https://doi.org/10.31449/inf.v48i13.6011 Informatica 48 (2024) 191–204 191 
Monitoring and Prediction of Settlement and Deformation of Ancient 
Building Foundations Based on Neural Networks 
 
Lei Gao
*
, Heng Wang 
School of Civil Engineering, Nanyang Normal University, Nanyang 474100, China 
E-mail: yshanmo@163.com 
*
Corresponding author 
Keywords: grey artificial neural network, settlement of ancient building foundations, deformation monitoring and 
prediction, deep beliefs, stress analysis 
Received: April 11, 2024 
With the rapid development of the tourism industry, the visual value of ancient buildings gradually 
increases. The prediction and protection of ancient building foundation settlement based on neural 
networks have been developed. When traditional methods are used to monitor and predict the 
settlement and deformation of ancient building foundations, complex factors such as water 
environment and geological conditions can bring noise to the experimental results. Deep belief was 
introduced into grey artificial neural networks to effectively denoise the corresponding model and 
enhance its ability to process data. Meanwhile, stress analysis was conducted on the ancient building 
foundation in the experiment to generate a composite model. Experiments were conducted on the 
Abfound dataset. Three models were compared to verify the predictive ability for ancient buildings, 
including random forest, to verify the superiority of the model. The dimensionality reduction 
capabilities of four models for building data were 4.6, 3.6, 3.2, and 3.9, respectively, indicating that 
the optimized model could effectively handle a large amount of data. The composite model had the 
highest accuracy in predicting the settlement of ancient building foundations, with an experimental 
data of 99.2%. These experiments confirmed that the proposed composite algorithm performed best in 
terms of noise reduction and prediction ability. This algorithm is suitable for predicting the settlement 
deformation of ancient building foundations. 
Povzetek: Raziskava uvaja inovativni model za napovedovanje posedanja in deformacij temeljev starih 
zgradb, ki temelji na nevronskem omrežju z uporabo globokega prepričanja (deep beliefs) za 
zmanjševanje šuma. Eksperimenti na Abfound podatkovnem naboru so pokazali, da ima sestavljeni 
model najvišjo točnost pri napovedovanju posedanja temeljev.
1 Introduction 
As the improvement of the national economy, residents' 
entertainment gradually focuses on urban buildings, and 
their protection requirements gradually increase [1-2]. 
Ancient buildings are an important component of cultural 
heritage, carrying memories of history and culture and 
possessing significant scientific value. The settlement and 
deformation of the foundation are the main problems they 
face [3]. The foundation often experiences settlement and 
deformation, due to the long history of urban construction 
and environmental changes, posing a serious threat to the 
safety and integrity of urban construction [4]. Many 
experts have proposed using neural networks to 
accurately predict them. However, these methods are only 
applicable to arbitrary building in limited terrain and 
humidity environments. The data accuracy of traditional 
neural networks is insufficient due to the complex natural 
factors. Recently, Grey Artistic Neural Network (GANN) 
has received attention due to its extensive search domain. 
However, the ordinary GANN has weak resolution ability 
and is prone to falling into local optima during operation. 
To address these issues, this study concatenated GANN 
to generate Series Grey Artistic Neural Network 
(SGANN) and introduced Deep Belief (DB) to generate a 
fusion model (DB-SGANN). A composite model 
(SPDB-SGANN) was generated by considering the 
Stability of Pile (SP) of arbitrary building. 
SPDB-SGANN improved the traditional grey prediction 
model and improved this model’s stability by introducing 
nonlinear fitting ability. In this study, the improved 
GANN was applied to the monitoring and prediction of 
foundation settlement of ancient buildings to avoid 
problems such as building inclination and cracks. The 
main content of this study includes four parts. Firstly, the 
current applications of GANN are summarized. Secondly, 
the usage of SP is introduced and introduced into 
DB-SGANN. The third part conducts simulation 
experiments. Finally, the model performance is analyzed 
and compared, and the shortcomings in this research are 
pointed out. The research on the prediction of settlement 
and deformation of ancient building foundation based on 
neural networks is very popular. However, there are few 

