# Optimizing the De-Noise Neural Network Model for GPS Time-Series Monitoring of Structures

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Identification Models

#### 2.1. Back-Propagation Neural Networks (BPN)

_{i}, i = 1,2,…n) assume an input unit and transmits these signals to the hidden units. Each hidden unit (Z

_{j}, j = 1,2,…m) calculates the sum of the weighted input signals, applies an activation function (f) and sends their result to the output unit [24]. The process of input signals to the hidden layer and output hidden layers can be represented as follow:

_{i}are the bias on the hidden node and weight factor from input to hidden units.

_{j}are the bias on the output node and weight factor from hidden to the output units.

_{k}(n) and δ

_{i}(n) are the error coefficients at the output and hidden nodes, respectively.

#### 2.2. Cascade- Forward Back-Propagation Neural Network (CFN)

#### 2.3. Adaptive Filter Neural Network (ADFN)

#### 2.4. Extended Kalman Filter Neural Network (EKFN)

_{p}and w

_{0}are coefficients and biases, these are lumped together into the weight vector w.

_{t}be the error made in approximating f by the NN, implementing the mapping λ for the input signal x

_{t}. Such a network can be represented as:

_{t}of the NN at times t = 1, 2,…n are as follow:

_{t}is the Kalman gain matrix, C

_{t}is a matrix of derivatives of λ

_{i}, R

_{t}and Q

_{t}are the covariance matrix for the process noise and measurement errors as shown in Equations (1) and (2). Herein, in this model assumed P

_{0}and R

_{t}symmetric positive definite matrices, Q

_{t}a symmetric positive semi definite matrix, and Equation (13) is initialized with a given w

_{0}[29].

## 3. Results and Discussions

#### 3.1. Simulation Noise Results

Models | BPN | CFN | ADFN | EKFN |
---|---|---|---|---|

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} |

R-Square | 0.987 | 0.986 | 0.997 | 0.992 |

^{−6}) values are shown with ADFN model. Therefore, it can be considered that the ADFN is the best model to predict the true position of the sensors’ monitoring for the noisy signals. Meanwhile, it can be shown that the models CFN and EKFN performed as second best, due to high fitting shown and low absolute and mean square errors for the two models. In addition, the CFN gives a quite low value of MAE (8.65 × 10

^{−4}). Therefore, the CFN, ADFN and EKFN models have shown better results than BPN which is recommended by Chen et al. [19]. In addition, the results show clearly that the NN model filter can be efficiently used to remove the white noise signals for the random process of structures. It implies the multi-step filtering procedure can be constrained to de-noise the noisy sensor recordings for the structural oscillations and to determine its oscillation amplitude and modal frequency; this outcome complies with the results obtained by Moschas and Stiros [1]. Based on these results, it can be concluded that the ADFN served most effectively to predict the accurate monitoring for the noisy signals, therefore, the de-noised signals can be used to evaluate the movements of structures. The next section contains a case study to investigate this conclusion.

