コンクリート工学年次論文集，Vol.27，No.2，2005- Technical paper -DEVELOPMENT OF EVALUATION SYSTEM FOR REINFORCED
CONCRETE BRIDGES
Bilal BAKHT*1, Hiroshi MUTSUYOSHI*2, Hayato TAKASE*3

ABSTRACTThe present study aims to develop an evaluation system for reinforced concrete bridges, constructed frommulti-layer neural networks with fuzzy logic in order to carry out fuzzy inference and machine learning.
The system evaluates the present performance of concrete bridge members in terms of serviceability,
which is based on durability and load-carrying capability, using simple visual inspection and technicalspecifications. The neural network employed facilitates refinement of the knowledge base using backpropagation method, and prevents the inference mechanism of the system from becoming a black box. The
results of the system when compared with the results of the bridge expert showed good agreement.
Keywords: serviceability, load-carrying capability, durability, fuzzy logic, expert system, neural network,
knowledge-base.

1. INTRODUCTION

Serviceability

Since 1990, bridge maintenance costs haveincreased in several developed countries to theextent where it is now more expensive to maintaindamaged bridges than to construct new ones.
According to a report, in Japan, by 2010,
approximately 35% of the bridges will be 50 yearsof age or older [1]. Therefore, the development of
a comprehensive Bridge Management System(BMS) for exiting bridges has become essential.
Such a system should enable, not only, theevaluation of bridge performance but also
prediction of remaining life and suggestion ofrehabilitation strategy taking into account thelimited funds available both for construction andmaintenance.
Kawamura et al [2] have developed an expert
system that can evaluate the performance ofconcrete bridges using knowledge and experienceacquired from the bridge experts. The objective of
the present study is to develop an independent
system with improved learning ability comparedwith the already developed system. The proposedsystem evaluates the present performance ofbridge members in terms of factors such asserviceability, load-carrying capability, anddurability. The input data for evaluating a concrete
bridgearethetechnical
specifications,environmental conditions, traffic volume, andLoad carrying capability

Durability

Overall damage

FlexuralcracksShearcracksCorrosioncracksCondition stateof free lime

Spalling of
concrete cover

Execution of work

Condition offree lime

Bond failure
cracksCondition stateof cracking

Crackconditions

Judgment item

Maximumcrack width

Input data

Fig. 1 Diagnostic process for main girders
other subjective information that can be obtained
through simple visual inspection.
The performance of a target bridge is evaluatedaccording to a diagnostic process [2], which ismodeled on the inference process used by domain
experts for evaluating bridges (see Fig.1). This
process is expressed by a hierarchical structure andhas twelve upper rated judgment items and fifty
lower rated judgment items. These judgment items
are evaluated by about 90 input data items. The
ultimate goal of this process is “serviceability.”
The relationship between judgment items andinput data is expressed by “If-Then” rules with

*1 Master Student, Department of Civil Engineering, Saitama University, JCI Member*2 Professor, Department of Civil Engineering, Saitama University, JCI Member*3 Undergraduate Student, Department of Civil Engineering, Saitama University-1621-

fuzzy variables (fuzzy rules). In a computer, using
Visual Basic, these rules have been transformed toa hierarchical neural network. The system refines
the knowledge base by applying the BackPropagation method [3]. The effectiveness ofhierarchical neural network and back propagation
was verified by comparison of the diagnostic
results of bridge expert and proposed system.

where, R : ith Fuzzy rule
x1 , ⋅⋅⋅, xm : Input items (input data such as technicalspecifications and results of visual inspection)y : Output item (judgment item)

2. PERFORMANCE EVALUATION

100)

In Fig.1, the lower rated judgment items, suchas “Condition state of flexural cracks aroundmidspan of main girders” (Condition state ofcracking) and “Condition state of free lime aroundmidspan of main girders” (Condition of free lime),are first evaluated by use of input data. The final
judgment item is “Serviceability”, which isevaluated according to the results of “Loadcarrying capability”, and “Durability”. Each ofthese judgment items is assigned a soundness
score, on a scale of 0-100, which is output of thesystem. The output score is categorized into one offive groups: 0-12.5, 12.6-37.5, 37.6-62.5, 62.687.5 and 87.6-100 as shown in Table 1.

