In structural health monitoring system, little research on the damage identification from different types of sensors applied to large span structure has been done in the field. In fact, it is significant to estimate the whole structural safety if the multitype sensors or multiscale measurements are used in application of structural health monitoring and the damage identification for large span structure. A methodology to combine the local and global measurements in noisy environments based on artificial neural network is proposed in this paper. For a real large span structure, the capacity of the methodology is validated, including the decision on damage placement, the discussions on the number of the sensors, and the optimal parameters for artificial neural networks. Furthermore, the noisy environments in different levels are simulated to demonstrate the robustness and effectiveness of the proposed approach.
Structural damage identification has taken increasing attention from the scientific and engineering communities because the unpredicted structural failure could cause catastrophic, economic, and human life loss. A reliable and effective damage identification methodology is significant to maintain safety and capacity of structures [
Although there are many accepted damage identification methods using ANNs, the optimizations, such as the structures and parameters of ANNs, as well as the damage indexes, are researched and improved in order to obtain more accurate results. Vibration-based damage identification method that utilized ANNs to identify defects of an experimental model was proposed [
However, the inputs of the ANNs are the features or measurements from single type of sensor, while suitable measurements from various types of sensors and data mining in various measurements can support more effective results [
The rest of the paper is organized as follows. In Section
The damage identification method is carried out by BP neural networks (BPNNs), whose full name is Back-Propagation Network. BPNN is a multilayer network, in which the weight value is trained by nonlinear differential equation. Because of the simple structure and fabricability of the BPNNs, it has been widely used in many research fields including function approximation, pattern recognition, information classification, data compression, and so on. However, there is still no clear criterion to determine the most appropriate network architecture for a certain system. Some scholars have proved that the neural network structure with two hidden layers can get better recognition results [
The inputs of the neural network for damage identification are selected as three scenarios: one is the strain damage parameter, one is the acceleration damage parameter, and the last one is the multiscale damage parameter combined with strain damage parameter and acceleration damage parameter [
The strain damage parameter vector is defined as
The acceleration damage parameter vector is defined as
The multiscale damage parameter vector is defined as
For the same input vectors of the neural network, different network architectures take different identification results. In order to evaluate whether the architecture of neural network is the optimal one or not, the absolute average error
Because the noise is usually accompanied by the measurements from sensors, the noisy measurements are given in different noise levels. The robustness of the proposed method can be proofed by estimating the antinoise performance of damage identification method. Here the noise level is the ratio of the root mean square (RMS) of the noise to the RMS of the signal time series [
The steel superstructure of Beijing National Aquatics Center is a new kind of polyhedron spatial frame structure, whose outside size is 176.5389 m in length, 176.5389 m in width, and 29.3786 m in height. Polyhedron space has high repeatability, where the polyhedral cell in internal structure just needs four kinds of rod length and three types of nodes. The steel structure of National Aquatic Center is analyzed by finite element software SAP2000, and the node is set to be rigid connection and the member is set to be space beam element. The members are subjected to bending moment, shear, tension, or compression and torsion, simultaneously [
The finite element model of Beijing National Aquatics Center.
The main natural frequencies of the intact structure can be obtained from structural modal analysis, which are shown in Table
The main natural frequencies of the intact shell structure.
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Mode | Period(s) | Mode mass participation factor | Mode | Period(s) | Mode mass participation factor | Mode | Period(s) | Mode mass participation factor |
2 | 0.780 | 0.773 | 1 | 0.839 | 0.753 | 3 | 0.734 | 0.215 |
4 | 0.599 | 0.033 | 4 | 0.599 | 0.026 | 8 | 0.484 | 0.004 |
7 | 0.491 | 0.022 | 7 | 0.491 | 0.038 | 16 | 0.351 | 0.017 |
10 | 0.425 | 0.010 | 9 | 0.443 | 0.014 | 27 | 0.298 | 0.017 |
14 | 0.359 | 0.005 | 17 | 0.338 | 0.003 | 28 | 0.296 | 0.079 |
18 | 0.334 | 0.004 | 19 | 0.333 | 0.010 | 29 | 0.289 | 0.048 |
The structural analysis for the polyhedron space frame is that the members are subjected to the normal force and biaxial bending moments, while most joints are not subjected to lateral force and the lateral force is so small to a small number of members. The maximum moment occurs at the two ends of member and the bending moments on the two ends are almost in the opposite direction. The analysis results for the structure which is subjected to seismic action in three directions [
The displacement peak points.