192   Informatica 48 (2024) 191–204                                                               L. Gao
 
et al. 
studies linking the depth belief method with it. In this 
study, the depth belief method is creatively introduced 
into the conventional GANN. A composite system is 
established based on the stress analysis of ancient 
building foundation. The practical significance of this 
study lies in monitoring and predicting the Settlement and 
Deformation of Accident Building Foundations (SDABF) 
and implementing protective measures for buildings. The 
article aims to inherit history and culture, thereby 
enriching the entertainment life of residents. 
2 Related works 
International research is widely distributed in the SDABF 
prediction. Huan et al. conducted research on various 
factors that affected the safety status of accident building 
to improve the accuracy of accident building safety 
assessment. They proposed a safety assessment model 
based on the structural entropy weighted matter element 
extension model. Meanwhile, the weights of each 
indicator were calculated by taking into account the 
influence of subjective and objective weights. The 
museum was used as a research case. The evaluation 
results were consistent with the actual damage 
investigation results and the actual situation of the 
building [5]. An and Sun comprehensively investigated 
the type of foundations of the adjacent buildings and 
explored the foundation pit support scheme to ensure the 
normal use of buildings. The finite difference method was 
used to analyze building foundation settlement. 
Reinforced concrete retaining piles were used to excavate 
and reinforce the foundation pit layer by layer. Their 
research provided a method for observing the foundation 
settlement of buildings, providing a good reference for 
safety assessment and evaluation of similar risk projects 
[6]. Ye et al. considered that shield tunneling construction 
would disturb the surrounding soil and affect the safety of 
nearby buildings. They analyzed the deformation 
monitoring of arbitrary building structures. A structural 
deformation monitoring method based on computer 
vision was developed to perform on-site monitoring of 
deformation under the influence of shield tunneling. 
Background correction was used to reduce the error 
caused by camera position changes. These experiments 
confirmed that their proposed computer vision method 
provided an effective method for structural safety 
assessment [7]. 
There is an increase in peripheral data during the 
construction of accidents, relying solely on neural 
networks for data extraction is insufficient. GANN 
gradually enters the vision of many scholars. Bozdağ 
believed that the steep slope of the slope was susceptible 
to rockfall events. Therefore, experimental investigations 
and numerical analysis were conducted. The danger of 
the slope was evaluated. Two-dimensional rockfall 
analysis was used to determine the jumping distance 
between detached and suspended blocks. These 
experiments confirmed that its research results provided 
preliminary data for describing risk management 
strategies and made scientific contributions to studying 
the hazards and risks caused by rockfall phenomena [8]. 
Borisov et al. described the study of urban construction 
from the 5th to 8th centuries. They used methods from 
soil science and archaeological botany. Soil profiles are 
made at different distances from the settlement. These 
experiments confirmed the potential risk of foundation 
settlement and deformation in ancient medieval sites. 
Burnt grains were used to store in the lower layer of the 
soil to solve this problem. These experiments confirmed 
the effectiveness of their method [9]. Di et al. analyzed 
the settlement of subway lines on soft soil foundations. 
The combination of different characteristic positions in 
subway lines was studied. The difference between a track 
slab and a bridge pier was analyzed. These experiments 
confirmed that about 85% of the station settlement was 
smaller than the settlement of adjacent shield tunnels. 
About 73% of the settlement at the tunnel connection 
channel was greater than the settlement on both tunnel 
sides. The stiffness conversion between different 
structures should be considered when designing subway 
structures on soft soil foundations [10]. A summary of the 
relevant works is shown in Table 1. 
 
 
Table 1: Summary of related works 
Author Time Main point 
Huan et al. [5] 2020 
A safety evaluation model of ancient wooden buildings based on the 
extension model of structural entropy weight is proposed. The influence of 
subjective and objective weights is considered comprehensively.  
An and Sun [6] 2020 
The foundation settlement and residual deformation of nearby buildings 
during subway station construction are analyzed by using finite difference 
method and deformation observation method. 
Ye et al. [7] 2021 
The three-dimensional deformation of ancient pagoda under the influence of 
shield tunnel excavation is monitored by computer vision method. 
Bozdağ [8] 2022 
The jump distance between the separated block and the suspended block is 
determined by two-dimensional rock fall analysis. 
Borisov et al. [9] 2022 Soil profiles are made at different distances from the settlement.  
Di et al. [10] 2020 
The measured differential settlement of subway lines is analyzed. The 
settlement of about 85% stations is less than that of adjacent shield tunnels. 

Monitoring and Prediction of Settlement and Deformation of… Informatica 48 (2024) 191–204  193 
The settlement of about 73% tunnel connecting channels is greater than that 
on both sides of the tunnels. 
 
To sum up, most of the previous research work 
focused on a single project example. The established 
prediction models have insufficient generalization ability. 
However, these models do not consider the timeliness of 
the bearing capacity of ancient building foundations 
under long-term load. That is, these models do not 
consider the influence of time factors. Neural networks 
have a strong nonlinear mapping ability. Big data and 
neural networks are used to analyze the regular trend of 
the bearing capacity and settlement of pile foundation 
under long-term load. This paper aims at predicting the 
bearing capacity and settlement of pile foundation under 
long-term load. The mathematical model for effectively 
predicting the bearing capacity and settlement timeliness 
of ancient building foundation will play a boosting role in 
the development of the safety evaluation of ancient 
buildings. 
 
3 The application of GANN in 
SDABF monitoring and prediction 
GANN combines grey system theory with Artificial 
Neural Network (ANN) and performs superior in 
prediction performance [11]. GANN improves the 
traditional grey prediction model and improves the 
stability of the prediction model by introducing nonlinear 
fitting ability. This study applies the improved GANN to 
SDABF monitoring and prediction to avoid problems 
such as building tilting and cracks. 
 
3.1 Construction of ANN based on DB 
The grey prediction model is a prediction method based 
on a small amount of data, which is suitable for situations 
such as small data volume and lack of complete 
information [12]. The grey prediction model describes 
and predicts the development trend of the system by 
establishing grey differential formulas. The grey 
prediction model has certain limitations when dealing 
with nonlinear and complex systems. GANN introduces 
ANN into the grey prediction model to fully utilize its 
nonlinear fitting ability to improve the prediction 
accuracy of the model. When introduced, the variables in 
these two models have the relationship in Eq. (1). 
 
0
1
20
xx
x
xx
−
=
−
           (1) 
 
In Eq. (1), the random data after ANN enters GANN 
is denoted as 
1
x . The minimum and maximum values are 
represented by 
02
, xx , respectively. 
x
 represents the 
raw data in ANN, which uses the inputting data as the 
inputting layer of neural network. The predicted results 
are obtained by calculating and adjusting the hidden layer 
and outputting layer [13-14]. During the training, GANN 
continuously adjusts the weights and thresholds of the 
network through backpropagation to minimize prediction 
errors. In this process, the weight and threshold 
calculation of the network follow Eq. (2). 
 