4. FUZZY INFERENCE PROCESS

R i : if x1 is A1 and ⋅⋅and xm is Am then y is Bi

A1 , ⋅⋅⋅, Am : Fuzzy variables
Bi : Constant (soundness score on the scale of 0-

This section describes in detail the fuzzy
inference process performed in the system. The
portion of Fig. 1 enclosed in a dotted box; namely,
the inference process that evaluates “Condition
state of cracking”, is explained as an instance.
Table 2 Fuzzy rules for evaluating condition
state of cracking
Antecedents

Table 1 Relation between soundness score &five categories
Category
Soundness score
Safe(87.6-100)
Fairly safe
(62.6-87.5)
Moderate(37.6-62.5)
Slightly dangerous(12.6-37.5)
Dangerous(0-12.5)

Condition State Description
The bridge has no problem.
There is no serious damage.
There are some damages that
require continuous inspection.
The bridge should be repaired
and/or strengthened.
The bridge should be removed
from service and requires
rebuilding.

3. KNOWLEDGE REPRESENTATIONIn the knowledge base of the system, thediagnostic process is stored in the form of “IfThen” rules with fuzzy variables. Consequently,
these rules enable the system to perform fuzzy
inference. The knowledge representation of thesystem is as follows:

No

Crack
conditions

Maximumcrack width

1
2
3
4
5
6
7
8
9

SevereSevereSevereModerate
Moderate
Moderate
Not severe
Not severe
Not severe

Very large
Large
Small
Very large
Large
Small
Very large
Large
Small

Consequent
Condition stateof cracking
Soundness score
Unsafe (0.0)
Severe (25)Moderate (50)
Severe (25)Moderate (50)
Mild (75)Moderate (50)
Mild (75)
Safe (100)Table 2 shows the fuzzy rules for evaluating
the judgment item “Condition state of cracking”.
For example, Rule No. 9 expresses the following
fuzzy rule; if ([Crack conditions] are {Notsevere}) and ([Maximum crack width] is {Small})then ([Condition state of cracking] is 100.0). Since
the antecedents of the rules employ fuzzy variables,
the initial form of membership functions for fuzzy
rules have been prepared as fuzzy sets (see Figs.
2(a) & (b)). The membership functions for “Crack
conditions” are singleton functions (see Fig. 2(a))
and for “Maximum crack width” are sigmoid
functions (see Fig. 2(b)). Table 3 shows an

Table 3 Partial inspection sheet
G-1.1

Cracking around midspans ofmain girders (Flexural cracks)
Crack conditions

G-1.2

Maximum crack width

G-1

(1)

i

■c Yes (go next)□d No (go to G-1.3)□c Severe ■d Moderate □e Not severe
0.3 mm-1622-

excerpt of the inspection sheet used for the system.
The solid squares indicate inspection results. The
results of multiple choice questions are translated
into numerical values and entered into the system.
For “Crack conditions” the fuzzy variables“Severe,” “Moderate,” and “Not severe”
correspond to input values 0.0, 0.5 and 1.0
respectively. Next, the inference process of“Condition state of cracking” diagnosis is
described below, and is performed in 4 steps.
Fuzzy sets
Not

A(x1) severeA(x2)SevereModerate

1

Small

Large

Very
large

1

0.5
x1
0

0.50

1.0

(a) Crack conditionsx2

0

0 0.1 0.25 0.35(b) Maximum crack
width (mm)

1
2
3
4
5
6
7
8
9

Fig. 2 Membership functions for input data
4.1 [Step 1] Data input
Input data are entered into the system. As
shown in Fig. 1 the diagnosis of “Condition stateof cracking” requires the input data [Crack
conditions] and [Maximum crack width (mm)].
Therefore, the values of G1-1 and G1-2 in Table
3; that is “Moderate” and 0.3 mm, are used as the
input data for the diagnosis.
No
1
2
3
4
5
6
7
8
9

Antecedents
Maximum crack
Crack conditions
width
Severe (0.0)
Very large (0.5)
Severe (0.0)
Large (0.5)
Severe (0.0)
Small (0.0)
Moderate (1.0) Very large (0.5)
Moderate (1.0)
Large (0.5)
Moderate (1.0)
Small (0.0)
Not severe (0.0) Very large (0.5)
Not severe (0.0)
Large (0.5)
Not severe (0.0)
Small (0.0)

Consequent(Soundness score)

No Fitness of rule0.50function that expresses the fuzzy set [Moderate](see Fig. 2(a)). Therefore the grade of themembership function is 1.0 for the fuzzy set[Moderate]. Similarly, considering the inspection
value of [Maximum crack width (mm)], which is0.3, the value matches two membership functions,which express the fuzzy sets for [Large] and [Verylarge]. Therefore, these grades of membershipfunctions are both 0.5 (see Fig. 2(b)). The left
hand section table in Fig. 3 indicates the fitness ofeach fuzzy variable in antecedents to theinspection results; namely, [Crack conditions] =0.5
(Moderate) and [Maximum crack width (mm)]=0.3.