The plastic hinge state of roof by moment
The plastic hinge state of roof by moment
The five bottom chord members around the node number 2039 are selected to be the damage case according to the analysis result of the structure which is subjected to seismic action. The selected damage locations are shown in Figure
The placements of the five damaged elements.
The placements of the elements
The five elements in model
The training, validation and prediction data for BPNN are from the structural analysis results on various damage models which are subjected to 36 kinds of earth pulsation load cases and the earth pulsations are simulated by white noises. For the first load case, the amplitudes of simulated white noise in
The acceleration time series in
The acceleration time series in
The acceleration time series in
For other load cases, amplitudes of each white noise in three directions only are changed, which implies that the acceleration amplitudes of earth pulsations in three directions are changed. The amplitudes of 36 kinds of simulated earth pulsations are shown in Table
The values of the load cases.
Number |
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1 | 0.100 | 0.080 | 0.060 |
2 | 0.150 | 0.120 | 0.090 |
3 | 0.175 | 0.140 | 0.105 |
4 | 0.200 | 0.160 | 0.120 |
5 | 0.225 | 0.180 | 0.135 |
6 | 0.250 | 0.200 | 0.150 |
7 | 0.275 | 0.220 | 0.165 |
8 | 0.300 | 0.240 | 0.180 |
9 | 0.325 | 0.260 | 0.195 |
10 | 0.350 | 0.280 | 0.210 |
11 | 0.375 | 0.300 | 0.225 |
12 | 0.400 | 0.320 | 0.240 |
13 | 0.425 | 0.340 | 0.255 |
14 | 0.450 | 0.360 | 0.270 |
15 | 0.475 | 0.380 | 0.285 |
16 | 0.500 | 0.400 | 0.300 |
17 | 0.525 | 0.420 | 0.315 |
18 | 0.550 | 0.440 | 0.330 |
19 | 0.575 | 0.460 | 0.345 |
20 | 0.600 | 0.480 | 0.360 |
21 | 0.625 | 0.500 | 0.375 |
22 | 0.650 | 0.520 | 0.390 |
23 | 0.675 | 0.540 | 0.405 |
24 | 0.700 | 0.560 | 0.420 |
25 | 0.725 | 0.580 | 0.435 |
26 | 0.750 | 0.600 | 0.450 |
27 | 0.775 | 0.620 | 0.465 |
28 | 0.800 | 0.640 | 0.480 |
29 | 0.825 | 0.660 | 0.495 |
30 | 0.850 | 0.680 | 0.510 |
31 | 0.875 | 0.700 | 0.525 |
32 | 0.900 | 0.720 | 0.540 |
33 | 0.925 | 0.740 | 0.555 |
34 | 0.950 | 0.760 | 0.570 |
35 | 0.975 | 0.780 | 0.585 |
36 | 1.000 | 0.800 | 0.600 |
The data for training, validation, and prediction.
Group | Damage model (elastic modulus after damage) | Load cases (number, as shown in Table |
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Validation group |
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6, 12, 18, 24, 30, 36 |
Prediction group |
|
5, 10, 15, 20, 25, 31 |
Training group | The other 14 kinds | The other 24 kinds |
According to Tables
The MAC value is used to evaluate the sensitivity of the selected damage parameters, where the smaller value of MAC is, the more sensitivity of the damage parameter is [
The candidate placements for strain sensors are shown in Figure
The previous placements of strain sensors.
The placements of strain sensors
The numbered strain sensors
Five scenarios on the number and placements of strain sensors are set as follows: (1)
For each strain damage parameter vector, the calculation results of sensitivity are shown in Table
The MAC values of damage parameter induced by strain sensors.