( ) ( )
( )
1
* / * 1
* * *
n
ii
i
We m R A m
Tv u m I A q

=
= + − 


=+



   (2) 
 
In Eq. (2), the data step size is denoted as 
u
. , mA 
represent the environmental errors of data features. The 
value range of data is represented by 
n
. The number of 
network layers is denoted as R . 

 represents the 
current dimension of the data. 
i
I and 
i
q are the 
resistance to data at different times. The improved GANN 
has been widely applied in various fields of prediction, 
especially in the disaster prediction. It can effectively 
handle nonlinear and time-varying data, which has high 
predictive stability. However, GANN requires 
appropriate parameter selection in Eq. (3). 
 
1
min 2
* * 0.9*
*
m Rc Ri Rg
Ri Rt


− 



    (3) 
 
In Eq. (3), Rc represents the compressive strength 
of the data in GANN. The structural rigidity of network is 
represented by Ri and is influenced by parameter 
1
 . 
The experimental errors caused by gravity and ambient 
temperature are recorded as 
Rg
 and Rt . 
2
 is a 
constant that takes a value within (  1,2 and is related to 
the minimum Ri [15]. Due to the incomplete and 
insufficient characteristics of the data processed in this 
study, SGANN is established in Fig. 1. 
 
Original sequence
Grey system
Residual sequence
 
Figure 1: Flow chart of SGANN 
 
From Fig. 1, SGANN combines the grey prediction 
model in grey system theory with ANN. The grey 
prediction model serves as the inputting layer. ANN 
serves as the outputting layer. The study concatenates the 
two to improve the accuracy and stability of prediction. A 
grey prediction model is used to preprocess the inputting 
data to obtain a prediction sequence. Then, the predicted 
sequence is used as input for further prediction and 
adjustment through ANN. This model can fully handle 

194   Informatica 48 (2024) 191–204                                                               L. Gao
 
et al. 
incomplete and uncertain data. Eq. (4) is the variable used 
when processing data. 
( )
( )
1
11
1
**
* * 1
*
p
i
i
i
i
s
Ex
Mo
s



−
=
=
 
−−
 
  

(4) 
In Eq. (4), the expansion modulus in SGANN is 
denoted as Ex , and its expansion fraction is represented 
by 
i
 . Mo represents the original modulus in the 
model, and its compression factor is denoted as 

. The 
total number of layers of SGANN is recorded as 
s
. 
i
s 
represents the i -th layer within it. In data processing, 
this study takes into account data collection, transmission, 
and storage processes to avoid data corruption and ensure 
data integrity and accuracy. DB and SGANN are 
integrated in Fig. 2. 
 
Network construction
Deep belief
Data acquisition Data processing
Calculation acquisition 
error
Calculation of 
processing error
Is the error 
less than the 
preset value?
Modification weight
Sample training
Y
N
 
Figure 2: Fusion of depth belief and SGANN 
 
Fig. 2 introduces DB-SGANN. According to Fig. 2, 
the basic idea of this model is to gradually learn the 
feature representation of the data from the bottom to the 
top through layer-by-layer training. Each layer learns 
some features of the data and passes them on as input to 
the previous layer. DB-SGANN can extract higher-level 
features by this layer and training. This model can be 
applied to data dimensionality reduction. After training, it 
will learn more abstract feature representations from the 
original data. In this process, Eq. (5) represents the data 
conversion before and after dimensionality reduction. 
( )
( )
( )
( )
22
22
* Di c E
Rd 

=

      (5) 
In Eq. (5), Di and Rd represent the data before 
and after dimensionality reduction, respectively. The data 
density is recorded as 

. E represents the elasticity 
between data. 
c
 is an internal parameter involved in 
data collection, which is related to machine performance. 
This method can reduce the redundancy of data while 
preserving the main information of the data. Data are 
analyzed through dimensionality reduction to improve 
modeling efficiency. In dimensionality reduction, the 
information preservation of data is balanced against the 
data information loss in Eq. (6). 
( ) ** Se m E f E Ei = + −     (6) 
In Eq. (6), the retained data is denoted as Se . Ei 
represents the composite modulus of the compressed data. 
The weighted environmental resistance in a stationary 
state is represented by f , which is related to data 
management methods [16]. The increasing coefficient 
method is used in Fig. 3. This method achieves data 
processing by increasing the coefficients of feature 
vectors. It is suitable for linear data and has high 
requirements for data distribution and the relationship 
between features, which meets the requirements of this 
study. 
 
Data survey area Output of achievements
Data browser
Monitoring data
Detection data
Survey planning
Bench calibrate
Measuring preset
Data alarm
Report of results
Statement of results
 
Figure 3: Flow chart of increasing coefficient method 

Monitoring and Prediction of Settlement and Deformation of… Informatica 48 (2024) 191–204  195 
 
From Fig. 3, the covariance matrix of the original 
data is first calculated. The eigenvalues are decomposed 
through the matrix to obtain the eigenvalues and 
corresponding eigenvectors. The eigenvalues represent 
the data variance in the corresponding eigenvector 
direction. The corresponding eigenvectors represent the 
data distribution in different directions. Based on the set 
dimensionality reduction goal, retained feature vectors 
are selected to describe changes in the data. Finally, the 
retained feature vectors are multiplied with the original 
data to obtain the managed data. This method can 
preserve the main information in the original data. Eq. (7) 
represents the comparison of information intensity 
between them. 
1
1
*
n
i
i
i
i
Me
Me H
Dp
=

=
       (7) 
In Eq. (7), the information intensities of the data 
before and after management are denoted as 
1
,
i
Me Me . 
The eigenvalues of the covariance matrix are represented 
by 
i
Dp . 
i
H represents the variance of the 
corresponding feature vector. Through this method, 
foundation settlement data are input. Potential features in 
the data are learned using the model. These features can 
help study the behavior of monitoring and predicting 
foundation settlement, thus taking corresponding 
measures for treatment and repair. 
In the pre-training stage: first, the state of the hidden 
node of the first layer network and the state value of the 
visible node are updated. According to the state value of 
the visible node, the state of the hidden node is updated 
again. Then, the offset of the threshold values of visible 
nodes and hidden nodes is dynamically updated. The state 
of the hidden node of the first layer network is used as the 
initial input of the second layer network until the 
pre-training of the second layer network is completed 
until the network is trained layer by layer. The matrix 
vectors of the network weight and threshold are 
established. The network weight and threshold are 
updated. The second batch data are input to complete the 
next round of training until all the data processing is 
complete. 
Prediction and analysis stage: the predicted value is 
output by softmax function. The data are de-normalized 
to evaluate the network prediction. 
 
