Prediction of efficiency of the filled-trench in layered soil through artificial neural network

Mehran Naghizadeh (Department of BIM and Digitalization, ICG Ingenieure GmbH, Dusseldorf, Germany)

Machine Learning and Data Science in Geotechnics

ISSN: 3029-0414

Article publication date: 16 January 2025

162

Abstract

Purpose

Vibrations are transmitted through the ground surface to building foundations, causing distress to structures and their occupants. Installing a wave barrier between the vibration source and buildings is a suitable method to mitigate ground vibration. However, the complexity arises in selecting the right trench design due to various influencing parameters. This paper aims to present a novel method to predict the efficiency of a geofoam-filled trench in mitigating ground vibrations within layered soil using an artificial neural network (ANN).

Design/methodology/approach

This study extends a parametric investigation conducted by Naghizadeh (Naghizadehrokni, 2022), where they identified key parameters influencing the trench’s efficiency. A multilayered feedforward neural network using the back-propagation training method was developed for the prediction task. The ANN model comprises input variables, including location, depth, width of the trench, thickness and shear wave velocity of the first layer as well as geofoam type. With a total of 18,750 data points from the parametric study, the network was trained and validated.

Findings

The accuracy of the trained model was evaluated using separate training, validation and testing data sets. Different neural network configurations were evaluated by comparing the coefficient of determination (

 R2) and mean square error. The optimal architecture was used to predict previous results, revealing the accuracy and effectiveness of the ANN approach. Furthermore, the ANN’s predictive performance was compared with finite element model results. The results indicate a high level of accuracy, with a regression R-value of 0.98 for the regression analysis of the entire data set.

Originality/value

After studying previous research, the author identified a need for a prediction model to evaluate the efficiency of geofoam-filled trenches. To meet this requirement, an ANN model was developed using data collected from Naghizadeh (Naghizadehrokni, 2022) to precisely predict the performance of these trenches.

Keywords

Citation

Naghizadeh, M. (2025), "Prediction of efficiency of the filled-trench in layered soil through artificial neural network", Machine Learning and Data Science in Geotechnics, Vol. 1 No. 1, pp. 35-45. https://doi.org/10.1108/MLAG-08-2024-0006

Publisher

:

Emerald Publishing Limited

Copyright © 2024, Mehran Naghizadeh.

License

Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode


1. Introduction

The number of people who are interested in living in the big towns is increasing. This growth in population results in the construction of more buildings and transport networks in and around the city. Therefore, residents will have more vibration problems from the vibration sources like passing trains, machine foundation, traffic and other constructional activities. The body and Rayleigh waves produced from these sources result in ground-born vibration. The vibration is transmitted through the ground surface to the foundation of the building and creates distress to the buildings and their inhabitants (Naghizadehrokni, 2022; Adam and Von Estorff, 2005).

The mitigation of structures vibration can be accomplished by providing more damping elements in the transmission path of incident waves by means of installation devices like an isolation trench. A wave barrier creates a finite material discontinuity for incoming waves by intercepting, scattering, diffracting and refracting wave propagation in soil, which can decrease the vibration amplitude beyond the obstacle (Haupt, 1997; Woods, 1968).

Different approaches, including experimental and numerical methods, have been carried out to solve the problem of vibration isolation by trench. Since experimental tests are expensive and the parameters to be assessed are fixed, a numerical model is an effective alternative method for assessing governing parameters in vibration isolation.

A series of field tests have been conducted by Alzawi and El Naggar (2011) and Ulgen and Toygar (2015) for finding the screening effectiveness of geofoam-filled obstacles as a soft barrier. The soil properties consisted of silty clay, clayey silt and sandy silt (Alzawi and El Naggar, 2011) and clayey sand resting on very stiff clay (Ulgen and Toygar, 2015). They used a harmonic load with the frequencies in the range of 30–70 Hz. The results showed that the vibration amplitude can be reduced up to 68% by installing a geofoam-filled barrier. Moreover, they have found that the performance of a geofoam-filled trench is dependent on the normalized depth. The optimum depths are suggested as 0.6λr and 1λr for near-field and far-field systems, respectively. In addition, it was concluded that the screening efficiency of the geofoam-filled trenches decreases with increasing the distance between the vibration source and trench.

