A Novel Visual System for Conducting Safety Evaluations of Operational Tunnel Linings

Abstract

Based on the lining structure of an operational tunnel, the AHP and Fuzzy mathematical models were used to determine the weight of the evaluation index and solve the membership matrix. The weighted-average Fuzzy comprehensive function was used to combine the two, and the Fuzzy–AHP evaluation model was built and programmed. According to the self-developed Fuzzy–AHP evaluation-programmed model, a visualized structure safety evaluation system for operational tunnels was developed by using MATLAB. The system’s functional design, program development, and computational visualized interface were implemented, and key codes were provided. The system can be divided into four modules: data management, fuzzy computation, predictive analysis and key disease indexes to focus on. In addition, the system can easily edit and modify the evaluation function, which includes not only the Fuzzy evaluation but also other types of evaluation functions applicable to other practical engineering projects, improving the applicability of the system. After that, the system was applied to the structure safety evaluation of a mountain tunnel, which provided the evaluation results and key indexes to focus on in the tunnel. Finally, the rationality of the system design was verified by constructing the corresponding BP–RBF combined neural network. This study provides a reference for the establishment of an intelligent structure safety warning system for operational tunnels.

1. Introduction

The long-term use of tunnels often results in severe rock disease problems (Figure 1) [1,2], which poses challenges for the structure safety of tunnels in their operational period. For example, cracks are one of the common rock diseases. Cracks in concrete tunnels are often caused by the heat of hydration, as it may lead to high material stresses in the early stages after casting [3]. These thermal cracks often appear as through cracks, resulting in structural damage and affecting the durability of the structure, and leading to severe damages and durability problems.

The structure safety state of an operational tunnel refers to the damage of the lining structure of the tunnel, so the evaluation of the state of tunnel structure safety is the process of considering the various states of damage in the tunnel structure. The structural damage states of operational tunnels can be comprehensively reflected by various forms of structural damage, which mainly include the lining cracking, lining weakening, water leakage, and lining cave [4,5,6]. Specifically, these include the crack length and width, lining deformation, lining peeling, strength index, thickness index, water leakage state, and cave depth. These diseases can bring many serious problems: lining cracking can cause a reduction in structural bearing capacity; tunnel headroom becomes smaller and intrudes into the building limit, which affects driving safety; leakage of water leads to corrosion of tunnel facilities and freezing damage; and when the caves in the lining are serious, the surrounding rock will become unstable and collapse.

However, there is insufficient research on the structure safety of operational tunnels, making it difficult to conduct standardized and quantitative safety evaluations [7,8]. Previous structure safety evaluations of tunnels mainly focused on the construction period, the purpose of which was to obtain the structure safety status in a timely manner and guide further construction [9,10]. With the increasing number of tunnels already constructed, structure safety evaluations of operational tunnels have received continuous attention, especially with respect to the development of quantitative evaluation methods instead of traditional qualitative methods. Some theoretical models have been applied in safety evaluations of operational tunnels. However, these methods have only demonstrated theoretical feasibility and have not been effectively applied in practical engineering projects [11,12,13,14,15,16]. One important reason is that the above models were too complex and specialized, resulting in insufficient applications. Therefore, there is an urgent need to develop a visualized safety evaluation system that is easy to operate for operational tunnels.

The development of a visualized system is based on an algorithmic model. A sound evaluation system must possess a well-developed algorithmic model, which serves as the core of the system. Research indicates that the Fuzzy–AHP model is an ideal model for evaluating structure safety due to its ability to effectively solve problems that are difficult to quantify, which makes the results more objective [17,18,19]. However, there have been few reports on the development of a programmable and visualized structure safety evaluation model for operational tunnel by combining Fuzzy and AHP.

The main work of this study is as follows: (1) Development of the evaluation system: This paper employs MATLAB to programmatically model the improved Fuzzy–AHP analysis method and develops a visualized system for evaluating the structure safety of operational tunnels based on self-designed program codes. The system is capable of not only rapidly assessing the safety status of tunnel structures, but also quantifying and accurately predicting the overall safety trends of the tunnel. (2) Full scale study: According to the lining structure of the operational tunnel, the AHP and Fuzzy mathematical models were used to determine the weight of the evaluation index and solve the membership matrix. The weighted-average Fuzzy comprehensive function was applied to combine the two, and then the Fuzzy–AHP evaluation model was built and programmed. (3) Evaluation of the results and feasibility of the evaluation system: The structure safety of a mountain operational tunnel was evaluated using the established system, and the evaluation results were compared with those obtained using the BP–RBF combined neural network, which demonstrated the feasibility, reasonableness, and accuracy of the evaluation system. This study provides a reference for the establishment of an intelligent structure safety warning system for operational tunnels.

