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IDENTIFICATION OF BRIDGES IN BARS DATABASE RATED BY WSD METHOD
AND AN INTELLIGENT DECISION SUPPORT SYSTEM TO CONVERT THE WSD-BASED
RATING TO LFD-BASED RATING
by
Hojjat Adeli
The Ohio State University
Job Number: 14765
Technical Report Submitted to
Ohio Department of Transportation
January 2004
1. Report No. FHWA/OH-2004/001
2. Government Accession No.
3. Recipient's Catalog No.
5. Report Date
January 2004 6. Performing Organization Code
4. Title and subtitle.
Identification of Bridges in BARS Database Rated by WSD Method and an Intelligent Decision Support System to Convert the WSD-Based Rating to LFD-Based Rating 8. Performing Organization Report No.
7. Author(s)
Dr. Hojjat Adeli 10. Work Unit No. (TRAIS)
11. Contract or Grant No. State Job No. 14765(0)
9. Performing Organization Name and Address The Ohio State University Department of Civil & Environmental Engineering and Geodetic Sciences 2070 Neil Avenue 470 Hitchcock Hall Columbus, OH 43210 13. Type of Report and Period Covered
Final Report 12. Sponsoring Agency Name and Address
Ohio Department of Transportation 1980 W Broad Street Columbus, OH 43223
14. Sponsoring Agency Code
15. Supplementary Notes
16. Abstract
An intelligent decision support system (IDSS) has been developed to help bridge engineers convert a WSD-based bridge rating to the LFD-based rating using two different soft computing approaches: case-based reasoning (CBR) and artificial neural networks. The former is used to predict the lateral bracing requirements and the latter is used to determine the LFD-based section properties. The LFD-based rating of steel bridges requires a detailed description of the steel girder’s geometric properties that may not be available. A counterpropagation neural (CPN) network model is presented for estimating the detailed section properties of steel bridge girders needed in the LFD-based rating based on the three cross-sectional properties used in the WSD-based rating of bridges: cross-section area, moment of inertia, and section modulus. It is demonstrated that with proper training of the CPN network using both standard wide-flange shapes and representative plate girder data, the proposed model can generate the detailed section properties needed for LFD-based rating of steel bridges accurately. The training set for the CPN network was based on the AISC W-shape database plus 100 plate girder designs. It can be readily extended to include additional plate girder designs. The CBR module for determining the steel bridge girder lateral bracing requirements is developed using lateral bracing design data from ODOT standard bridge design drawings dating as far back as 1939 and as recently as 1997. The IDSS has been developed using the object-oriented features of Microsoft Visual Basic and the spreadsheet program, Microsoft Excel (the version released in 2000). The computational models and the IDSS created in this research can be used by bridge engineers as an intelligent decision support system to convert the WSD-based bridge rating to LFD-based bridge rating substantially faster than the conventional approach. 17. Key Words
Allowable stress design, bridge engineering, bridge rating, case-based reasoning, intelligent decision support system, load factor design, neural networks
18. Distribution Statement
No Restrictions. This document is available to the public through the National Technical Information Service, Springfield, Virginia 22161
19. Security Classif. (of this report)
Unclassified
20. Security Classif. (of this page)
Unclassified
21. No. of Pages
22. Price
Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
IDENTIFICATION OF BRIDGES IN BARS DATABASE RATED BY WSD METHOD
AND AN INTELLIGENT DECISION SUPPORT SYSTEM TO CONVERT THE WSD-BASED
RATING TO LFD-BASED RATING
Principal Investigator
Hojjat Adeli Lichtenstein Professor
The Ohio State University
Sponsored by Ohio Department of Transportation
and Federal Highway Administration
Prepared in Cooperation with the Ohio Department of Transportation and the U.S. Department of
Transportation, Federal Highway Administration "The contents of this report reflect the views of the authors who are responsible for the facts and the accuracy of the data presented herein. The contents do no necessarily reflect the official views or policies of the Ohio Department of Transportation or the Federal Highway Administration. This report does not constitute a standard, specification or regulation."
1
Table of Content
Page Summary and Organization of the Report 3
Part I Counterpropagation Neural Network Model for Steel Girder Bridge Structures 5 Abstract 6 Introduction 7 Architecture of Neural Networks 8 Training the Network 10 Testing the Network 13 CPN Performance and Results 15 Determining LFD-Based Section Properties for Plate Girders 16 Enhanced CPN Network for Steel Plate Girder Bridges 18 Enhanced CPN Network Trained with Plate Girder Data 19 Conclusions 20 Acknowledgment 21 List of Tables 22 References 28 List of Figures 30 Part II An Intelligent Decision Support System to Convert WSD-Based Bridge Rating to LFD-Based Bridge Rating 38 Abstract 39 Introduction 39 Overall Structure for the WSD-to-LFD Conversion Model 42 Database Management 43 Case-Based Reasoning 47 Determining Lateral Bracing requirements Directly 52 BARS-PC IDSS Interface 55 Example Problem 56 Conclusions 57 Acknowledgment 57 References 58 List of Figures 63 Appendix - Users Manual 71
2
Summary and Organization of the Report
The Ohio DOT is required to load rate all bridges under its jurisdiction to calculate their
safe live load carrying capacities. The rating of bridges in Ohio is mandated by the federal law
and the Ohio Revised Code. A new load rating is required for any given bridge whenever there
are changes in the conditions of the bridge such as addition of a new wearing surface, structural
damage due to a traffic accident, surface rusting of steel members (causing a reduction in their
cross-sectional areas), or loss of tension in tendons in prestressed members. ODOT engineers
perform the task of bridge rating in-house using the computer program AASHTO BARS. In the
past, the ratings were primarily based on the original design method which in most cases was the
working stress design (WSD) approach. In 1995, FHWA required that all new bridge ratings,
regardless of their method of design, be based on the load factor design (LFD) method. ODOT in
compliance with FHWA requirements switched to LFD-based method of rating for all new
bridge ratings. However, the current master data library has a mixture of more than 9000 WSD-
and LFD-based data files of which about 70% are based on WSD. Depending on the type of the
bridge the amount of work and efforts required to convert a WSD data file to LFD data file can
be substantial. As an example, a steel girder bridge file may require re-coding 90% of the data in
the computer.
An intelligent decision support system (IDSS) has been developed to help bridge
engineers convert a WSD-based bridge rating to the LFD-based rating using two different soft
computing approaches: case-based reasoning (CBR) and artificial neural networks. The former is
used to predict the lateral bracing requirements and the latter is used to determine the LFD-based
section properties.
3
This report consists of two parts presented as two different manuscripts and a short Users
Manual included in the Appenix. The LFD-based rating of steel bridges requires a detailed
description of the steel girder’s geometric properties that may not be available. In the first
manuscript, a counterpropagation neural (CPN) network model is presented for estimating the
detailed section properties of steel bridge girders needed in the LFD-based rating based on the
three cross-sectional properties used in the WSD-based rating of bridges: cross-section area,
moment of inertia, and section modulus. It is demonstrated that with proper training of the CPN
network using both standard wide-flange shape and representative plate girder data, the proposed
model can generate the detailed section properties needed for LFD-based rating of steel bridges
quite accurately. The training set for the CPN network was based on the AISC W-shape database
plus 100 plate girder designs. It can be readily extended to include additional plate girder
designs.
In the second manuscript, the CBR part of the model is described. The CBR module for
determining the steel bridge girder lateral bracing requirements is developed using lateral
bracing design data from ODOT standard bridge design drawings dating as far back as 1939 and
as recent as 1997.
The IDSS has been developed using the object-oriented features of Microsoft Visual
Basic and the spreadsheet program, Microsoft Excel (the version released in 2000). The
computational models and the IDSS created in this research can be used by bridge engineers as
an intelligent decision support system to convert the WSD-based bridge rating to LFD-based
bridge rating substantially faster than the conventional approach.
4
Part I
Counterpropagation Neural Network Model
for Steel Girder Bridge Structures
5
Counterpropagation Neural Network Model for Steel Girder Bridge Structures
Gene F. Sirca, Jr.1 and Hojjat Adeli 2, Fellow, ASCE
ABSTRACT: Bridge load rating is based on the method of design: Working Stress Design
(WSD) or Load Factor Design (LFD). A large number of older bridges were designed and
load rated based on the WSD code using the AASHTO BARS (Bridge Analysis & Rating
System). These WSD-based bridge ratings now have to be converted to the LFD-based
rating. The LFD-based rating of steel bridges in BARS requires a detailed description of the
steel girder’s geometric properties that may not be available in the WSD-based data files. In
this research, a counterpropagation neural network model has been developed for estimating
the detailed section properties of steel bridge girders needed in the LFD-based rating based
on the three cross-sectional properties used in the WSD-based rating of bridges: cross-section
area, moment of inertia, and section modulus. It is demonstrated that with proper training of
the network using both standard wide-flange shape and representative plate girder data, the
proposed model can generate the detailed section properties needed for LFD-based rating of
steel bridges quite accurately. The result of this research can be used in an intelligent
1 Graduate Student, Department of Civil and Environmental Engineering and Geodetic
Science, The Ohio State University, 470 Hitchcock Hall, 2070 Neil Avenue, Columbus, Ohio
43210
2 Professor, Department of Civil and Environmental Engineering and Geodetic Science, The
Ohio State University, 470 Hitchcock Hall, 2070 Neil Avenue, Columbus, Ohio 43210
6
decision support system (IDSS) to help bridge engineers convert a WSD-based bridge rating
to the LFD-based rating.
INTRODUCTION
Up until 1995, bridge load ratings were based on the design method used, which, in most
cases, was the WSD method. Since 1995, the FHWA requires that for the consistency of
results all bridge load ratings, regardless of the method used for the original design, be based
on the LFD method (FHWA, 1995). In order to comply with the FHWA requirements,
ODOT has switched to the LFD method for all new bridge ratings. In addition, all existing
bridges previously rated using the WSD method in BARS must also be converted to the LFD
method. The current BARS computer master library of rated bridges contains a mixture of
about 9,000 WSD- and LFD-based data files with approximately 70% of those files being
WSD-based. For bridge types such as reinforced and prestressed concrete girder bridges, the
conversion from WSD to LFD is a relatively simple task since the majority of data for both
design methods are the same. This is generally not the case for steel bridges. Steel bridges
rated by the WSD method have critical data missing to make the proper conversion to the
LFD method.
To rate a steel girder bridge, using either method, the girder’s section properties must be
inputted into BARS-PC (PC version of AASHTO BARS). The bridge-rating engineer has
two input options, a non-detailed description of the section properties or a detailed
description. The non-detailed description includes only the cross sectional area, moment of
inertia, and section modulus of each girder cross-section. The detailed description requires
information about each of the individual elements that make up the steel girder cross section
7
such as the areas of the web and flange elements, their individual moments of inertia and the
distances from their centroids to a reference axis.
The LFD-based bridge rating method in BARS requires a detailed description of the steel
girder’s geometric properties while the WSD-based method allows the engineer to use either
the non-detailed or detailed description. A majority of all bridges load rated by the WSD
method is based on the non-detailed description. When trying to convert data of a WSD-
based rated steel bridge to that based on LFD, it is not possible to directly determine the
information required by the detailed description from the information provided by the non-
detailed description. When making the conversion manually, the engineer must refer to a
table of common structural shapes to match the moment of inertia and section modulus
provided by the non-detailed description with those of a common shape in order to ascertain
the properties required by the detailed description. This process can take a considerable
amount of time for the volume of bridges that need conversion from WSD-based rating to
LFD-based rating.
In this article, a counterpropagation neural network model is presented for determining
the detailed section properties of steel bridge girders needed in the LFD-based rating based on
the three cross-sectional properties used in the WSD-based rating of bridges: cross-section area
(A), moment of inertia (Ix), and section modulus (Sx).