Naghizadehrokni et al. conducted some experimental tests to assess the impact of a geofoam-filled barrier on mitigating incoming waves. In addition, both 2D and 3D numerical models were developed and validated using field test results. These models aimed to evaluate the screening effectiveness of geofoam-filled trenches in both near-field and far-field scenarios. The investigation focused on understanding how the geometric and dimensional characteristics of the trench influenced its performance. A comparative analysis was conducted under a harmonic load with a frequency of 50 Hz. The results revealed that achieving an effective level of efficiency in near-field isolation required a trench depth of approximately 1λr and a width of about 0.2λr for all three systems. However, in the far-field scheme, depth played a negligible role for single and double-wall barriers, while it significantly influenced the effectiveness of the triangle wall system (Naghizadehrokni et al., 2020; Naghizadeh et al., 2022).

An artificial neural network (ANN) is a computational model inspired by the structure and functions of biological neural networks in the human brain. It functions as an artificial counterpart to the human nervous system, receiving, processing and transmitting information (Rezania, 2008; Naghizadehrokni and Ziegler, 2020). In recent years, ANNs have found extensive application in various domains of geotechnical engineering, showing promising outcomes (Motlagh and Naghizadehrokni, 2022).

Recent research by Es-haghi et al. (2023) applied machine learning (ML) to estimate the true air-entry value of soil using grain size distribution curves. By leveraging a large data set and advanced algorithms, their model significantly improved prediction accuracy compared to traditional methods. This approach not only streamlined complex geotechnical analyses but also demonstrated the potential of ML in predicting critical soil parameters, which could be beneficial for evaluating geofoam-filled trench efficiency.

Jayawardana et al. (2019) investigate the potential of artificial neural networks (ANN) as an intelligent and effective tool for predicting the efficiency of geofoam-filled trenches in mitigating ground vibrations. Their study is based on a data set generated from a 2D finite element parametric study, considering frequencies from 8 to 50 Hz and soil shear wave velocities between 100 and 300 m/s. Their study explores the impact of trench geometry, including depth, width and location. However, their model was limited to specific frequencies and soil conditions, which may not generalize well to other trench configurations or soil types. Using a multilayer feedforward neural network with a backpropagation algorithm and two hidden layers, their model achieves impressive results. The proposed method extends this work by incorporating a broader range of soil layers and trench parameters, ensuring better generalization.

Sreekantan et al. (2024) conducted a study using ANN and extreme gradient boosting models to evaluate and predict key geofoam design parameters. Their research focused on parametric evaluation and highlighted the use of ML to improve design predictions. Despite the high accuracy achieved, the study primarily focuses on static design parameters and does not address dynamic vibration scenarios. The results demonstrated high prediction accuracy for critical geofoam parameters, emphasizing the applicability of ANN in optimizing geofoam designs for geotechnical purposes. In contrast, the current study evaluates dynamic trench performance under real-world vibration conditions, making it more applicable for practical vibration mitigation design.

Furthermore, the ANN model developed by Fang et al. (2019) was used to predict soil-ground vibrations caused by moving trains. The trained data was the result of the field and numerical simulation. The speed of the train in this study was 67 km/h with the train axel weight of 160 KN. The elastic modulus of the soil one and two were 17.7 and 16.9 MPa, respectively, with the density of 1.8 and 2.0 gr/cm3 for the first and second layer. The outcomes indicate that the predictive approach maintains the maximum error below 6.41% and the average error below 2.29% when used for estimating acceleration vibration levels.

Hung and Ni (2007) focused on the application of multiple neural networks to estimate the screening effect of surface waves by in-filled trenches. For data collection, a boundary element method program was developed to predict trench efficiency. Their study involved a harmonic load with a vertical load amplitude of 1 KN/m2 and a vibration frequency of 50 Hz. The soil under investigation was characterized as medium to dense sand with a Rayleigh wave velocity of 250 m/s, unit weight of 17.5 kN/m3 and a Poisson’s ratio of 0.4. They used three ANN, including a backpropagation network, a generalized regression neural network (GRNN) and a radial base function network, to evaluate the performance of the filled trenches. The findings revealed that the GRNN displayed superior accuracy in assessing the efficacy of screening trenches when compared to other models.

After studying previous research, the author identified a need for a prediction model to evaluate the efficiency of geofoam-filled trenches. To meet this requirement, an ANN model was developed using data collected from Naghizadehrokni (2022) and Naghizadeh et al. (2022) to precisely predict the performance of these trenches.

