095 0.119 0.131 0.177 0.016 0.023 0.028 0.035 Dcase_BAA 0.096 0.129 0.140 0.200 0.018 0.027 0.034 0.041 Dcase_NAA 0.107 0.144 0.170 0.191 0.028 0.038 0.046 0.057 Dcase_ABA 0.093 0.124 0.142 0.181 0.020 0.030 0.036 0.045 Dcase_ANA 0.095 0.145 0.160 0.204 0.021 0.038 0.047 0.056 Dcase_AAB 0.091 0.126 0.137 0.178 0.019 0.028 0.034 0.042 Dcase_AAN 0.117 0.149 0.157 0.180 0.021 0.030 0.037 0.045 Dcase_BBA 0.094 0.123 0.144 0.175 0.019 0.030 0.038 0.045 Dcase_BNA 0.093 0.143 0.167 0.202 0.021 0.037 0.048 0.056 Dcase_NBA 0.106 0.143 0.166 0.207 0.028 0.042 0.052 0.062 Dcase_NNA 0.102 0.156 0.184 0.244 0.033 0.058 0.074 0.085 Dcase_BAB 0.102 0.138 0.160 0.184 0.022 0.032 0.039 0.048 Dcase_BAN 0.137 0.172 0.159 0.218 0.028 0.036 0.04 0.052 Dcase_NAB 0.104 0.148 0.192 0.216 0.027 0.043 0.054 0.063 Dcase_NAN 0.143 0.189 0.188 0.235 0.036 0.048 0.056 0.070 Dcase_ABB 0.097 0.131 0.141 0.184 0.022 0.033 0.039 0.048 Dcase_ABN 0.115 0.150 0.152 0.181 0.023 0.034 0.043 0.052 Dcase_ANB 0.095 0.161 0.171 0.225 0.023 0.040 0.051 0.060 Dcase_ANN 0.100 0.158 0.162 0.230 0.026 0.043 0.055 0.066 Dcase_BBB 0.089 0.129 0.152 0.184 0.024 0.035 0.042 0.051 Dcase_BBN 0.130 0.170 0.160 0.221 0.030 0.041 0.046 0.058 Dcase_NBB 0.103 0.159 0.201 0.227 0.036 0.059 0.074 0.087 Dcase_BNN 0.135 0.171 0.179 0.265 0.034 0.053 0.065 0.078 Dcase_NNB 0.098 0.148 0.193 0.248 0.043 0.079 0.099 0.115 Dcase_NNN 0.133 0.184 0.210 0.298 0.050 0.084 0.109 0.127
Table 4.11 (Continue) III. ∆max(acc.) (g)
(=damage case – baseline) IV. ∆max(acc /.) baseline (%) Case
1F 2F 3F 4F 1F 2F 3F 4F
AAA / / / / / / / /
Dcase_BAA 0.001 0.010 0.009 0.023 0.6 8.3 6.9 13.0 Dcase_NAA 0.012 0.025 0.039 0.014 12.3 21.0 29.5 7.9 Dcase_ABA -0.002 0.005 0.011 0.004 -1.8 4.3 8.0 2.0 Dcase_ANA 0.000 0.026 0.029 0.027 0.2 21.7 22.1 15.0 Dcase_AAB -0.004 0.007 0.006 0.001 -3.9 6.0 4.9 0.8 Dcase_AAN 0.022 0.030 0.026 0.003 23.6 24.8 19.8 1.5 Dcase_BBA -0.001 0.004 0.013 -0.002 -1.6 3.0 10.2 -1.4 Dcase_BNA -0.002 0.024 0.036 0.025 -1.9 20.0 27.5 13.9 Dcase_NBA 0.011 0.024 0.035 0.030 11.2 20.1 27.0 16.9 Dcase_NNA 0.007 0.037 0.053 0.067 7.4 31.1 40.5 37.9 Dcase_BAB 0.007 0.019 0.029 0.007 7.5 