**Figure 5.**Comparison of the simulation results (

**a**) Back-Propagation Neural Network (BPN); (

**b**) Cascade- Forward Back-Propagation Neural Network (CFN); (

**c**) Adaptive Filter Neural Network (ADFN); (d) Extended Kalman Filter Neural Network (EKFN).

#### 3.2. GPS-Bridge Movement Application: Case Study

**Figure 8.**Dynamic performance for z direction. (

**a**) Long period displacement; (

**b**) Short period displacement; (

**c**) Multi filter method (MFM) de-noise frequency contents; (

**d**) ADFN de-noise frequency contents.

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} |

## 4. Conclusions

- (1)
- 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.
- (2)
- 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.
- (3)
- 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.
- (4)
- 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.
- (5)
- 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.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Moschas, F.; Stiros, S. Measurement of the dynamic displacements and of the modal frequencies of a short-span pedestrian bridge using GPS and an accelerometer. Eng. Struct.
**2011**, 33, 10–17. [Google Scholar] [CrossRef] - Moschas, F.; Stiros, S. Noise characteristics of high-frequency, short-duration GPS records from analysis of identical, collocated instruments. Measurement
**2013**, 46, 1488–1506. [Google Scholar] [CrossRef] - Gorski, P. Investigation of dynamic characteristic of tall industrial chimney based on GPS measurements using random decrement method. Eng. Struct.
**2015**, 83, 30–49. [Google Scholar] [CrossRef] - Yia, T.H.; Lia, H.N.; Gub, M. Experimental assessment of high-rate GPS receivers for deformation monitoring of bridge. Measurement
**2013**, 46, 420–432. [Google Scholar] [CrossRef] - Jeon, H.; Shin, J.U.; Myung, H. The displacement estimation error back-propagation (DEEP) method for a multiple structural displacement monitoring system. Meas. Sci. Technol.
**2013**. [Google Scholar] [CrossRef] - Psimoulis, P.; Ghilardi, M.; Fouache, E.; Stiros, S. Subsidence and evolution of the Thessaloniki plain, Greece, based on historical leveling and GPS data. Eng. Geol.
**2007**, 90, 55–70. [Google Scholar] [CrossRef] - Gikas, V. Three-dimensional laser scanning for geometry documentation and construction management of highway tunnel during excavation. Sensors
**2012**, 12, 11249–11270. [Google Scholar] [CrossRef] [PubMed] - Kaloop, M.; Kim, D. De-noising of GPS structural monitoring observation error using wavelet analysis. Geomat. Nat. Hazard. Risk
**2014**. [Google Scholar] [CrossRef] - Oludolapo, O.A.; Jimoh, A.A.; Kholopane, P.A. Comparing performance of MLP and RBF neural network models for predicting South Africa’s energy consumption. J. Energ. South. Afr.
**2012**, 23, 40–46. [Google Scholar] - Binti-Idris, A.; Bin-Rahim, R.F.; Ali, D. The effect of additive white gaussian noise and multipath rayleigh fading on ber statistic in digital cellular network. In Proceedings of the International RF and Microwave Conference, Putrajaya, Malaysia, 12–14 September 2006.
- Haykin, S. Kalman Filtering and Neural Networks; John Wiley & Sons, Inc.: New York, NY, USA, 2002. [Google Scholar]
- Wang, J.W.; Wang, J.; Sinclair, D.; Watts, L. Designing a neural network for GPS/INS/PL integration. In Proceedings of the International Global Navigation Satellite System Society IGNSS Symposium, Sydney, Australia, 17–21 July 2006.
- Zhang, X.; Liu, Y.; Yang, M.; Zhang, T.; Young, A.; Li, X. Comparative study of four time series methods in forecasting typhoid fever incidence in China. PLoS ONE