3.2 DB-SGANN and SDABF monitoring and 
prediction models 
Due to the long history of ancient buildings, the bearing 
capacity of the foundation will be affected, leading to 
settlement. SDABF is caused by various factors, 
including the physical properties of the foundation soil 
and changes in groundwater level. These factors may lead 
to deformation, thereby affecting the structural safety of 
the accident building [17-18]. This study draws the 
arbitrary building foundation map in Fig. 4 and analyzes 
the properties of the foundation soil to conduct a detailed 
evaluation of it. 
 
(a) Exterior view of ancient buildings
 
Second step 
(breccia)
Three steps (sandstone)
Sand filling
Subgrade
One step (breccia)
(b) Simplified overall model of the ancient building
16m
16m 
Figure 4: Topology diagram of ancient building 
foundation structure 
 
Fig. 4 (a) is the actual exterior map of the ancient 
building. According to the actual size of the actual survey 
data of the ancient building, the main body of the model 
is basically built according to the real size of the temple 
structure. To facilitate the simulation and calculation, the 
central tower, four corner towers of the three-storey 
platform, four corner towers of the second-storey 
platform, and two promenade buildings of the first-storey 
platform are converted into equivalent pressure loads 
according to their volumes and applied on the surface of 
the platform. The foundation depth of the model is 16 
meters below the surface. The first step is 16 meters in 
the plane range. This calculation unit adopts the kN and 
m system. The simplified model is shown in Fig. 4 (b). In 
Fig. 4 (b), the foundation soil is silty soil sand. The upper 
layer of foundation soil is filled sand, that is, fine sand. 
The first and second floors are breccia. The three steps 
are sandstone. These structures are distributed in the soil. 
The soil properties have a significant impact on the 
settlement performance of the foundation. The study 
establishes the relationship between the various 
properties of soil and the settlement of the foundation SP 
in Eq. (8). 
 

196   Informatica 48 (2024) 191–204                                                               L. Gao
 
et al. 
( ) ( )
( ) ( ) ( ) ( )
* 2 * tan
2 * tan * 2 * tan
c s m
t t p p
St
So So h So
So h So So h So
=
+
++
(8) 
 
In Eq. (8), the arbitrary building foundation SP is 
represented by St . 
c
So represents the compressive 
performance of the foundation soil. The strength of soil 
resistance to external forces is recorded as 
s
So . These 
two attributes are the inherent properties of soil, and their 
external factors include water content, saturation, and 
viscosity, represented by 
,,
m t p
So So So
, respectively. h 
represents the depth of excavation, which can affect the 
stress of the underlying layer of the building foundation. 
Eq. (9) is the connection between them. 
 
( ) 2* * *
*
Ub Co h Ob
Fs
Ub Co
+
=     (9) 
 
In Eq. (9), Ub and Co represent the stresses on 
the upper layer and reinforcement zone, respectively. The 
total friction force possessed by nearby soil is recorded as 
Ob , which directly affects the stability of the building. In 
ancient buildings, the walls supporting the building 
typically use edge stakes, which are embedded into the 
building foundation to provide additional durability. In 
these ancient buildings, edge stakes play an important 
role, enabling the building to withstand thousands of 
years without collapsing. Therefore, an architectural 
diagram of ancient building side piles is drawn based on 
the internal structure of the building in Fig. 5. 
 
Base frame 1
Base frame 2
Calibration point
Side pile point
Horizontal frame
Side centerline Test point
Starting point
C
B
A1
A2
 
Figure 5: Structural diagram of ancient buildings with side piles 
 
Fig. 5 shows the hierarchical analysis diagram of the 
edge pile of the accident building. The study first 
establishes test and calibration points for edge piles in 
buildings and divides them into basic and horizontal 
boxes. Then, the starting point and edge pile point are 
maintained at the lower end of edge pile, both of which 
are closely related to the settlement of the building. A 
study is conducted to fuse DB-SGANN with it to 
generate SPDB-SGANN to analyze its SP capability, 
with Eq. (10) as the fusion method. 
2
1
0
*
2*
i
Ve Fs
Ve
 −
=
        (10) 
In Eq. (10), the input vector of the fusion model is 
denoted as 
0
Ve . The output vector at the SGANN end is 
represented by 
1
Ve . The vector of the center points of 
both is denoted as 

. 
i
 represents the norm of the 
vector. At this point, the method can vectorize the 
obtained data, which has a significant advantage in 
avoiding redundant data. However, there are differences 
between the foundation structure of ancient buildings and 
modern architectures, mainly reflected in the lack of 
protective structures. Therefore, the ancient buildings are 
susceptible to external factors such as the hydrological 
environment in Eq. (11). 
( )
1
*
n
si
i
Wa Wa T x
=
=

      (11) 
In Eq. (11), 
s
Wa is the output value of 
SPDB-SGANN considering the impact of water 
environment. The water pressure at each node of the edge 
pile is represented by 
i
Wa . 
n
 represents the total nodes. 
The unit influence in this model is represented by ( ) Tx, 
which is related to the number of perception units in Eq. 
(12). 
( ) ( )
1
0.5*
I
ii
i
T x t ff
=
=−

    (12) 
In Eq. (12), 
i
t represents the computational layer of 
neural network. 
i
ff is the original SDABF data. This 
method can be used to obtain SDABF prediction model in 
Fig. 6. 