2. The Fuzzy–AHP Evaluation Model and Its Programming

The improved Fuzzy–AHP model combines both Fuzzy and AHP using the following procedure [20]: (1) the weights of the indexes were determined by AHP, (2) the membership matrix was solved using Fuzzy, and then (3) the two were combined using the weighted-average Fuzzy comprehensive function.

2.1. Hierarchical Indexes and Classifications for Structure Safety Evaluations of Operational Tunnels

There are numerous factors that can influence the structure safety of operational tunnels, among which the most important are lining cracking, lining weakening, water leakage, and lining cave. The selection of appropriate evaluation indexes plays a crucial role in ensuring the accuracy of the evaluation results [21]. Based on related research [22,23,24], an evaluation index system that conformed to the structure safety characteristics of the operational tunnel was established, as shown in Figure 2.

The four-level classification method serves as the basis for assigning a structure safety level. The levels are defined as follows: A—slight damage; B—moderate damage; C—severe damage; D—dangerous state.

2.2. Programming of Fuzzy–AHP Model

The key to establishing a visualized system is to construct a programmatic computational model. The Fuzzy–AHP model was programmed and then embedded into the visualized interface based on self-written codes.

2.2.1. Fuzzy Comprehensive Evaluation Programmatic Model

Based on Fuzzy comprehensive evaluation theory [20], the Fuzzy comprehensive evaluation function “Fuzzy.m” was formed using self-written codes (please note that some underlines were for emphasis and distinction and did not affect the meaning of the codes):

① function R=Fuzzy (num1, num2, ~numm);

② R=zeros(m, n);

T=zeros(1, m);

③ T(1, 1)=num1; T(1, 2)=num2;

T(1, 3)=num3~T(1, m)=numm;

④ for i=1:m;

R(i, ) = F _i, (T(1, i), S(i, )..);

end

Num1 to numm in ① represent the influencing factors at the index layer, which are the actual monitoring values from the operational tunnel. R in ② is an m-row and n-column empty matrix used to store the membership matrix. Codes ③ and ④ mean the represent the actual monitoring values input into the membership functions to calculate the membership matrix (Fuzzy relationship matrix).

2.2.2. Determination of Index Weights

For hierarchical structures, if there are several membership relationships from the top to bottom, several indicator-factor judgment matrices need to be established. After establishing the judgment matrices, the key is to calculate the maximum eigenvalue of the judgment matrix and the eigenvector corresponding to the eigenvalue. The above eigenvector is the weight.

The improved Fuzzy–AHP model used the e^0/4~e^8/4 scaling method instead of the traditional 1~9 scaling method to construct the corresponding judgment matrix and quantitatively determine the index weight, which can avoid the boundary ambiguity issue [25].

Table 1. Weight values of evaluation indexes for all layers.

Criterion Layer	Index Layer	Weight Values
Lining cracking A1	Crack length and width A11	0.4109
	Lining deformation A12	0.3781
	Lining peeling A13	0.2110
Lining weakening A2	Strength index A21	0.5622
	Thickness index A22	0.4378
Leakage water A3	Leakage water state A31	1.0000
Lining cave A4	Cave depth A41	1.0000

presents the weight values of the evaluation indexes in each layer, which were obtained by using the “eig function” in MATLAB.

The MATLAB codes used to solve the eigenvalues and eigenvectors (weights) in the AHP model are as follows:

Define “M function” as MAX-eigvalvec.m;

function[eigval, w] = MAX-eigvalvec(A);

% Obtain the maximum eigenvalue and normalized eigenvector, where A is the judgment matrix;

① [eigvec,eigval]=eig(A);

② maxeigval=max(eigval);

③ v=eigvec(:,index’);

④ W=v./sum(v);

⑤ end

The codes result in the fast calculation of both the eigenvalues and eigenvectors of the judgment matrix in MATLAB. “eig(A)” in ① is to call the “eig function” in MATLAB, resulting in the calculation of the eigenvalues and eigenvectors of the judgment matrix A. The codes in ② result in the solution of the maximum eigenvalue. The codes in ③ result in the solution of the eigenvector corresponding to the maximum eigenvalue. The codes in ④ result in the normalization of the eigenvectors (normalization of the comparative weights), the aim of which is to ensure the sum of all weights is equal to 1. The normalized weights are more conducive to the comparative evaluation of things.