Time steps | Scenario on the number and placements of strain sensors | ||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |
5 | 0.921 | 0.598 | 0.803 | 0.610 | 0.216 |
7 | 0.727 | 0.362 | 0.669 | 0.290 | 0.372 |
9 | 0.403 | 0.203 | 0.002 | 0.048 | 0.338 |
11 | 0.903 | 0.679 | 0.844 | 0.715 | 0.342 |
13 | 0.631 | 0.441 | 0.761 | 0.361 | 0.558 |
15 | 0.526 | 0.284 | 0.005 | 0.082 | 0.257 |
In order to validate the effectiveness of the strain damage parameter, the noisy measurements are considered, where the strain measurements, the noisy strain measurements, and the noise are shown in Figures
The time series of the strain sensor without noise.
The time series of the strain sensor with noise.
The time series of noise with 4% noise level.
The MAC values of strain damage parameter vector using noisy measurements are compared in Tables
The MAC values of stain damage parameter vector extracted from different load cases.
Noise levels | Damage extents | ||||
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0.00 | 0.0051 | 0.0050 | 0.0048 | 0.0047 | 0.0046 |
0.01 | 0.0477 | 0.0709 | 0.3940 | 0.2398 | 0.1891 |
0.02 | 0.0579 | 0.0650 | 0.2540 | 0.0139 | 0.0313 |
0.04 | 0.0001 | 0.2316 | 0.1417 | 0.0008 | 0.0180 |
0.08 | 0.0001 | 0.0373 | 0.0012 | 0.2914 | 0.0024 |
0.10 | 0.3863 | 0.0268 | 0.0010 | 0.0036 | 0.0118 |
The MAC values of stain damage parameter vector extracted from the same load case.
Noise levels | Damage extents | ||||
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0.00 | 1.0000 | 0.9998 | 0.9989 | 0.9961 | 0.9905 |
0.01 | 0.4538 | 0.5548 | 0.2523 | 0.6695 | 0.0366 |
0.02 | 0.0072 | 0.0011 | 0.0037 | 0.0129 | 0.0000 |
0.04 | 0.0042 | 0.0068 | 0.0235 | 0.0261 | 0.0015 |
0.08 | 0.1638 | 0.1018 | 0.0064 | 0.0010 | 0.0000 |
0.10 | 0.0692 | 0.0682 | 0.2063 | 0.0292 | 0.0657 |
It can be known from Tables
The candidate placements for accelerometers are shown in Figure
The previous placements of accelerometer.
Five scenarios on the number and placements of accelerometers are set as follows: (1)
For each acceleration damage parameter vector, the calculation results of sensitivity are shown in Tables
The MAC values of acceleration damage parameter in
Mode | Number of accelerometers | ||||
---|---|---|---|---|---|
9 | 6 | 6 | 5 | 4 | |
2 | 0.042 | 0.367 | 0.602 | 0.533 | 0.049 |
4 | 0.055 | 0.522 | 0.033 | 0.533 | 0.906 |
7 | 0.055 | 0.264 | 0.092 | 0.335 | 0.611 |
10 | 0.036 | 0.216 | 0.440 | 0.954 | 0.224 |
14 | 0.001 | 0.010 | 0.002 | 0.331 | 0.001 |
18 | 0.242 | 0.405 | 0.348 | 0.472 | 0.148 |
The MAC values of acceleration damage parameter in
Mode | Number of accelerometers | ||||
---|---|---|---|---|---|
9 | 6 | 6 | 5 | 4 | |
1 | 0.234 | 0.933 | 0.608 | 0.230 | 0.581 |
4 | 0.010 | 0.861 | 0.002 | 0.060 | 0.810 |
7 | 0.009 | 0.779 | 0.062 | 0.162 | 0.046 |
9 | 0.086 | 0.900 | 0.204 | 0.417 | 0.268 |
17 | 0.100 | 0.648 | 0.085 | 0.071 | 0.737 |
19 | 0.221 | 0.842 | 0.231 | 0.020 | 0.669 |
The MAC values of acceleration damage parameter in
Mode | Number of accelerometers | ||||
---|---|---|---|---|---|
9 | 6 | 6 | 5 | 4 | |
3 | 0.003 | 0.027 | 0.102 | 0.423 | 0.007 |
8 | 0.397 | 0.021 | 0.222 | 0.464 | 0.044 |
16 | 0.081 | 0.299 | 0.024 | 0.201 | 0.004 |
27 | 0.039 | 0.041 | 0.236 | 0.014 | 0.082 |
28 | 0.039 | 0.041 | 0.236 | 0.014 | 0.082 |
29 | 0.010 | 0.018 | 0.054 | 0.074 | 0.023 |
In order to analyze the effectiveness of the selected acceleration damage parameter vectors, the MAC values on noisy acceleration measurements are discussed. The acceleration measurements, the noisy acceleration measurements, and the noise are shown in Figures
The time series of the accelerometer without noise.