2. Artificial neural network

Since modern computers are becoming more powerful, researchers try to use machines to perform calculations of complicated models. Artificial intelligence (AI) is known as the process of simulating human intelligence in machines for thinking like humans and mimic their actions (Naghizadehrokni, 2022). AI can interpret and learn external data and use those learnings to reach specific aims through flexible adaptation. AI encompasses various techniques, including ML, where algorithms learn from data to achieve specific objectives through adaptive learning. Deep learning is a subset of ML that has a network for learning from data. ML is a technique to figure out a model from data. After developing the model, it will be applied to real field data (Oliveira et al., 2022).

The ML technique is categorized into three different groups based on the training model, including (Reed and Marks, 1999):

  1. supervised learning

  2. unsupervised learning

  3. reinforcement learning

There is input and ground truth for each training data set in supervised learning. The main duty of the supervised learning technique is to produce a correct output from the input using training data. Conversely, the unsupervised learning technique contains inputs without ground truth. Classification and regression are two types of application of the supervised learning technique. Classification is the problem of identifying the classes to which the data belong. In contrast, regression predicts value. Vibration isolation problem is categorized as a regression problem (Shahin et al., 2001).

ML models serve diverse purposes, such as ANN for classification and regression, convolutional neural networks for image analysis and recurrent neural networks for time series data. ANN, inspired by human neural networks, acts as an artificial nervous system to process information (Motlagh and Naghizadehrokni, 2022).

In this context, this study focuses on applying ANN to predict the vibration mitigation performance of geofoam-filled trenches, which refers to their ability to reduce the amplitude of ground vibrations. The efficiency is quantified by comparing vibration levels before and after trench installation, expressed as a percentage reduction in vibration intensity. This metric captures how effectively the geofoam-filled trenches act as barriers to attenuate vibrations and protect nearby structures.

An ANN is a computational model that is inspired by the structure and functions of biological neural networks in human brains. ANN acts like an artificial human nervous system for receiving, training and transmitting information. ANN is the most exciting and powerful branch of ML, in which a computer model learns to perform tasks directly from data.

2.1 Neurons

The principal idea behind a neural network is based on imitating the structure of neurons and the cells in the brain for performing some tasks like recognizing patterns and making decisions.

Figure 1 shows a biological neuron, which is the fundamental unit of the brain and the nervous system. The cells responsible for receiving input from the external world via dendrites process it through a function and give the output through axons. A neuron does not have any storage for saving data; it just transmits signals from one neuron to another (Gurney, 1997).

An artificial neuron is a mathematical function based on biological neurons. Table 1 represents the analogy between the human brain and ANN.

A perceptron is a model based on biological neurons for the supervised learning of binary classifiers. This model enables neurons to learn and process data in a training set once. Single and multilayer are two types of perceptron. A single perceptron with two layers, including input and output layers, is presented in Figure 2.

Nodes X1, X2 and X3, which are called features, are the input, and w1, w2 and wn are the weights for the corresponding features. Weights show the strength of the features. Each feature is multiplied by a connection weight and pulsed through a summation function. Then a bias, which is a constant value, is added to the weighted sum for shifting the result of an activation function.

The summation is passed through the activation function. An activation function introduces nonlinearity to the neural network through converting the weighted sum of features into the output signal.

The activation function, which is attached to each neuron in the network, determines the output of a neural network. In addition, it helps to normalize the output of each neuron to a range of [0,1] or [−1,1]. A neural network without an activation function is a linear regression model. There are two different kinds of activation functions including linear and nonlinear functions. The nonlinear activation functions are the most applicable in neural networks. The most popular nonlinear activation functions include:

  • Sigmoid activation function;

  • Tanh or hyperbolic tangent activation function; and

  • ReLU (Rectified Linear Unit) activation function

A sigmoid function is an exponential function having a characteristic “S” shape curve, and it takes real value as input, and the output value is in the range of [0,1]. It was chosen for this study because the output being predicted (efficiency) is a percentage, and the Sigmoid function is well-suited for such bounded outputs. In addition, Sigmoid provides smooth gradient transitions that are effective in regression tasks involving small data sets and nonlinear relationships.

Tanh is an activation function like sigmoid in terms of shape, but the range of output of this function is [−1,1]. Therefore, the inputs to the next layers will not always be the same sign. The applicability of the functions is more for classification between two classes. Both Tanh and sigmoid functions are used in feedforwards neural networks.