2.2.3. Determination of Membership Function

The calculation of the membership matrix in MATLAB is one of the important aspects. The traditional manual membership matrix is very complicated to solve. When there are dozens of sections, the calculation difficulty and complexity are very large, and the accuracy of the traditional calculation cannot be guaranteed at all. Therefore, this article uses MATLAB to program the solution of the membership matrix, which can solve the membership matrix quickly and precisely. The program is divided into four parts, namely, lining cracking, lining weakening, water leakage, and lining cave. The membership matrix can be calculated by the membership function (Formulas (1)–(3) described below).

According to the membership function determination rule, the “ridge-shaped distribution function” was selected. There are three main types of ridge-shaped distribution:

(1)

Partial-small type

$$R(x)=\left\{\begin{array}{cc}0& x\le a_1 \hfill \\ {\displaystyle \frac{1}{2}}-{\displaystyle \frac{1}{2}}\sin {\displaystyle \frac{\pi }{a_2-a_1}}(x-{\displaystyle \frac{a_1+a_2}{2}})& a_1<x\le a_2\hfill \\ 0& x>a_2\hfill \end{array}\right.$$

(1)

(2)

Inter-mediate type

$$R(x)=\left\{\begin{array}{cc}0& x\le a_1 \hfill \\ {\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}\sin {\displaystyle \frac{\pi }{a_2-a_1}}(x-{\displaystyle \frac{a_1+a_2}{2}})& a_1<x\le a_2\hfill \\ 1& a_2<x\le a_3\hfill \\ {\displaystyle \frac{1}{2}}-{\displaystyle \frac{1}{2}}\sin {\displaystyle \frac{\pi }{a_2-a_1}}(x-{\displaystyle \frac{a_1+a_2}{2}})& a_3<x\le a_4\hfill \\ 0& x>a_4 \hfill \end{array}\right.$$

(2)

(3)

Partial-large type

$$R(x)=\left\{\begin{array}{cc}0& x\le a_1 \hfill \\ {\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}\sin {\displaystyle \frac{\pi }{a_2-a_1}}(x-{\displaystyle \frac{a_1+a_2}{2}})& a_1<x\le a_2\hfill \\ 1& x>a_2\hfill \end{array}\right.$$

(3)

In Formula (1)–(3), where a means the grading standard of the evaluation index, based on both actual engineering and relevant specifications, membership R(x) indicates the degree where x belongs to R: the closer R(x) is to 0, the smaller the degree where x belongs to R(x); the closer R(x) is to 0.5, the fuzzier the degree to where x belongs to R; the closer R(x) is to 1, the greater the degree where x belongs to R(x).

3. Function Design and Implementation of Visualized System

The visualized system was developed on the MATLAB platform, effectively integrating functional modules such as data management that not only allow for manual input, but also accept real-time monitoring data through the designated interface, which can connect to the real-time monitoring system of an operational tunnel. This system also provides the following: Fuzzy computation; predictive analysis; and key disease indexes to focus on. Based on both the safety evaluation index and Fuzzy–AHP evaluation model, the structure safety evaluation of an operational tunnel was conducted through model analysis and functional application.

The development of the visualized system was based on the MATLAB GUI platform, incorporating the control modules in “untitled.fig”. The program design was based on the attributes, events, and methods of encapsulated modules and application objects, which not only enhance the computational capability of the model but also establish interconnections and coupling among various modules, resulting in a unified whole.

The establishment of the structure safety evaluation system for operational tunnels involves several key issues that are addressed by using MATLAB: (1) the input of monitoring data; (2) the calculation of the Fuzzy relation matrix by calling the Fuzzy comprehensive evaluation function; and (3) the structure safety level and corresponding key disease indexes to focus on. The evaluation system workflow is illustrated in Figure 3.

The codes for the structure safety evaluation program for operational tunnels are complex and professional, which is not conducive to its application in the safety evaluations of tunnel engineering. Our system uses GUIDE in MATLAB to create the GUI-visualized interface, easily achieving human–machine interactions. The implementation steps mainly include setting the GUI object layout. This involves opening the object property viewer and setting the corresponding properties of the object, and writing the callback functions. The purpose of writing callback functions is to invoke pre-written subfunctions (Fuzzy–AHP evaluation programmatic model), which are typically saved in the form of M-files in a fixed path within MATLAB. This step is crucial for creating the visualized interface, the specific operation process of which is as follows: right-click the Push Button, select View Callbacks, and then select the Callback (Figure 4).