The time series of the accelerometer with noise.
The acceleration noise with 10% noise level.
The MAC values of acceleration damage parameter vector using noisy measurements are compared in Tables
The MAC values of acceleration damage parameter vector extracted from different load cases.
Noise levels | Damage extents | ||||
---|---|---|---|---|---|
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0.00 | 0.1057 | 0.0843 | 0.0673 | 0.0568 | 0.0512 |
0.01 | 0.1601 | 0.1471 | 0.1013 | 0.0769 | 0.0765 |
0.02 | 0.0957 | 0.0912 | 0.0140 | 0.0146 | 0.0914 |
0.04 | 0.0301 | 0.0229 | 0.1233 | 0.0617 | 0.0809 |
0.08 | 0.6297 | 0.4090 | 0.3884 | 0.5173 | 0.3854 |
0.10 | 0.0028 | 0.0039 | 0.0024 | 0.0015 | 0.0039 |
The MAC values of acceleration damage parameter vector extracted from the same load case.
Noise levels | Damage extents | ||||
---|---|---|---|---|---|
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0.00 | 0.9999 | 0.9976 | 0.9868 | 0.9573 | 0.9064 |
0.01 | 0.9994 | 0.9832 | 0.9772 | 0.9725 | 0.9987 |
0.02 | 0.9659 | 0.9552 | 0.9213 | 0.9900 | 0.7671 |
0.04 | 0.9574 | 0.9265 | 0.9902 | 0.9799 | 0.9832 |
0.08 | 0.7293 | 0.2113 | 0.8939 | 0.1842 | 0.5951 |
0.10 | 0.9585 | 0.8510 | 0.2923 | 0.9885 | 0.3672 |
It can be known from Tables
Based on the optimal selection on the strain damage parameter and the acceleration damage parameter, the sensitivity of multiscale damage parameter is analyzed. The MAC values of multiscale damage parameter vector using noisy measurements are compared in Tables
The MAC values of multiscale damage parameter vector extracted from different load cases.
Noise levels | Damage extents | ||||
---|---|---|---|---|---|
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0.00 | 0.0378 | 0.0297 | 0.0233 | 0.0194 | 0.0173 |
0.01 | 0.0578 | 0.1018 | 0.0877 | 0.0385 | 0.0632 |
0.02 | 0.0871 | 0.0632 | 0.0141 | 0.0145 | 0.0149 |
0.04 | 0.0014 | 0.0373 | 0.0001 | 0.0011 | 0.0003 |
0.08 | 0.0029 | 0.0028 | 0.0011 | 0.1455 | 0.0090 |
0.10 | 0.0001 | 0.0001 | 0.0013 | 0.0010 | 0.0028 |
The MAC values of multiscale damage parameter vector extracted from the same load case.
Noise levels | Damage extents | ||||
---|---|---|---|---|---|
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0.00 | 0.9998 | 0.9966 | 0.9805 | 0.9342 | 0.8550 |
0.01 | 0.9991 | 0.9799 | 0.9534 | 0.9685 | 0.9976 |
0.02 | 0.7203 | 0.7306 | 0.8239 | 0.9694 | 0.6904 |
0.04 | 0.2148 | 0.2052 | 0.3055 | 0.3178 | 0.0898 |
0.08 | 0.0291 | 0.1810 | 0.8410 | 0.0998 | 0.5351 |
0.10 | 0.3614 | 0.7199 | 0.2158 | 0.8808 | 0.0038 |
It can be seen from Tables
Five kinds of training groups are chosen to obtain the optimal predicted values which can be used to compare the effectiveness of the multiscale damage parameter and sole-scale damage parameter. Based on the training group and all the 24 kinds of load cases listed in Table
According to the empirical equation (
The number of neurons in hidden layers of neural networks.