Monitoring and Prediction of Settlement and Deformation of… Informatica 48 (2024) 191–204  197 
 
Y
N
Starting
Project overview
Building settlement
Data processing
Network modeling
Building settlement prediction
Is the data accurate?
Building settlement prediction
Ending
 
Figure 6: Structure diagram of SDABF prediction 
 
Fig. 6 is an introduction to the SPDB-SGANN 
prediction of SDABF. From Fig. 6, the study first inputs 
the geological data of ancient buildings. The factors of 
foundation settlement are determined according to the 
data. Then, the mechanical parameters of the soil are 
tested to calculate the foundation settlement. The 
settlement of foundation under different load conditions 
is analyzed based on the soil mechanical parameters and 
geological data. The parameters for predicting the 
settlement of ancient building foundation are output. 
Finally, the weight factors of the model are adjusted 
based on the proposed model in Eq. (13). 
( )
1
Fa Fa T x
 −
=+      (13) 
In Eq. (13), the weight of the model is related to the 
influence of the model units. Random weight is 
represented by 
Fa

. 
1
Fa
 −
 represents its nearest 
neighbor. The feature attention of SPDB-SGANN is 
optimized through this step, thereby improving the 
settlement prediction performance of the model. In the 
actual excavation of foundation, the study calculates the 
error of geological data in Eq. (14). 
 
( )
( )
0.5
2
/
tt
t t
t
t t
Yp Yr Yr
Merror
N
Yp Yr
Rmse
N

−
 =




−


=


  


   (14) 
 
In Eq. (14), Merror represents the average error. 
Rmse represents the root mean square error. 
, Yp Yr
 
represent the eigenvalues and mean values in the data, 
and the total number is represented by N . The small 
, Yp Yr
 indicate that the predicted and true values have a 
small difference, indicating good model performance. 
The adjustment factor of calibration targets is introduced 
to obtain the minimum value of both in Eq. (15) to 
evaluate the performance of models between different 
datasets. 
2
2
**
j
Ad Merror Rmse   = +   (15) 
 
In Eq. (15), the adjustment factor of the target is 
denoted as 

. The total errors before and after 
adjustment are 
,
j
Ad  
. This method has good 
interpretability and intuitiveness in predicting SDABF, 
which has low sensitivity to outliers. 
In this paper, the pre-processed data are input into 
the network model in the input layer. Feature extraction is 
carried out in the convolution layer and pooling layer. 
The extracted features are input into the mean pooling 
layer for average extraction of all information after the 
feature extraction of the last layer of pooling layer is 
completed. Finally, these features are input into the 
Softmax classifier for data target decision. The extraction 
operation of feature 
( ) , l i j
y
 is shown in Eq. (16). 
 
( ) ( ) ( )
1
,
0
W
l j l j j
l i j
i
j
y K x


−
+
=
=
     (16) 
In Eq. (16), 
( )
lj
i
K

 represents the l weight of the 
i convolution kernel in the j

 layer. 
( )
l j j
x

+
 
represents the l target region in the 
j
 layer. W is 
the width of the convolution kernel. The input layer is the 
time-frequency graph of training bearings. The 
convolution kernel size of the first layer is 5*5. The step 
size is 2*2. The convolution kernel of the second and 
third layers is 3*3. The step size of the third layer is 2*2. 
The size of the pooling region of the three layers is 2*2. It 
is necessary to fill the eigenvalues to keep the size of the 
eigenvalues after each convolution and pooling 
unchanged. That is, adding zeros around the feature map 
makes the feature map complete. 
Next, the SPDB-SGANN algorithm network 
conducts self-learning to train the neural network model 
until the error between the theoretical output value and 
the actual output value reaches the minimum. The 
network training time is too long due to the excessive 
number of samples in the training set and the one-time 
training of so many data sets. Meanwhile, the network 
parameters (weights and biases) are updated slowly, 
resulting in poor results. Therefore, 128 groups are 
randomly selected from all training data each time to 
update and train network parameters. The convolutional 
layer in the network model uses Relu activation function. 
The fully connected layer uses Sigmoid activation 
function. The learning efficiency of the Adam 
optimization algorithm is 0.001. The dropout is set to 0.5 
to prevent overfitting of the training process data. 
 

198   Informatica 48 (2024) 191–204                                                               L. Gao
 
et al. 
4 Application effect of composite 
model SPDB-SGANN in SDABF 
monitoring and prediction 
This study conducted SDABF monitoring and prediction 
experiments on the Abfound dataset to analyze the 
practical application effect of the model. In this dataset, 
there were a total of 2520 pieces of data on building 
foundations of different ages, including various terrains 
such as sand and tundra. Therefore, experiments were 
conducted on two parameters of existence time and 
geographical location, respectively, on the included 
accident building. 
 