15.9 22.1 4.1 Dcase_BAN 0.042 0.053 0.028 0.041 44.7 44.8 21.4 23.4 Dcase_NAB 0.009 0.029 0.061 0.039 9.2 24.5 46.9 22.2 Dcase_NAN 0.048 0.070 0.057 0.058 50.5 58.7 43.3 32.6 Dcase_ABB 0.002 0.012 0.010 0.007 2.6 10.3 7.3 3.7 Dcase_ABN 0.020 0.031 0.021 0.004 21.4 25.7 15.8 2.1 Dcase_ANB 0.000 0.042 0.040 0.048 0.4 35.4 30.5 26.9 Dcase_ANN 0.005 0.039 0.031 0.053 5.3 32.8 23.7 29.9 Dcase_BBB -0.006 0.010 0.021 0.007 -6.3 8.4 16.0 4.0 Dcase_BBN 0.035 0.051 0.029 0.044 36.7 43.2 22.1 25.0 Dcase_NBB 0.008 0.040 0.070 0.050 8.0 33.6 53.5 28.1 Dcase_BNN 0.040 0.052 0.048 0.088 42.1 43.7 36.6 49.7 Dcase_NNB 0.003 0.029 0.062 0.071 2.7 24.6 47.5 40.0 Dcase_NNN 0.038 0.065 0.079 0.121 40.0 54.5 60.2 68.5
Table 4.12 Statistical summaries of the strain records from the FBG sensors at BE I. Max. response (µ strain)
) max(ε
II. Standard deviation (µ strain) )
( std ε Case
FBG1 FBG3 FBG5 FBG7 FBG1 FBG3 FBG5 FBG7 AAA 238.1 184.2 143.1 109.6 44.5 36.8 28.2 20.5 Dcase_NNB 419.7 385.1 230.2 171.5 220.5 196.9 107.1 75.4 Dcase_NNN 427.8 385.8 318.0 187.0 195.7 176.9 129.8 66.9
Table 4.12 (Continue)
FBG1 FBG3 FBG5 FBG7 FBG1 FBG3 FBG5 FBG7
AAA 18.7 20.0 19.7 18.7 / / / /
Table 4.13 Statistical summaries of the strain records from FBG the sensors at TE I. Max. response (µ strain)
) max(ε
II. Standard deviation (µ strain) )
( std ε Case
FBG2 FBG4 FBG6 FBG8 FBG2 FBG4 FBG6 FBG8 AAA 241.5 188.2 151.5 111.6 46.1 37.8 30.1 20.9 Dcase_NNB 429.7 387.2 251.8 174.6 226.1 198.1 118.1 76.8 Dcase_NNN 434.72 384.2 338.5 196.8 201.2 176.7 138.7 70.8
Table 4.13 (Continue)
FBG2 FBG4 FBG6 FBG8 FBG2 FBG4 FBG6 FBG8
AAA 19.1 20.1 19.8 18.7 / / / /
Table 4.14 Statistical summaries of the strain records from the FBG sensors at BW I. Max. response (µ strain)
) max(ε
II. Standard deviation (µ strain) )
( std ε Case
FBG9 FBG10 FBG11 FBG12 FBG9 FBG10 FBG11 FBG12 AAA 250.0 190.1 142.8 98.1 47.0 38.2 28.5 19.2 Dcase_NNB 449.3 389.6 233.2 167.7 235.9 199.2 108.1 70.6 Dcase_NNN 455.1 390.6 316.5 185.3 209.9 179.1 129.5 62.7
Table 4.14 (Continue)
FBG9 FBG10 FBG11 FBG12 FBG9 FBG10 FBG11 FBG12
AAA 18.8 20.1 20.0 19.5 / / / /