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1st hidden layer | 2nd hidden layer |
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4 | 2 | 13 | 6 |
6 | 2 | 15 | 6 |
6 | 4 | 15 | 7 |
8 | 5 | 17 | 8 |
The data from validation groups are used to choose the optimal architecture of the neural networks which have the different sets and number of neurons in the hidden layer. It is shown in Table
The identification errors of neural networks based on strain damage parameters.
Training functions | Sets | Neurons | Noise levels | Maximum error | |||||
---|---|---|---|---|---|---|---|---|---|
0.00 | 0.01 | 0.02 | 0.04 | 0.08 | 0.10 | ||||
T_LM | 192 | (13,6) | 0.057 | 0.195 | 0.264 | 0.180 | 0.156 | 0.164 | 0.264 |
T_LM | 192 | (15,6) | 0.118 | 0.365 | 0.202 | 0.182 | 0.231 | 0.230 | 0.365 |
T_LM | 192 | (15,7) | 0.064 | 0.256 | 0.185 | 0.172 | 0.714 | 0.117 | 0.714 |
T_LM | 192 | (17,8) | 0.066 | 0.346 | 0.252 | 0.153 | 0.172 | 0.198 | 0.346 |
T_LM | 240 | (13,6) | 0.040 | 0.202 | 0.151 | 0.186 | 0.161 | 0.162 | 0.202 |
T_LM | 240 | (15,6) | 0.068 | 0.156 | 0.151 | 0.134 | 0.279 | 0.127 | 0.279 |
T_LM | 240 | (15,7) | 0.046 | 0.182 | 0.135 | 0.925 | 0.172 | 0.150 | 0.925 |
T_LM | 240 | (17,8) | 0.077 | 0.343 | 0.194 | 0.246 | 0.165 | 0.157 | 0.343 |
T_LM | 264 | (13,6) | 0.086 | 0.400 | 0.182 | 0.509 | 0.228 | 0.164 | 0.509 |
T_LM | 264 | (15,6) | 0.239 | 0.380 | 0.174 | 0.750 | 0.149 | 0.160 | 0.750 |
T_LM | 264 | (15,7) | 0.082 | 0.164 | 0.176 | 0.151 | 0.197 | 0.192 | 0.197 |
T_LM | 264 | (17,8) | 0.041 | 0.245 | 0.222 | 0.163 | 0.309 | 0.172 | 0.309 |
T_LM | 288 | (13,6) | 0.044 | 0.136 | 0.390 | 0.145 | 0.112 | 0.165 | 0.390 |
T_LM | 288 | (15,6) | 0.144 | 0.157 | 0.196 | 0.142 | 0.122 | 0.149 | 0.196 |
T_LM | 288 | (15,7) | 0.067 | 0.242 | 0.224 | 0.178 | 0.404 | 0.257 | 0.404 |
T_LM | 288 | (17,8) | 0.095 | 0.158 | 0.268 | 0.109 | 0.128 | 0.141 | 0.268 |
T_LM | 336 | (13,6) | 0.082 | 0.111 | 0.125 | 0.103 | 0.255 | 0.114 | 0.255 |
T_LM | 336 | (15,6) | 0.039 | 0.149 | 0.245 | 0.126 | 0.273 | 0.193 | 0.273 |
T_LM | 336 | (15,7) | 0.044 | 0.169 | 0.130 | 0.081 | 0.128 | 0.484 | 0.484 |
T_LM | 336 | (17,8) | 0.040 | 0.322 | 0.196 | 0.149 | 0.067 | 0.055 | 0.322 |
The choice of the best neural network based on the strain damage parameters.