Partial core codes which were self-written in the callback function are as follows:

function pushbutton1_Callback(hObject, eventdata, handles)

str1=get(handles.edit1,‘String’);

num1=str2double(str1);

str2=get(handles.edit2,‘String’);

num2=str2double(str2);

str3=get(handles.edit3,‘String’);

num3=str2double(str3);

str4=get(handles.edit4,‘String’);

num4=str2double(str4);

str5=get(handles.edit5,‘String’);

num5=str2double(str5);

str6=get(handles.edit6,‘String’);

num6=str2double(str6);

str7=get(handles.edit7,‘String’);

num7=str2double(str7);

str8=get(handles.edit8,‘String’);

num8=str2double(str8);

% Monitoring data input

R1=Ff1(num1,num2,num3,num4);

R2=Ff2(num5,num6);

R3=Ff3(num7);

R4=Ff4(num8);

% Forming the membership matrix based on the membership function (2.2.3 Determination of membership function)

wA1=[0.4109,0.3781,0.2110];

wA2=[0.5622,0.4378];

wA3=[1];

wA4=[1];

% index weight

Taking 4 monitoring data for lining cracking as an example:

C1=jq(wA1,R1);

% Fuzzy composition

B1=C1./sum(C1);

% normalization

wB1=[4 3 2 1];

G1=dot(wB1,B1);

if G1>3.5&&G1<=4

H1=(‘A—slight damage’);

set(handles.edit9,‘string’,num2str(H1));

end

% First-level evaluation

.......

.......

E=[B1;B2;B3;B4];

wA=[0.5696,0.1741,0.1632,0.0931];

C=jq(wA,E);

B=C./sum(C);

wB=[4 3 2 1];

G2=dot(wB,B);

set(handles.edit13,‘string’,num2str(G2),‘FontSize’,15);

.......

if G2>2.5&&G2<=3.5

str1=[‘This section of the lining has been evaluated as having B—moderate damage, which is primarily characterized by insufficient lining strength and thickness, as well as the leakage of water and back cave of the lining. Appropriate measures should be taken to address these issues 10];

str2=[str1]

set(handles.edit14,‘string’,str2,‘FontSize’,20);

end

% Second-level evaluation (or overall evaluation)

The above codes result from the input of 8 representative monitoring data (corresponding to the Table 1 index layer: crack length, crack width, lining deformation, lining peeling depth, actual strength/design strength of lining, actual thickness/design thickness of lining, leakage of water, and lining cave depth), the call of the index weights, and the membership matrix. Taking 4 monitoring data of lining cracking as an example, the Fuzzy evaluation matrix was synthesized by combining the index weight wA1 with the membership matrix R1. The first-level structure safety value G1 was then obtained, allowing for a quantitative evaluation of structure safety state in the criterion layer. Based on the first-level evaluation, the second-level evaluation (or overall evaluation) was implemented and finally the second-level structure safety value G2 and the key disease indexes to focus on were obtained.

In addition, the system provides convenient editing and modification of monitoring-data input procedures and subfunctions, such as membership functions or other types of structure safety evaluation functions, which allows for the addition of new monitoring items or changes to the evaluation functions according to practical engineering needs. As a result, the system can continuously adjust its computational model in response to different tunnels with different environmental conditions, making it practical and extensive.

Table 2. Tunnel structure safety levels and values.

Structure Safety Level	Structure Safety Value
Slight damage (A)	$4.0\ge G>3.5$
Moderate damage (B)	$3.5\ge G>2.5$
Severe damage (C)	$2.5\ge G>1.5$
Dangerous state (D)	$1.5\ge G\ge 1.0$

shows the tunnel structure safety levels and values.

The following codes result in the judgment and visualized output of the safety levels (taking the lining cracking as example):

if G1>3.5&&G1<=4

H1=(‘A—slight damage’);

set(handles.edit1,‘string’,num2str(H1));

else if G1>2.5&&G1<=3.5

H2=(‘B—moderate damage’);

set(handles.edit1,‘string’,num2str(H2));

else if G1>1.5&&G1<=2.5

H3=(‘C—severe damage’);

set(handles.edit1,‘string’,num2str(H3));

else G1>=1&&G1<=1.5

H4=(‘D—dangerous state’);

set(handles.edit1,‘string’,num2str(H4));

end

4. Engineering Case Analysis

4.1. Project Overview

The tunnel is a mountain operational tunnel. The left tunnel has a length of 400 m, while the right has a length of 375 m. The starting and ending milepost number of the right line is K+005–K+380. There were many diseases in the tunnel lining, such as cracks (Figure 5a), water leakage (Figure 5b), etc.