ReLu, which stands for Rectified Linear Units, is another type of nonlinear activation function, which stands for Rectified Linear Units. Mathematically, this function R(z) can be defined using max function over the set of 0 and the input z, R(z) = max(0, z). Figure 3 represents the pictures of all three activation functions.

In the last step, information will be transferred to output. If the predicted output with ANN is equal to actual output, which is called label, the algorithm will be finished; otherwise, there will be an error and it returns to back to neurons for adjusting the weights and bias, and this process will continue until the error is minimized.

3. Feedforward networks

Feedforward or multilayered perceptrons are an ANN, which combines many layers of perceptrons. A feedforward network leads to information only in a forward direction from an input layer through a hidden layer and finally to an output layer. In this network, all nodes are fully connected, and the weights are recognized into layers that feed into each other.

Figure 4 represents a multilayered feedforward neural network in which the first and the last layers are called input and output, respectively. The layers between the input and output are called hidden layers. The number of hidden layers is adjustable based on the complexity of a problem. The application of hidden neurons is to intervene between input and output data. In a feedforward neuron network, every neuron in each layer is fully connected to every other neuron in the next forward layer.

Performing a forward-pass of a network gives us the predicted value. Thus, the “goodness” of the predicted value should be evaluated by comparing the predicted and actual values. This is the duty of a cost function. Different cost functions are including mean square error (MSE), root mean square error (RMSE) and correlation (corr), which are used to measure the error between the predicted value with a feedforward neural network and the actual value. MSE is the average squared difference between the predicted and actual value. RMSE is the standard deviation of the predicted errors, and it shows how data are concentrated around the line of the best fit. Corr represents how independent variables are related to each other.

The weights W and biases b are the most important factors in converting an input to impact the output. Therefore, training a neural network means finding the proper value for weights and biases. Generally, the process of adjusting the weights and biases between input data and hidden neurons for minimizing the cost function is called training a neural network.

A neural network can be considered shallow, which processes the inputs, and an output layer, which presents the result of the model. On the other hand, a deep neural network usually has between 2 and 8 hidden layers of neurons.

3.1 Backpropagation

A backpropagation algorithm is the most popular learning algorithm in training a feedforward neural network for a supervised problem. In this procedure, the measured error through a cost function is propagated back to all weights and biases to decrease error. In summary, backpropagation is adjusting the weights and biases of all connections in a network repeatedly to minimize errors. An error describes how a set of parameters in a network fits a data set.

There are several algorithms for optimizing errors, including:

  • Gradient descent

  • Newton method

  • Gauss–Newton method

  • Levenberg–Marquardt algorithm

The gradient descent method is a first-order iterative optimization technique to adjust the weights and biases in the backpropagation phase to reach the best output. To find an appropriate value for weights and biases, a derivative of the cost function should be taken with respect to the weights and biases. A gradient descent algorithm works as follows:

  1. Initialize the weights randomly ∼ N(0, σ2)

  2. Loop until convergence:

  3. Returning weights

where η is the learning rate, which is one of the most important parameters in the gradient descent technique. The learning rate determines the speed of a neural network training process. A small value of learning rate leads to an optimal set of weights, but it may take a long time. On the other hand, a large learning rate results in training the model faster; we may face the risk of missing the optimal weight. Step decay is a proper method for finding the optimal learning rate in which the learning rate is reduced by some percentages after a set of training epochs. Newton’s method is a second-order algorithm, in which the Hessian matrix is used instead of the Jacobian Matrix. The goal of this algorithm is to find better training directions through using the second derivatives of an error function. The conjugate gradient algorithm can be regarded as a method between Newton’s and gradient descent procedures. The search process in this method is performed along a conjugate direction, which can result in faster convergence than with gradient descent directions.

The Gauss–Newton method, which is used to solve nonlinear least square problems, is a developed model of the Newton method. The assumption in this method is that the objective function in the parameters near the optimal solution is quadratic. The Gauss–Newton method usually converges with a medium-sized problem much faster than the gradient descent method.

The Levenberg–Marquardt algorithm is an iterative technique that is commonly used to solve nonlinear least-squares problems. The LM method can be defined either as a combination of the gradient descent optimization method when the parameters are far from their optimal values or the Gauss–Newton optimization procedures when the parameters are close to their optimal value.