Training functions | Sets | Neurons | Noise levels | Maximum error | |||||
---|---|---|---|---|---|---|---|---|---|
0.00 | 0.01 | 0.02 | 0.04 | 0.08 | 0.10 | ||||
T_LM | 288 | (15,6) | 0.144 | 0.157 | 0.196 | 0.142 | 0.122 | 0.149 | 0.196 |
T_SCG | 192 | (15,6) | 0.286 | 0.275 | 0.177 | 0.266 | 0.199 | 0.206 | 0.286 |
T_RP | 264 | (15,7) | 0.261 | 0.229 | 0.391 | 0.308 | 0.295 | 0.335 | 0.391 |
T_GDM | 192 | (15,6) | 1.073 | 0.572 | 1.031 | 1.633 | 0.826 | 1.580 | 1.633 |
T_GDX | 240 | (17,8) | 0.493 | 0.304 | 0.392 | 0.593 | 0.297 | 0.087 | 0.593 |
T_CGF | 192 | (13,6) | 0.251 | 0.214 | 0.169 | 0.153 | 0.268 | 0.305 | 0.305 |
T_BFG | 192 | (15,6) | 0.499 | 0.484 | 0.198 | 0.184 | 0.184 | 0.240 | 0.499 |
The choice of the best neural network based on the acceleration damage parameters.
Training functions | Sets | Neurons | Noise levels | Maximum error | |||||
---|---|---|---|---|---|---|---|---|---|
0.00 | 0.01 | 0.02 | 0.04 | 0.08 | 0.10 | ||||
T_LM | 264 | (13,6) | 0.083 | 0.153 | 0.158 | 0.148 | 0.167 | 0.168 | 0.168 |
T_SCG | 192 | (15,7) | 0.196 | 0.486 | 0.429 | 0.307 | 0.365 | 0.223 | 0.486 |
T_RP | 240 | (15,6) | 0.075 | 0.194 | 0.296 | 0.276 | 0.261 | 0.256 | 0.296 |
T_GDM | 288 | (15,6) | 0.838 | 1.008 | 1.190 | 0.679 | 1.021 | 1.462 | 1.462 |
T_GDX | 240 | (15,6) | 0.172 | 0.105 | 0.274 | 0.195 | 0.204 | 0.332 | 0.332 |
T_CGF | 240 | (15,7) | 0.156 | 0.230 | 0.151 | 0.173 | 0.201 | 0.197 | 0.230 |
T_BFG | 192 | (15,7) | 0.303 | 0.428 | 0.339 | 0.193 | 0.211 | 0.144 | 0.428 |
It can be known from Tables
The identification errors of forecasted cases based on strain damage parameters.
Number | Damage extents | Load cases | Noise levels | Maximum error | |||||
---|---|---|---|---|---|---|---|---|---|
0.00 | 0.01 | 0.02 | 0.04 | 0.08 | 0.10 | ||||
1 |
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5 | 0.186 | 0.086 | 0.247 | 0.124 | 0.145 | 0.129 | 0.247 |
2 |
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10 | 0.013 | 0.022 | 0.084 | 0.097 | 0.274 | 0.048 | 0.274 |
3 |
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15 | 0.046 | 0.087 | 0.037 | 0.002 | 0.037 | 0.065 | 0.087 |
4 |
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20 | 0.030 | 0.041 | 0.278 | 0.021 | 0.114 | 0.102 | 0.278 |
5 |
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25 | 0.036 | 0.144 | 0.140 | 0.042 | 0.103 | 0.109 | 0.140 |
6 |
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31 | 0.019 | 0.104 | 0.180 | 0.138 | 0.108 | 0.165 | 0.180 |
The identification errors of forecasted cases based on acceleration damage parameters.
Number | Damage extents | Load cases | Noise levels | Maximum error | |||||
---|---|---|---|---|---|---|---|---|---|
0.00 | 0.01 | 0.02 | 0.04 | 0.08 | 0.10 | ||||
1 |
|
5 | 0.147 | 0.012 | 0.209 | 0.145 | 0.118 | 0.210 | 0.210 |
2 |
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10 | 0.108 | 0.112 | 0.077 | 0.244 | 0.086 | 0.041 | 0.244 |
3 |
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15 | 0.002 | 0.065 | 0.159 | 0.007 | 0.054 | 0.232 | 0.232 |
4 |
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20 | 0.071 | 0.265 | 0.104 | 0.146 | 0.006 | 0.034 | 0.265 |
5 |
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25 | 0.018 | 0.251 | 0.068 | 0.078 | 0.101 | 0.013 | 0.251 |
6 |
|
31 | 0.011 | 0.283 | 0.029 | 0.108 | 0.061 | 0.174 | 0.283 |
The identification errors of the forecasted cases based on optimal neural networks.