ARCHITECTURE OF NEURAL NETWORKS
Artificial neural networks have been used recently to recognize complicated patterns and
to solve problems considered too complex to be modeled by traditional computational methods
satisfactorily (Adeli and Hung, 1995; Adeli and Park, 1998; Adeli and Karim, 2001). Civil
8
engineering applications of neural networks have increased in recent years and continue to
increase. A state-of-the-art review of journal articles on civil engineering applications of neural
networks is presented in a recent article by Adeli (2001).
A counterpropagation neural (CPN) network model is developed for determining the
detailed section properties required for the WSD-to-LFD data file conversion process. The
algorithm is a forward-only CPN network that utilizes both supervised and competitive
unsupervised learning (Hecht-Nielsen, 1987, Adeli and Park, 1995). The basic architecture of
the counterpropagation neural network for determining the detailed section properties consists of
an input layer with three input nodes (equal to the number of input variables representing the
WSD-based non-detailed description), a competition layer with 295 nodes (equal to the number
of wide flange shapes used in the database), an interpolation layer with eleven nodes (equal to
the number of output variables that define the LFD-based detailed description plus an additional
node used for network testing), and eleven output nodes (Figure 1). Every node in the input
layer is connected to each node in the competition layer. Every node in the competition layer is
connected to the interpolation node and to each other with inhibitory connections. Inhibitory
connections are used to temporarily deactivate winning nodes in the competition layer,
prohibiting them from participating in the competition for the other training instances in the
current iteration. The input nodes of the CPN network represent the structural member’s cross-
sectional area, A, moment of inertia with respect to the major axis, Ix, and section modulus with
respect to the major axis, Sx.
The output nodes, op,k, represent the detailed section properties where k refer to the kth
output node (k=1,..,10) and p refers to the pth training example. Referring to the W-shape cross
section in Figure 2, the first ten constituents of the output vector are h, the overall height of the
9
section, and A1, Ix1, dy
1, A2, Ix2, dy
2, A3, Ix3, dy
3, the area, moment of inertia, and distance from the
element’s neutral axis to the reference axis, of the top flange, web, and bottom flange,
respectively. The first ten terms of the output vector represent the necessary input for the
detailed description of the BARS-PC Card Type 12 (AASHTO, 1994). The eleventh term of the
output vector, Ioutput, is used during network testing, defined later in this work.
In order to produce discrete output, the conventional CPN network shown in Figure 1 is
modified by replacing the interpolation layer with a second competition layer, consisting of m
sets of eleven nodes, where m is the number of winning nodes from the first competition layer,
and adding a filter layer consisting of eleven nodes. The new network is presented in Figure 3.
In the case of geometric property conversion, m is taken to be five, chosen heuristically. The
filter layer is used to select the best output from the m sets based on some acceptability criteria to
be defined later. For the case of determining LFD-based section properties, the CPN network
may not produce output with a moment of inertia, Ix, greater than the input moment of inertia in
order to produce a conservative bridge rating.
TRAINING THE NETWORK
The CPN network used for WSD-to-LFD data conversion of steel bridge girder
geometric properties is trained using the geometric properties of common structural shapes,
namely, wide-flanged sections. The training data consist of values of A, Ix and Sx for common
wide-flange shapes, from the AISC design manual (AISC, 1995, 1998), and their corresponding
elemental section properties required for the LFD-based method of bridge rating. This includes
the moments of inertia and cross-sectional areas of the flange and web elements and the
10
distances from their centroids to the reference axis. Table 1 presents a sample partial listing of
the data used to train the network.
The training of the CPN network is accomplished in two phases (Figure 4). In the first
phase, the weights of the links connecting the nodes in the input layer to the nodes in the
competition layer are determined using unsupervised learning. In the second phase, the weights
of the links connecting the competition layer to the nodes in the interpolation layers are
determined leaving the previously trained weights in the first phase unchanged. For each
training instance, the network weights are updated using the “conscience” mechanism proposed
by DeSieno (1988) where each node can win only once per iteration. This is achieved by
temporarily deactivating the winning node, prohibiting it from participating in competition with
the remaining non-winning nodes.
Phase I
1. Generate a set of randomly chosen weights for the connection strengths between the
nodes in the input layer and the nodes in the competition layer and between the nodes in
the competition layer and the node in the interpolation layer.
2. For each set of training examples xp,i (1 ≤ p ≤ P, P = number of training examples)
calculate the Euclidean distance between the input vector xp and the weight vector w (of
links connecting the input and competition layers):
( )2/1
..1
2
,
2
,⎭⎬⎫
⎩⎨⎧
−= ∑= cNj
ipijj xwd (1)
where Nc is the number of nodes in the competition layer, wj,i is the connection weight
of the link between node i in the input layer and node j in the competition layer.
11
3. For the given training example, nodes in the competition layer compete with each other.
Among the active nodes, the node with the shortest Euclidean distance, dj , wins. The
winning node output, Zj, is set to 1.0 and all other node outputs are set to 0.
⎭⎬⎫
⎩⎨⎧ ≠<
=otherwise0
allforif0.1 jiddZ ij
j (2)
4. The connection weight between node i in the input layer and node j in the competition
layer, wj,i, is updated according to the Kohonen (1988) learning rule:
( ) ( ) ( ) jijij Znijwipxnwnw ⎥⎦⎤
⎢⎣⎡ −+=+ ,,1 ,, α (3)
where n is the iteration number. Once the connection weight is updated, node j is added
to the set of temporarily deactivated nodes in the competition layer. Following Adeli
and Park (1995), we use the following expression for the learning coefficient, a,
expressed as a function of the iteration number:
( )21
1+
=n
α (4)
instead of using an arbitrary problem-dependant learning ratio in the range of 0 and 0.8
suggested by Hecht-Nielson (1987). Eq. (4) provides a means of reducing the magnitude
of the weight changes after each iteration which helps to stabilize the weight
computations and improve network performance.
Phase II
12
The connection weight between the winning node j of the competition layer and the node
k in the interpolation layer, wk,j, is updated according to the Grossberg (1982) learning
rule:
(5) ( ) ( ) ( ) jjkjk Zkpynjkwnwnw ⎥⎦⎤
⎢⎣⎡ −+=+ ,,1 ,, α
where yp,k is the desired output k of training example p. We use the same Eq. (4) for the
learning coefficient, α, in Eq. (5).
TESTING THE NETWORK
The network is tested using a new set of data independent of the training data. The CPN
test cycle is presented in Figure 5. The test data are actual samples from the BARS-PC master
library, not from the AISC data. In a typical CPN network, more than one node in the
competition layer may win during network testing. This allows the network to produce an output
vector from interpolation between two or more winning competition layer nodes. The CPN
testing cycle in this work is based on one winning node in the competition layer because for the
WSD-to-LFD data conversion problem the output must be a discrete value, a standard W-shape
that best represents the WSD-based data.
The first competition layer is configured to yield output, Zj, equal to one for weight
vectors closest to the given input vector, for m winning nodes, and equal to zero for weight
vectors not included in the set of winning nodes:
13
(Zj)n = 1.0 if (Zj)n ⊂ Sw (for n = 1..m) (6)
(Zj)n = 0 if Zj ⊄ Sw
where n is one of m winning nodes and Sw is the set of all the winning nodes. The set of m
winning nodes is passed to the filter layer to satisfy the acceptability criterion. This is
accomplished by computing the dot product of the weight vector obtained from Eq. (5) and the
vector of winning node outputs:
n=1,…..,m (7) jj
jknkp Zwo ∑= ,, )*(
An output is generated for each set of winning nodes, n, of m sets of winning nodes and are then
ranked from highest to lowest values of Ioutput.
The winning set of nodes from the second competition layer is the set with the largest
network-generated (overall) moment of inertia that is less than or equal to the network-input
moment of inertia.
(8) ⎭⎬⎫
⎩⎨⎧ ≤
=otherwise0if0.1
,inputoutput
nk
IIZ
The output for each node in the winning set of nodes is one and zero for all others. The
inequality Ioutput ≤ Iinput in Eq. (8) is the acceptability criterion used in the filter layer to insure
that the network output produces a conservative bridge rating. If the inequality in Eq. (8) does
not hold for any of the m sets of nodes, then the value for m must be increased to include a larger
number of potential winning sets of nodes. The final network output is calculated according to:
op,k = Zk,n (o*p,k)n (9)
The CPN network output is similar to a table lookup except that the weight vectors are
determined by network training, not in an ad hoc manner (Mehrotra, et al., 1997).
14
CPN PERFORMANCE AND RESULTS
Figure 6 illustrates a typical convergence history for training the CPN network. The
number of iterations ranges from 275 to 315, which is close to the number of training
examples of 295. Each iteration adjusts the network weights until the network error
approaches zero. The mean squared error, E, is defined as:
%100)(
2,
2,, ∗
−=
kp
kpkp
y
yoE . (10)
The variation in the total number of iterations can be attributed to the initial random
generation of the weights, prior to network training.
Table 2 presents the results from testing the network using actual BARS-PC input data.
For comparative purposes, only the overall cross-sectional area, A, moment of inertia, Ix, and
section modulus, Sx are shown. The computed values of A, Ix, and Sx based on the CPN
network are compared with their respective input values to determine how closely the WSD-
based section properties match a standard AISC W-shape. The error is broken down into
matching vector components. In Table 2, error values shown in parentheses are negative
values, or non-conservative in nature. Since the moment of inertia is chosen to be the basis
for the acceptability criteria, error in estimating this variable is always positive. Small
negative error values for the cross-sectional area and section modulus, although non-
conservative, are acceptable. Positive error values for A and Sx are acceptable (they are on
the conservative side).
The error values in Table 2 are in the range of –7.31 to 10.06% (with an average error
value of –1.19%) for the cross-sectional area, 0 to 9.46% (with an average error value of
15
3.88%) for the moment of inertia, and –5.01 to 8.14% (with an average error value of 0.65%)
for the section modulus. The network can be improved further with a larger database of
structural shapes beyond the commonly used W-shapes, for example, including plate girders.
This enhancement would be especially beneficial for converting BARS-PC files containing
structural shapes with high moments of inertia and disproportionately small overall cross-
sectional areas.
DETERMINING LFD-BASED SECTION PROPERTIES FOR PLATE GIRDERS
To overcome the difficulties in obtaining representative data for converting plate girder
sections with large moments of inertia and small cross-sectional areas, an algorithm is
developed that determines the LFD-based detailed section properties directly from the WSD-
based section properties. The algorithm is based on the following relationships, assuming a
doubly symmetric I-shape:
(11) wfff tthtbA )2(2 −+=
hI
S xx
2= (12)
( )[ ]333 2121)2(
121
fffwx thhbthtI −−+−= (13)
where bf is the width of the flanges, tf is the thickness of the flanges, and tw is the web
thickness. Values for A, Sx, and Ix are given and h can be calculated directly using Eq. (12).
Equations (11) and (13) are combined to produce the equations for finding the flange
thickness and width:
16
( )( )
( )( ) ⎪
⎪
⎭
⎪⎪
⎬
⎫
⎪⎪
⎩
⎪⎪
⎨
⎧
−−+++−−−
−−+++−+−
=>
htAhtAIhttAhhAhtAh
htAhtAIhttAhhAhtAh
t
w
wxwww
w
wxwww
tff
4482333
4482333
min423222
423222
0 (14)
33
3
)2()2(12
f
fwxf thh
thtIb
−−
−−= (15)
The algorithm is structured as a minimization routine for finding the smallest tf, defined by
Equation (14), for a discrete set of tw.
Minimize: tf
Subject To: ⎭⎬⎫
⎩⎨⎧
∈2,875.1,75.1,625.1,5.1,375.1,25.1
,125.1,1,875.0,75.0,625.0,5.0,375.0wt
Once the minimal value for tf is found, bf is calculated according to Equation (15). The
values for h, tf, tw, and bf are then used to generate the LFD-based detailed section properties.
