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M. R. Kaloop et al. / Advanced Engineering and Research (AER) 00 (2016) 0000~0000

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

Mosbeh R.Kaloop1, a and Jong Wan Hu2, b

1Incheon Disaster Prevention Research Center, Incheon National University, 12-1 Songdo-dong, Yeonsu-gu, Incheon, 406-840, Republic of Korea

2 Department of Civil and Environmental Engineering, University of Incheon, Incheon, 406-840, Republic of Korea

aeat@conf.org, bietp@conf.org, cidprc@incheon.ac.kr (Corresponding Author)

(Manuscript Received 000 0, 2009; Revised 000 0, 2009; Accepted 000 0, 2009) -please leave blank

Abstract. The Global Positioning System (GPS) monitoring system is recently used widely in structures and other applications. Notwithstanding, the GPS accuracy still suffers from its errors, and that affects the measurements, particularly the short-period displacement component of structures. Therefore, this paper aims to use neural network prediction models to improve the GPS monitoring time series data. Four methods are applied and used with neural network solutions, which are Back-propagation, Cascade-forward back-propagation, Adaptive filter, and Extended Kalman filter to estimate the optimize model which can be recommended. The noise simulation with the bridge short-period GPS monitoring displacement component of one Hz sampling frequency is used to validate the four models. The results show that the Adaptive filter neural network is recommended to be used as a tool for de-noising the observations, particularly for the GPS displacement components of structures. In addition, it is expected of this model to have an important influence in the design of structures in the low frequency contents responses and measurements.

Keywords: GPS, De-Noise, Monitoring, Neural Network

Introduction

The extracted displacement components of structures are one of the important structural health monitoring (SHM) parameters, which can be used to predict the behavior of different types of structure applications. A real-time monitoring system using Global Positioning System (GPS) in SHM is now add more advantages for monitoring displacement components behavior (static, semi-static, and dynamic components) of structures with high sampling frequency [1-3]. GPS is one of the best sensors for deformation monitoring, that’s because the high sensitivity and lower labor consuming than that of traditional geodetic survey techniques and other sensors [4-5]. However, the drawbacks and errors still affect the accuracy of the GPS measurements. In addition, Moschas and Stiros [2] have concluded that the noise characteristics of short duration records describing dynamic effects are not well understood, that is may be because the high rate of GPS sensors; however the noise characteristics should be studied to know its properties and characteristics.

Moschas and Stiros [2, 6] have represented the identification of signal that can be defined as a real challenge for the geodesy, structure, and earthquake engineering. Linear and non-linear identification methods can be used to predict the displacement components of different structure applications [7-9]. Linear theory methods are used widely to study the structures behavior under small displacements around a safe state, but this approach does not provide information concerning other characteristics of non-linear systems, such as the magnitude and frequency of any limit-cycle oscillations. For this purpose, non-linear movement analysis is required.

Nowadays, the Neural Networks (NN) can be designed and trained to perform complex functions and solve problems that are difficult for conventional computers and traditional solution methods [10]. The NN models seem to be highly accurate prediction models [7]. NN consist of an input layer, a hidden layer, and an output layer. Each layer is formed by a number of nodes, and each node represents a neuron. Wang et al. [10] and Zhang et al. [11] have summarized the design of NN as follow: NN models are composed of simple elements operating in parallel; a NN models can be trained to perform a particular function by adjusting the values of the weights between elements so that a particular input leads to optimal output [10]. The adjustment of NN depends on a comparison of the output and the target. NN aided adaptive and Kalman filters were used to smooth and filter the dynamic GPS monitoring data [12-13]. El-Rabbany and El-Diasty [14] have used NN models for de-noising Micro-Electro-Mechanical Systems (MEMS)-based inertial data. Moreover, many studies have used NN models to predict a position of monitoring application with integrated GPS/inertial navigation system (INS) [15-16]. These previous studies have revealed that the strength of NN models can be used to predict and de-noise solutions of different monitoring sensor error problems. In the present study, however, we compare different NN models with and without aid filters to optimize NN models that can be used to de-noise the GPS dynamic measurements noises and to extract the displacement components of structures.

Identification Models

The stochastic NN models output only identification system are derived from the state-space models, which expresses the equation of movement as a first-order differential equation, as shown in Fig.1. This equation can be discredited as in (2), where the system is observed by (1).

Fig. 1 Design NN stochastic model identification system.

x_(i+1)=Ax_i+q_i (1)

y_i=Cx_i+e_i (2)

where, x_i is state vector of structures movement responses from N models; y_i is output vector at m locations on the structure and q_iand e_i are Gaussian-distributed process noise and measurement errors vector sequences matching the state and output responses. The coefficients A and C are known as state and output matrices, which are calculated based on NN method. The following models are used widely to predict, smooth, and adjust time series of monitoring points positions with different applications [12-14, 17-18].

