- freely available
Sensors 2015, 15(9), 24428-24444; https://doi.org/10.3390/s150924428
2. Identification Models
2.1. Back-Propagation Neural Networks (BPN)
2.2. Cascade- Forward Back-Propagation Neural Network (CFN)
2.3. Adaptive Filter Neural Network (ADFN)
2.4. Extended Kalman Filter Neural Network (EKFN)
3. Results and Discussions
3.1. Simulation Noise Results
|MAE||0.0093||8.65 × 10−4||0.0024||0.0037|
|MSE||1.22 × 10−4||1.206 × 10−5||7.98 × 10−6||3.174 × 10−5|
3.2. GPS-Bridge Movement Application: Case Study
|Parameter||Original Signal||MFM Model||ADFN Model|
|MAE (mm)||5.789 × 10−3||5.119 × 10−3||4.018 × 10−3|
|MSE (mm)||7.575 × 10−5||5.872 × 10−5||3.742 × 10−5|
|STD (mm)||8.703 × 10−3||7.663 × 10−3||6.117 × 10−3|
|Absolute Max (mm)||8.861 × 10−2||5.611 × 10−2||4.773 × 10−2|
- The multi-step filtering procedure can be constrained to de-noise the noisy measurements of the oscillations of structures, and to determine its oscillation amplitude and modal frequency. In addition, it is concluded that the ADFN is the best model and thus suggested for use to de-noise the GPS measurements. In addition, the ADFN model is observed to be more effective and accurate than MFM model for de-noising short-period components of displacements of GPS real monitoring data in time and frequency domains.
- The apparent displacement measurements contain noises that can be considered as vibration and background noises. Moreover, the ADFN model increased the accuracy of short-period displacement by 83.3% in the x and y directions and by 93.8% in the z direction.
- The de-noised short-period displacement component of the measurements has decreased the power spectrum density to 98%. This means that the noise has high effect on the high and low frequency vibration modes of structures. From the frequency modes calculations, it is assumed that the low frequency modes of the short-period displacement component values are between 0–0.2 Hz.
- The GPS measurements with a sampling rate of 1.0 Hz may in fact underestimate the amplitude of displacement components, this problem, however, can be expected to overcome with the modern high-frequency GPS.
- The de-noised short-period displacement component based on NN predictive models is expected to have significant implications in the SHM and the design of structures in the low-frequency content.
Conflicts of Interest
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