The assumption that a WSD-based steel section is doubly symmetric is reasonable if the
section’s top and bottom flange sizes are approximately equal. This assumption presents a
problem, however, if the steel section is singly symmetric with a bottom flange size that is
substantially different from the top flange size. Singly symmetric cases, with large
differences between the sizes of top and bottom flanges, may cause the algorithm to produce
an undesirably large flange thickness or imaginary numbers in Eq. (14).
17
ENHANCED CPN NETWORK FOR STEEL PLATE GIRDER BRIDGES
For a steel plate girder bridge, first the enhanced CPN network is used to find the detailed
properties needed for the LFD-based rating of the bridge. Then, the mean squared value of
the input vector comprising of the cross-sectional area, section modulus, and moment of
inertia is compared with the corresponding mean squared value of the same parameters
derived from the output vector. When the difference is greater than certain predefined
threshold the procedure described in the previous section is used.
The results from network testing of 39 plate girder shapes are presented in Table 3, which is
comprised of the error between actual and network-generated values of LFD-based detailed
section property data, where the numbers in parentheses indicate non-conservative values. In
Table 3, the first thirty shapes are doubly-symmetric and the remaining nine shapes are
singly-symmetric plate girders.
Error values replaced by “ – “ indicate that a feasible solution could not be found. Error
values in Table 3 range from –1.8 to 1.3% with an average of 0.003%, for test samples that
are known to be doubly symmetric plate girders. The error values for test samples that are
known to be singly symmetric are quite high. It is apparent from the Table that the enhanced
network is a significant improvement over the previous network without the enhancement for
finding LFD-based section properties of doubly symmetric sections. This is not the case,
however, for singly symmetric sections. The network needs to be improved further with the
addition of commonly used singly symmetric plate girders to the CPN training data set in
order to overcome the problems with the doubly symmetric assumption used by the plate
girder algorithm described in the previous section.
18
ENHANCED CPN NETWORK TRAINED WITH PLATE GIRDER DATA
To overcome problems with the doubly symmetric assumption in the previous section,
the enhanced CPN network is trained with common wide-flange shapes from the AISC design
manual plus one hundred of the most common plate girder shapes used in bridge design, selected
from LFD-based, singly symmetric, steel plate girder designs in the BARS-PC master library.
Table 4 lists a portion of the new plate girder data used to train the network. The choice of
which singly symmetric plate girder designs to use in network training, of the thousands of
designs contained in the master library, was made by selecting the most frequently used plate
girder bridge designs and limiting the number to one hundred.
With the inclusion of the plate girder data, the CPN network in Figure 3 is modified by
increasing the number of nodes in the competition layer from 295 to 395, leaving the remaining
structure of the former CPN network intact.
The training convergence history of the enhanced CPN network, illustrated in Figure 7, is
similar to the training history of the CPN network without enhancements (Figure 6). The
number of iterations required for the network error to approach zero ranges from 380 to 412.
As mentioned previously, the variation in the total number of iterations can be attributed to
the initial random generation of the weights, prior to network training.
The procedure described in the previous section for determining the LFD-based detailed
section properties for plate girders is used only for cases where the enhanced CPN network is
unable to produce acceptable results, primarily for doubly symmetric plate girders that
cannot be represented by a common AISC wide-flange shape accurately.
19
The results from testing the enhanced CPN network are presented in Table 5, which is
comprised of the error between actual and network-generated values of LFD-based detailed
section property data, where the numbers in parentheses indicate non-conservative values.
The error values in Table 5 range from –1.818 to 1.333% with an average of 0.002%. It is
apparent from Table 5 that the network enhanced with plate girder training data is a
significant improvement over the previous network without the enhancement. For all of the
test cases, the network is capable of generating LFD-based detailed section properties that
are almost identical to the actual data. This is true for WSD-to-LFD converted steel bridge
structures consisting of both singly and doubly symmetric plate girders and AISC wide-
flange shapes.
CONCLUSIONS
This research was indeed out of necessity and not as an academic exercise. It solves an
actual problem encountered by Bridge Engineers at the Ohio Department of Transportation. The
computational model developed in this research has been implemented in an intelligent decision
support system currently in use.
One may suggest the use of a manual look-up table for W-shape geometric data which
may be possible if all of the steel bridge data resemble W-shape section property data. However,
this is not the case. A fair number of steel bridges contained in the ODOT bridge database do
not use W-shapes but plate girders. A manual look-up table may be created for plate girder data.
But, it will be very tedious and time-consuming to create and use, and therefore impractical. The
computational model proposed in the paper simply provides an efficient and automated
approach.
20
The training set was based on the AISC W-shape database plus 100 plate girder designs.
It can be readily extended to include additional plate girder designs.
ACKNOWLEDGEMENT
This manuscript is based on a research project sponsored by the Ohio Department of
Transportation and Federal Highway Administration.
21
LIST OF TABLES
Table 1 A sample partial listing of the data used to train the network
Table 2 Results from testing the network using actual BARS-PC input data.
Table 3 Results from network testing of 39 plate girder shapes
Table 4 Data from LFD-based, singly symmetric, steel plate girder designs in the BARS-PC
master library
Table 5 Results from testing the enhanced CPN network
22
23
Dat
a Po
int
AI x
S xh
A11
d y1
A22
d2
A3I x3
d y3
(W-S
ectio
n)(in
2 )(in
4 )(in
3 )(in
.)(in
2 )(in
4 )(in
.)(in
2 )(in
4 )(in
.)(in
2 )(in
4 )(in
.)
W44
x285
83.8
2460
011
2044
.02
20.9
05.
4643
.14
41.4
956
65.8
422
.01
20.9
05.
460.
89W
44x2
4872
.821
400
983
43.6
218
.60
3.85
42.8
335
.01
4777
.87
21.8
118
.60
3.85
0.79
W44
x224
65.8
1920
088
943
.31
16.7
12.
7942
.60
31.7
843
39.2
021
.66
16.7
12.
790.
71W
44x1
9858
.016
700
776
42.9
114
.41
1.79
42.3
028
.73
3921
.72
21.4
614
.41
1.79
0.61
W40
x328
96.4
2680
013
4040
.00
30.9
87.
7339
.14
33.2
536
99.6
920
.00
30.9
87.
730.
87W
40x2
9887
.624
200
1220
39.6
928
.08
5.81
38.9
030
.33
3374
.45
19.8
528
.08
5.81
0.79
W40
x268
78.8
2150
010
9039
.37
25.1
24.
1938
.66
27.4
130
49.2
019
.69
25.1
24.
190.
71W
40x2
4471
.719
200
983
39.0
622
.31
2.95
38.4
325
.94
2886
.57
19.5
322
.31
2.95
0.63
W40
x221
64.8
1660
085
838
.67
18.8
61.
7838
.14
25.9
428
86.5
719
.34
18.8
61.
780.
53W
40x1
9256
.513
500
708
38.2
014
.70
0.84
37.7
925
.94
2886
.57
19.1
014
.70
0.84
0.42
W40
x655
192.
056
500
2590
43.6
259
.72
62.3
741
.85
71.9
880
09.2
321
.81
59.7
262
.37
1.77
W40
x593
174.
050
400
2340
42.9
953
.91
46.8
741
.38
65.3
972
71.4
521
.50
53.9
146
.87
1.62
W40
x531
156.
044
300
2090
42.3
448
.04
33.9
040
.89
58.8
065
34.8
721
.17
48.0
433
.90
1.46
W8x
185.
361
.915
.28.
141.
730.
016
7.97
51.
720
8.02
14.
070
1.73
30.
016
0.16
5W
8x15
4.4
4811
.88.
111.
260.
010
7.95
31.
833
8.54
54.
055
1.26
50.
010
0.15
8W
8x13
3.8
39.6
9.91
7.99
1.02
0.00
67.
863
1.72
08.
021
3.99
51.
020
0.00
60.
128
W8x
103.
030
.87.
817.
890.
810.
003
7.78
81.
272
5.92
93.
945
0.80
80.
003
0.10
3W
6x25
7.3
53.4
16.7
6.38
2.77
0.04
86.
153
1.75
04.
364
3.19
02.
766
0.04
80.
228
W6x
205.
941
.413
.46.
202.
200.
024
6.01
81.
422
3.54
63.
100
2.19
70.
024
0.18
3W
6x15
4.4
29.1
9.72
5.99
1.56
0.00
95.
860
1.25
83.
137
2.99
51.
557
0.00
90.
130
W6x
164.
732
.110
.26.
281.
630.
022
6.07
81.
422
3.54
63.
140
1.63
20.
022
0.20
3W
6x12
3.6
22.1
7.31
6.03
1.12
0.00
75.
890
1.25
83.
137
3.01
51.
120
0.00
70.
140
W6x
92.
716
.45.
565.
900.
850.
003
5.79
30.
930
2.31
92.
950
0.84
70.
003
0.10
8W
5x19
5.5
26.2
10.2
5.15
2.16
0.03
34.
935
1.15
81.
776
2.57
52.
163
0.03
30.
215
W5x
164.
721
.38.
515.
011.
800.
019
4.83
01.
030
1.57
92.
505
1.80
00.
019
0.18
0W
4x13
3.8
11.3
5.46
4.16
1.40
0.01
43.
988
0.97
20.
975
2.08
01.
401
0.01
40.