4.2. Source of Monitoring Data

K+050–K+350 in the right line was selected as the evaluation object. Fiber optic sensors were used to monitor lining cracks (Figure 6a,b).

A ZC3-A rebound tester was used to test the lining strength (Figure 7a), and ground penetrating radar was used to detect the lining thickness and the presence of caves (Figure 7b), etc.

Consequently, 30 sections were divided and numbered from 1 to 30. Each evaluation section was approximately 10 m in length, as shown in

Table 3. Structure safety monitoring data in the mountain tunnel.

Section	Crack Length /m	Crack Width/mm	Lining Deformation	Lining Peeling Depth /mm	Strength Index	Thickness Index	Water Leakage State	Lining Cave Depth /mm
1	2.3	0.4	0.00	8	0.90	0.70	drip	30
2	0.0	0.0	0.07	0	1.00	0.80	seepage	41
3	1.5	1.6	0.50	13	0.42	0.90	drip	37
4	4.5	0.6	0.80	20	0.38	0.50	drip	351
5	3.0	0.7	0.60	21	0.50	0.60	drip	589
6	4.0	1.1	0.70	12	0.40	0.50	seepage	121
7	1.8	0.4	0.01	6	0.90	0.51	seepage	31
8	2.3	1.2	0.02	5	0.80	0.43	drip	265
9	3.9	1.1	0.02	0.3	0.92	0.44	drip	65
10	0.2	0.3	0.06	0.5	0.70	0.52	drip	44
11	2.1	1.8	0.04	0.2	0.93	0.76	drip	143
12	0.3	0.2	0.05	9	0.80	0.82	drip	34
13	0.5	1.3	0.03	12	0.91	0.20	drip	31
14	4.2	1.8	0.12	11	0.61	0.73	seepage	189
15	1.8	1.3	0.30	13	0.87	0.78	seepage	35
16	1.1	2.1	0.07	16	0.45	0.83	seepage	409
17	0.2	0.1	0.65	8	0.60	0.81	seepage	210
18	0.3	0.2	0.76	12	0.63	0.52	seepage	25
19	1.2	0.1	0.21	14	0.47	0.72	drip	302
20	4.7	0.7	0.49	16	0.52	0.78	drip	34
21	2.2	0.5	0.38	10	0.50	0.49	drip	40
22	2.5	1.5	0.10	7	0.64	0.43	drip	54
23	3.4	1.4	0.04	9	0.97	0.65	drip	28
24	3.1	1.9	0.42	16	0.92	0.70	drip	245
25	2.6	2.0	0.30	13	0.82	0.53	drip	20
26	9.0	0.5	0.60	1	0.79	0.56	gush	54
27	5.4	0.5	0.03	16	0.80	0.49	drip	25
28	4.7	0.2	0.15	2	0.92	1.00	drip	93
29	0.1	0.2	0.01	1	0.91	0.62	drip	43
30	4.3	0.4	0.00	3	1.00	0.75	drip	32

.

Please note that the lining deformation in the Table above refers to the ratio of the deformation amount to the internal limit distance; the strength and thickness indexes are the ratios of the measured values to the design values. Therefore, these three indexes are dimensionless and unitless.

4.3. Visualized Evaluation and Result Analysis

The monitoring data from Table 3 were input into the visualized system. The evaluation results are shown in

Table 4. Results of structure safety system evaluations.

Section Number	Evaluation of Lining Cracking	Evaluation of Lining Weakening	Evaluation of Water Leakage	Evaluation of Lining Cave	Overall Structure Safety Value	System Evaluation Results
1	A	B	B	B	3.4711	B
2	A	A	A	B	3.8307	A
3	B	C	B	B	2.8485	B
4	C	D	B	C	2.2418	C
5	B	D	B	D	2.4022	C
6	B	D	A	C	2.6805	B
7	A	B	A	B	3.6181	A
8	A	C	B	C	3.3241	B
9	A	B	B	B	3.5150	A
10	A	C	B	B	3.3193	B
11	A	B	B	C	3.5553	A
12	A	B	B	B	3.4494	B
13	A	B	B	B	3.3348	B
14	A	D	A	C	3.2526	B
15	B	A	A	B	3.3684	B
16	A	C	A	C	3.2036	B
17	B	C	A	C	2.8930	B
18	B	D	A	B	2.6392	B
19	A	D	B	C	2.9589	B
20	B	C	B	B	2.8213	B
21	B	D	B	B	2.8858	B
22	A	D	B	B	3.1257	B
23	A	B	B	B	3.4711	B
24	B	B	B	C	3.0424	B
25	B	C	B	B	2.9614	B
26	B	C	D	B	2.4260	C
27	B	C	B	B	2.9485	B
28	A	A	B	B	3.7214	A
29	A	B	B	B	3.5862	A
30	A	B	B	B	3.6294	A

.

