ARTIFICIAL NEURAL NETWORK MODEL FOR …€¦ · with ACI 318 guidance, except for load factor and reinforcement percentage. This manual has an approach similar to that of ACI 350R-89

http://www.iaeme.com/IJCIET/index.asp 265 [email protected]

International Journal of Civil Engineering and Technology (IJCIET)

Volume 9, Issue 2, February 2018, pp. 265–274, Article ID: IJCIET_09_02_026

Available online at http://http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=9&IType=2

ISSN Print: 0976-6308 and ISSN Online: 0976-6316

© IAEME Publication Scopus Indexed

ARTIFICIAL NEURAL NETWORK MODEL FOR

FLEXURAL DESIGN OF CONCRETE

HYDRAULIC STRUCTURES

Oday M. Albuthbahak and Hayder H. Alkhudery

Faculty of Engineering, University of Kufa, Najaf, Iraq

ABSTRACT

As a computer technique, Artificial Neural Networks (ANNs) have expanded in use

with engineering fields. ANNs have been used in many civil engineering problems and

some of them were used in the design of concrete structural elements and have shown

a good degree of success. This paper presents an ANN model for the strength design

of reinforced-concrete hydraulic structure according to the requirements of the

Engineering Manual 1110-2-2104. Structural design is a sequential process needs

iteration, assumption, checking the limits, ...etc, and that can be programmed with

some judgments of the designer. 288 cases of design samples have been calculated

using excel sheets and Microsoft visual basic programming language. 200 samples of

design randomly selected have been used for training of (4-10-10-2) ANN model. 50

samples have been selected for validation, and 38 for prediction processes. The

predicted design outputs were the thickness of hydraulic concrete section and

corresponding steel reinforcements. Visual Gene Developer software of ANN

prediction for general purposes has been used with a feed-forward neural network

with a standard back-propagation learning process. The suggested artificial neural

network model has predicted the output data of design for concrete sections, and the

results have shown a satisfactorily match with the actual output data of design.

Key words: Artificial Neural Networks; Engineering Manual 1110-2-2104; Strength

design of concrete hydraulic structure; Feed-forward neural network; Back-

propagation learning algorithm.

Cite this Article: Oday M. Albuthbahak and Hayder H. Alkhudery, Artificial Neural

Network Model for Flexural Design of Concrete Hydraulic Structures. International

Journal of Civil Engineering and Technology, 9(2), 2018, pp. 265-274.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=9&IType=2

1. INTRODUCTION

The first to suggest the idea of neural networks came from the work of brain neurons that can

be likened to a biological electrical network to process information to the brain. In these

networks, Donald O. Hebb suggested that the neural synapse plays a key role in guiding the

computing process and this prompted to think about the idea of connectivity and artificial

neural networks. It consists neural networks artificial than a neurons or processing units,



linked together to form a network of nodes, and all communication between these nodes have

a set of values called weights contribute to the identification resulting from each processing

units based on the values that entered the unit [1].

In general, all the neural networks arranged in layers of artificial cells: the inner layer, the

outer layer and the in between layers or hidden layers exist between inner and outer layer.

Each cell in one of these layers is related to all neurons in the layer that followed, and all

neurons in the layer that precede it. Each communication between one neuron and another is

characterized by a binding value called weight (weighting), it constitutes the importance of

the link between these two neurons. The neuron multiplying each entered value received from

neurons in the previous layer weights of connection of these neurons, then collecting all the

multiplication outputs, and then subjecting the result to continued converter varies depending

on the type of neuron. The result of continued converter is a neuron output that carries out to

the subsequent layer neurons [2].

One of the most important forms of neural networks: feed-forward neural network, which

it is a group of holding neural arranged in layers. These neurons are connected with each other

so that each neuron is usually associated with a layer of all neurons in the next layer (neurons

are not linked with each other at the same layer). The typical arrangement for these networks

is three neural layers called (input layer, hidden layer, output layer). Input layer does not carry

out any computational process they simply place of the network supplying data, the input

layer then supply (transfer information) to hidden layer and then hidden layer supplying the

output layer. The real data processing is in the hidden layer and output layer [3].

Back-propagation is a training algorithm in which the information flows in one direction

at a time, either forward or backward, that aims to adjust the weights of these network

connections. When there is an adequate number of neurons, the network will be able to

training to do things with the help of training algorithm [4].