3.2 Data preparation

The size of a database plays a significant role in training a neural network. Large database results in a more accurate model but requires a lot of computational time. On the other hand, too small database results in a less accurate model and requires less computational time. Therefore, the database should be big enough to result in an accurate model and optimal computational time, too. When the input data in the database has different ranges, the database needs to be normalized. Normalization is applied to a neural network to produce a set of data values within the same magnitude. When the features are different in terms of magnitude, the fluctuations of some parameters with bigger ranges may decrease the influence of the parameters with smaller ranges. Nevertheless, the features with smaller ranges may be more important in predicting the desired output. Therefore, all the data should be normalized to have the same range to ignore the influence of different ranges in ANN. All features are normalized to be in the range of [−1,1] through equation (1).

(1) (Xj)n=2(XjminXjmaxXjminXj)1
where Xj is the feature, (Xj)n is the scaled input feature, minXj and maxXj are the lower and upper limits of input features, respectively.

3.3 Implementing feedforward neural network

A multilayered feedforward neural network with the back-propagation training method is developed to predict the efficiency of the geofoam-filled trench. The feedforward network is used for supervised learning tasks with the results of the parametric study in Naghizadehrokni (2022) and Naghizadeh et al. (2022). The main goal of the developed ANN in this study is to approximate a regression function to predict the efficiency of the geofoam-filled trench.

The architecture of the network includes input, output and two hidden layers. The optimum number of neurons in each hidden layer is selected based on trial and error. The structure of the network represents the full connection of any nodes in one layer to all other nodes in the next layer, and the information only moves forward into the network, from the input to the hidden layers and finally to the output node. The input layer receives the features, which govern the parameters in the vibration isolation topic, and the output is corresponded to predict the efficiency of the barrier based on the input layer.

The database includes 18,750 data points from parametric study because of changing key parameters in the vibration isolation topic by Naghizadehrokni (2022) and Naghizadeh et al. (2022). The efficiency of the geofoam-filled barrier is presented as a percentage, which is the average of the ratio of vertical velocity of the soil after and before installing the trench, respectively, through equation (2).

(2) Efficiency=(1A¯r)*100
The data set used in this study covers six key governing factors that influence the efficiency of geofoam-filled trenches. These factors include trench location (X), which determines the placement of the trench relative to the vibration source, and the depth (D) and width (W) of the trench, which are critical dimensions impacting vibration isolation. In addition, the thickness of the first soil layer (L) and shear wave velocity (Vs) of the soil define the geotechnical properties, while the geofoam type (EPS12 to EPS29) represents variations in material used for vibration damping. This comprehensive data set ensures that a wide range of trench configurations and soil conditions are covered. Table 2 presents the governing factors and the ranges.

There is a full connection between all neurons, and each connection between two nodes has a weight, which is assigned to the connection randomly. The weight shows the strength of the connection between two nodes. When the network receives a value for one feature in the input layer, this value is passed to the next node via a connection, and the value will be multiplied by the weight assigned to that connection. Thereafter, a weighted sum for all incoming connections is computed, and this sum, after adding the value of bias, is passed to an activation function. The process is represented in equation (3):

(3) Y=Activation((weight*inputs)+bias)
The activation function transfers the inputs to their corresponding output, which is between lower and upper limits. Since the vibration isolation topic is a nonlinear problem, sigmoid function, which is a nonlinear activation function, is used for the developed ANN.

Backpropagation algorithm is one of the best supervised learning algorithms for a multilayer feedforward neural network. The backpropagation with Levenberg–Marquardt algorithm, which is explained in 3.1, is selected to update the weights and biases values of the developed ANN.

The learning error is calculated through equation (4):

(4) Error=12(tiσi)2
where ti is the calculated efficiency of the trench through FEM and σi is the predicted value by a feedforward neural network. In the whole process of training the neural network, the error between predicted and actual value of the efficiency of the trench is measured and used to update the weights and biases of all neurons through the LM algorithm. T

The architecture of the developed ANN is presented in Figure 5. After testing various configurations, the optimal model was selected based on minimizing the MSE and preventing underfitting or overfitting. The final architecture includes two hidden layers with 10 and 15 neurons, respectively. The input layer consists of six variables (location, depth, width, first-layer thickness, geofoam type and shear wave velocity), while the output layer predicts the efficiency of the geofoam-filled barrier as a percentage. Sigmoid activation functions were chosen due to their smooth output transitions, which suit the percentage-based output. The Levenberg–Marquardt algorithm was applied for efficient weight updating, known for its rapid convergence on smaller data sets, making it an ideal choice for this study.