Taking the previous five sections (numbers 1~5) as an example (Table 4), the structure safety values of Sections 2–5 were 3.8307, 2.8485, 2.2418, and 2.4022, respectively. Section 2 was classified as A-level, indicating slight damage to the structure, which does not compromise traffic safety. Therefore, this section was relatively safe, and only needed continued observation, without taking special safety measures, and maintenance. Sections 1 and 3 were classified as B-level, indicating moderate damage to the structure that may potentially affect traffic safety. The evaluation of lining weakening in Section 3 was C, so the strength and thickness of lining should be of particular concern. For example, the lining strength can be improved by grouting and supporting. Sections 4 and 5 were classified as C-level, indicating severe damage to the structure that poses a threat to traffic safety and thus requires immediate action to be taken. Taking Section 4 as an example, the evaluation of lining cracking, lining weakening and lining cave were C, D, and C, respectively, which requires immediate safety measures and maintenance; lining cracks and deformation can be treated by jointing reinforcement and shotcrete, the lining strength can be improved by grouting and supporting, and lining cave can be treated by backfilling and grouting.

The safety levels of Sections 4 and 5 were lower than those of the previous sections, indicating that the system has a strong sensitivity to monitoring data. Observations showed that the monitoring data in these two sections were significantly different from those in the previous sections. When the monitoring data changed in an unfavorable direction, the overall structure safety performance also weakened significantly. It was also observed that the lining crack length and width had a significant impact on structure safety, which corresponded to the weight design in the AHP model and conformed to engineering experiences. In addition, for system architecture, multi-level evaluation can enhance evaluation efficiency and quickly identify key disease indexes to focus on. For instance, Sections 1 and 3 (both B), Sections 4 and 5 (both C) had the same safety level (second-level evaluation or final evaluation), but there were still differences. By observing Columns 2 to 5 in Table 4 that represents the structure safety level of the first-level evaluation, it can be seen which index had a greater impact. This two-level evaluation mode can quickly find the key diseases to focus on and improve the evaluation efficiency.

The visualized system interface for structure safety evaluation is shown in Figure 8.

As for the entire tunnel structure (K+050-K+350), the absence of D-level damage (second-level evaluation) indicated that the overall safety of the tunnel structure was still within a controllable range, requiring only local reinforcement. Additionally, the following can be observed from Table 4: there were numerous cracks in the tunnel lining with larger lengths and widths; there were different degrees of lining peeling and falling blocks; and there were many instances of water leakage that were not serious.

Figure 9 presents a distribution diagram of the structure safety levels for each section of the operational tunnel. The blue color represents level A, yellow represents level B, orange represents level C, and red represents level D. The numbers in the diagram indicate the section number and their corresponding overall structure safety values. As can be observed from the diagram, sections with either safety level A or B accounted for 13.3% and 76.6%, respectively, while the remaining sections were at level C. Level B had the highest proportion, indicating that the overall tunnel was in the moderate state of damage. Although there was no need for large-scale renovations of the tunnel, all sections at level C were critical sections that were identified for immediate intervention.

4.4. Verification of BP–RBF Combined Neural Network

4.4.1. Matlab Implementation of BP–RBF Neural Network Evaluation Model

Neural networks can evaluate and predict things that are difficult to quantify [26,27,28]. The BP–RBF neural network combines the advantages of both BP and RBF neural networks. Therefore, the BP–RBF neural network was applied to the comparative method in our study. It is worth noting that reducing the complexity of the dataset can potentially improve the accuracy of the BP–RBF network [29,30], which will be studied in subsequent work.

For the neural network evaluation, eight disease indexes, including crack length, crack width, lining deformation, depth of lining peeling, actual strength/design strength of lining, actual thickness/design thickness of lining, water leakage, and depth of lining cave, were selected as the input variables, which were consistent with the visualized system evaluation. The number of neurons in the input layer of the neural network was 8, and the structure safety level was divided into four levels. The output-layer safety-level vectors included the following: A—slight damage (0 0 0 1); B—moderate damage (0 0 1 0); C—severe damage (0 1 0 0); D—dangerous state (1 0 0 0). The sample data determination referred to the normalization of the input data, as the actual monitoring data units were different and there was no unified dimension.