Back-propagation neural networks (BPN)

This method is a type of feed forward artificial neural networks. In feed forward neural networks, the data flow processed in one direction and the prediction output obtained based on the current input sets. The architecture of BPN is shown in Fig. 2. The training algorithm depends on the weights assumed; which is initialized as small random values. In feed-forward stage; the input signals (xi, i=1,2,…n) assumed a input unit and transmits these signals to the hidden units. Each hidden unit (Zj, j=1,2,..m) calculates the sums regression weights of input signals and that can be obtained the neuron or activation function (f) and send their result to output unit [18]. The process of input signals to the hidden layer and output hidden layers can be represented as follow:

(3)

In (3) the term b and wi are the bias on the hidden node and weight factor from input to hidden units.

The same for the output layer, the output of BPN can be represented as follow:

(4)

In (4) the term c and wj are the bias on the output node and weight factor from hidden to the output units.

The weights and bias of the output node are updated using gradient-descent based delta-learning rule as follow [9,15]:

(5)

Similarity, the weight and bias of the hidden node are updated as:

(6)

where the weight and bias correction terms can be solved as:

(7)

where, is the learning rate and and are the error coefficients at the output and hidden nodes respectively.

The output error can be calculated by comparing the predicted values with the target outputs. The smaller output error is a better fit of the model. In the case of error does not achieve the accuracy needs required, the network weights should be re adjusted along the opposite direction of the network to the required minimum network error is eventually achieved [11, 19].

Fig. 2 Back-propagation neural networks architecture.

Cascade- forward back-propagation neural network (CFN)

CFN model shown in Fig. 3 is similar to feed-forward networks, but the different is it includes a weight connection from the input to hidden and output layers and from each layer to the sequential layers. However, this process of the feed-forward networks with more layers and weight affects might learn complex relationships more quickly [20]. CFN model is similar to BPN in using the back propagation algorithm for weights generating and updating, but the main advantages of this network is that the output neurons related to input and hidden layer of neurons [15, 20]. So, the output CFN is the sums of all previous layers as follow:

(8)

Fig. 3 Cascade- forward Back-propagation neural networks architecture.

Adaptive filter neural network (ADFN)

The adaptive filter aided neural networks can be used to reduce the sensor noises from unknown noise resources [13, 21]. The operation of such an adaptive filter involves two basic processes; which are a filtering process to produce an output in response to an input sequence; and an adaptive process for the control of adjustable parameters used in the filtering process [21, 22]. In this model, feed forward artificial neural networks were used with adaptive filter to update the weight coefficients. Kaloop and Kim [13] concluded this model and used to de-noise the long period of bridge movement components, but in this study used to estimate the accurate short period displacement component. Fig. 4 shows the ADFN architecture and (9), (10) concluded the methodology used:

(9)

(10)

where, w is the filter weight coefficient, is the step, M is the filter order.

Fig. 4 Adaptive filter neural networks architecture.

Extended Kalman filter neural network (EKFN)

The Kalman filter is a finesses tool to changes the actual system parameters; moreover, it is better tracking ability to the mutation status; and lower sensitivity to system noise, measurement noise and the initial statistical properties [16]. Nowadays, the Extended Kalman Filter (EKF) has been used widely in the application of estimation nonlinear model parameters for the neural networks [18]. In the EKF the nonlinear terms are approximated by linear terms of first order using Taylor expansion. In this model used feed forward artificial neural networks with extended Kalman filter to update the weight coefficients of artificial neural networks model. Based on stochastic model in (1) and (2) and consider a nonlinear system described in [9, 23], it can be assumed an input output mapping of the k-th unit (k=1,2…v) of the l-th (l=1,2,..m) layer is given by:

(11)

where, and are coefficients and biases, these are lumped together into the weight vector .

Now, let ζt be the error made in approximating f by the NN implementing the mapping λ for the input signal xt. Such a network can be represented as:

t=1,2,….n (12)

Herein, the weights optimization used EKF to estimate the of the NN at times t=1,2,..n as follow:

(13)

where,

(14)

(15)

is the Kalman gain matrix, is a matrix of derivatives of, Rtand Qtare the covariance matrix for the process noise and measurement errors as shown in (1) and (2). Herein in this model assumedP0 and Rt symmetric positive definite matrices, Qt a symmetric positive semi definite matrix, and (13) is initialized with a given w0 [23].