Dcase_BAA 22.2 23.7 23.2 21.7 10.2 8.0 9.1 10.2 Dcase_NAA 27.5 25.7 28.0 28.3 45.0 34.9 25.7 13.3 Dcase_ABA 23.1 24.8 24.8 24.1 14.2 16.6 -4.4 11.8 Dcase_ANA 28.3 30.1 28.9 26.6 25.7 61.1 8.1 29.4 Dcase_AAB 20.1 21.3 22.1 21.0 11.3 15.6 1.3 8.9 Dcase_AAN 23.2 26.7 26.9 23.3 19.7 14.2 37.1 14.6 Dcase_BBA 23.8 25.1 25.3 23.0 24.3 19.6 11.6 10.4 Dcase_BNA 27.6 29.1 28.3 24.3 26.0 61.6 25.1 31.4 Dcase_NBA 30.5 29.1 29.0 27.7 48.7 46.0 39.0 28.4 Dcase_NNA 35.1 33.7 31.2 26.8 60.9 86.7 58.0 59.0 Dcase_BAB 24.9 25.6 26.6 24.8 29.0 26.0 8.1 16.4 Dcase_BAN 23.0 24.7 23.8 20.7 40.9 32.7 65.5 41.0 Dcase_NAB 30.4 29.5 30.8 28.3 59.3 51.2 27.2 33.3 Dcase_NAN 28.9 29.5 31.7 27.2 67.2 50.6 68.6 44.0 Dcase_ABB 24.1 26.2 26.5 24.6 15.0 15.8 4.8 10.8 Dcase_ABN 24.5 27.2 29.3 28.2 25.5 24.5 41.4 6.9 Dcase_ANB 28.1 30.4 29.1 26.2 32.2 66.0 25.6 31.8 Dcase_ANN 30.2 31.8 29.2 24.9 33.1 71.3 82.4 52.9 Dcase_BBB 25.2 25.3 26.2 24.0 32.9 33.6 18.5 26.5 Dcase_BBN 24.7 26.6 25.7 23.0 48.5 39.4 73.7 41.4 Dcase_NBB 36.3 35.9 36.2 34.4 79.7 64.7 48.7 46.1 Dcase_BNN 32.3 32.1 27.8 23.3 50.2 83.2 103.1 75.3 Dcase_NNB 52.5 51.1 46.3 42.1 79.7 104.9 63.3 70.9 Dcase_NNN 46.1 45.9 40.9 33.8 82.1 105.4 121.6 88.8
Table 4.15 Statistical summaries of the strain records from the RSGs
I. Max. response (µ strain) )
max(ε
II. Standard deviation (µ strain)
) ( std ε Case
RSG1 RSG2 RSG3 RSG4 RSG1 RSG2 RSG3 RSG4
AAA 166.4 144.9 121.3 96.2 36.6 33.5 27.5 21.1
Dcase_BAA 185.4 156.3 129.1 103.9 45.4 41.5 33.8 25.3 Dcase_NAA 236.7 196.3 152.0 112.6 73.8 57.1 47.8 34.0 Dcase_ABA 192.3 169.1 116.0 113.7 48.9 45.5 31.1 27.2 Dcase_ANA 214.7 235.9 139.4 123.9 63.5 73.7 39.9 33.6 Dcase_AAB 188.6 167.6 121.9 107.8 45.7 43.1 32.5 25.5 Dcase_AAN 203.1 167.2 169.0 112.8 49.4 46.3 46.5 26.7 Dcase_BBA 210.1 179.5 137.6 117.6 56.9 49.6 37.5 27.3 Dcase_BNA 210.9 232.8 164.2 119.6 64.9 75.2 46.4 33.9 Dcase_NBA 246.4 215.3 175.2 131.8 83.5 69.5 52.5 37.1 Dcase_NNA 266.8 273.6 188.8 136.9 119.3 114.7 73.4 50.6 Dcase_BAB 213.6 184.3 135.4 105.5 58.1 50.1 36.8 28.7 Dcase_BAN 240.7 188.6 194.1 123.8 60.1 52.0 51.9 30.3 Dcase_NAB 266.3 221.2 165.4 137.5 86.7 70.9 51.1 37.6 Dcase_NAN 278.4 221.1 201.9 134.5 89.4 72.6 72.0 40.5 