3.4 Results

The developed network is used to predict the efficiency of the geofoam-filled trench using six input variables. Approximately 13,000 data are used to train the network, and the rest of data are used to test the model. The magnitude of the gradient, the number of validation checks and epochs are used to terminate the training. The values for these criteria are selected as 1e- 7, −6 and 1,000, respectively. The number of validation checks shows the number of successive epochs, in which validation performance fails continuously for more than six epochs. The developed network is terminated by reaching the maximum number of validation checks. The performance of the network in training, validation and test data sets is presented in Figure 6. The best validation performance occurs at epoch 60 and the training continued for more than 6 iterations before the training stopped. The results show that the training, validation and test curves decay in a similar way. Since there is no unexpected increase in the result of the test curve, it can be concluded that over-fitting does not occur in the network.

Creating a regression plot, which shows the relationship between the outputs of the network and the target, is another procedure for validating the model. The extracted outputs and targets of all the data are plotted in Figure 7, and the results represent a proper fit. The figure includes a dashed line, which represents the perfect result (output=target) and a solid line, which is the best-fit linear regression line between the output and the target. The regression R-value = 0.98 for a total response based on the whole data set indicates an acceptable performance for the developed network. Most of the points are located on the fitted line, and some points are located under and above the fitted line. The computed R-value shows the capability of the network to give a reasonable prediction of the efficiency with a success rate of 98.1%. In engineering contexts, this accuracy can provide confidence in using the ANN model for predicting trench efficiency, reducing the need for time-consuming simulations and facilitating faster decision-making in design and implementation.

To evaluate the prediction capability of the developed network, another linear regression analysis is conducted on the network for three subsets, including training, validation and testing data, and the results are presented in Figure 8. The corresponding coefficient of determination (R2) for all training, validation and data testing, which are 0.988, 0.977 and 0.972, respectively, demonstrate acceptable agreement between predicted and actual values of the efficiency of the trench.

Finally, the computed coefficients for assessing the performance of the network in training, validating and testing data are presented in Table 3. The values of MSE and correlation coefficients for all the data represent that the model predicts efficiency well.

While the model performs well on the data set used for training and testing, its generalization capability should be evaluated across a broader range of geological conditions and trench configurations not included in the current training data. Future studies should focus on testing the model’s performance in diverse soil profiles and variable trench configurations to ensure robustness in real-world applications.

However, the proposed method has limitations. The model may be prone to overfitting, especially with complex data sets, despite measures taken to avoid it. The ANN’s performance heavily depends on the quality and diversity of the training data. In addition, while the ANN provides efficient predictions after training, the training process itself can be computationally intensive, particularly when dealing with larger data sets.

3.5 Validating artificial neural network model

To demonstrate the capability of the developed network for predicting the efficiency of the geofoam-filled trench, 100 new data with completely new parameters of the trench, which are different from the training and test data for the ANN, are analyzed through the finite element model (Plaxis), and the results are compared to the predicted value by the trained ANN model. The R-value coefficient is used to compare the predicted and the real value of the efficiency. Figure 9 represents the calculated R-value for the validation data, which is 0.86, and this value indicates an acceptable performance of the ANN model.

Figure 10 shows the predicted and real value of the efficiency with different parameters of the trench. The result represents that the predicted value by the ANN model follows almost the same pattern as the real value. In addition, the MSE and RMSE coefficients are calculated through measuring the value of error.

The comparison of the results shows acceptable agreement between the predicted and real value of the efficiency, and it shows that the developed ANN model can successfully predict the efficiency of the geofoam-filled barrier in a layered soil based on the new parameters.

4. Conclusions

In this study, a multilayered feed-forward neural network with back-propagation training model has been developed using the results of the parametric study in Naghizadehrokni (2022) and Naghizadeh et al. (2022) to estimate the efficiency of the geofoam-field barriers. Based on the results, the following conclusions can be drawn:

  • The training of the artificial neural network showed a high capability to predict the efficiency of the geofoam-filled trench. The regression R-value = 0.98 for a total response based on the whole data set indicates an excellent performance for the developed network. The computed R-value shows the capability of the network in providing a reasonable prediction of the efficiency with a success rate of 98.1%;

  • The developed model is also validated with 100 new data with completely new parameters, which were analyzed through the finite element model, and the results showed an accuracy of 86% for predicting new data, which is an acceptable performance; and

  • The developed models can be used as a preliminary design tool to predict the efficiency of a trench based on the existing dimensions without doing any calculations.

