Dự báo lún theo thời gian cho xây dựng đường ở Bắc Ninh và Hải Dương bằng mạng nơ ron nhân tạo

. So sánh kết quả dự đoán 
của các mô hình với kết quả thực tế có thể thấy: 
nên sử dụng mạng nơ-ron nhân tạo (ANN) để dự 
báo lún theo thời gian trong quá trình thi công 
đường. 
Từ khóa: Dự đoán, mạng nơ ron nhân tạo 
(ANN), lún mặt đất, xây dựng đường. 
1. Introduction 
Artificial neural network is a branch of the 
‘artificial intelligence’, which also includes case-
based reasoning, expert systems, and genetic 
algorithms [19]. The efficient manipulation of large 
amounts of data and the ability to generalize results 
are the main advantages of neural networks [23]. 
Thus, the applications of the artificial neural network 
have been found in innumerable fields [2, 4, 10-15, 
18, 21, 22]. 
In the last few decades, artificial neural networks 
(ANNs) have been successfully applied to virtually 
every problem in the predictions of the settlement 
problems. Alkroosh and Nikraz [10] simulated the 
load-settlement behavior of pile foundations 
embedded in sand and mixed soils (subjected to 
axial loads) by artificial neural networks (ANNs). The 
results indicated that the ANN model performed very 
well after comparing predictions from the ANN with 
predictions of number of currently adopted load-
transfer methods. Ismail and Jeng [13] developed a 
high-order neural network (HON) for simulating the 
pile load–settlement curve using properties of the 
pile and SPT data along the depth of pile 
embedment as inputs. The HON model presented 
better predictions than the predictions of elastic and 
hyperbolic models. Shahin, Jaksa [8] presented a 
new hand-calculation design formula for settlement 
prediction of shallow foundations on granular soils 
based on a more accurate settlement prediction 
from an artificial neural network model. The model 
had five inputs (the footing width, net applied footing 
load, average blow count, obtained using a standard 
penetration test (SPT) over the depth of influence of 
the foundation as a measure of soil compressibility, 
footing geometry, and footing embedment ratio), 
and one output (foundation settlement). Shahin, 
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Jaksa [20] developed a set of charts incorporating 
the uncertainty associated with the ANN method, 
which enable the designer to make informed 
decisions about the level of risk correlated with 
predicted settlements. 
It can be seen that there is not much research 
on predicting the settlement over time. In this paper, 
an ANN model is developed and compared with two 
traditional methods (Asaoka method and the method 
of Asaoka combined with Polynomial) in predicting 
the settlement of two cases of road construction. 
The parameters of two traditional methods are 
referenced from Tran, Nguyen [9]. The criterions to 
evaluate the accuracy of the models are the R 
squared (R
2
) and the mean square error (MSE). The 
relative conclusions would be drawn by comparing 
the criterions of these models, and the predictions 
data of these models with the monitoring data. 
2. Overview of artificial neural networks 
Artificial neural networks (ANNs) are numerical 
modeling techniques inspired by the functioning of 
the human brain and nervous system [7]. 
The purpose of ANNs is similar to conventional 
statistical models, which is to determine the 
relationship between the model inputs and 
corresponding outputs. However, ANNs only use the 
data and do not require predefined mathematical 
equations of the relationship between the inputs 
data and outputs data. This allows ANN to get past 
the limitations of the conventional models. 
A Multi-layer feed-forward with the back-
propagation algorithm training is used in this study 
[6]. The multi-layer feed-forward neural network is 
composed of several processing elements (called 
nodes or neurons). The processing elements are 
fully or partially connected via connection weights, 
and they are often classified into layers: an input 
layer; an output layer; and hidden layers (layers in 
between). 
Many authors have already described the 
structure and operation of ANNs. Figure 1 shows 
the structure and operation of an ANN depicted by 
Shahin [7]. At each processing element, the input 
from the processing element of the previous layer 
(xi) is multiplied by an adjustable connection weight 
(wji), and weighted inputs are summed and a bias 
(θj) is added or subtracted. The combined input (Ij) is 
then passed through a non-linear transfer function 
(f(.)) (e.g. sigmoidal function or tanh function) to 
produce the output of the processing element (yj). 
The training of the multi-layer feed-forward 
neural network starts at the input layer, after that, a 
learning rule is used to obtain the network output 
(Figure 1). The weights and the bias are adjusted in 
order to get the smallest possible error between the 
desired output and the output which is obtained from 
the preview step. As soon as the training phase is 
accomplished, the trained model would be validated 
by an independent testing set. Several of the steps 
used to develop an ANN are discussed by Maier 
and Dandy [5]. 
Figure 1. Structure and operation of an ANN [7] 
3. Development of the ANN model 
The ANN model is created with the aid of the 
software package PYTHON Version 3.6. The 
constructed sites of two roads were located in Bac 
Ninh and Hai Duong province with different soil 
types and geotechnical conditions. The data used to 
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Tạp chí KHCN Xây dựng - số 3/2021 63 
calibrate and validate the ANN model are shown in Table 1 and Table 2. 