(0.0) * (0.5) = 0.0(0.0) * (0.5) = 0.0(0.0) * (0.0) = 0.0(1.0) * (0.5) = 0.5(1.0) * (0.5) = 0.5(1.0) * (0.0) = 0.0(0.0) * (0.5) = 0.0(0.0) * (0.5) = 0.0(0.0) * (0.0) = 0.0

Fitness of rule
(%)
0.0
0.0
0.0
0.5 (50%)
0.5 (50%)
0.0
0.0
0.0
0.0

0.0
0.0
0.0
0.5
0.5
0.0
0.0
0.0
0.0

*
*
*
*
*
*
*
*
*

0.0
25.0
50.0
25.0
50.0
75.0
50.0
75.0
100

= 0.0
= 0.0
= 0.0
= 12.5= 25.0
= 0.0
= 0.0
= 0.0
= 0.0

(Input Data)
Maximum crack
width 0.3 mm &Crack condition
0.5 (moderate)
37.5(Total sum)
Soundness score[ Step 4 ]Fig. 4 Fuzzy inference process ➁4.3 [Step 3] Calculation of fitness of each rule
Step 3 calculates the fitness of each rule toinput values. All fitness values of fuzzy variablesin the same fuzzy rule are multiplied. Next theirsum is calculated and finally each value is divided
by the sum to calculate fitness of each rule (seeFig.3). For the input data entered, the values in theright-hand section in Fig. 3 are estimated. Rule No.
4 and Rule No. 5 both have a fitness of 50%.
4.4 [Step 4] Calculation of soundness score
In the final step, all fitness values of fuzzy rules
are multiplied by the respective soundness score in
the consequent and their sum is calculated. Hencefor the input data entered, the system outputs thesoundness score of 37.5 (see Fig. 4).

Total sum = 1.0[ Step 1 & Step 2 ][ Step 3 ]Fig. 3 Fuzzy inference process ➀5. FUZZY INFERENCE BASED ON NEURALNETWORK

4.2 [Step 2] Calculation of grades
Step2 calculates the grades of membershipfunctions used in the antecedents of fuzzy rules. In
this example, since the partial inspection sheet (seeTable 3) shows multiple-choice value “Moderate”
for the input data [Crack conditions], this multiplechoice value corresponds to the input value 0.5.
This input value matches only one membership

In the expert system, the inference mechanism
for evaluating a judgment item is constructed witha hierarchical neural network consisting of 4 layers
for crack conditions and 5 layers for maximum
crack width as shown in Fig. 5. The knowledge
for diagnosing “Condition state of cracking”; thatis to say, Table 2 and Figs. 2(a) & (b) (fuzzy
rules and membership functions for fuzzy sets), are-1623-

ASevere(x1)Input 1.0, if x1 = 1.0
Input 0.0, if x1 ≠ 1.0

I1
x1

Input 1.0, if x1 = 0.5

1Ⅰ2

AModerate(x1)0.0ⅡInput 0.0, if x1 ≠ 0.5

3
25.0

ANot severe(x1)Crackconditions

Input 1.0, if x1 = 0.0

4Ⅲ

Input 0.0, if x1 ≠ 0.0

25.0(0.0, 0.5, 1.0)

a
70.0

I2
x2
Maximumcrack width
(mm)

46.7
-70.0
-46.7

AVery large(x2)
IV

-21.0

b

21.0

50.0

6

V

7

ASmall(x2)

8

VI

d

75.0

O1

50.0

Condition
state

75.0

of cracking

100soundness
score

9

8.17

(A)

5

ALarge(x2)

-8.17

c

50.0

(B)

(C)

(D)

(E)