Dcase_ABB 195.7 171.4 128.2 102.9 52.3 48.8 36.9 28.7 Dcase_ABN 210.7 186.2 171.5 105.8 55.7 52.2 53.1 30.6 Dcase_ANB 222.9 240.5 151.1 131.8 68.6 79.4 47.9 36.1 Dcase_ANN 225.4 243.4 212.1 129.0 73.9 85.1 69.5 38.4 Dcase_BBB 223.6 191.6 148.2 114.6 63.3 55.1 40.8 30.6 Dcase_BBN 253.7 205.6 208.3 129.7 68.7 59.3 58.2 33.9 Dcase_NBB 302.4 234.4 186.6 145.6 121.5 94.7 72.5 52.8 Dcase_BNN 255.0 260.0 244.2 147.9 96.7 99.8 81.0 45.0 Dcase_NNB 298.8 300.9 207.0 148.0 162.8 158.3 92.3 67.6 Dcase_NNN 307.1 302.7 273.2 171.8 173.4 170.7 134.2 72.6
Table 4.15 (Continue)
RSG1 RSG2 RSG3 RSG4 RSG1 RSG2 RSG3 RSG4
AAA 22.0 23.1 22.7 21.9 / / / /
Dcase_BAA 24.5 26.5 26.2 24.4 11.4 7.9 6.4 8.0 Dcase_NAA 31.2 29.1 31.4 30.2 42.3 35.5 25.4 17.0 Dcase_ABA 25.4 26.9 26.8 23.9 15.6 16.7 -4.3 18.3 Dcase_ANA 29.6 31.2 28.6 27.1 29.1 62.8 15.0 28.9 Dcase_AAB 24.2 25.7 26.6 23.6 13.4 15.7 0.6 12.1 Dcase_AAN 24.3 27.7 27.5 23.7 22.1 15.4 39.3 17.3 Dcase_BBA 27.1 27.6 27.3 23.2 26.3 23.9 13.5 22.3 Dcase_BNA 30.8 32.3 28.3 28.4 26.8 60.7 35.4 24.4 Dcase_NBA 33.9 32.3 30.0 28.1 48.1 48.6 44.5 37.1 Dcase_NNA 44.7 41.9 38.9 37.0 60.4 88.9 55.7 42.4 Dcase_BAB 27.2 27.2 27.2 27.2 28.4 27.2 11.7 9.7 Dcase_BAN 25.0 27.6 26.7 24.5 44.7 30.2 60.1 28.8 Dcase_NAB 32.5 32.0 30.9 27.3 60.0 52.7 36.4 43.0 Dcase_NAN 32.1 32.9 35.7 30.1 67.3 52.6 66.5 39.8 Dcase_ABB 26.7 28.5 28.8 27.9 17.7 18.3 5.7 7.0 Dcase_ABN 26.4 28.1 31.0 28.9 26.7 28.5 41.4 10.0 Dcase_ANB 30.8 33.0 31.7 27.4 34.0 66.0 24.6 37.0 Dcase_ANN 32.8 35.0 32.8 29.8 35.5 68.0 74.9 34.2 Dcase_BBB 28.3 28.7 27.5 26.7 34.4 32.3 22.2 19.2 Dcase_BBN 27.1 28.8 27.9 26.1 52.5 41.9 71.8 34.8 Dcase_NBB 40.2 40.4 38.8 36.3 81.8 61.8 53.9 51.4 Dcase_BNN 37.9 38.4 33.2 30.4 53.3 79.5 101.4 53.8 Dcase_NNB 54.5 52.6 44.6 45.7 79.6 107.7 70.7 53.8 Dcase_NNN 56.5 56.4 49.1 42.3 84.6 108.9 125.3 78.6
Table 5.1 Modal parameters of the test structure in healthy condition (AAA)
Mode 1 2 3 4
Frequency (Hz) 1.69 5.04 8.14 10.22 Damping ratio (%) 3.32 1.38 1.40 2.01
A4 1.000 1.000 0.427 0.288
A3 0.846 -0.130 -0.729 -0.729
A2 0.628 -0.914 -0.137 1.000
Mode shape
A1 0.336 -0.830 1.000 -0.705
Table 5.2 Modal parameters of Dcase_BAA