. 
Table 1. Road surface settlement over time in the first case [9] 
No 
Time 
(day) 
Field data 
(mm) 
No 
Time 
(day) 
Field data 
(mm) 
No 
Time 
(day) 
Field data 
(mm) 
1 1 -2 14 63 -60 27 115 -290 
2 6 -6 15 68 -65 28 118 -295 
3 10 -9 16 71 -70 29 125 -310 
4 14 -13 17 75 -94 30 131 -325 
5 20 -19 18 78 -112 31 138 -340 
6 24 -29 19 82 -125 32 145 -360 
7 27 -32 20 86 -141 33 152 -381 
8 31 -35 21 92 -155 34 159 -395 
9 35 -37 22 96 -172 35 166 -411 
10 39 -42 23 100 -189 36 173 -425 
11 46 -49 24 104 -214 37 179 -439 
12 52 -54 25 108 -242 
13 57 -56 26 110 -262 
Table 2. Road surface settlement over time in the second case [9] 
No 
Time 
(day) 
Field data 
(mm) 
No 
Time 
(day) 
Field data 
(mm) 
No 
Time 
(day) 
Field data 
(mm) 
1 4 -1 17 280 -52 33 515 -92 
2 23 -3 18 298 -53 34 522 -95 
3 43 -4 19 319 -54 35 531 -99 
4 61 -6 20 333 -55 36 547 -103 
5 90 -7 21 350 -57 37 566 -108 
6 111 -8 22 363 -58 38 578 -112 
7 140 -10 23 375 -60 39 587 -115 
8 158 -13 24 384 -61 40 599 -117 
9 165 -19 25 398 -65 41 613 -118 
10 172 -25 26 403 -68 42 636 -118 
11 181 -28 27 417 -74 43 662 -121 
12 197 -35 28 438 -78 44 683 -123 
13 209 -38 29 459 -81 45 704 -125 
14 226 -45 30 474 -82 46 726 -126 
15 237 -47 31 494 -86 47 782 -127 
16 254 -50 32 502 -89 
3.1 Data division and preprocessing 
Monitoring data includes time and settlement, 
thus, the time was chosen as an input variable and 
settlement was chosen as an output variable. 
The data have been divided into two subsets, 
training set for model calibration and validation set 
for model verification. All the methods in this paper 
are developed for the purpose of predicting the 
settlement at the next step. Thus, the data from the 
beginning to 159 days and the data from the 
beginning to 683 days are allocated for the training 
data in the first and the second case, respectively. 
The last three monitoring data are used for model 
verification. 
In order to minimize the dimension and to make 
sure all variables get equal attention during training, 
the preprocessing is conducted by scaling the input 
and output variables between 0.0 and 1.0. The 
scaled value of each variable x, xn, is calculated as 
follows: 
xn = x / xmax [1] 
Where: xmax is maximum values of each variable x. 
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3.2 Model architecture, weight optimization and stopping criterion 
Figure 2. Variation of loss against epoch 
Figure 3. Effect of number of hidden layer nodes on performance of ANN model 
The model geometry (i.e. the number of hidden 
layers, the number of hidden nodes in each layer) 
and weight optimization (i.e. learning rate and 
momentum term) play a major role in the 
development of the ANN models. 
 Hornik, Stinchcombe [3] noted that a network 
with one hidden layer can approximate any 
continuous function provided that sufficient 
connection weights are used. Thus, one hidden 
layer is used in this ANN model. 
ReLU and tanh are selected as transfer 
functions in the hidden and output layers (ReLU and 
tanh are activation functions, which outputs a small 
value for small inputs, and a larger value if its inputs 
exceed a threshold; ReLu: f(x) = max(0,x); Tanh: 
f(x) = (e
x 
- e
-x
)/(e
x 
+ e
-x
)). The 5000 training cycles 
(epochs) is used to terminate the training process, 
which is the same as the training cycles previously 
published by Shahin [7]. This number basically 
satisfies the requirement that there is no increase in 
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Tạp chí KHCN Xây dựng - số 3/2021 65 
the error. The training loss at the end of the training 
process does not fluctuate and does not increase 
(see Figure 2). 
 Caudill [1] noted that 2I+1 hidden layer nodes 
are the upper limit needed to map any continuous 
function for a network with I number of inputs. 
However, based on the effect of the number of 
hidden nodes on the performance of ANN model 
(Figure 3), the ANN model with 5000 hidden nodes 
has the lowest prediction error (the highest value of 
the R squared and the lowest value of the mean 
square error). The number of hidden nodes using for 
ANN model in this paper is much more than the 
number of hidden nodes recommended and used by 
Caudill [1] before. 
The learning rate is a tuning parameter in an 
optimization algorithm that determines the step size 
at each iteration while moving toward a minimum of 
a loss function [17]. The effect of learning rate on 
the performance of ANN models is shown in Figure 
4. It can be seen that the ANN model with the 
learning rate of 0.01 has the lowest prediction error. 