Fig. 5 Neural Network for evaluating “Condition state of cracking”
implemented in the computer by the neuralnetwork shown in Fig. 5. Therefore, the neuralnetwork can carry out the fuzzy inference
mentioned in the previous section. In the present
study, the layers of the network are referred to as
layers (A), (B), (C), (D) and (E), respectively.
These layers have neurons of three different types.
The neurons in layers (A), (C) and (E) are linear
neurons. The neurons in layer (B) are sigmoid
neurons. The neurons in layer (D) are referred toas normalization neurons. The Arabic numerals in
the layer (D) neurons correspond to the number(No.) in Table 2. Therefore, clearly theconnections from layer (C) to layer (E) express afuzzy rule. A boxed value represents the initialconnection weight between neurons or the initialthreshold for a neuron.
Next is described the manner in which theinitial values of weight and threshold are set. The
layers (A)-(B)-(C) in the network identify the
fuzzy sets in antecedents of fuzzy rules for
maximum crack width only. If the membershipfunction of a fuzzy set is an increasing function ora decreasing function, the form is identified by asigmoid function in layer (B). If the membershipfunction is a convex function, the form isidentified by the combination of two sigmoid
functions in layer (B). For crack conditions since
singleton functions have been used, which canhave three input values only, thus behaving likecrisp sets, layer (B) has not been used (see Fig. 5).
The weights (ω ) between layer (A) neurons andlayer (B) neurons, and the thresholds (θ ) of the(B) neurons are calculated according to theequations given in reference [2]. For increasing
and decreasing functions the equations are thesame as mentioned in the reference [2], however,for convex function the equation has been
modified. The modified form of the equation is asfollows.
➀ Approximation of convex functionω1 = h / Aω = − h / C 2θ1 = − h( B − A) / Aθ 2 = + h( B + C ) / C x1 = B, A( x1 ) = 1.0
 x2 = B − 2 A, A( x2 ) = 0.0
 x3 = B + 2C , A( x3 ) = 0.0
x , x , x ∈ X , x < x23
 1 2 3(5)Note that h is a real number, which satisfies
f (h) ≈ 1.0 where, f (h) : is sigmoid function. In thepresent study, h = 3.5. The weights between layer(B) neurons and layer (C) neurons are set to 1.0. In

Table 4 Partial questionnaire sheet➀ What is the damage degree of flexural cracks?

Dangerous Slightly dangerous
Moderate
Fairly safe
Safe
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100-1624-

addition, initial weights between layer (C) neurons
and layer (D) neurons are also set to 1.0. The
initial weights between layer (D) neurons andlayer (E) neurons are set according to Table 2.
These weights express soundness scores describedin consequent of fuzzy rules. Consequently, when
input data are entered into the system, layers (A)(B)-(C) perform the processing of [Step 1] and[Step 2] described earlier. Next, layers (C)-(D)perform the processing of [Step 3]. Finally, layers(D)-(E) perform the processing of [Step 4].

needs the inspection results to fill out thequestionnaire. The results of questionnaire survey
and visual inspection were used as training data forcarrying out machine learning.

6. MODIFICATION OF FUZZY RULE BY
MACHINE LEARNING
The elements modified by machine learning
are the weights between layer (A) neurons andlayer (B) neurons, the thresholds of layer (B)neurons, and the weights between layer (D)neurons and layer (E) neurons. The weights oflayers (A)-(B) and the thresholds of layer (B)neurons are used in order to express membershipfunctions in antecedents of fuzzy rules for
maximum crack width only. Consequently, weight
alteration after learning indicates the slope
alteration of the corresponding membershipfunction, and threshold alteration after learning
indicates the axis movement of the membershipfunction in the horizontal direction. In the learningof layers (D)-(E) weight, the proposition inconsequent of fuzzy rules is changed. For instance,
if the weight between a layer (D) neuron and alayer (E) neuron is changed from 10.0 to 20.0, theproposition described in consequent of fuzzy ruleis changed from ([Condition state of cracking] is10.0) to ([Condition state of cracking] is 20.0).
7. VERIFICATION OF EFFECTIVENESS OF
MACHINE LEARNING
The proposed system is developed in Visual
Basic programming language and runs on a
personal computer. In this section, the system isapplied to an existing bridge (one span), which isan RC T-girder-type bridge, in order to test
validity of the learning capability. The target
bridge is located in Saitama prefecture.
7.1 Questionnaire survey of domain expert
and visual inspection of bridges
The purpose of the questionnaire survey ofdomain expert is to acquire teaching datanecessary for learning (see Table 4); where as the
purpose of visual inspection of bridge (see Figs. 6,& 7) is to collect inspection data to be entered into
the system (see Table 3). The domain expert also

Fig. 6 Side view of the bridge inspected

Fig. 7 Main girder deterioration
7.2 Practical application and verification of theevaluation system
A set of survey forms, prepared for the bridgein Fig. 6 consisted of three different handouts;
inspection record sheets to be used to record visualinspection results, a model drawing of the bridgeon which the respondent wrote down whatevercame to his mind during inspection, andquestionnaire sheets to obtain teaching datarequired for machine learning.
Table 5 summarizes the results of the main
girder diagnosis by the system (DR) and domain
expert (TD) in addition to the learned results (LR)and errors before and after learning. Twelve upper
judgment items have been listed to show theeffectiveness of machine learning, however, in all
there are sixty two judgment items including upperand lower. The letters S, F-s, M, S-d, and D in theparentheses represent Safe, Fairly safe, Moderate,
Slightly dangerous, and Dangerous. These labelsclassify the values given in the table into five