173
WSD
-bas
ed D
ata
LFD
-bas
ed D
ata
I xI x
y
Table 1
Table 2
BARS-PC LFD-based Data (ANN Output) ErrorStructure A I x S x A I x S x A I x S x
I.D. (in2) (in4) (in3) (in2) (in4) (in3) (%) (%) (%)
020024 47.09 9738.8 541 49.5 9290 549 (5.12) 4.61 (1.48)020024 58.43 13483.8 705.4 61.8 13200 719 (5.77) 2.10 (1.93)020024 51.04 11445.5 603.1 53.6 11300 623 (5.02) 1.27 (3.30)020024 39.7 7796.1 438.6 41.6 7450 448 (4.79) 4.44 (2.14)020018 55.5 12722.9 667.3 57 12100 664 (2.70) 4.90 0.49020018 44.16 9012.1 502.9 44.7 8160 487 (1.22) 9.46 3.16010225 61.78 11664.5 704.4 59.1 11500 684 4.34 1.41 2.90010282 8.18 304.1 40.6 7.68 301 38.4 6.11 1.02 5.42020006 64.88 15095.2 785.7 68.1 15000 809 (4.96) 0.63 (2.97)020006 53.54 11281.5 621.2 50 10500 580 6.61 6.93 6.63020234 47.09 9738.8 541 49.5 9290 549 (5.12) 4.61 (1.48)020234 57.11 12103.4 663.6 57 12100 664 0.19 0.03 (0.06)020234 57.59 13224.6 705.3 61.8 13200 719 (7.31) 0.19 (1.94)020234 75.12 18348.2 965.7 76.5 17300 953 (1.84) 5.71 1.32020234 65.08 15817.2 843.6 67.6 15000 837 (3.87) 5.17 0.78020279 55.59 11263.8 631.4 50 10500 580 10.06 6.78 8.14020279 44.71 8147.6 486.4 41.6 7450 448 6.96 8.56 7.89020282 57.11 12103.4 663.6 57 12100 664 0.19 0.03 (0.06)020282 75.11 18348.2 965.7 76.5 17300 953 (1.85) 5.71 1.32020282 69.29 15951.6 828.1 67.6 15000 837 2.44 5.97 (1.07)020345 38.3 6710 406 38.3 6710 406 0.00 0.00 0.00020363 47.09 9738.8 541 49.5 9290 549 (5.12) 4.61 (1.48)020363 89.48 22218.1 1158.3 88.3 20300 1110 1.32 8.63 4.17020363 67.73 14988.4 835.5 70.9 14200 829 (4.68) 5.26 0.78020363 84.98 20743.6 1076.5 88.3 20300 1110 (3.91) 2.14 (3.11)020363 64.34 15100.4 770.4 68.1 15000 809 (5.84) 0.66 (5.01)
WSD-based Data
Table 3
24
BARS-PC
Structure A 1 I 1 d 1 A 2 I 2 d 2 A 3 I 3 d 3
I.D. (in2) (in4) (in) (in2) (in4) (in) (in2) (in4) (in)
010013 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 (0.769) 0.000 0.000 0.045 0.000 0.000 (0.769) (0.364)
0.000 0.030 0.006 0.000 (0.004) (0.019) 0.000 0.030 (0.267)
010023 0.000 0.000 0.000 0.000 0.028 0.000 0.000 0.000 0.000
0.000 0.000 (0.002) 0.000 0.049 0.010 0.000 0.000 (0.571)
0.000 0.000 0.006 0.044 0.119 0.009 0.000 0.000 (0.844)
0.000 0.000 0.002 0.000 0.044 (0.006) 0.000 0.000 (1.053)
010186 0.000 0.482 (0.010) 0.000 0.000 (0.014) 0.000 0.482 (0.256)
0.000 0.024 (0.007) 0.000 0.005 0.023 0.000 0.024 0.308
020080 0.000 0.225 0.000 0.000 0.000 0.000 0.000 0.225 0.000
0.000 (0.105) (0.007) 0.000 0.005 0.023 0.000 (0.105) 0.444
0.000 0.154 0.011 0.000 0.000 0.000 0.000 0.154 (0.800)
040119 0.000 0.250 0.000 0.000 0.000 0.000 0.000 0.250 0.000
0.000 0.024 0.000 0.000 (0.020) (0.020) 0.000 0.024 0.308
040339 0.000 0.446 (0.009) 0.000 (0.000) 0.000 0.000 0.446 1.333
0.000 0.148 0.000 0.000 0.000 0.000 0.000 0.148 0.000
0.000 0.274 (0.004) 0.000 (0.004) (0.018) 0.000 0.274 0.444
0.000 (0.011) (0.009) 0.000 0.001 0.000 0.000 (0.011) 0.571
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000
0.000 0.023 (0.004) 0.000 (0.003) (0.017) 0.000 0.023 0.308
040435 0.000 (1.554) 0.000 0.000 0.022 0.000 0.000 (1.554) (1.818)
0.000 0.020 (0.008) 0.000 0.000 0.000 0.000 0.020 0.800
0.000 0.182 0.000 0.000 0.000 0.000 0.000 0.182 0.000
0.013 0.149 0.000 0.000 (0.013) 0.000 0.013 0.149 (0.414)
060215 29.218 - (18.400) - - (19.009) 65.387 (33.655) -
120258 0.000 0.128 (0.004) 0.000 (0.004) (0.019) 0.000 0.128 0.444
0.000 0.026 (0.010) 0.000 0.000 0.000 0.000 0.026 0.571
130638 0.000 0.160 0.000 0.000 (0.035) 0.000 0.000 0.160 0.800
0.000 (0.031) 0.000 0.000 0.000 0.000 0.000 (0.031) 0.000
150255 (11.33) - (12.23) (37.03) (26.02) (16.61) 40.62 - -
180124 - - (3.74) 15.36 39.38 (9.80) 3.79 - -
181204 - - 76.60 - - 5.33 - - -
181208 - - (3.87) 33.66 - (6.20) - 50.00 44.00
181310 - - (1.72) 39.25 - (2.55) - - -
- - (0.08) 46.35 - (1.61) - - -
- - (1.38) 41.10 - (2.31) - - -
186933 26.84 46.90 (12.05) (41.08) - (11.54) 58.85 - 36.00210227 (0.38) - (6.51) (25.30) (25.89) (8.17) 24.71 - -
Error between Actual and CPN-generated values (%)BARS-PC
Structure A 1 I 1 d 1 A 2 I 2 d 2 A 3 I 3 d 3
I.D. (in2) (in4) (in) (in2) (in4) (in) (in2) (in4) (in)
010013 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 (0.769) 0.000 0.000 0.045 0.000 0.000 (0.769) (0.364)
0.000 0.030 0.006 0.000 (0.004) (0.019) 0.000 0.030 (0.267)
010023 0.000 0.000 0.000 0.000 0.028 0.000 0.000 0.000 0.000
0.000 0.000 (0.002) 0.000 0.049 0.010 0.000 0.000 (0.571)
0.000 0.000 0.006 0.044 0.119 0.009 0.000 0.000 (0.844)
0.000 0.000 0.002 0.000 0.044 (0.006) 0.000 0.000 (1.053)
010186 0.000 0.482 (0.010) 0.000 0.000 (0.014) 0.000 0.482 (0.256)
0.000 0.024 (0.007) 0.000 0.005 0.023 0.000 0.024 0.308
020080 0.000 0.225 0.000 0.000 0.000 0.000 0.000 0.225 0.000
0.000 (0.105) (0.007) 0.000 0.005 0.023 0.000 (0.105) 0.444
0.000 0.154 0.011 0.000 0.000 0.000 0.000 0.154 (0.800)
040119 0.000 0.250 0.000 0.000 0.000 0.000 0.000 0.250 0.000
0.000 0.024 0.000 0.000 (0.020) (0.020) 0.000 0.024 0.308
040339 0.000 0.446 (0.009) 0.000 (0.000) 0.000 0.000 0.446 1.333
0.000 0.148 0.000 0.000 0.000 0.000 0.000 0.148 0.000
0.000 0.274 (0.004) 0.000 (0.004) (0.018) 0.000 0.274 0.444
0.000 (0.011) (0.009) 0.000 0.001 0.000 0.000 (0.011) 0.571
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000
0.000 0.023 (0.004) 0.000 (0.003) (0.017) 0.000 0.023 0.308
040435 0.000 (1.554) 0.000 0.000 0.022 0.000 0.000 (1.554) (1.818)
0.000 0.020 (0.008) 0.000 0.000 0.000 0.000 0.020 0.800
0.000 0.182 0.000 0.000 0.000 0.000 0.000 0.182 0.000
0.013 0.149 0.000 0.000 (0.013) 0.000 0.013 0.149 (0.414)
060215 29.218 - (18.400) - - (19.009) 65.387 (33.655) -
120258 0.000 0.128 (0.004) 0.000 (0.004) (0.019) 0.000 0.128 0.444
0.000 0.026 (0.010) 0.000 0.000 0.000 0.000 0.026 0.571
130638 0.000 0.160 0.000 0.000 (0.035) 0.000 0.000 0.160 0.800
0.000 (0.031) 0.000 0.000 0.000 0.000 0.000 (0.031) 0.000
150255 (11.33) - (12.23) (37.03) (26.02) (16.61) 40.62 - -
180124 - - (3.74) 15.36 39.38 (9.80) 3.79 - -
181204 - - 76.60 - - 5.33 - - -
181208 - - (3.87) 33.66 - (6.20) - 50.00 44.00
181310 - - (1.72) 39.25 - (2.55) - - -
- - (0.08) 46.35 - (1.61) - - -
- - (1.38) 41.10 - (2.31) - - -
186933 26.84 46.90 (12.05) (41.08) - (11.54) 58.85 - 36.00210227 (0.38) - (6.51) (25.30) (25.89) (8.17) 24.71 - -
Error between Actual and CPN-generated values (%)
25 25
26
AI x
S xh
A1I x1
d y1
A2I x2
d y2
AD
ata
Poin
t(in
2 )(in
4 )(in
3 )(in
.)(in
2 )(in
4 )(in
.)(in
2 )(in
4 )(in
.)(in
156
.013
140
704
36.8
87.
880.
370
36.5
039
.70
7800
18.3
88.
442
66.5
1659
086
037
.75
10.5
00.
875
37.2
544
.20
9040
18.8
111
.81
310
7.0
2812
114
2838
.21
16.8
81.
780
37.6
472
.10
1610
018
.54
18.0
04
75.9
1905
897
738
.25
10.5
00.
875
37.7
553
.60
1130
019
.06
11.8
15
48.6
1592
961
244
.19
10.5
00.
670
43.7
518
.38
2701
22.3
119
.69
650
.018
467
737
45.0
014
.00
1.16
744
.50
16.0
324
4222
.63
20.0
07
51.4
1708
563
444
.96
10.2
30.
639
44.5
320
.25
3108
22.6
420
.92
835
.013
691
567
50.2
59.
000.
422
49.8
818
.00
3456
25.5
08.
009
43.8
1958
265
352
.00
9.00
0.42
251
.63
18.8
439
6526
.13
16.0
010
54.4
2641
885
455
.50
10.5
00.
492
55.1
326
.88
6470
27.8
817
.00
1176
.043
985
1414
57.2
521
.00
3.93
856
.50
27.0
065
6128
.75
28.0
012
68.5
4114
411
7460
.50
14.0
01.
167
60.0
029
.00
8130
30.5
025
.50
1361
.438
580
1003
65.0
09.
000.
422
64.6
331
.38
1029
532
.88
21.0
0
8891
.379
550
1851
75.0
016
.00
1.33
74.5
045
.31
1984
837
.75
30.0
089
89.3
8011
918
7676
.50
16.0
01.
3376
.00
46.2
521
105
38.5
027
.00
9010
4.2
1043
1323
2479
.00
21.0
03.
9478
.25
47.1
922
415
39.7
536
.00
9110
4.1
1027
8722
9982
.25
17.5
02.
2881
.63
59.6
331
404
41.2
527
.00
9210
5.6
1165
3124
3888
.38
16.0
01.
3387
.88
64.5
939
927
44.3
125
.00
WSD
-bas
ed D
ata
LFD
-bas
ed D
ata
Table 4 3
I x3d y
3
2 )(in
4 )(in
.)
0.27
00.
313
0.75
00.
438
1.50
00.
500
0.75
00.
438
2.82
60.
656
2.60
40.
625
2.43
20.
590
0.16
70.
750
1.33
30.
500
1.41
70.
500
7.14
60.
875
4.78
10.
750
3.93
80.
750
5.63
0.75
5.06
0.75
12.0
01.
005.
060.
753.
260.
6393
126.
313
1701
2791
90.0
016
.00
1.33
89.5
087
.75
5630
745
.13
22.5
02.
930.
6394
133.
217
6153
3517
91.7
527
.00
5.06
91.0
066
.19
4295
646
.13
40.0
013
.33
1.00
9515
0.3
1953
7839
8296
.25
27.0
05.
0695
.50
93.2
567
572
48.1
330
.00
5.63
0.75
9614
3.5
1826
6534
5798
.00
18.0
01.
5097
.50
95.5
072
582
49.2
530
.00
5.63
0.75
9717
5.6
2437
3045
6110
0.00
27.0
05.
0699
.25
108.
5684
247
50.2
540
.00
13.3
31.
0098
173.
529
4213
4999
110.
0027
.00
5.06
109.
2510
6.50
1006
6255
.25
40.0
013
.33
1.00
9920
6.0
4526
3071
4712
2.00
40.0
013
.33
121.
0011
8.00
1369
1961
.00
48.0
016
.00
1.00
100
219.
550
6242
7516
124.
0040
.00
13.3
312
3.00
119.
5014
2207
62.2
560
.00
31.2
51.