There are many different architectures of neural networks, each of them has the

characteristic to be used for modeling a specific problem. The feed-forward neural networks

with back-propagation learning algorithms are considered very important especially in the

uses intelligent classification of data not already familiar, and it is the most generally used in

structural engineering [5].

Structural design is sequential steps which are restricted by selected building code

requirements and the most important step is the first step. Assumptions, iteration, comparison,

checking ... etc., all are processes necessary for the structural design. In this days the

computer programs are efficient and accurate in structural analysis, but these programs are not

enough for design because they require human expertise and judgment [6]. The artificial

neural network is a new technique which discovered to simulate the human brain and has been

used in many applications of engineering [2], [7].

US Army Corps of Engineers has produced Engineering Manual 1110-2-2104 for strength

design of reinforced concrete hydraulic structures in 30 June 1992 and reviewed in 20 August

2003. The manual represents a guidance for designing reinforced concrete hydraulic

structures by strength deign method. The manual provides the designer with design

procedures in sufficient details and examples of their application. The procedure is consistent

with ACI 318 guidance, except for load factor and reinforcement percentage. This manual has

an approach similar to that of ACI 350R-89 [8].

Artificial Neural Network Model for Flexural Design of Concrete Hydraulic Structures


2. ENGINEERING MANUAL 1110-2-2104 DESIGN PROCEDURE

For singly reinforced concrete flexural members subjected to combined flexure and

compressive axial load the ratio of tension reinforcement ρ is limited to a recommended value

of 0.25ρb, where ρb is the tension reinforcement ratio at balanced condition. The upper limit of

0.375ρb is permitted to avoid investigation of serviceability and economy, and maximum

permitted upper limit of 0.5ρb when excessive deflections are not predicted [8]. These limits of

reinforcement ratio will be taken in consideration to avoid further investigation for

serviceability requirements due to service load.

A step-by-step procedure has been detailed in Appendix D of the manual. Below the

summarized steps and equations of design, collected from the manual, are presented. The

design equations specified for rectangular flexural member subjected to pure bending or

bending moment combined with axial load. The required parameters and data are; concrete

compressive strength fć, steel yield strength fy, ultimate moment Mu, ultimate axial load Pu,

width of concrete rectangular section b, concrete cover c, and ratio of tensile reinforcement

ratio to balanced one ρ/ρb which is specified to above-mentioned values as recommended by

the manual in item (3-5) of maximum tension reinforcement.

Step 1: Assuming thickness h of the concrete section, taking in consideration minimum

thickness limited by the manual.

Step 2: Computing required nominal strength Mn, and Pn from the following equations:

n u

n u

( u h fc ⁄ )

Step 3: Calculating the effective depth d, factor β1, ratio kd, minimum effective depth that a

singly reinforced member may have and maintain steel ratio requirements dd, depth of stress

block at limiting value of balanced condition ad, and bending moment capacity at limiting

value of balanced condition MDS from the following equations:

d h c

fc

for f c a and for f c a

kd

(ρ

ρ )

c

c fy

Es

where c is the maximum concrete strain at the extreme compression fiber = 0.003

d √ n

fc kd (

kd

)

ad kdd

D fc ad (d

ad

) (d

h

) n

Step 4: For no axial load (Pu =0), d should be greater than dd, and for (Pu >0), MDS should be

greater than Mn, otherwise the thickness h of concrete section should be increased and

repeating steps from step 2.



Step 5:Calculating ratio of stress block depth to the effective depth ku, and the required area of

steel reinforcement As taking in consideration the minimum tension reinforcement ratio ρmin

equal to 0.0028.

ku √ n n (d h ⁄ )

fc d

s fc

ku d n

fy

Step 6: Checking that ϕPn is less than the lesser of 0.1bh fć and ϕPb. Otherwise, the thickness

h of concrete section should be increased and repeating steps from step 2 again, where;

k Es c

Es c fy

( fc k d sfy)

It is obvious that the design procedure needs assumption as a first step, checking for some

conditions, and an iteration processes to reach the optimum design for the thickness of the

concrete section, and then specifying the required area of steel reinforcement.

3. DEVELOPMENT OF NEURAL NETWORK MODEL

The aim of this research is to construct an artificial neural network mode to strength design of

reinforced-concrete hydraulic structures using EM 1110-2-2104. To build such network a set

of design examples should be prepared. These examples should have design parameters each

one has a range of values.