Results and Discussions

After the GPS data collections, the output of the GPS software is the time series of rover monitoring point coordinates in the WGS84. The transformer coordinates of monitoring points to local coordinates monitoring points with directions of monitoring members is apparent monitoring displacement. A long period displacement component of structures is a filter of apparent displacement which contains a semi-static displacement and background noise, whereas the short period displacement component; which is supervised the long period component from apparent displacement; is contains a dynamic displacement and some noise [2]. This study is focused on the de-noising the short period monitoring displacement component because of the importance of this in time and frequency modes calculations for the structural dynamics. In this section used a MATLAB simulation noise reduction to simulate complex noise and verification the designed model and applied the model chooses in a bridge monitoring data as a case study.

Simulation noise results

Additive white Gaussian noise is a basic noise model used in information theory to simulate the effect of many random processes that can be occurred in nature [8]. This noise model channel can be modeled for satellite and deep space communication links applications [8]. In this study used additive white Gaussian noise MATLAB code to create a noise as shown in Fig. 5. The NN models design in a previous section are tested to decrease the noise value created to zero target value as shown in Fig. 5. The Multilayer perceptron (MLP) network is considered, furthermore only one hidden layer hyperbolic tangent and one output linear activation function are confidence. The Table 1 shows the mean absolute error (MAE) and mean square errors (MSE), which are used to statistic the accuracy of the model. The R-square is used to measure the fitness between target and prediction value, the R-square value closer to one indicates a better fit.

(a)

(b)

(c)

(d)

Fig. 5. Comparison simulation results a) BPN, b) CFN, c) ADFN, d) EKFN

Table 1. Performance analysis for simulation de-noise NN models.

Models

BPN

CFN

ADFN

EKFN

MAE

0.0093

8.65e-4

0.0024

0.0037

MSE

1.22e-4

1.206e-5

7.98e-6

3.174e-5

R-Square

0.987

0.986

0.997

0.992

From Fig. 5 and Table 1, it can be seen that the ADFN is a best model can be used to de-noise the sensors monitoring noise. In the same time, it can be shown that the models CFN and EKFN are also can be used as second models. In addition, it can be seen that the CFN gives a quite low value of MAE. But, it can be shown clearly that the filter with neural network models are make a good fitness models can be used in the case of noise removed to discuss a dynamic behavior of structures. It means that the multi-step filtering procedure can be constrained to de-noise the noisy sensors recordings of the oscillations of structures and determine its oscillation amplitude and modal frequency, this result complies with the resulted obtained by Moschas and Stiros [6].

GPS-Bridge movement application: Case Study

In this section used a case study Zhujiang Huangpu long span bridge (Fig. 6) deck GPS monitoring [13, 24] to validate the ADFN model. This bridge is composed of a 705 m-long cable-stayed bridge and an 1108 m-long cable-suspended bridge, and located in China. The monitoring system as shown in [24] contains 10 deck and 3 tower monitoring points with one base point as reference station refresh the real time kinematic (RTK) correction message for the monitoring points. The sampling frequency of GPS used is one Hz to decrease the cost of the monitoring system. The observations were split into single hour observations for the processing purposes. A local bridge coordinate system was established to be used in the analysis and the evaluation of the observed data. The x data represent the relative displacement changes along the longitudinal direction of the bridge; the y data represent the relative displacement changes along the transverse direction of the bridge while the z data represent the relative displacement changes along the altitude direction of the bridge. The relative displacement changes of the bridge deck will be in millimeters. In this study used a fixation monitoring point (point 1, as shown in Fig. 6) to study the effective of ADFN model on the de-noise GPS measurement errors and detect the dynamic behavior of stiff bridge monitoring point of short period displacement component in time and frequency domains.

1

Fig.6. General view of bridge and selection monitoring study point

Fig. 7 shows one day apparent displacement, long period and short period monitoring point displacement component. Herein, the long period component is extracted by using a moving average filter with span 855. The short period displacement component is computed based on supervised the long period component from apparent displacement. The last step is de-noising the short period component used ADFN model.

From the fixation of monitoring point, and Fig.7, it can be seen that the displacement components in x and y directions are greater than z direction displacement. In addition, it can be seen that the standard deviation of x,y and z directions are 0.154,0.174 and 0.033 mm for the apparent displacement, respectively. It means that the noises cover the apparent displacement is vibration and background noises. In addition, it can be seen that the correlation between the apparent and long period component is high in three direction of monitoring point. And the correlation between three direction movements is high. It means that the effective of moving average is high to extract the long period monitoring movements, and the state of structure is healthy. Also, it can be seen that the time history of short period displacement component for the x and y are greater than it in z direction, and the maximum short period for x direction is 0.09 mm. That is because the monitoring point fixation. From the short period displacement component and de-noise model used calculation, it can be seen that the model is increased the accuracy of short period by 83.3% in x and y directions and 93.8% in z direction. In addition, from the time history of the long period component, it can be seen that the displacement of monitoring point is very small, and the maximum displacement is 0.19 mm in x direction. That is because the availability movement of this point in this direction. From these results, it can be concluded that the ADFN model can be permitted to de-noise the noisy GPS recordings of the oscillations of a stiff points monitoring of bridges and determine its oscillation amplitude and modal frequency. 