25
Table 5 BARS-PC
Structure A 1 I 1 d 1 A 2 I 2 d 2 A 3 I 3 d 3
I.D. (in2) (in4) (in) (in2) (in4) (in) (in2) (in4) (in)
010013 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 (0.769) 0.000 0.000 0.045 0.000 0.000 (0.769) (0.364)
0.000 0.030 0.006 0.000 (0.004) (0.019) 0.000 0.030 (0.267)
010023 0.000 0.000 0.000 0.000 0.028 0.000 0.000 0.000 0.000
0.000 0.000 (0.002) 0.000 0.049 0.010 0.000 0.000 (0.571)
0.000 0.000 0.006 0.044 0.119 0.009 0.000 0.000 (0.844)
0.000 0.000 0.002 0.000 0.044 (0.006) 0.000 0.000 (1.053)
010186 0.000 0.482 (0.010) 0.000 0.000 (0.014) 0.000 0.482 (0.256)
0.000 0.024 (0.007) 0.000 0.005 0.023 0.000 0.024 0.308
020080 0.000 0.225 0.000 0.000 0.000 0.000 0.000 0.225 0.000
0.000 (0.105) (0.007) 0.000 0.005 0.023 0.000 (0.105) 0.444
0.000 0.154 0.011 0.000 0.000 0.000 0.000 0.154 (0.800)
040119 0.000 0.250 0.000 0.000 0.000 0.000 0.000 0.250 0.000
0.000 0.024 0.000 0.000 (0.020) (0.020) 0.000 0.024 0.308
040339 0.000 0.446 (0.009) 0.000 (0.000) 0.000 0.000 0.446 1.333
0.000 0.148 0.000 0.000 0.000 0.000 0.000 0.148 0.000
0.000 0.274 (0.004) 0.000 (0.004) (0.018) 0.000 0.274 0.444
0.000 (0.011) (0.009) 0.000 0.001 0.000 0.000 (0.011) 0.571
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000
0.000 0.023 (0.004) 0.000 (0.003) (0.017) 0.000 0.023 0.308
040435 0.000 (1.554) 0.000 0.000 0.022 0.000 0.000 (1.554) (1.818)
0.000 0.020 (0.008) 0.000 0.000 0.000 0.000 0.020 0.800
0.000 0.182 0.000 0.000 0.000 0.000 0.000 0.182 0.000
0.013 0.149 0.000 0.000 (0.013) 0.000 0.013 0.149 (0.414)
060215 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
120258 0.000 0.128 (0.004) 0.000 (0.004) (0.019) 0.000 0.128 0.444
0.000 0.026 (0.010) 0.000 0.000 0.000 0.000 0.026 0.571
130638 0.000 0.160 0.000 0.000 (0.035) 0.000 0.000 0.160 0.800
0.000 (0.031) 0.000 0.000 0.000 0.000 0.000 (0.031) 0.000
150255 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
180124 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
181204 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
181208 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
181310 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
186933 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000210227 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Error between Actual and CPN-generated values (%)
27
REFERENCES
AASHTO (1994), Bridge Analysis and Rating System, BARS-PC, Release 5.5, Mod 3.2, User
Manuals I and II, American Association of State Highway and Transportation Officials,
Washington, D.C.
Adeli, H. (2001), “Neural Networks in Civil Engineering, 1989-2000”, Computer-Aided Civil
and Infrastructure Engineering, Vol. 16, No. 2, pp. 126-147.
Adeli, H. and Hung, S. L. (1995), Machine Learning - Neural Networks, Genetic Algorithms,
and Fuzzy System, John Wiley, New York, 1995.
Adeli, H. and Karim, A. (2001), Construction Scheduling, Cost Optimization, and Management
– A New Model Based on Neurocomputing and Object Technologies, Spon Press, London.
Adeli, H., and Park, H. S. (1995), “Counterpropagation Neural Networks in Structural
Engineering.” Journal of Structural Engineering, 121(8), ASCE, pp. 1205-1212.
Adeli, H. and Park, H.S. (1998), Neurocomputing for Design Automation, CRC Press, Boca
Raton, Florida.
AISC (1995), Manual of Steel Construction, Allowable Stress Design, American Institute of
Steel Construction, Chicago, IL.
AISC (1998), Manual of Steel Construction, Load & Resistance Factor Design, American
Institute of Steel Construction, Chicago, IL.
DeSieno, D. (1988), “Adding a conscience to competitive learning”, IEEE International
Conference on Neural Networks, San Diego, CA, SOS Printing, Vol. 1, pp. 117-124.
Grossberg, S. (1982). Studies of Mind and Brain. Reidel Press, Boston, Mass.
Hecht-Nielsen, R. (1987). “Counterpropagation Networks”, Applied Optics, 26:23, pp. 4979-
4985.
28
Kohonen, T. (1998). Self-organized and Associative Memory. Springer-Verlag, New York, N.Y.
Mehrotra, K., Mohan, C. K., and Ranka, S. (1997). Elements of Artificial Neural Networks, MIT
Press, Cambridge.
29
LIST OF FIGURES Figure 1: Architecture of CPN network used for training for determining the geometric
properties conversion from WSD- to LFD-based rating of bridges.
Figure 2: Detailed description of geometric properties of BARS-PC Input Data Form Card
Type 12.
Figure 3: Architecture of modified CPN network used for testing for determining the
geometric properties conversion from WSD- to LFD-based rating of bridges.
Figure 4: CPN Training Cycle.
Figure 5: CPN Testing Cycle.
Figure 6: CPN network training convergence history using steel wide-flange shapes only.
Figure 7: CPN network with plate girder data training convergence history.
30
Figure 1
31
Figure 2
32
Figure 3
33 33
Phase I Phase II
Training input vector xp
be
w
Adjust the weight vector
No
Desired output vector py
Calculate Euclidean distance tween input and weight vectors:
( )2/1
..1
2
,
2
,⎭⎬⎫
⎩⎨⎧
−= ∑= ENj
ipijj xwd
Select the winning node
Adjust the weight vector
( ) ( ) ( ) jijij Znijwipxnwn ⎥⎦⎤
⎢⎣⎡ −+=+ ,,1 ,, α
where ( )21
1+
=n
α
( ) ( ) ( ) jkpjkjkjk Zynwnwnw ][ ,,,, 1 −+=+ α
where ( )21
1+
=n
α
Yes
Save the stable weights
Check Convergence
Check Convergence
No
Yes
Stop
Figure 4
34
Input vector xp
Calculate Euclidean distance between input and weight vectors:
( )2/1
..1
2
,
2
,⎭⎬⎫
⎩⎨⎧
−= ∑= ENj
ipijj xwd
Select the winning nodes
Calculate Competition Layer Output:
( )
⎪⎪
⎭
⎪⎪
⎬
⎫
⎪⎪
⎩
⎪⎪
⎨
⎧⊂
−
−
= ∑∑
=
=
otherwise0
if1
..1
..1wj
mnn
mnjn
j
SZdm
dd
Z
Calculate output:
( )c
jNj
jkcml ZwaE
⎟⎟⎠
⎞⎜⎜⎝
⎛= ∑
= ..1,,'
Figure 5
35
CPN Convergence History
0
50
100
150
200
250
0 10 20 30 40 50
Iteration
Roo
t Mea
n Sq
uare
sys
tem
err
or (%
)
Competition Layer
Interpolation Layer
295. . .
Figure 6
36
CPN Convergence History
0
20
40
60
80
100
120
140
160
180
200
0 10 20 30 40 50
Iteration
Roo
t Mea
n Sq
uare
sys
tem
err
or (%
)
Competition Layer
Interpolation Layer
395. . .
Figure 7
37
Part II
An Intelligent Decision Support System
to Convert WSD-Based Bridge Rating to
LFD-Based Bridge Rating
38
An Intelligent Decision Support System
to Convert WSD-Based Bridge Rating to LFD-Based Bridge Rating
Gene F. Sirca, Jr.2 and Hojjat Adeli3, Fellow, ASCE
ABSTRACT: In 1995, the FHWA required that all bridges, regardless of the design method
used for the original design, be based on the Load Factor Design (LFD) method. In order to
comply with the FHWA requirements, state departments of transportation have converted to the
LFD method for all new bridge ratings. Further, all existing bridges previously rated using the
Working Stress Design (WSD) method must be converted to the LFD method. Consequently,
thousands of bridges must be re-rated using the LFD method. Steel bridges rated by the WSD
method have critical data missing to make the proper conversion to the LFD method. This article
presents a methodology and an intelligent decision support system (IDSS) to help bridge
engineers convert a WSD-rated bridge to the LFD-rating system with little human effort using
case-base reasoning and artificial neural networks. The proposed methodology can help bridge
engineers create the missing LFD-based data efficiently and quickly with minimum amount of
work. This research demonstrates how bridge engineers can use a novel computing paradigm and
modern computer tool to convert an antiquated database to current design.
INTRODUCTION
The Federal Highway Administration (FHWA) requires the Ohio Department of
Transportation (ODOT) to rate all bridges under its jurisdiction for their safe live load carrying
2 Graduate Student, Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, 470 Hitchcock Hall, 2070 Neil Avenue, Columbus, Ohio 43210 2 Professor, Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, 470 Hitchcock Hall, 2070 Neil Avenue, Columbus, Ohio 43210
39
capacities in accordance with National Bridge Inspection Standards (NBIS) and the Ohio
Revised Code (ORC). To date, ODOT is responsible for over 12,000 bridges, which includes
new, existing and rehabilitated structures. The FHWA defines a bridge as a highway structure of
length 20 feet (6.1 m), or more (FHWA, 1995), while the ORC defines a bridge to be any
structure that carries a highway load and has a total length of 10 feet (3.05 m) or more (ORC,
2000). The ORC requires that warning signs be posted on bridges where the safe load carrying
capacity of the structure is determined to be less than the load limits prescribed by the ORC.
Therefore, it is vital to know the load carrying capacity of a bridge in order to insure public
safety.
A new bridge rating is required for all new and rehabilitated bridges. New ratings are
also required for any existing bridge that has incurred changes in its overall design such as an
addition of a new wearing surface, structural damage due to a traffic accident, excessive surface
rusting of steel members that causes a reduction in their cross-sectional area, or loss of tension in
tendons in prestressed concrete members. ODOT engineers determine bridge ratings using the
computer program AASHTO BARS (Bridge Analysis and Rating System) (ODOT, 2000). More
recently, a PC version of the BARS program is used called BARS-PC.
Each ODOT BARS-PC data file is organized according to different input forms or “Card
Types” that represent different descriptive data of the bridge structure (AASHTO, 1994). The
card type defines the kind of information that is contained on the card and its relationship to the
structural analysis process and bridge rating. For example, Card Type 16 refers to data relating
to the lateral support and stiffener spacing of steel bridge girders. The data files contained in the
ODOT master library consist of lines of data derived from these input forms. Each file contains
40
bridge-rating data pertaining to the structural design of a given bridge based on the working
stress design (WSD) or load factor or strength design (LFD) method.
Up until 1995, bridge ratings were based on the design method used, which, in most
cases, was the WSD method. In 1995, the FHWA required that all bridges, regardless of the
design method used for the original design, shall be based on the LFD method (FHWA, 1995).
In order to comply with the FHWA requirements, ODOT has switched to the LFD method for all
new bridge ratings. In addition, all existing bridges previously rated using the WSD method
must be converted to the LFD method. The current master library of rated bridges contains a
mixture of about 9,000 WSD- and LFD-based data files with approximately 70% of those files
being WSD-based. For some bridge types such as reinforced and prestressed concrete girder
bridges, the conversion from WSD to LFD is a relatively simple task since the majority of data
for both design methods are the same. This is generally not the case for steel bridges.
Steel bridges rated by the WSD method have critical data missing to make the proper
conversion to the LFD method. For example, a steel girder bridge rated by either method
requires input into the BARS-PC program that describes the girder’s section properties. For the
WSD-based bridge rating, a non-detailed description of the section properties including only the
cross sectional area, moment of inertia, and section modulus of each girder cross-section would
suffice. For the LFD-based rating, however, a detailed description of the section properties is
required including information about individual elements making up the steel girder cross
section such as the total height of the section, and the areas of the web and flange elements and
their individual moments of inertia and the distances from their centroids to a reference axis.