3.1. Creation of Design Cases

The design parameters taken into account were; ultimate moment Mu ranging from 150 kN.m

to 400 kN.m with 50 kN.m steps (6 cases), concrete compressive strength fć ranging from 20

MPa to 35 MPa with 5 MPa steps (4 cases), ultimate axial load Pu ranging from 0 to 450 kN

with 150 kN steps (4 cases), and ratio of tensile reinforcement ratio to balanced one ρ/ρb with

values of 0.25, 0.375, and 0.5 (3 cases). These values have been chosen to cover a wide range

of possible design cases. The total number of design examples are equal to 6*4*4*3=288

cases.

The width of the concrete structure has been taken equal to 1m (1000mm) as a unit strip,

the concrete cover c is constant and equal to 58mm, and the yield strength of steel

reinforcement is constant and equal to 420 MPa, because other steel grades are not

recommended by the EM 1110-2-2104 for the reasons mentioned in item (2-2. Quality) of the

manual [8]. For each set of input data, the minimum design thickness h of the concrete section

and area of steel reinforcement As have to be calculated.

An Excel sheets have been constructed to calculate the required h and As. The first sheet

was built to calculate the design parameters described-above in design procedure steps, see

Fig.1. The initial value of concrete section thickness was assumed to be 200mm. The iteration

processes have been done with aid of Microsoft Visual Basic for Applications (micro). The

incremental value of thickness h was 10mm for each iteration. For each new value of h,

checking the differences between d and dd or Mn and MDS have to be achieved, as mentioned

in step 4 of the design procedure. Final checking for the applied loads, if they within limits



specified in step 6, was done in the last column of the sheet, see Fig.1. A thorough review for

each design case has been achieved to make the final adjustments.

Figure 1 EM 1110-2-2104 Part of Excel Sheet of Design

Other sheets were constructed to separate pure input and output data without formulas and

to make randomization to them. Finally, the randomized data have been divided into 3 groups,

(Training data, validation data, and Prediction data). The total examples of design cases were

288 cases. Two hundred case were selected randomly for training samples, and fifty cases for

validation samples and the rest (38 case) were used as a prediction samples.

3.2. Artificial Neural Network software

Visual Gene Developer is one of the free software that contains artificial neural network

prediction package for general purposes. The software can be used for gene design,

optimization, or artificial neural network. Each package is able to work independently.

Artificial neural network package has software environment and tools which can be easily

used. The learning algorithm is a feed-forward neural network with a back-propagation. This

algorithm is used to train networks and it provide some different transfer functions [9].

3.3. Input and Output vectors

The input vector was carefully chosen for this model which was [Input1=fć, Input2=Mu,

Input3=Pu, Input4=ρ/ρb]. Consequently, the output vector for the neural network model was

[Output1=h, Output2=As]. Each vector has been normalized by dividing all values of a single

parameter by a number slightly larger than the maximum value of the parameter. Therefore,

all values of input and output vectors will range between 0 to 1. The normalization processes

are mandatory for the artificial neural network software.

3.4. Network topology and setting of training parameters

To set up the most suitable network configuration no specified method known yet [10], [11],

[12]. A trial and error processes have been used to provide fast training and the most reliable

predictions. After examining some network configurations, it has been observed that the

network with 10 neurons each in two hidden layers has the best behavior in training and

predicting. The behavior can be monitored by the regression analysis table and chart.

Therefore, a topology of (4-10-10-2) has been selected for this network model from a number

of examined configurations.



Also, the values and selections for the parameters of training-setting have been specified

using the method of try and error. As an example, when the training is stuck as the sum of

error is oscillated. In that case, learning rate should be reduced. Thus, the parameters of

training setting were; Learning rate equal to 0.0003, Momentum coefficient equal to 0.1,

Hyperbolic tangent selected to be the Transfer function, 1000000 as maximum training

cycles, and Target error of 0.00001. The initialization method of threshold and weight factor

was set to be random. The used Artificial Neural Network topology and all other settings are

depicted in Fig.2.

Figure 2 Used Artificial Neural Network configuration

3.5. Training and Validation Data of the Network

The training of this network has been completed using the Back-Propagation algorithm (BP).

Also, a validation process of the network has been carried out to assess the network for the

other set of data that are not used in training of the network.