**2013**. [Google Scholar] [CrossRef] [PubMed] - Jwo, D.; Huang, H. Neural network aided adaptive extended Kalman filtering approach for DGPS positioning. J. Navig.
**2004**, 57, 449–463. [Google Scholar] [CrossRef] - Kaloop, M.; Kim, D. GPS-structural health monitoring of a long span bridge using neural network adaptive filter. Surv. Rev.
**2014**, 46, 7–14. [Google Scholar] [CrossRef] - Akyılmaz, O.; Çelik, R.N.; Apaydın, N.; Ayan, T. GPS monitoring of the Fatih Sultan Mehmet suspension bridge by using assessment methods of neural network. Spat. Inf. Sci.
**2004**, 34, 702–707. [Google Scholar] - Kaloop, M.R.; Hu, J.W. Stayed-cable bridge damage detection and localization based on accelerometer health monitoring measurements. Shock Vib.
**2015**, in press. [Google Scholar] - Pantazis, G.; Alevizakou, E.G. The use of artificial neural networks in predicting vertical displacements of structures. Int. J. Appl. Sci. Technol.
**2013**, 3, 1–8. [Google Scholar] - Chen, Y.; Akutagawa, M.; Katayama, M.; Zhang, Q.; Kinouchi, Y. Neural network based EEG denoising. In Proceedings of the 30th Annual International IEEE EMBS Conference, Vancouver, BC, Canada, 20–24 August 2008.
- El-Rabbany, A.; El-Diasty, M. An efficient neural network model for de-noising of MEMS-based inertial data. J. Navig.
**2004**, 57, 407–415. [Google Scholar] [CrossRef] - Malleswarana, M.; Vaidehib, V.; Sivasankari, N. A novel approach to the integration of GPS and INS using recurrent neural networks with evolutionary optimization techniques. Aerosp. Sci. Technol.
**2014**, 32, 169–179. [Google Scholar] [CrossRef] - Chen, X.; Shena, C.; Zhang, W.; Tomizuka, M.; Xu, Y.; Chiu, K. Novel hybrid of strong tracking Kalman filter and wavelet neural network for GPS/INS during GPS outages. Measurement
**2013**, 46, 3847–3854. [Google Scholar] [CrossRef] - Roy, N.; Ganguli, R. Filter design using radial basis function neural network and genetic algorithm for improved operational health monitoring. Appl. Soft Comput.
**2006**, 6, 154–169. [Google Scholar] [CrossRef] - Oliveira, M.A. An application of neural networks trained with kalman filter variants (ekf and ukf) to heteroscedastic time series forecasting. Appl. Math. Sci.
**2012**, 6, 3675–3686. [Google Scholar] - Bachir, G.; Habib, M.; Amar, K.; Youcef, L. The GRNN and the RBF Neural Networks for 2D Displacement Field Modelling. Case study: GPS Auscultation Network of LNG reservoir (GL4/Z industrial complex—Arzew, Algeria). Available online: http://www.fig.net/resources/proceedings/fig_proceedings/fig2012/papers/ts01f/TS01F_gourine_mahi_et_al_5684.pdf (accessed on 18 September 2015).
- Goyal, S.; Goyal, G.K. Cascade and feed-forward back-propagation artificial neural network models for prediction of sensory quality of instant coffee flavoured sterilized drink. Can. J. Artif. Intell. Mach. Pattern Recognit.
**2011**, 2, 78–82. [Google Scholar] - Mistry, D.; Kulkarni, A.V. Noise cancellation using adaptive filter base on neural networks. ITSI Trans. Electron. Electron. Eng.
**2013**, 1, 87–91. [Google Scholar] - Chang, C.L.; Juang, J.C. An adaptive multipath mitigation filter for gnss applications. EURASIP J. Adv. Signal Proc.
**2008**. [Google Scholar] [CrossRef] - Alessandri, A.; Cuneo, M.; Pagnan, S.; Sanguineti, M. On the convergence of EKF-based parameters optimization for neural networks. In Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, USA, 9–12 December 2003.
- Kaloop, M. Bridge safety monitoring based-GPS technique: Case study Zhujiang Huangpu Bridge. Smart Struct. Syst.
**2012**, 9, 473–487. [Google Scholar] [CrossRef]

© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kaloop, M.R.; Hu, J.W.
Optimizing the De-Noise Neural Network Model for GPS Time-Series Monitoring of Structures. *Sensors* **2015**, *15*, 24428-24444.
https://doi.org/10.3390/s150924428

**AMA Style**

Kaloop MR, Hu JW.
Optimizing the De-Noise Neural Network Model for GPS Time-Series Monitoring of Structures. *Sensors*. 2015; 15(9):24428-24444.
https://doi.org/10.3390/s150924428

**Chicago/Turabian Style**

Kaloop, Mosbeh R., and Jong Wan Hu.
2015. "Optimizing the De-Noise Neural Network Model for GPS Time-Series Monitoring of Structures" *Sensors* 15, no. 9: 24428-24444.
https://doi.org/10.3390/s150924428