Another piece of missing data needed by the LFD-based method for rating steel girder
bridges using BARS-PC, not included in the WSD-based method, is information regarding the
41
spacing of lateral bracing of the girders. Short of physically inspecting each bridge rated under
the WSD method, determining this missing data is no easy task. The engineer must make an
intelligent decision regarding the lateral bracing based on the available WSD-based data used to
rate the bridge. This is accomplished by evaluating design criteria that would have been used for
the original design. For example, if a bridge was originally designed in 1952, the engineer
would refer to the design guidelines of that era to determine the lateral bracing requirements that
would have been used.
An intelligent method of determining the detailed section properties of steel bridge
girders and cross bracing requirements is advanced to convert a WSD-rated bridge to the LFD-
rating system with little human effort. One approach is to use case-based reasoning (CBR)
(Watson, 1997). Using artificial neural networks (ANNs) is another approach (Adeli and Hung,
1995; Adeli and Park, 1998; Adeli and Karim, 2001).
Recently, the authors presented a counterpropagation neural network model for
estimating the detailed section properties of steel bridge girders needed in the LFD-based rating
based on the three cross-sectional properties used in the WSD-based rating of bridges: cross-
section area, moment of inertia, and section modulus (Sirca and Adeli, 2003). It is shown that
with proper training of the network using both standard wide-flange shape and representative
plate girder data, the proposed model can generate the detailed section properties needed for
LFD-based rating of steel bridges quite accurately.
OVERALL STRUCTURE OF THE WSD-TO-LFD CONVERSION MODEL
The goal of this research is to create an intelligent decision support system (IDSS) for
converting all WSD-based data files contained in the ODOT master library to LFD-based files.
The process used to achieve this employs the use of both case-based reasoning and artificial
42
neural networks. The former is used to predict the lateral bracing requirements and the latter is
used to determine the LFD-based section properties. The overall structure of the WSD-to-LFD
conversion model is presented in Figure 1. Referring to Figure 1, the following steps summarize
the WSD-to-LFD conversion process.
1) Is the data file WSD- or LFD- based? The master library files that are LFD-based
contain the letter “L” next to the file number. All other files are presumed to be
WSD-based. If the file is found to contain LFD-based data, go to step 6. Otherwise,
go to step 2.
2) Determine the bridge type. If the structure is a structural steel (SS) or composite steel
and concrete (CSC) bridge, go to step 3. If the structure is a reinforced concrete
(RC), prestressed concrete (PSC), composite prestressed concrete (CPS), or
composite reinforced concrete (CRC) bridge, go to step 5 (no special conversion
process is necessary). If the file contains data pertaining to any other bridge type, it
is “tagged” as being beyond the scope of the BARS-PC program and is returned to
the master library. Then, go to step 6.
3) Go to the CBR module to determine the lateral bracing requirements for the “Bridge
Analysis and Rating System Input Data Form Card Type 16”. The details of the
process used in the CBR module are discussed in a subsequent section. The module
updates the file with lateral bracing information and the conversion process proceeds
to the next step.
4) Go to the neural network module to determine the LFD-based section properties
description for the “Bridge Analysis and Rating System Input Data Form Card Type
12”. The details of the process used in the neural network module are presented in
43
Sirca and Adeli (2003). The module determines the Card Type 12 data and modifies
the data file accordingly. The process continues with step 5.
5) Change columns 66-69 of “Bridge Analysis and Rating System Input Data Form Card
Type 01” from *77* (or blank) to *LF*. Columns 66-69 represent a batch process
control code that indicates the characteristics by which the structures in the batch are
to be analyzed (AASHTO, 1994). The card is changed to indicate that the data
contained in the file represents the LFD-based data. Once the file is updated, proceed
to the next step.
6) Add “L” to the file name. This procedure changes the file name to reflect the fact
that it represents LFD-based data. For example, a WSD-based file might be named
“311432”, representing its Structure I.D. The file containing LFD-based data would
be named “311432L”.
One of the goals of the WSD-to-LFD conversion IDSS presented in this work is to create
an all-inclusive user-friendly interface, allowing the bridge engineer to submit a single file or
batches of files. Decision blocks that require user interaction, such as whether to continue after
discovering one of the files in a given batch is already LFD-based, must be programmed to
provide a seamless process. The IDSS must also contain a user-friendly Graphical User
Interface (GUI) to help make the program as foolproof as possible. To best facilitate these
features, the IDSS is developed using Microsoft Visual Basic© within the popular spreadsheet
program, Microsoft Excel©. Visual Basic provides many of the object-oriented-programming
(OOP) features common to C++ or Java (Adeli and Yu, 1991). An advantage of using Visual
Basic compared to using C++ or Java is that most engineers are already familiar with Excel and
44
its interface. Thus, learning to use the WSD-to-LFD conversion IDSS should be easier than
learning to use an entirely new program with an unfamiliar interface.
DATABASE MANAGEMENT
The BARS-PC master library contains data, used as input into the AASHTO BARS-PC
Bridge Analysis and Rating System, for about 9,000 bridges. The data is stored in the master
library as strings of Unicode text, where each row represents a string of data used by the BARS-
PC program to generate a bridge rating. Each column in the master library corresponds to the
individual characters that make up a string of BARS-PC input data. A sample of data from the
master library is presented in Figure 2. In this figure, the first two columns represent the BARS-
PC card number and columns 3 to 8 represent the 6-digit Structure I.D. where each Structure I.D.
represents a different bridge in the master library. The rows of data strings are sorted, in
descending order of the card and Structure I.D. numbers. The remaining columns in the master
library file represent different bridge parameters depending on the card type. For example in
Card Type 16, columns 9-11 represent the “Flexural Member ID”, column 12 represents data
that indicates to the BARS-PC program whether the lateral supports are placed symmetrically,
columns 13 and 14 represent the bridge “Span Number”, column 15 represents data that indicates
the position of the lateral supports, columns 16 and 17 represents the “Range Number” of groups
of common lateral bracing spacings, columns 18-27 represent the “Range Length” identified by
the range number in columns 16 and 17, columns 28-31 represent the “Support Code” for the
lateral bracing, columns 32-43 represent data pertaining to the spacing of equally spaced lateral
bracing points within a range, columns 44 and 45 are not used and are left blank, and columns 46
and 55 represent data pertaining to the maximum stiffener spacing within the defined range, and
the remaining columns are not used for this card type (AASHTO, 1994).
45
Each "file" in the master library file (Figure 2) consists of rows of data strings that share
a common Structure I.D. Part of the difficulty in converting WSD-based data files to LFD-based
files is not just choosing which rows of data from the master library to convert, but what to
convert on each row. To help resolve these issues, in this research, the master library is
transformed into a Microsoft© Access database.
A sample of the transformed spreadsheet database is presented in Figure 3. The database
is created with the first three columns representing the data string’s position in the database,
BARS-PC input data form card type, and Structure I.D. The remaining columns in the database
represent BARS-PC input data columns which represent the same design parameters included in
the master library file (Figure 2) and in the same order. Part of the master library transformation
includes breaking the strings of text into individual characters. Each row of the transformed
database consists of 80 columns, which corresponds to the largest number of columns contained
in a BARS-PC data input card. This division of the rows of text strings into individual
characters is necessary because each card type contains a unique configuration of characters
independent of the other card types. For example, a string of data that describes the geometric
properties of the bridge girder(s) are different from a string of data that describes the bridge
structure type, such as steel girder, and span information, primarily due to differences their
respective columnar position of data on each row. Individual characters from each data string
are combined, as needed, into smaller strings of useful information during the WSD-to-LFD
conversion process. Since the transformed database consists of an array of data, the process of
combining characters is simply a matter of looping through rows and columns of master library
data and storing the information into a new array, one array for each smaller string of combined
characters.
46
Once the WSD-to-LFD conversion process is complete, the IDSS output, which is in the
form of strings of text, must be placed on a spreadsheet in the form of individual characters of
text. This presents a challenge in that the IDSS output, which is primarily floating-point
numerical output, must be placed into a fixed number of cells defined by the BARS-PC data
type. To illustrate the point, consider the BARS-PC data field on Card Type 12 for the height of
the LFD-based steel section. The data field consists of six characters. If, for example, the IDSS
output for the height is the value “56.34375”, which is obviously greater than six characters, then
the output must be rounded to six characters in order to comply with the BARS-PC data format.
To achieve this, an algorithm is developed that uses only the required number of characters in
addition to separating the numerical output into individual characters. From the aforementioned
example, the value for height, generated by the IDSS, is converted into six individual characters:
“5”, “6”, “.”, “3”, “4”, and “4”.
CASE-BASED REASONING
47
General
Case-based reasoning is a problem-solving paradigm for solving new problems based on
previously solved problems (Maher, et al., 1995; Maher and Pu, 1997; Riesbeck and Schank,
1989). Derived from the way human experts solve problems by drawing from experience, case-
based reasoning can be used to determine the lateral bracing requirements by drawing from a
case base of previously solved problems. For example, given the year in which a steel girder
bridge was built, in addition to its length and number of spans, a CBR system can determine the
lateral bracing specifications by drawing information from a case base consisting of lateral
bracing design data from past years.
Case-based reasoning differs from direct database retrieval in that CBR does not require an
exact match (Richter, 1998). Thus, CBR is advantageous over database retrieval in its ability to
handle “fuzzy” matches (Watson, 1997; Dubois, et al., 1999). The CBR retrieval algorithm
looks for similarities between the new reference case and the cases in the case base and ranks the
matches according to their relative similarity to the reference case (Leake, 1996).
A major advantage of CBR, compared with rule-based or knowledge-based systems
(Adeli and Balasubramanyam, 1988; Adeli, 1988; Adeli, 1990a&b), is that the knowledge
acquisition process used to develop the case base is relatively straightforward; it consists of
collecting and documenting cases with the premise that new cases can be added easily. In
contrast, in rule-based systems the knowledge is presented in the form of production rules. For
example, the case base used for solving the lateral bracing determination problem includes data
derived from past ODOT standard bridge design drawings (ODOT, 1939-1997). New references
that successfully match a case in the case base may be adapted, using the matched case’s output
48
data, and added to the base as a new case. This eliminates the need to re-derive the case-
matching procedure from scratch (Leake, 1996).
Part of the development process in creating a successful CBR system is to minimize the
number of potential unsuccessful references to the case base. Early in the development process,
the CBR system designer must determine the appropriate relevance of the data contained in the
case base with respect to the reference case and the desired solution for all possible references.
Some fields, representing the data in the case base such as the year the bridge was designed, may
be more important than other fields, such as span length(s), in terms of consistently providing a
correct solution. This is another advantage of CBR over direct database retrieval in that direct
retrieval can provide only one solution based solely on the data at hand.
Case-Based Reasoning Shell
The CBR shell, Induce-It (Inductive Solutions, 1997), is used to create and manage the
CBR module for the IDSS presented in this work. The CBR module is created according to the
following steps. First, the data field parameters are set to compute new reference similarities
with the cases. This includes selecting case data types, textual or numerical, and creating field
names that represent the case data such as the year in which the bridge was designed, the span
length(s) of the bridge, and the number of cross-frame spaces. The next step is to assign weights
to the data fields to determine field significance. Then, the field and case similarity functions are
chosen. The similarity function used in this work will be introduced in the next section. The
final step is to create the case base. This is accomplished by assigning data to each field that
represents each case. Calculating scores based on field similarity determines similarity of the
new reference case with the cases in the case base. The similarity scores are normalized to yield
49
values between 0 (least similar) and 1 (exact match). The field-matched scores are stored in an
inductive database that mirrors the case database, and is used to determine the overall case
similarity (The inductive database is a tool used by the CBR shell to rank the matches by the
reference case to the cases stored in the case base). This is accomplished by calculating a score
for each case based on weighted field relevance and similarity. The case scores are used to rank
the cases in the case base in order of similarity to the reference case.
