Applications of Backpropagation and Conjugate Gradient Neural Networks in Structural Engineering


  • 1A Department of Civil Engineering, Amity School of Engineering and Technology, Amity University, Noida, Uttar Pradesh 201301, India
  • 2Amity Institute of Molecular Medicine and Stem Cell Research,

Amity University, Noida, Uttar Pradesh 201301, India

department of Civil Engineering, School of Engineering and Technology, Kaziranga University, Jorhat, Assam.

'Corresponding author. E-mail: This email address is being protected from spam bots, you need Javascript enabled to view it


This chapter briefly describes the backpropagation and conjugate networks in structural engineering. The fu st portion of the section deals with the basic framework of backpropagation and conjugate gradient network. The second portion presents the literature review of research works associated with the application of neural networks hi structural engineering. The third section deals with the pros and cons of neural networks. The final part deals with the identification of the problems associated with the neural networks and emphasis on possible solutions to overcome the issues. Finally, conclusions derived from the research study are provided.


Artificial intelligence is a system specifically designed to exhibit human-like behavior in decision making for solving complex problems. The decisions made by artificial intelligence are quick, efficient, and straightforward. Artificial intelligence is an interdisciplinary subject, which has inherent advantages over traditional modeling and statistical methods. The developed artificial neural networks (ANNs) are useful in the collection, analysis, and processing of data on a large scale. After that, the difference between actual and target values is computed to propose an activation function.

Artificial intelligence combines different fields such as computer science, neuropsychology, psychology, and information technology. The ANN is often used in the field of civil engineering due to its efficiency and lesser time consumption in different aspects such as modeling, design, analysis, and optimization, which are veiy complex, time-consuming, and prone to error. The field of structural engineering employs techniques of data collection, especially for predicting the strength of concrete. The ANN can be trained based on the experimental dataset for prediction of desired output parameters.

The first section deals with a brief introduction to the ANN, along with a detailed description of its elements. The final portion of this section presents a brief discussion on the backpropagation (BP) network. The second section offers a comprehensive literature review spanning over three decades about the implementation of the ANN in structural engineering problems. Finally, the last portion elucidates the shortcomings of different types of ANNs and provides recommendations to overcome these shortcomings.


The biological networks are quite complex and veiy difficult to explain. A human brain is comprised of hundreds of biological neurons, and it is impossible to represent these neurons using a mathematical model. However, a simple neural network model resembling the functioning of the actual brain can represent complex mathematical problems and can yield accurate results. The artificial neuron receives the input signals from the brain. After that, output data and every information or peripheral data of this neuron are generated, which can be used as the input data for further iterations. The activation function processes the data from surroundings received by the input layer in the hidden layers. The output layer receives these processed data, which forms a solution of the problem. The input layer may comprise of n number of neurons, but every neuron receives one input data only.


The weight coefficients are integral elements of the neural network, and weight coefficient is assigned to each neuron depending on its sensitivity to the output parameter. The input signal can be obtained by multiplying the input parameter with its weight coefficient. The weights are described as wl, w2, and w3 and input data are marked as kl, k2, and k3. Therefore, equivalent weights can be calculated as wlkl + w2k2 + w3k3. The zero weight coefficients show that there is no relationship between input and output data.


The field of structural engineering often employs BP networks and BP algorithm to achieve accuracy. BP networks consist of several hidden layers with different weights. The technique of supervised learning is used in BP networks to calculate the discrepancy between expected and actual outputs.

The functioning of the BP network is as follows:

  • • Providing the training data to a given sample of ANN.
  • • The network output is compared with the expected output.
  • • Estimation of the network error.
  • • The adjustment of weights to reduce the error.

The multilayer perception is used in conjunction with the BP network. The relationship between weights of individual elements should be accurately determined for the training of multilayer perception. The calculated error depends on the combination of weight coefficients. The main aim of training a perception is to determine the minimum failure for any possible combination. The gradient descent technique can be adopted to achieve this purpose.

The BP algorithm refers to a training algorithm of feedforward neural networks or multilayer perceptions. The network weights are initially set to a random value or an absolute minimum of the error surface. The BP algorithm calculates the gradient of the error surface, and changes in weights are determined for the steepest slope. The weights will converge to minima for small error surface. The BP algorithm is summarized as follows.

  • • Initialize weights of the network.
  • • The first input vector is derived from the dataset used for training.
  • • The output is obtained by propagating the input vector through the network.
  • • The desired output is compared against actual output to estimate error.
  • • The error signals are transmitted in the reverse network direction.
  • • To weights are adjusted to minimize the overall error.
  • • The repetition of steps is done to reduce the overall error to a permissible limit.

The training can be subclassified into two different types.

  • Online training: In this training, the corresponding weights of the network are changed after the presentation of each pattern.
  • Batch training: In this type of training, the error weights are updated at each iteration.

The training iterations are repeated number of tunes till a satisfactory performance is obtained for a particular problem. The training should terminate when the performance of the individual test data reaches a maximum value. However, it may not result in error minimization necessarily. The counter-propagation algorithm is associated with two parameters that can be adjusted significantly, learning rate and the learning speed, which determines the size of the step adopted during the learning process of the descent of the iterative gradient. A significant value leads to the generation of the network error, but if this step is small and time-consuming

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