Mode 1 2 3 4
Frequency (Hz) 1.68 4.94 7.89 10.17
Damping ratio (%) 2.54 1.23 0.54 3.04
A4 1.000 1.000 0.557 0.254
A3 0.844 -0.100 -0.893 -0.775
A2 0.629 -0.935 -0.206 1.000
Mode shape
A1 0.340 -0.887 1.000 -0.672
MAC 1.000 0.999 0.989 0.998
Table 5.3 Modal parameters of Dcase_NAA
Mode 1 2 3 4
Frequency (Hz) 1.60 4.78 7.77 9.88
Damping ratio (%) 1.80 0.28 0.49 2.53
A4 1.000 1.000 0.582 0.317
A3 0.857 -0.035 -0.870 -0.809
A2 0.649 -0.879 -0.303 1.000
Mode shape
A1 0.370 -0.932 1.000 -0.618
MAC 1.000 0.992 0.979 0.993
Table 5.4 Modal parameters of Dcase_ABA
Mode 1 2 3 4
Frequency (Hz) 1.70 5.09 7.93 10.15
Damping ratio (%) 2.11 0.50 1.27 2.68
A4 1.000 1.000 0.449 0.249
A3 0.843 -0.149 -0.769 -0.871
A2 0.648 -0.835 -0.197 1.000
Mode shape
A1 0.344 -0.786 1.000 -0.757
MAC 1.000 0.998 0.998 0.993
Table 5.5 Modal parameters of Dcase_ANA
Mode 1 2 3 4
Frequency (Hz) 1.63 5.02 7.84 9.85 Damping ratio (%) 1.78 0.69 4.64 4.26 A4 1.000 1.000 0.415 0.388 A3 0.856 -0.121 -0.614 -0.923 A2 0.671 -0.823 -0.214 1.000 Mode shape
A1 0.326 -0.829 1.000 -0.640
MAC 0.999 0.998 0.989 0.982
Table 5.6 Modal parameters of Dcase_AAB
Mode 1 2 3 4
Frequency (Hz) 1.68 5.03 7.97 10.10 Damping ratio (%) 2.80 0.33 2.23 1.32
A4 1.000 1.000 0.609 0.277 A3 0.852 -0.119 -0.951 -0.836 A2 0.638 -0.885 -0.176 1.000 Mode shape
A1 0.337 -0.827 1.000 -0.709
MAC 1.000 1.000 0.981 0.996
Table 5.7 Modal parameters of Dcase_AAN
Mode 1 2 3 4
Frequency (Hz) 1.63 4.84 7.70 9.65 Damping ratio (%) 2.92 0.28 1.22 1.64 A4 1.000 0.955 0.692 0.284 A3 0.852 -0.042 -1.000 -0.723 A2 0.602 -1.000 -0.134 1.000 Mode shape
A1 0.317 -0.909 0.928 -0.866
MAC 1.000 0.993 0.955 0.991
Table 5.8 Modal parameters of Dcase_BBA
Mode 1 2 3 4
Frequency (Hz) 1.62 4.89 7.72 10.08 Damping ratio (%) 2.50 1.64 0.53 2.52
A4 1.000 1.000 0.558 0.351 A3 0.855 -0.075 -0.829 -0.807 A2 0.649 -0.855 -0.252 1.000 Mode shape
A1 0.354 -0.832 1.000 -0.565
MAC 1.000 0.998 0.988 0.986
Table 5.9 Modal parameters of Dcase_BNA
Mode 1 2 3 4
Frequency (Hz) 1.60 4.91 7.49 9.68 Damping ratio (%) 1.75 1.03 0.56 1.32 A4 1.000 1.000 0.532 0.361 A3 0.859 -0.086 -0.755 -0.954 A2 0.654 -0.934 -0.294 1.000 Mode shape