Once the CBR system is created, it goes through a fine-tuning process. The process
involves modifying the weights, re-defining case parameters, adding and/or deleting cases,
specifying new case base fields or removing old ones. The purpose of fine-tuning is to maximize
the quality of the similar case matches by adjusting the architecture of the CBR system.
Determining Lateral Bracing Requirements using CBR
The CBR module for determining the steel bridge girder lateral bracing requirements is
developed using lateral bracing design data from ODOT standard bridge design drawings dating
as far back as 1939 and as recent as 1997. After 1997, lateral bracing requirements are
determined according to the ODOT Bridge Design Manual (ODOT, 2000). The year the bridge
was built is the most important factor in determining the correct lateral bracing spacing due to
the number of changes that were made to the design process through the years. The other
parameters needed to determine the lateral bracing spacing is the number of spans and the span
length(s). The CBR model used for solving the lateral bracing determination problem is
presented in Figure 4.
The case base created for the WSD-to-LFD conversion process does not contain every
case recorded (since 1939) for determining the lateral bracing requirements due to redundancies
50
in the data. New issues of the ODOT standard bridge drawings often include changes to other
aspects of bridge design, leaving the lateral bracing design unchanged. It is therefore possible to
omit the redundant cases without affecting the integrity of the case base. After eliminating the
redundant cases, 39 cases are included in the case base of the bridge rating IDSS.
Table 1 presents the data used to develop the case base for determining the lateral bracing
requirements for the 39 representative cases of lateral bracing design. The numerical data type,
designated by n, is used to represent the following case base fields: year, middle_span_length,
and end_span_length. The textural data type (Lenz, et al., 1998) is used for the first field, cases,
which carries a weight of zero, which means that the field does not play a role in the case-
matching process. The second field, the year of bridge construction, holds the greatest
significance and carries a weight of one. The two remaining fields hold equal significance and
carry weights less than one. The weight values are chosen heuristically, based on the general
knowledge of bridge design and discussions with bridge-rating engineers. Since the case base is
relatively small and is constructed with only three weighted data fields, the weights of the
middle_span_length and end_span_length fields can be any value less than one but greater than
zero to produce the same results. A database of lateral bracing spacing information for each case
is kept separate from the case base and is used only when a successful match is made. A
successful match, to be defined subsequently, causes the IDSS to pull information from the
lateral bracing spacing database for the WSD-to-LFD conversion process.
The fields of each reference case are compared to the corresponding fields of the cases in
the case base to obtain a similarity score for each case. The individual field-match scores are
stored in the inductive database for use in generating the overall case score. A linear weighted
similarity function is used to calculate the overall case scores:
51
∑∑
=
==
nii
niii
j w
vwcaserefSimilarity
,1
,1),( n = number of fields (1)
where ref is the reference case, casej is the jth case in the case base, wi is the importance weight
of the ith field, vi is the similarity of field i between the reference case and case j of the case base
determined by:
),( , jiii CRSimilarityv = 10 ≤≤ iv (2)
and Ri is the ith reference field and Ci,j is the corresponding field value of the jth case in the case
base. For numerical data types, vi is the ratio between Ri and Ci,j. For textual data types, vi is 0
or 1 where 1 is a direct match and 0 is not.
Nearest-neighbor matching is used to rank the matches between the reference case and
the cases in the case base (Kolodner, 1993) to aid in the solution verification process. In this
approach, the scores are ranked from the highest to the lowest value. The highest scores
represent the best matches. In order for a match to be considered successful, it must first be
verified. The following relationships must be true for a match to be correct. First, starting with
the highest ranked match, the match must yield a score greater than or equal to some acceptable
value, such as 95%, chosen heuristically. Second, the matched case will have a span length
greater than the reference case in order to insure a conservative bridge rating.
A successful match with the case base causes the IDSS to generate lateral bracing data,
formatted according to BARS Input Data Form Card Type 16 from the associated database of
lateral bracing information.
52
DETERMINING LATERAL BRACING REQUIREMENTS DIRECTLY
Since the case base used to determine the lateral bracing requirements during the WSD-
to-LFD conversion process is relatively small, it is possible to determine the lateral bracing
spacing directly, without the use of case-based reasoning. An algorithm is developed to handle
the task.
The CBR module is transformed into a simple algorithm that determines the lateral
bracing spacing requirements, Smax, using two input variables, the year in which the bridge was
designed, Y, and the total length of the bridge, L (in feet). The case base of the CBR module
consists of representative lateral bracing designs from a discrete number of years, or years where
a significant change was made with respect to lateral bracing design. In the direct algorithm,
each significant design year is defined as a unique lateral spacing design criterion. There are six
different lateral bracing design criteria used in the algorithm from design years 1941, 1945,
1949, 1955, 1963, and 1997.
The algorithm works in two parts. The first part of the algorithm determines the lateral
bracing design criterion and the second part determines the maximum lateral bracing spacing. A
generalized form of the algorithm follows.
Part I: determine lateral bracing design criterion: If Y <1945 then use 1941 lateral bracing design
If 1945 ≤ Y < 1949 then use 1945 lateral bracing design
If 1949 ≤ Y < 1955 then use 1949 lateral bracing design
If 1955 ≤ Y < 1963 then use 1955 lateral bracing design
If 1963 ≤ Y < 1997 then use 1963 lateral bracing design
If 1997 ≤ Y then use 1997 lateral bracing design
Part II: determine maximum lateral spacing (in feet):
53
1941 Lateral Bracing Design:
If L < 25 then Smax = 7
If 25 ≤ L < 35 then Smax = 8
If 35 ≤ L < 60 then Smax = 9
If 60 ≤ L < 78 then Smax = 10
If 78 ≤ L < 104 then Smax = 11
If 104 ≤ L < 130 then Smax = 12
If 130 ≤ L < 156 then Smax = 13
If 156 ≤ L then Smax = 14 1945 Lateral Bracing Design:
If L < 104 then Smax = 10
If 104 ≤ L < 130 then Smax = 11
If 130 ≤ L < 195 then Smax = 12
If 195 ≤ L then Smax = 13 1949 Lateral Bracing Design:
If L < 25 then Smax = 7
If 25 ≤ L < 30 then Smax = 8
If 30 ≤ L < 78 then Smax = 9
If 78 ≤ L < 97.5 then Smax = 10
If 97.5 ≤ L < 156 then Smax = 11
If 156 ≤ L then Smax = 12 1955 Lateral Bracing Design:
If L < 130 then Smax = 10
If 130 ≤ L < 195 then Smax = 11
If 195 ≤ L < 208 then Smax = 12
If 208 ≤ L then Smax = 13
54
1963 Lateral Bracing Design:
If L < 97.5 then Smax = 9
If 97.5 ≤ L < 156 then Smax = 10
If 156 ≤ L < 195 then Smax = 11
If 195 ≤ L < 234 then Smax = 12
If 234 ≤ L then Smax = 13
1997 Lateral Bracing Design:
Smax = 15
For a given bridge of total length L, designed in year Y, the algorithm is capable of
determining the LFD-based lateral bracing requirements by determining the maximum lateral
bracing spacing Smax directly from the inputs, using the aforementioned relationships. The
algorithm is more efficient than the CBR module with respect to CPU usage since it does not
require the use of a separate programming shell such as Induce-It. Frequent calls to Induce-It
functions during the WSD-to-LFD conversion process take a considerable amount of time, even
considering the small size of the case base. Another advantage over the CBR approach, using
Induce-It, is that the algorithm is directly integrated with the IDSS program, which provides
seamless transfer of input and output. The advantage of using the CBR approach, on the other
hand, is that new cases can be added easily without any need for rewriting any part of the code.
BARS-PC IDSS INTERFACE
The BARS-PC IDSS uses a user-friendly GUI interface that allows the bridge engineer to
interact directly with the program with little user input. The interface contains options for
converting one file or batches of several files (Figure 5). The third tab on the interface contains
a window to modify the paths to the database, output file location, and BARS-PC program
55
directory. The output windows on the interface correspond to each of the LFD-based section
properties such as h, A1, Ix1, d1, A2, Ix
2, d2, A3, Ix3, and d3. Additionally, output windows are
provided for the overall section properties such as A, Ix, and Sx, and for the name of the AISC
shape or plate girder shape, such as “W44x285” or “SPG”, where “SPG” stands for “Synthetic
Plate Girder”. The output windows allow the bridge engineer to review the program’s output for
the LFD-based detailed section properties before creating a new BARS-PC-format file. The
windowed output on the interface handles multiple instances (more than one steel shape for a
given structure file) by the use of a button that toggles through different converted outputs.
In lieu of viewing the output on the interface, the bridge engineer may choose to view the
output by selecting the “Show Section Properties” button or “Show Lateral Bracing” button.
Selecting either option opens a spreadsheet with output data for the LFD-based detailed section
properties or lateral bracing. Selecting the “Show Converted File” option opens a spreadsheet
with the entire newly converted LFD-based file in database format (broken text strings).
Selecting the “Convert to BARS-PC Format” option runs computer code that transforms the
newly converted database-format file to BARS-PC format. Specifically, the code combines the
rows of broken text strings into rows of Unicode text. A final option on the single-mode status
interface is to run the BARS-PC program directly from the IDSS.
EXAMPLE PROBLEM
The bridge rating IDSS is used to solve the WSD-to-LFD conversion problem in the
following example. A sample of the imported data is presented in Figure 6. The bridge rating
IDSS analyzes the data to determine if the structure is already LFD-based. If not, it determines
the structure type and how to make the WSD-to-LFD conversion. In this example, the structure
56
type is “SS”, or, “steel structure”. The program proceeds to determine the LFD-based detailed
section properties and lateral bracing requirements.
Once the bridge rating IDSS has completed the WSD-to-LFD conversion process, the
“BARS-PC IDSS Single-Mode Status” interface is presented to the bridge engineer (Figure 7).
The output of the newly converted LFD-based file is presented in spreadsheet format, similar to
the spreadsheet depicted in Figure 3. The output can also be presented in unicode text format,
similar to the format depicted in Figure 2.
CONCLUSIONS
The proposed system was developed out of necessity. Currently, the Ohio Department of
Transportation converts the data manually, where a bridge engineer converts the WSD-based
data to LFD-based data by either updating the data from recent bridge inspection reports or by
using engineering judgment. This process is both time-consuming and error-prone. The
conversion process may take a bridge engineer as much as a full working day where the
proposed intelligent decision support system can make the same conversion in a matter of
seconds. The proposed CBR technology and intelligent decision support system help bridge
engineers create the missing LFD-based data efficiently and quickly with minimum amount of
work. This research demonstrates how bridge engineers can use a novel computing paradigm and
modern computer tool to convert an antiquated database to current design.
ACKNOWLEDGEMENT
57
This manuscript is based on a research project sponsored by the Ohio Department of
Transportation and Federal Highway Administration.
REFERENCES
AASHTO (1994), Bridge Analysis and Rating System, BARS-PC, Release 5.5, Mod 3.2, User
Manuals I and II, American Association of State Highway and Transportation Officials,
Washington, D.C.
Adeli, H., Ed. (1988), Expert Systems in Construction and Structural Engineering, Chapman and
Hall, New York.
Adeli, H., Ed. (1990a), Knowledge Engineering – Volume One - Fundamentals, McGraw-Hill
Book Company, New York.
Adeli, H., Ed. (1990b), Knowledge Engineering – Volume Two - Applications, McGraw-Hill
Book Company, New York.