4.1 The predictive ability and internal 
performance of SPDB-SGANN in SDABF 
The settlement prediction model was established using 
MATLAB software. The relevant parameters were set as 
follows: the maximum number of iterations of the neural 
network was 10, the maximum number of trainings was 
100, the learning rate was 0.01, and the minimum error of 
the training target was 0.001. The neural network 
structure was determined as 4-9-1 (4 neurons in the input 
layer, 9 neurons in the hidden layer, and 1 neuron in the 
output layer). 36 weights from the input layer to the 
hidden layer, 9 weights from the hidden layer to the 
output layer, and 10 thresholds were obtained. The 55 
weights and thresholds of the neural network were 
optimized. The optimal initial weights and thresholds 
were assigned to the neural network for settlement 
prediction. The model was used for simulation training. 
The predicted values of the neural network before and 
after optimization were compared with the measured 
values. 
Due to the limited data in Abfound, this study 
evenly divided it into two groups. The incidence building 
types in each group were basically the same. The 
equipment selection and parameter settings in the 
experiment were first conducted before the experiment to 
carry out the experiment effectively. Then, the internal 
performance test of SPDB-SGANN was conducted. 
Meanwhile, experiments were conducted on Random 
Forest (RF), Artificial Fish Swarm Algorithm (AF), and 
Generalized Predictive Control (GPC) to validate the 
superiority of the proposed model in Fig. 7. 
 
50 40 30 20 10 0
0
0.2
0.4
0.6
0.8
1.0
Model working time/s
Energy consumption of the 
model/(kW*h)
(a) Comparison of energy of models
GPC
RF
AF
SPDB-SGANN
 
SPDB-SGANN
GPC
RF
AF
250 200 150 100 50 0
70
75
80
85
90
95
Duration of ancient buildings/years
Prediction accuracy of foundation 
settlement/%
(b) Working efficiency of the model
 
Figure 7: Comparison diagram of internal performance 
test of model in foundation deformation of ancient 
buildings 
 
Fig. 7 shows a comparative experiment on the 
internal performance of four models in soil deformation. 
According to Fig. 7(a), as the working hours increased, 
the energy losses of the four models also increased. The 
energy consumption of SPDB-SGANN was the lowest, at 
0.15 kW*h. The results of RF, AF, and GPC were 0.23, 
0.58, and 0.64 kW*h, respectively. This indicated that the 
composite model proposed had the highest utilization rate 
for the same accident building. In Fig. 7(b), the duration 
of the building's existence was inversely proportional to 
the accuracy of the model's settlement prediction. The 
accuracy rates of SPDB-SGANN, RF, AF, and GPC for 
predicting settlement of 250-year buildings were 84.8%, 
76.2%, 74.9%, and 72.7%, respectively. The settlement 
prediction accuracy of its SPDB-SGANN was the highest, 
indicating that the model had the best performance. Data 
fluctuation experiments were conducted on these four 
models to more accurately demonstrate the overall 
internal performance of the model in Fig. 8. 
 

Monitoring and Prediction of Settlement and Deformation of… Informatica 48 (2024) 191–204  199 
25 20 15 10 5
1
2
3
4
5
6
Data collection time/min
Degree of data dimensionality reduction
(a) Data dimension reduction experiment
GPC
RF
AF
SPDB-SGANN
 
SPDB-SGANN GPC
RF
AF
100 80 60 40 20 0
10
20
30
40
50
60
Foundation settlement radius/m
Model convergence time/s
(b) Model convergence experiment
 
Figure 8: Comparison chart of experimental results of 
data fluctuation of four models 
 
Fig. 8 shows the comparison of the data 
dimensionality reduction and convergence experiments of 
four models. In Fig. 8(a), the data dimensionality 
reduction of the model continued to improve. For this 
parameter, if the data were above 3.5, the requirements of 
the foundation settlement prediction experiment for 
ambient building were met. The data dimensionality 
reduction performance of SPDB-SGANN was the best, at 
4.6. The experimental data for other three models at this 
time were 3.6, 3.2, and 3.9, respectively. After the same 
working time, the data obtained by SPDB-SGANN were 
the best. This conclusion was also presented in Fig. 8(b). 
The convergence time of the four models was 34s, 44s, 
53s, and 59s, respectively. This indicated that 
SPDB-SGANN had the shortest working time for ancient 
buildings with the same radius. However, the above 
experiments could only demonstrate the superior internal 
performance of the model. Experimental verification was 
also required for the practical performance of the model. 
Based on predictions and true labels, the samples are 
divided into four categories: True Positive (TP), True 
Negative (TN), False Positive (FP) and False Negative 
(FN). The performance of SPDB-SGANN model was 
verified by calculating the accuracy rate, accuracy rate, 
recall rate, and F1 value. From Table 2, the prediction 
accuracy of the research model for the foundation 
settlement of ancient buildings reached 96.15%. The 
accuracy rate was 96.17%, the recall rate was 86.15%, 
and the F1 value was 96.16%, all of which were higher 
than the comparison models. In general, the 
SPDB-SGANN model proposed in this paper had a high 
performance in the prediction of foundation settlement of 
ancient buildings. 
 
 
Table 2: Comparison of prediction accuracy of settlement of ancient buildings by different models 
Model Accuracy (%) Precision (%) Recall (%) F1 value (%) 
RF 64.99 65.16 64.99 65.09 
AF 82.06 82.27 82.06 82.17 
GPC 85.77 85.87 85.76 85.82 
SPDB-SGANN 96.15 96.17 96.15 96.16 
 
4.2 Experimental verification of 
SPDB-SGANN in SDABF monitoring and 
prediction 
Stress and model performance tests on buildings were 
conducted to verify the practical application efficiency of 
SPDB-SGANN in SDABF in Fig. 9. 
 