(a)

(b)

(c)

Fig.7. Long (left) and Short (right) period displacement for a) x, b) y, c) z directions

(a)

(b)

(c)

Fig.8. Frequency of short period before and after de-noise GPS monitoring point a) x, b) y, c) z directions

Fig. 8 shows the frequency calculation for the short period component and de-noises displacement. The frequency and power are calculated using Fast Fourier Transformation (FFT). The high pass filter is used to calculate the frequency for the monitoring point greater than 0.02 Hz. From this Fig., it can be seen that the power spectrum density of signal is decreased to about 98% in three directions for the monitoring point. It means that the noise is high affected on the low and high frequency modes calculation, and the noise can be misleading the frequency mode in high and low frequency modes. In addition, it can be seen clearly that the low frequency modes of short period displacement component values are appears in between 0-0.2 Hz. However, it can be concluded that the spectral analyses revealed low-frequency colored noise, statistically significant below 0.2 Hz, and this result complies with the resulted obtained by Moschas and Stiros [2]. Also, it can be seen that the frequency models of short period component are more clearly with de-noise signal, especially in z direction. It means that this model is more effective for frequency modes calculation.

However, finally the output of this study is that it reveals the potential of GPS to measure the displacement history and the modal frequencies of stiff monitoring point of structures. Model frequency up to 0.5 Hz is not included in this paper because the availability of GPS monitoring sampling frequency, also of course shown that GPS measurements with a sampling rate of 1Hz may in fact underestimate the amplitude of displacements components, these problems however can be expected to be overcome with the modern high-frequency GPS. In addition, study the availability for the NN models used to de-noise the GPS vibration measurements in low frequency mode effects. These results are expected to have important implications in the Structural Health Monitoring and the design of Structures, especiallyfor the low frequency modes analyze.

Conclusions

Neural Network models are used in this study to select the best model for improved operational health monitoring of structures based on GPS geodetic survey technique. Four models are used to de-noise the GPS monitoring applications, which are Back-propagation, Cascade-forward back-propagation, Adaptive filter, and Extended Kalman filter. An updated weight for NN models is used as the main factor to de-noise monitoring GPS applications. The results of the four models are compared to suggest and recommend the optimum de-noise model which can be used in GPS monitoring for measuring the deformation of structures. The following conclusions are drawn from this study:

•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 can be concluded that the ADFN model is the best model which is recommended to de-noise the GPS measurements.

•The apparent displacement measurements contain noises that can be considered as vibration and background noises. Moreover, it is concluded that 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 highly affected the high and low frequency vibration modes of structures. In addition, from the frequency modes calculations, it can be 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 one Hz may in fact underestimate the amplitude of displacement components, this problem however can be expected to be overcome with the modern high-frequency GPS.

•The de-noised short-period displacement component is expected to have important implications in the SHM and the design of structures in the low frequency content.

Acknowledgment

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT, and Future Planning (Grant No. 2013R1A2A2A01068174).

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© 2016 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 (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

Dr. Jong Wan Hu received his MS degrees from (1) G.W.W. School of Mechanical Engineering and (2) School of Civil and Environmental Engineering, respectively, in Georgia Institute of Tech-nology. He then received his Ph.D. degree from School of Civil and Environmental Engineering, Georgia Institute of Technology. Dr. Hu was a Post-Doctorate Research Fellow at Structural, Mechanics, and Material Research Group in Georgia Institute of Technology. Dr. Hu is currently an Associate Research Fellow at the Korea Institute of S&T Evaluation and Planning (KISTEP) and also an Assistant Administrator at the National S&T Council (NSTC). He has been active in the member of ASME and ASCE. He research interests are in the area of computational solid mechanics, composite materials, and plasticity modeling.

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7

x 10

-6

De-Noise Power

De-Noise

Short-period Comp. Disp.

00.050.10.150.20.250.30.350.40.450.5

0

1

2

3

4

5

x 10

-4

Short-period Power

Frequency (Hz)

00.050.10.150.20.250.30.350.40.450.5

0

0.2

0.4

0.6

0.8

1

x 10

-5

De-Noise Power

De-Noise

Short-period Comp. Disp.

00.050.10.150.20.250.30.350.40.450.5

0

0.2

0.4

0.6

0.8

1

x 10

-4

Short-period Power

Frequency (Hz)

00.050.10.150.20.250.30.350.40.450.5

0

0.2

0.4

0.6

0.8

1

x 10

-6

De-Noise Power

De-Noise

Short-period Comp. Disp.