Input vector | Sets | Neurons | Noise levels | Maximum error | |||||
---|---|---|---|---|---|---|---|---|---|
0.00 | 0.01 | 0.02 | 0.04 | 0.08 | 0.10 | ||||
Strain | 288 | (15,6) | 0.055 | 0.081 | 0.161 | 0.071 | 0.130 | 0.103 | 0.161 |
Acceleration | 264 | (13,6) | 0.059 | 0.165 | 0.108 | 0.121 | 0.071 | 0.117 | 0.165 |
The multiscale damage parameter, combined with the strain damage parameter and the acceleration damage parameter, is used to discuss the effectiveness of damage evaluation. The same procedure on selecting the optimal architecture of neural network is processed to the multiscale damage parameter, where the Levenberg-Marquardt algorithm is the best training function for multiscale damage parameter. The errors of the prediction scenarios are listed in Table
The identification errors of forecasted cases based on multiscale damage parameters.
Number | Damage extents | Load cases | Noise levels | Maximum error | |||||
---|---|---|---|---|---|---|---|---|---|
0.00 | 0.01 | 0.02 | 0.04 | 0.08 | 0.10 | ||||
1 |
|
5 | 0.179 | 0.100 | 0.009 | 0.043 | 0.021 | 0.003 | 0.179 |
2 |
|
10 | 0.109 | 0.110 | 0.051 | 0.112 | 0.083 | 0.110 | 0.110 |
3 |
|
15 | 0.173 | 0.152 | 0.118 | 0.135 | 0.006 | 0.122 | 0.173 |
4 |
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20 | 0.166 | 0.028 | 0.353 | 0.019 | 0.164 | 0.025 | 0.353 |
5 |
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25 | 0.065 | 0.005 | 0.061 | 0.109 | 0.218 | 0.053 | 0.218 |
6 |
|
31 | 0.001 | 0.125 | 0.115 | 0.210 | 0.063 | 0.124 | 0.210 |
The identification errors of forecasted cases based on three different input vectors.
Input vectors | Sets | Neurons | Noise levels | Maximum error | |||||
---|---|---|---|---|---|---|---|---|---|
0.00 | 0.01 | 0.02 | 0.04 | 0.08 | 0.10 | ||||
Strain | 288 | (15,6) | 0.055 | 0.081 | 0.161 | 0.071 | 0.130 | 0.103 | 0.161 |
Acceleration | 264 | (13,6) | 0.059 | 0.165 | 0.108 | 0.121 | 0.071 | 0.117 | 0.165 |
Combination | 336 | (19,6) | 0.059 | 0.096 | 0.118 | 0.126 | 0.085 | 0.106 | 0.126 |
The paper proposed an effective damage identification method based on the multiscale measurements from strain sensors and accelerometers using artificial neural networks. The conclusions are obtained as follows. According to the principle of MAC, the method of sensitivity analysis on structural damage index is given and the optimal damage parameter vector is determined. The optimal architectures of neural networks using the strain damage parameter and acceleration damage parameter as the input are discussed and selected, while the identification errors are listed for each scenario in prediction groups. The optimal architecture of neural networks using the multiscale damage parameter as the input is discussed and selected, while the identification errors are compared with those using the sole-scale damage parameter, such as strain damage parameter and acceleration damage parameter. The proposed damage identification method is proofed to be effective and the identification errors of performance are better. The proposed method can be used for a real large span space structure and the elastoplastic analysis should be processed at the beginning of selecting unfavorable structural members.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the National Science Foundation of China (Grant no. 51308162), Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIT.NSRIF.2015085), and the Supporting Project for Junior Faculties of Harbin Institute of Technology Shenzhen Graduate School.