Normalization is generally used to map data within a specified range, removing the dimensions and units of the different dimensional data. The most common normalization method is Min–Max normalization (Equation (4)). Min–Max normalization, also known as deviation normalization, is a linear transformation of raw data that maps the resulting values between [0.1–0.9]. This normalization method is more suitable for the case of relatively concentrated values such as

$$x_n=0.1+0.8{\displaystyle \frac{x_i-x_{\min }}{x_{\max }-x_{\min }}}$$

(4)

where x_n represents the normalized data, x_i refers to the original monitoring data, x_min represents the minimum value in a set of input data, and x_max represents the maximum value in a set of input data. The normalization process adopts a self-designed normalization program based on Equation (4), and the normalization codes are as follows:

function R=guiyi2(A1,A2,A3,A4,A5,A6,A7,A8)

x=[A1,A2,A3,A4,A5,A6,A7,A8];

R=zeros(1,8);

[min_of_x]=min(x);

[max_of_x]=max(x);

R(1,1)=0.1+0.8*(A1-[min_of_x])/([max_of_x]-[min_of_x]);

R(1,2)=0.1+0.8*(A2-[min_of_x])/([max_of_x]-[min_of_x]);

R(1,3)=0.1+0.8*(A3-[min_of_x])/([max_of_x]-[min_of_x]);

R(1,4)=0.1+0.8*(A4-[min_of_x])/([max_of_x]-[min_of_x]);

R(1,5)=0.1+0.8*(A5-[min_of_x])/([max_of_x]-[min_of_x]);

R(1,6)=0.1+0.8*(A6-[min_of_x])/([max_of_x]-[min_of_x]);

R(1,7)=0.1+0.8*(A7-[min_of_x])/([max_of_x]-[min_of_x]);

R(1,8)=0.1+0.8*(A8-[min_of_x])/([max_of_x]-[min_of_x]);

end

The normalization of the sample input data in Table 3 is shown in

Table 5. Normalization of input data.

Section Number	Crack Length	Crack Width	Lining Deformation	Lining Peeling Depth	Strength Index	Thickness Index	Water Leakage State	Lining Cave Depth
1	0.1613	0.1107	0.1000	0.3133	0.1240	0.1187	0.1533	0.9000
2	0.1000	0.1000	0.1014	0.1000	0.1195	0.1156	0.1195	0.9000
3	0.1236	0.1258	0.1017	0.3751	0.1000	0.1105	0.1346	0.9000
4	0.1094	0.1005	0.1010	0.1448	0.1000	0.1003	0.1037	0.9000
5	0.1034	0.1003	0.1001	0.1279	0.1000	0.1001	0.1020	0.9000
6	0.1239	0.1046	0.1020	0.1769	0.1000	0.1007	0.1040	0.9000
7	0.1462	0.1101	0.1000	0.2546	0.1230	0.1129	0.1256	0.9000
8	0.1069	0.1036	0.1000	0.1150	0.1024	0.1012	0.1060	0.9000
9	0.1478	0.1133	0.1000	0.1034	0.1111	0.1052	0.1244	0.9000
10	0.1025	0.1044	0.1000	0.1080	0.1117	0.1084	0.1353	0.9000
11	0.1115	0.1098	0.1000	0.1009	0.1050	0.1040	0.1110	0.9000
12	0.1059	0.1035	0.1000	0.3109	0.1177	0.1181	0.1459	0.9000
13	0.1121	0.2180	0.1000	0.4092	0.1302	0.1044	0.1509	0.9000
14	0.1173	0.1071	0.1000	0.1461	0.1021	0.1026	0.1037	0.9000
15	0.1346	0.1231	0.1000	0.3928	0.1131	0.1111	0.1161	0.9000
16	0.1020	0.1040	0.1000	0.1312	0.1007	0.1015	0.1018	0.9000
17	0.1004	0.1000	0.1021	0.1301	0.1019	0.1027	0.1034	0.9000
18	0.1032	0.1000	0.1181	0.4806	0.1139	0.1103	0.1258	0.9000
19	0.1029	0.1000	0.1003	0.1368	0.1010	0.1016	0.1050	0.9000
20	0.2005	0.1050	0.1000	0.4703	0.1007	0.1069	0.1360	0.9000
21	0.1367	0.1024	0.1000	0.2942	0.1024	0.1022	0.1327	0.9000
22	0.1356	0.1208	0.1000	0.2024	0.1080	0.1049	0.1282	0.9000
23	0.1961	0.1389	0.1000	0.3564	0.1266	0.1175	0.1561	0.9000
24	0.1088	0.1048	0.1000	0.1510	0.1016	0.1009	0.1052	0.9000
25	0.1934	0.1690	0.1000	0.6157	0.1211	0.1093	0.1690	0.9000
26	0.2271	0.1000	0.1015	0.1075	0.1043	0.1009	0.1523	0.9000
27	0.2720	0.1151	0.1000	0.6117	0.1247	0.1147	0.1631	0.9000
28	0.1392	0.1004	0.1000	0.1159	0.1066	0.1073	0.1159	0.9000
29	0.1017	0.1035	0.1000	0.1184	0.1167	0.1114	0.1370	0.9000
30	0.2075	0.1100	0.1000	0.1750	0.1250	0.1188	0.1500	0.9000

.