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Table 5 Results of main girder diagnosis
Judgment items
DR
TD
Error
LR
TD
Error
Girder design
66.02 (F-s) 90 (S)
23.98
89.90 (S)90 (S)
0.10
Girder execution
75.00 (F-s) 40 (M) 35.00 40.09 (M) 40 (M) 0.09
Service condition
87.73 (S)90 (S)
2.27
90.08 (S)90 (S)
0.08
Material deterioration
66.33 (F-s) 40 (M) 26.33 40.10 (M) 40 (M) 0.10
Flexural cracks
87.50 (S) 30 (S-d) 57.50 30.10 (S-d) 30 (S-d) 0.10
Shear cracks
100.0 (S) 30 (S-d) 70.00 30.09 (S-d) 30 (S-d) 0.09
Corrosion cracks
77.97 (F-s) 30 (S-d) 47.97 30.08 (S-d) 30 (S-d) 0.08
Bond cracks
100 (S)
100 (S)
0.00
100 (S)
100 (S) 0.00
Whole damage
85.99 (F-s) 55 (M) 30.99 55.10 (M) 55 (M) 0.10
Load-carrying capacity 49.71 (M)
90 (S)
40.29
89.90 (S)90 (S)
0.10
Durability
82.91 (F-s) 50 (M) 32.91 50.08 (M) 50 (M) 0.08
Serviceability
71.40 (F-s) 80 (F-s)
8.60
79.90 (F-s) 80 (F-s) 0.1
Total error
Before learning
365.84 After learning
1.02
DR: Diagnosed Results, TD: Teaching Data, LR: Learned Results
categories, the criteria used by the respondent forthis categorization having been mentioned earlier.
For the bridge inspected, the total error before
learning is 365.84, however after learning the error
reduces drastically to 1.02. For the individual
judgment item, no error is more than 0.1. This
proves the effectiveness of machine learning.
However, since the reliability of the systemdepends on information on the distribution ofbridge damage used for neural network learning,
we must increase the number of sample bridge
data sets used for learning and acquire data sets forvarious damage conditions.

Moreover, the proposed neural network
contributes to prevent the inference mechanism
from becoming a black box. The system wasapplied to the main girders of existing bridge inorder to verify the effectiveness of machinelearning method. The knowledge base was refinedfrom the results of questionnaire survey of domain
expert. Good agreement between the target values
and the values after learning confirms theeffectiveness of the learning method in the system.
In order to enhance the reliability of the expert
system, the knowledge base must be refined
through application to a greater number of bridges
with various damage conditions.

8. CONCLUSIONSACKNOWLEDGMENTS
In the present study, an evaluation system forreinforced concrete bridges has been developed
independently, with improved learning ability
compared with the system developed by
Kawamura et al [2]. The diagnostic tree (see Fig.
1) is the same as used by Kawamura et al [2],however, machine learning algorithms have been
written for all the judgment items (sixty two in
number); unlike Kawamura et al [2], who connect
the input data items directly with the upper
judgment items (eleven in number for theirsystem). The approach adopted in the present
study increased the task in terms of writing thecode and collecting teaching data for all the
judgment items; however, the errors between theteaching data and system’s output after learning,
reduced drastically compared with the systemdeveloped by Kawamura et al [2].
The developed system not only performs fuzzy
inference but also facilitates refinement of theknowledge base, based on data such as inspection
results and questionnaire survey of domain expert.

The authors would like to acknowledge
Professor Ayaho MIYAMOTO and Research
Associate Kei KAWAMURA for their support
during the system’s development.
REFERENCES[1] Miyamoto, A., Kawamura, K., and Nakamura,
H., “Development of a Bridge Management
System for Existing Bridges,” J. of Advancesin Engineering Software, Elsevier, Vol. 32,
2001, pp. 821-833.
[2] Kawamura, K., and Miyamoto, A., “Condition
state evaluation of Existing Reinforced
Concrete Bridges Using Neuro-Fuzzy Hybrid
System,” J. of Computers and Structures,
Elsevier, Vol. 81, 2003, pp. 1931-1940.
[3] Rumelhart, D.E., Hinton, G.E., Williams, R., J.,“Learning
Representations
byBack
Propagating Errors,” Nature, Vol. 323(9),1986, pp. 533-6.

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