Adeli, H. and Balasubramanyam, K.V. (1988), Expert Systems for Structural Design – A New
Generation, Prentice-Hall, Englewood Cliffs, New Jersey.
Adeli, H. and Hung, S. L. (1995), Machine Learning - Neural Networks, Genetic Algorithms,
and Fuzzy System, John Wiley, New York, 1995.
Adeli, H. and Karim, A. (2001), Construction Scheduling, Cost Optimization, and Management
– A New Model Based on Neurocomputing and Object Technologies, Spon Press, London.
58
Adeli, H. and Park, H.S. (1998), Neurocomputing for Design Automation, CRC Press, Boca
Raton, Florida.
Adeli, H. and Yu, G (1991), “Computer-Aided Design Using Object-Oriented Programming
Paradigm and Blackboard Architecture.” Microcomputers in Civil Engineering, pp. 177-190.
Aha, David W. (1998), “The Omnipresence of Case-Based Reasoning in Science and
Application,” Knowledge-Based Systems, 11, Elsevier Science, pp. 261-273.
AISC (1995), Manual of Steel Construction, Allowable Stress Design, American Institute of
Steel Construction, Chicago, IL.
AISC (1998), Manual of Steel Construction, Load & Resistance Factor Design, American
Institute of Steel Construction, Chicago, IL.
Dubois, D., Esteva, F., Garcia, P., Godo, L., López de Màntaras, R., and Prade, H. (1999),
“Case-Based Reasoning: A Fuzzy Approach,” Fuzzy Logic in Artificial Intelligence : selected
papers / IJCAI ’97 workshop, Nagoya, Japan, Springer-Verlag, Berlin, Germany, pp. 79-90.
Ellman, J. (1995), “An Application of Case Based Reasoning to Object Oriented Database
Retrieval,” Progress in Case-Based Reasoning : first United Kingdom workshop, Salford, UK,
Watson, Ian D. (ed.), Springer-Verlag, Berlin, Germany, pp. 134-141.
FHWA (1993), “Bridge Ratings for the National Bridge Inventory,” Federal Highway
Administration Policy Memorandum, United States Department of Transportation, Washington,
D.C.
FHWA (1995), Recording and Coding Guide for the Structure Inventory and Appraisal of the
Nation’s Bridges, Federal Highway Administration, United States Department of Transportation,
Washington, D.C.
59
Fuchs, M. and Fuchs, M. (1997), “Applying Case-Based Reasoning to Automated Deduction”,
Case-Based Reasoning Research and Development : second international conference / ICCBR-
97, Providence, RI, Leake, David (ed.), Springer-Verlag, Berlin, Germany, pp. 23-32.
Inductive Solutions (1997), Induce-It User Manual, Inductive Solutions, Inc., New York, NY.
Kolodner, Janet (1993), Case-Based Reasoning, Morgan Kaufmann Publishers, Inc., San Mateo,
CA.
Leake, D.B., Ed. (1996), Case-Based Reasoning, Experiences, Lessons and Future Dircections,
AAAI Press/The MIT Press, Menlo Park, CA.
Lenz, M., Hübner, A., and Kunze, M. (1998), “Textural CBR”, Case-Based Reasoning
Technology : from foundations to applications, Lenz, Mario (ed.), Springer-Verlag, Berlin,
Germany, pp. 115-137.
Maher, M.L., Balachandran, M.B., and Zhang, D.M. (1995), Case-Based Reasoning in Design,
Lawrence Eribaum Associates, Mahwah, NJ.
Maher, M.L., and Pu, P. (1997), Issues and Applications of Case-Based Reasoning in Design,
Lawrence Erlbaum Associates, Inc., Mahwah, NJ.
ODOT (1939-1997), Construction and Material Specifications, Ohio Department of
Transportation, Office of Contracts, Columbus, OH.
ODOT (2000), Bridge Design Manual, Ohio Department of Transportation, Columbus, OH.
ORC (2000), Ohio Revised Code, Anderson Publishing Co., Cincinnati, OH.
Richter, M. M. (1998), “Introduction”, Chapter one in Case-Based Reasoning Technology : from
foundations to applications, Lenz, M., Ed., Springer-Verlag, Berlin, Germany, pp. 1-15.
Riesbeck, C.K., Schank, R.C. (1989), Inside Case-based Reasoning, Lawrence Erlbaum
Associates, Publishers, Hillsdale, NJ.
60
Sirca, G. and Adeli, H. (2003), "Counterpropagation Neural Network Model for Steel Girder
Bridges", Journal of Bridge Engineering, ASCE, accepted for publication.
Watson, I. (1995), “An Introduction to Case-Based Reasoning,” in Progress in Case-Based
Reasoning : first United Kingdom workshop, Salford, UK, Watson, I. D., Ed., Springer-Verlag,
Berlin, Germany, pp. 3-16.
Watson, I. (1997), Applying Case-Based Reasoning, Morgan Kaufmann Publishers, Inc., San
Mateo, CA.
61
Table 1: Sample lateral bracing case base.
Types: t n n n nMaps: (case<=ref)
middle_ end_span_ Cross FrameField Names: cases year span_length length Spaces
Weights: 0 1 0.9 0.9 -Reference: 1935 43 36
Result: CSB-12-39-8 1939 45 36 10
Scores0.940024255 CSB-45-2 1945 40 32 90.983878076 CSB-45-3 1945 45 36 110.921020933 CSB-45-4 1945 50 40 110.869592361 CSB-45-5 1945 55 44 130.826735219 CSB-45-6 1945 60 48 130.790471482 CSB-45-7 1945 65 52 150.75938828 CSB-45-8 1945 70 56 15
0.732449504 CSB-45-9 1945 75 60 150.708878076 CSB-45-10 1945 80 64 150.867850293 CSB-15-40-1 1940 35 28 90.940939994 CSB-15-40-2 1940 40 32 90.984793814 CSB-15-40-3 1940 45 36 100.921936672 CSB-15-40-4 1940 50 40 10
0.8705081 CSB-15-40-5 1940 55 44 110.827650957 CSB-15-40-6 1940 60 48 110.791387221 CSB-15-40-7 1940 65 52 120.760304019 CSB-15-40-8 1940 70 56 130.733365243 CSB-15-40-9 1940 75 60 140.709793814 CSB-15-40-10 1940 80 64 150.688995495 CSB-15-40-11 1940 85 68 160.721854605 CSB-12-39-1 1939 25 20 60.758399456 CSB-12-39-2 1939 27.5 22 70.794944306 CSB-12-39-3 1939 30 24 70.831489157 CSB-12-39-4 1939 32.5 26 80.868034007 CSB-12-39-5 1939 35 28 80.904578858 CSB-12-39-6 1939 37.5 30 90.941123708 CSB-12-39-7 1939 40 32 90.984977529 CSB-12-39-8 1939 45 36 100.922120386 CSB-12-39-9 1939 50 40 110.870691815 CSB-12-39-10 1939 55 44 120.79293381 CSB-5-50-1 1950 30 24 7
0.829478661 CSB-5-50-2 1950 32.5 26 70.866023511 CSB-5-50-3 1950 35 28 90.902568362 CSB-5-50-4 1950 37.5 30 90.939113212 CSB-5-50-5 1950 40 32 90.982967033 CSB-5-50-6 1950 45 36 110.92010989 CSB-5-50-7 1950 50 40 11
0.868681319 CSB-5-50-8 1950 55 44 130.825824176 CSB-5-50-9 1950 60 48 13
62
List of Figures Figure 1: Overall Structure of the WSD-to-LFD Conversion Model.
Figure 2: Sample BARS-PC Master Library Text File.
Figure 3: Sample BARS-PC Master Library Database in Spreadsheet Format.
Figure 4: CBR Model to Determine the Lateral Bracing Requirements.
Figure 5: BARS-PC IDSS Interface – Single File Option.
Figure 6: IDSS Example – Data Import.
Figure 7: IDSS Example – Output Form for SS or CSC Structure Types.
63
Retrieve ODOT BARS-PC Data File from Master Library
Step 1
Is Data File WSD- or LFD-
based?
Det
erm
ine
Type
of
Stru
ctur
e
WSD LFD Add “L” to Filename
Convert Another
File?
Stop SS?
Yes
No
No
Yes
CSC?
Yes
No
3
Step 2
Start WSD-to-LFD
Conversion Model
Step
Change Columns 66-69 of Card Type 01 From *77* (or blank) to *LF* (from WSD-based Data toLFD-based Data)
Go To CBR Module to Determine
Lateral Bracing Requirements for Card Type 16
(see Figure 3)
RC? Yes
4
StepGo To CPN Module to Determine
LFD-based Detailed Section Properties Description for
Card Type 12
(see Figures 4 and 8)
No
CRC? Yes
No
5
StepAdd “L” to Filename
PSC? Yes
No
CPS? Yes
Change Columns 66-69 of Card Type 01 From *77* (or blank) to *LF* (from WSD-based Data to
LFD-based Data)
Step 6
Stop
Yes
No
No
Error: Beyond the Scope of BARS-PC
Convert Another
File?
Figure 1
SS: Structural Steel CSC: Composite Steel and Concrete RC: Reinforced Concrete CRC: Reinforcing Steel Concrete PSC: Prestressed Concrete CPS: Composite Prestressed Concrete
64
Figure 2
65
Figure 3
66
Input
New Reference Case
e
Si
ICa
RaHig
t
Lateral Bracing Spacing
A
Compar
CASE BASE
Calculate milarity Score
ndex to Next se in Case Base
nk Scores Fromhest to Lowest
Outpu
Figure 4
dapt Highest Ranked Case
67
Figure 5
68
Figure 6
69
Figure 7
70
Appendix User's Manual
A) Notes to the User General
When using the program for the first time, make sure that the paths to the database and
output file directories are updated - refer to the “IDSS Settings” tab of the worksheet, or, on the
program’s graphical user’s interface (GUI).
The current version of the program contains worksheets with critical program settings
that are not write-protected. Take extra care not to change anything on the “ANN Weights”
worksheet.
Batch Mode
There are two ways to generate a list of structure IDs when using the “batch mode”. The
first is to manually input each structure ID using the program’s built-in feature. The second is to
create a list manually by placing a list of structure IDs on the “Batch List” worksheet. If the
second option is used, it is important to format the worksheet cells as “Text” so that the leading
zero remains intact (where applicable). The structure ID list may be placed on the worksheet by
cutting and pasting or by manually generating the list in a single column starting with the second
row on the “Batch List” worksheet.
IMPORTANT: do not overwrite the upper left cell of the “Batch List” worksheet. This
contains the number of structure IDs contained in the list. Also, if manually creating a structure
71
ID list, be sure to update the upper left cell with the correct number of structure IDs. Using the
program’s built-in feature updates this number automatically.
B) Basic Operation
Step 1
Open “BARS-PC IDSS beta1.xls” and press the “BARS-PC IDSS” button located on the “IDSS
Output” worksheet. This opens a GUI prompting for the user’s initials.
Step 2
Enter the user initials (the text format may be upper or lower case); press “Done” when finished.
This opens the main IDSS interface.
Step 3
(Single File)
Enter the six-digit structure ID and press the “Convert” button to run the IDSS program.
(Batch Mode)
Generate a list of six-digit structure IDs (manually or using the interface), then press the
“Convert” button to run the IDSS program. In batch mode, the output files (in *.dat format) are
generated automatically.
Step 4
(Single File only)
Once the WSD-to-LFD conversion process has been completed, the “BARS-PC IDSS Single-
Mode Status” interface is presented. Selecting the “Show Converted File” option opens a
spreadsheet with the newly converted LFD-based file in database format. Pressing the “Convert
to BARS-PC Format” button causes the IDSS program to transform the newly converted
database-format file to BARS-PC format (Unicode text), in the form of a *.dat file.
72