This program invokes the MATLAB BP–RBF neural network toolbox through the “newff” function and applies the “train” function to train the network (the training data comes from Sections 1~20 in Table 5). The performance curve of the BP–RBF neural network is shown in Figure 10.

4.4.2. Prediction of BP–RBF Combined Neural Network Model

Based on the trained network, the “sim” function simulation was called in the MATLAB command window to predict the last 10 sections and then compare them with the results of the visualized system evaluation. The program codes are as follows:

Q=[0.1367,0.1024,0.1000,0.2942,0.1024,0.1022,0.1327,0.9000;

……

0.2075,0.1100,0.1000,0.1750,0.1250,0.1188,0.1500,0.9000];

% Read the sample data

Q=Q′

B=sim(net,Q)

% Calculate network simulation output

The prediction results that were calculated by the trained BP–RBF combined neural network model are shown in

Table 6. Prediction results calculated by BP–RBF neural network.

Section	Target Safety Level	Target Level Vector	Predict Output Vector	Predict Safety Level	Error
21	B	0 0 1 0	0.0179  0.0248 0.9854  −0.0279	B	0.0439
22	B	0 0 1 0	0.0066  0.0239 1.0215  0.0137	B	0.0356
23	B	0 0 1 0	0.0681  0.0319 0.8828  −0.0370	B	0.1441
24	B	0 0 1 0	0.0124  −0.0023 0.9961  0.1014	B	0.1023
25	B	0 0 1 0	0.1337  0.0416 0.0118  0.7696	B	0.2699
26	C	0 1 0 0	0.0273  0.0264 −0.0248  0.9675	C	0.0558
27	B	0 0 1 0	0.0033  0.0216 0.0030  1.0242	B	0.0327
28	A	0 0 0 1	0.0070  0.0172 −0.0104  1.0103	A	0.0302
29	A	0 0 0 1	0.0035  0.0217 0.0721  0.9237	A	0.1073
30	A	0 0 0 1	0.0806  0.0505 0.0049  0.8668	A	0.1637

.

As demonstrated in Table 6 and Figure 10, the BP–RBF combined neural network model exhibited consistent results when predicting the structure safety status of the last 10 sections when compared to the desired objectives. The average error was 0.0986, and the “Best Validation Performance” reached a value of 0.0099342 at epoch 4.

4.5. Comparison of Visualized System and BP–RBF Combined Neural Network Evaluations

Table 7. Comparison of visualized system and BP–RBF combined neural network evaluations.

Sections	Visualized System	BP–RBF Combined Neural Network
21	B	B
22	B	B
23	B	B
24	B	B
25	B	B
26	C	C
27	B	B
28	A	A
29	A	A
30	A	A
Validation/epoch		0.0099342/4
training epochs		9
Average error		0.0986

presents a comparison between the system evaluation and the BP–RBF combined neural network prediction. It can be seen that the safety evaluation results of the visualized system and neural network model were consistent, indicating that the visualized system evaluation is both scientific and reasonable.

5. Conclusions

The visualized structure safety evaluation system for operational tunnels, based on self-developed Fuzzy–AHP programmed model, was developed by using MATLAB, and the rationality of the system was verified by the BP–RBF combined neural network.

• The user-friendly interface of the visualized system simplified operations and integrated functions such as data input, management, analysis, and application. This system solved the problem of large amounts of monitoring data that were difficult to calculate and analyze, and promoted the development of structure safety evaluations from qualitative to quantitative results for operational tunnels.
• The system can conveniently edit and modify core calculation functions, such as membership functions, based on different practical engineering projects, which improves the applicability of the system. In addition, this system provides an important construction method for the programming and visualization of other kinds of evaluation models.
• Based on the monitoring data, the system was applied to the structure safety evaluation of a mountain tunnel during its operational period. The system provided the evaluation results of each section of the tunnel and key disease indexes to focus on, which was conducive to the sustainable operation of the tunnel.