A1 0.319 -0.855 1.000 -0.547
MAC 1.000 0.999 0.985 0.967
Table 5.10 Modal parameters of Dcase_NBA
Mode 1 2 3 4
Frequency (Hz) 1.58 4.76 7.59 9.49 Damping ratio (%) 1.47 0.50 0.65 3.27 A4 1.000 1.000 0.564 0.312 A3 0.863 -0.025 -0.807 -0.826 A2 0.657 -0.883 -0.336 1.000 Mode shape
A1 0.363 -0.957 1.000 -0.685
MAC 1.000 0.990 0.977 0.996
Table 5.11 Modal parameters of Dcase_NNA
Mode 1 2 3 4
Frequency (Hz) 1.55 4.72 7.38 9.62 Damping ratio (%) 0.72 0.66 0.34 0.62 A4 1.000 1.000 0.520 0.352 A3 0.868 -0.014 -0.682 -0.982 A2 0.668 -0.918 -0.382 1.000 Mode shape
A1 0.349 -0.934 1.000 -0.546
MAC 1.000 0.992 0.964 0.962
Table 5.12 Modal parameters of Dcase_BAB
Mode 1 2 3 4
Frequency (Hz) 1.63 4.90 7.81 10.04 Damping ratio (%) 2.31 0.25 0.88 1.08
A4 1.000 1.000 0.610 0.294 A3 0.855 -0.063 -0.920 -0.808 A2 0.653 -0.844 -0.205 1.000 Mode shape
A1 0.355 -0.824 1.000 -0.671
MAC 1.000 0.997 0.983 0.997
Table 5.13 Modal parameters of Dcase_BAN
Mode 1 2 3 4
Frequency (Hz) 1.59 4.72 7.74 9.70 Damping ratio (%) 2.58 0.11 0.31 2.17 A4 1.000 0.985 0.675 0.246 A3 0.859 -0.014 -1.000 -0.948 A2 0.619 -1.000 -0.094 1.000 Mode shape
A1 0.335 -0.946 0.863 -0.847
MAC 1.000 0.991 0.941 0.985
Table 5.14 Modal parameters of Dcase_NAB
Mode 1 2 3 4
Frequency (Hz) 1.60 4.84 7.71 9.99 Damping ratio (%) 1.49 0.21 0.79 0.62 A4 1.000 1.000 0.632 0.289 A3 0.860 -0.044 -0.942 -0.808 A2 0.667 -0.835 -0.273 1.000 Mode shape
A1 0.371 -0.889 1.000 -0.603
MAC 0.999 0.993 0.975 0.992
Table 5.15 Modal parameters of Dcase_NAN
Mode 1 2 3 4
Frequency (Hz) 1.56 4.63 7.67 9.65 Damping ratio (%) 1.42 0.04 0.20 2.33 A4 1.000 0.978 0.698 0.282 A3 0.862 0.026 -1.000 -0.703 A2 0.627 -0.959 -0.163 1.000 Mode shape
A1 0.348 -1.000 0.803 -0.771
MAC 1.000 0.983 0.923 0.998
Table 5.16 Modal parameters of Dcase_ABB
Mode 1 2 3 4
Frequency (Hz) 1.68 5.02 7.86 10.07 Damping ratio (%) 2.31 0.31 1.67 1.12
A4 1.000 1.000 0.559 0.262 A3 0.848 -0.118 -0.871 -0.832 A2 0.637 -0.888 -0.171 1.000 Mode shape
A1 0.337 -0.815 1.000 -0.680
MAC 1.000 1.000 0.991 0.995
Table 5.17 Modal parameters of Dcase_ABN
Mode 1 2 3 4
Frequency (Hz) 1.64 4.84 7.77 9.58
Frequency (Hz) 1.64 4.84 7.77 9.58