Visual Gene Developer software has a separate window for regression analysis. The

regression coefficients (R2), slope, and y-intercept of output variables for training and

validation data were monitored with each learning cycle. With this window, the convergence

rate with each cycle of training can be traced. Figs. 3 shows the convergence level at 24,255

cycles of training with elapsed time of 1 minute and 54 seconds. The regression analysis

shows that the regression coefficients for training and validation data were above 95%. In

regression analysis window, Out1 and Out2 represent h and As, respectively.

Fig. 4 shows the data set of the network at 140,771 cycles of training, which was the last

training cycle. Actually, the program has been stopped at this point of training. The total

processing time was 11 minutes and 7 seconds. The regression coefficients for training and

validation data were all a ove % The training can e continued y pressing “continue

training” utton But no more advantages with the continuity in this stage because of the slow

rate of change of convergence.



Figure 3 Convergence rate by regression analysis at training cycle of 24255

Figure 4 Convergence rate by regression analysis at training cycle of 140771 (Last cycle)

After stopping the training and validation processes, the output data of validation were de-

normalized and saved. Figs.5 (a)-(b) represents a graph for the validation output data versus

the design data, for h and As respectively. The linear fitting results of Figs.5 (a)-(b) coincide

with the data shown in regression analysis window of last training cycle. The two graphs

show a high level of confidence of trained network.



3.6. Prediction Data of the Network

As a prediction step, the neural network has been tested with 38 randomly selected samples

that were not used in training and validation process. Here, the trained network model should

capable of prediction of the depth of the concrete section h, and the required area of steel

reinforcement As. To investigate the confidence level in the relation between the actual

designed value of h and As and the predicted ones, two charts have been constructed for this

purpose as illustrated in Figs. 6(a)-(b). The results of the linear fit, for the two charts, were

presented from which the high values of coefficients of regression can be seen. So, it can be

said that the trained network gave excellent prediction values for the design outputs.

a h As

Figure 5 Regression analysis for output validation data versus design data

a h As

Figure 6 Regression analysis of prediction versus actual design outputs



The relationship between the designed depth of concrete section h and the required area of

steel reinforcement As for that section is not linear, and this can be observed from the actual

design outputs. To see this nonlinearity and how much the actual design outputs coincide with

the validated and predicted ones, a sample of twenty cases were randomly selected and then

represented in Figs. 7(a)-(b). It is obvious that the values, predicted by the trained network

model, of design outputs coincide satisfactorily with results of actual design cases.

a Validation output rediction output

Figure 7 Sample of Prediction and Validation output with actual output of design

4. CONCLUSIONS

Hydraulic concrete structures need special requirements in strength design and serviceability.

Engineering Manual 1110-2-2104 is an important manual and exhibits a clear and sequential

procedure for the strength design of the hydraulic concrete structures. It has a similarity in

design approach with ACI 350R-89. It is not difficult to program such a design procedure, but

the design outputs can’t e accepted without designer judgment

The artificial neural network is a new computer technology that has gained a wide range

of use in civil engineering fields, especially for structural analysis and design. In this paper,

an artificial neural network model has been developed to strength design of hydraulic

reinforced-concrete structures with the requirements of Engineering Manual 1110-2-2104. In

this manual, the design steps should start with an assumption of a thickness of the concrete

section, and then an iteration process has to be used to find the optimal thickness of the

concrete section of the hydraulic structure. Consequently, the required area of steel

reinforcement can be calculated, as part of the strength requirements. The designer should do

a review of the output design data and may make a redesign to some parameters according to

his judgment from practice.

In literature and as having observed in this work, no specific method to choose the number

of hidden layers, learning rate, momentum coefficient, transfer function, initialization method

of the threshold, and initialization method of weight factor other than trial and error method.

The developed neural network has been trained with 200 samples, that cover a wide range

of design parameters, in 140771 training cycle in less than 12 minutes. With excellent

accuracy, the developed neural network has shown the ability to predict the optimal thickness



of concrete section and the corresponding area of steel reinforcement. Thus, it could be

concluded that the developed neural network model can be a safe and powerful alternative for

structural design of reinforced-concrete hydraulic structures with requirements of EM 1110-2-

2104.

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Documents

ARTIFICIAL NEURAL NETWORK MODEL FOR …€¦ · with ACI 318 guidance, except for load factor and reinforcement percentage. This manual has an approach similar to that of ACI 350R-89