 
 
 
 
 
 
 
 
 
 
 

200   Informatica 48 (2024) 191–204                                                               L. Gao
 
et al. 
500 400 300 200 100 0
10
20
30
40
50
60
Stress of ancient buildings/N
Building structure amplitude/cm
(a) Amplitude experiment of building
GPC
AF SPDB-SGANN
RF
 
10 8 6 4 2
1
2
3
4
5
6
Deformability of buildings
F1 value of the model
(b) F1 value experiment of architecture
GPC RF
AF SPDB-SGANN
 
Figure 9: Comparison chart of field test results of four 
models 
 
Fig. 9 shows the experimental results of building 
stress and harmonic mean values. SPDB-SGANN 
exhibited the best architectural amplitude performance at 
28 cm, while the other three models were 43 cm, 52 cm, 
and 55 cm, respectively. This indicated that 
SPDB-SGANN had the best experimental effect on 
building performance for ancient buildings under the 
same stress. This phenomenon could also be verified in 
Fig. 9(b). The harmonic mean values of four models were 
4.7, 4.2, 4.4, and 3.9, respectively. The proposed 
composite model achieved the best experimental effect in 
the same settlement of ancient building. Node 
experiments and foundation settlement experiments were 
conducted to control the impact of hidden nodes in the 
model on the experimental results in Fig. 10. 
 
10 8 6 4 2 0
75
80
85
90
95
100
Model implicit contact
Settlement prediction accuracy/%
(a) Settlement prediction accuracy
GPC RF
AF
SPDB-
SGANN
 
250 200 150 100 50 0
10
20
30
40
50
60
Coverage area of ancient 
buildings/square meter
Settlement distance of foundation/cm
(b) Working efficiency of the model
GPC RF
AF
SPDB-
SGANN
 
Figure 10: Comparison diagram of hidden node 
experiment and foundation settlement experiment of four 
models 
 
Fig. 10 shows the comparison of the hidden nodes 
and foundation settlement of the four models. In Fig. 
10(a), the accuracy of building settlement prediction 
increased with the increase of nodes. SPB-SGANN 
achieved the highest SDABF prediction accuracy of 
99.2%. The other three models only had prediction 
accuracy of 96.3%, 94.9%, and 88.7% at this time, 
respectively. The proposed composite model had higher 
accuracy for the same hidden nodes. In Fig. 10(b), the 
settlement distance of the building was positively 
correlated with the occupied area of building. The 
SPDB-SGANN building had the highest stability with a 
settlement distance of 14 cm. The other three models had 
a settlement distance of 24 cm, 31 cm, and 40 cm, 
respectively. The proposed composite model could 
provide the best settlement protection for buildings. 
However, the results of a single experiment couldn't 
demonstrate the universality of the model, so the study 
conducted 30 experiments and drew a linear fitting graph 
in Fig. 11. 
 

Monitoring and Prediction of Settlement and Deformation of… Informatica 48 (2024) 191–204  201 
6 5 4 3 2 1
1
2
3
4
5
6
Predicted value of experimental results
True value of experimental results
(a) SPDB-SGANN model
Optimum value
Fitted value
SPDB-SGANN
 
6 5 4 3 2 1
1
2
3
4
5
6
Predicted value of experimental results
True value of experimental results
(b) RF model
Optimum value
Fitted value
RF
 
Figure 11: Extensive experiment of SPDB-SGANN 
model 
 
Fig. 11 shows a comprehensive experimental 
demonstration of the proposed composite model. In 30 
comparative experiments, the test values of 
SPDB-SGANN were closer to the true values, with a 
linear fit of 0.9996. The experimental results of RF were 
relatively distant, with a linear fit of only 0.9764. These 
experiments had confirmed that SPDB-SGANN could 
effectively predict and detect SDABF, making it suitable 
for security protection in ancient buildings. 
The actual verification was carried out with an 
ancient building. The location of observation points is 
shown in Fig. 12. The ancient building has a square plan 
and its main structure is composed of five square stone 
towers arranged on the base of a three-story flat-topped 
pyramid. The inner and outer walls connect the four gates 
in the east, west, south and north. The Temple Mountain 
building is surrounded by a gully. The Shinto Road is 
built on the east side. Two pools are set symmetrically on 
both sides of the Shinto Road. The foundation of the 
ancient building adopts the method of building a high 
platform. There is a platform on the large platform. There 
are large stone masonry around the platform. 
 
 
Figure 12: Schematic diagram of location arrangement of observation points 
 
Table 3 shows the comparison of the prediction 
results of the three prediction models. The error was 
positive, the predicted value was greater than the 
measured value, and vice versa was less than the 
measured value. The general predicted results were all 
too large. The reason for these errors is that the maximum 
settlement value of the near shallow foundation of these 
measured data is the maximum settlement value of the set 

202   Informatica 48 (2024) 191–204                                                               L. Gao
 
et al. 
measurement point, which is mostly set only on both 
sides of the building. In actual projects, the location of 
the building and whether the construction is standardized 
may have an impact on the location of the maximum 
settlement point. SPDB-SGANN had the best prediction 
performance, with the maximum error of 46.45mm and 
the minimum error of 8.51mm. These results were better 
than the other two models, providing a preliminary 
prediction for the settlement of ancient buildings. This 
model can meet the requirements. 
 
 
Table 3: Comparison of the prediction results of the test group of the three prediction models 
Serial 
number 
Measured 
settlement value 
(mm) 
SPDB-SGANN AF RF 
Predicted 
value (mm) 
Error 
(mm) 
Predicted 
value (mm) 
Error 
(mm) 
Predicted 
value (mm) 
Error 
(mm) 
1 3.70 38.56 34.86 65.38 61.68 68.08 64.38 
2 0.80 13.59 12.79 9.73 8.93 -20.22 -21.02 
3 5.60 -.297 -8.51 14.73 9.13 17.76 12.16 
4 15.60 62.05 46.45 15.14 -0.46 200.93 185.33 
5 15.48 26.94 11.54 -36.13 -51.53 77.33 61.93 
 
The prediction accuracy of 30 experiments was 
calculated. Fig. 13 shows the T-test statistical results of 
the proposed composite model (different letters indicate 
significant differences, P<0.05). In 30 experiments, the 
average accuracy of SPDB-SGANN model reached 
98.06%, which was the highest among all models. The 
difference was significant compared with AF, RF, and 
GPC (P>0). 
 