The prediction errors tend to increase at the larger 
learning rate. The gradient descent optimization 
algorithm is Adam optimizer. It already incorporates 
something like momentum, thus, the momentum 
term is not examined. 
Figure 4. Effect of learning rate on performance of ANN model 
4. Comparison of ANN model with difference 
methods 
The performance of the ANN models and two 
traditional methods for the first case is summarized 
in Table 3. It may be seen that the ANN 1 model 
performs well; as it has the highest value of R 
squared (0.9996), and lowest value of mean 
squared errors (7.6) for the training data set. 
However, the next three predicted data (validation 
set) of the ANN 1 model does not even draw a line 
of best fit between predicted data and field data 
(Figure 4 and Figure 5). It also validates that, like all 
empirical models, ANNs perform best in 
interpolation rather than extrapolation [16]. 
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66 Tạp chí KHCN Xây dựng - số 3/2021 
Table 3. Performance of the models for first case 
Name of Method Equation (or Model architecture) 
R squared 
(traning data) 
MSE 
Asaoka 1*0423.10372.6  titi SS 
0.9976 37.4 
Asaoka + 
Polynomial 
1
32
*9096.0
*474.4*0117.0
*4776.0838.9



ti
ii
iti
S
tt
tS
0.9985 24.0 
ANN 1 5000 Hidden nodes; lr 0.01; epochs 5000 0.9996 7.6 
ANN 2 5000 Hidden nodes; lr 0.008; epochs 5000 0.9992 51.7 
Table 4. Field data and Prediction data for first case 
Time 
(day) 
Measurement (mm) 
Prediction (Diviation) (mm) 
Asaoka Asaoka + Polynomial ANN 1 
166 -411 -418 (-7) -407 (4) -406 (5) 
173 -425 -434 (-9) -419 (6) -414 (11) 
179 -439 -449 (-10) -429 (10) -418 (21) 
Figure 5. Settlement for first case 
The method and the model performs well in 
predicting the next three data (validation set) is the 
Asaoka combined with Polynomial (AP) and ANN 2 
(with 5000 Hidden nodes, learning rate 0.008 and 
epochs 5000). Though their criterions to evaluate 
the accuracy of the models in the training data set 
are not the best (the values of R squared are not the 
highest and the values of mean squared errors are 
not the lowest). This may due to the training data is 
not enough in this case. 
Table 5 shows the performance of the ANN 1 
model and two traditional methods for the second 
case. The ANN 1 model also performs well for the 
training data, as it has the highest value of R 
squared (0.9993), and lowest value of mean 
squared errors (1.2). However, in this case, the next 
three predicted data of ANN 1 model have a very 
small deviation from the field data (Table 6). It may 
be because the road has moved to the stage of the 
commissioning work. All the data given by the ANN 
1 model creates the best fit line between predicted 
data and field data (Figure 6). Thus, when the 
training data is enough, the ANN method provides a 
more accurate prediction than traditional methods. 
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Tạp chí KHCN Xây dựng - số 3/2021 67 
Table 5. Performance of the models for the second case 
Name of Method Equation (or Model architecture) 
R squared 
(traning data) 
MSE 
Asaoka 1*9987.09164.2  titi SS 0.9980 2.9 
Asaoka + 
Polynomial 
1
3825
*9598.0
*10*2.2*10*3
*0207.0159.1





ti
ii
iti
S
tt
tS
 0.9981 2.8 
ANN 1 5000 Hidden nodes; lr 0.01; epochs 5000 0.9993 1.2 
Table 6. Field data and Prediction data for the second case 
Time 
(day) 
Measurement (mm) 
Prediction (Diviation) (mm) 
Asaoka Asaoka + Polynomial ANN 1 
704 -125 -126 (-1) -127 (-2) -125 (0) 
726 -126 -128 (-2) -129 (-3) -126 (0) 
782 -127 -129 (-2) -130 (-3) -127 (0) 
Figure 6. Settlement for the second case 
5. Conclusion 
After comparing the accuracy of ANN method 
with the accuracy of traditional methods (Asaoka 
method and the method of Asaoka combined with 
Polynomial) for predicting the settlement of two case 
histories, the following conclusions can be drawn. 
- The ANN model with 5000 hidden nodes has 
the lowest prediction error in predicting settlement 
over time (time is input variable and settlement is 
output variable). The number of hidden nodes is 
much more than the hidden nodes discussed by 
Caudill [1]; 
- The criterions to evaluate the accuracy of the 
ANN model are much better than other models, 
however, the accuracy of the next three predicted 
data of the ANN models (validation set) is not good 
if it does not have enough training data (i.e. 34 data 
in the first case history); 
- If the training data is enough (i.e. 44 data in the 
second case history) the accuracy the ANN model 
for the next three predicted data (validation set) is 
extremely high, and ANN model should be used for 
predicting settlement over time without knowing 
parameters related to the surcharge and soil. 
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Ngày nhận bài: 18/8/2021. 
Ngày nhận bài sửa: 07/9/2021. 
Ngày chấp nhận đăng: 08/9/2021. 
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