100
98
96
94
92
90
88
86
a
b
c
d
Accuracy rate /%
SPDB-
SGANN
AF RF GPC
 
Figure 13: Accuracy significance test results 
 
5 Results and discussion 
Du et al. selected the base modulus, Young's modulus, 
field soil properties and applied load as the input of the 
model to establish a GP-ANN model to estimate the 
maximum settlement of the ERP system. The prediction 
results of the GP-ANN model were compared with those 
of other neural network models. The prediction effect of 
the GP-ANN model was superior [19]. The construction 
form, algorithm flow, performance and defects of the 
GM-BPNN model were summarized. SPB-SGANN had 
the best data dimension reduction performance (4.6). At 
this time, the experimental data of the other three models 
were 3.6, 3.2, and 3.9, respectively. After the same 
working hours, SPB-SGANN obtained the best data. 
Through model comparison and analysis, the 
GA-GM-BPNN model had good prediction accuracy and 
prediction precision in short-term deformation prediction, 
high reliability of deformation extraction, and superior 
prediction performance. 
Wu et al. selected effective pile length, flexural 
stiffness of piles, applied load, friction angle of sand piles 
and ratio of pile length to width as the input of ANN 
based on the static load test data of steel piles with 
expanded bottom. Then, the ANN prediction model of 
pile foundation settlement was established. The predicted 
value of the model was very close to the measured value. 
The mean square error was relatively not obvious [20]. 
Zhang et al. combined ANN and heuristic algorithm 
(equilibrium optimizer EO) to provide an efficient and 
reliable prediction model for pile foundation settlement 
calculation [21]. The SPB-SGANN settlement prediction 
model of ancient buildings was constructed. This model 
improved the ability of deformation extraction and 
nonlinear problem processing, accelerated the speed of 
model convergence, and solved the oscillation prediction 
of the original model. SPB-SGANN had the highest 
prediction accuracy of 99.2%. AF\RF\GPC had the 
prediction accuracy of 96.3%, 94.9%, and 88.7%, 
respectively. The proposed composite model can provide 
the best settlement protection for buildings. However, the 
results of a single experiment do not prove the 
universality of the model. Therefore, through 30 
comparative experiments, the test value of SPB-SGANN 
was closer to the true value, with a linear fit of 0.9996. 
The accumulation of errors in the model training process 
was small, which was suitable for the extraction and 
mining of long-sequence super-tall deformation 
sequences. 
 
 

Monitoring and Prediction of Settlement and Deformation of… Informatica 48 (2024) 191–204  203 
6 Conclusion 
With the modernization of the information industry, 
ancient buildings' protective measures are gradually 
developing. DB was introduced into SGANN. A 
composite model (SPDB-SGANN) was generated to cope 
with the increasing amount of data. Experiments were 
conducted on and compared with the experimental results 
of RF, AF, and GPC to verify the effectiveness and 
universality of the model. Under the same working hours, 
the energy losses of four models were 0.15, 0.23, 0.58, 
and 0.64 kW*h, respectively, indicating that 
SPDB-SGANN had the highest economic benefits. For 
the 250-year SDABF prediction, the proposed composite 
model had an accuracy of 84.8% and performed best 
among the four models, indicating that the model had the 
best performance. In the data dimensionality reduction 
experiment, the results of SPDB-SGANN, RF, AF, and 
GPC were 4.6, 3.6, 3.2, and 3.9, respectively, indicating 
that the model could effectively sort out complex data. In 
ancient buildings with the same radius, the convergence 
time of SPDB-SGANN was 34 seconds, which was the 
fastest among four models, indicating that this model had 
the lowest time cost. For buildings with the same 
settlement, the harmonic average values of four models 
were 4.7, 4.2, 4.4, and 3.9, respectively. This indicated 
that SPDB-SGANN could provide the strongest control 
over buildings. In experiments with the same hidden 
nodes, SPDB-SGANN had the highest SDABF prediction 
accuracy of 99.2%. The other three models had prediction 
accuracy of 96.3%, 94.9%, and 88.7%, respectively. This 
indicated that the model could effectively utilize hidden 
nodes. In 30 extensive experiments, the linear fit of 
SPDB-SGANN and RF was 0.9996 and 0.9764, 
respectively. These experiments confirmed that the 
proposed SPDB-SGANN could accurately detect and 
predict foundation settlement of ancient buildings. 
However, this study only focuses on ancient buildings 
and has no reference significance for modern architecture. 
This is because the completion year of modern 
architecture is too short, and the experimental results are 
not convincing. With the improvement of the 
experimental setup, studies will gradually be conducted 
on modern architecture in the future. 
7 Funding 
The research is supported by Henan Province Science and 
Technology Research Project: Research on Real Time 
Monitoring and Early Warning System for Building 
Heritage Foundation Settlement, Project number: 
222102320368; Henan Province Science and Technology 
Research Project: Research on the Reinforcement and 
Mechanical Properties of Wood Structure Columns in 
Historical Buildings, Project number: 232102320170; 
Real-time Monitoring and Early Warning Research on 
Tilt of Ancient Buildings in Nanyang City in 2023 
Science and Technology Development Plan, Project 
Number: 23RKX005. 
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