The ANN model can be integrated into engineering workflows to enhance design efficiency, though further validation across a broader range of soil profiles and configurations is recommended for more general applicability.

Figures

A biological neuron

Figure 1

A biological neuron

A single perceptron

Figure 2

A single perceptron

Activation functions in artificial neural networks

Figure 3

Activation functions in artificial neural networks

A multilayered feedforward neural network

Figure 4

A multilayered feedforward neural network

The architecture of developed ANN

Figure 5

The architecture of developed ANN

Performance of the network for training, validation and test data sets

Figure 6

Performance of the network for training, validation and test data sets

Extracted outputs and targets of all the data

Figure 7

Extracted outputs and targets of all the data

Results of subsets including training, validation and testing data

Figure 8

Results of subsets including training, validation and testing data

Calculated R-value for the validation data

Figure 9

Calculated R-value for the validation data

Predicted and real value of the efficiency of geofoam-filled trench

Figure 10

Predicted and real value of the efficiency of geofoam-filled trench

Analogy between the human brain and artificial neural network

Biological neuron Artificial neuron
Cell Node
Dendrites Input
Synapse Weights
Axon Output

Source: Author’s elaboration

Governing factors and the ranges in ANN

Feature Min Max
Location (X) 3 (m) 15 (m)
Depth (D) 2 (m) 7 (m)
Width (W) 0.3 (m) 1.5 (m)
Thickness of first layer (L) 2 (m) 10 (m)
Geofoam type (EPS) EPS12 EPS29
Shear wave velocity (Vs) 200 (m/s) 400 (m/s)

Source: Author’s elaboration

Performance of the network for training, validating and test data

Data set R-square Correlation coefficient MSE RMSE
Training test 0.96 0.98 14.47 3.8
Testing test 0.95 0.97 16.61 4.076

Source: Author’s elaboration

References

Adam, M. and Von Estorff, O. (2005), “Reduction of train-induced building vibrations by using open and filled trenches”, Computers and Structures, Vol. 83 No. 1, pp. 11-24.

Alzawi, A. and El Naggar, M.H. (2011), “Full scale experimental study on vibration scattering using open and in-filled (GeoFoam) wave barriers”, Soil Dynamics and Earthquake Engineering, Vol. 31 No. 3, pp. 306-317.

Es-Haghi, M.S., Rezania, M. and Bagheri, M. (2023), “Machine learning-based estimation of soil’s true air-entry value from GSD curves”, Gondwana Research, Vol. 123, pp. 280-292.

Fang, L., Yao, J. and Xia, H. (2019), “Prediction on soil-ground vibration induced by high-speed moving train based on artificial neural network model”, Advances in Mechanical Engineering, Vol. 11 No. 5, p. 1687814019847290.

Gurney, K. (1997), An Introduction to Neural Networks. Book, CRC press, University of Sheffield.

Haupt, W.A. (1997), “Wave propagation in the ground and isolation measures”, International Conferences on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, Vol. 2, pp. 985-1016.

Hung, C.C. and Ni, S.H. (2007), “Using multiple neural networks to estimate the screening effect of surface waves by in-filled trenches”, Computers and Geotechnics, Vol. 34 No. 5, pp. 397-409.

Jayawardana, P., Thambiratnam, D.P., Perera, N., Chan, T. and De Silva, G.S. (2019), “Use of artificial neural network to evaluate the vibration mitigation performance of geofoam-filled trenches”, Soils and Foundations, Vol. 59 No. 4, pp. 874-887.

Motlagh, S.A.T. and Naghizadehrokni, M. (2022), “An extended multi-model regression approach for compressive strength prediction and optimization of a concrete mixture”, Construction and Building Materials, Vol. 327, pp. 126828.

Naghizadeh, M., Ziegler, M. and Fuentes, R. (2022), “Vibration screening in layered soil by geofoam-filled barrier”, 3rd International Conference on Natural Hazards Infrastructure.

Naghizadehrokni, M. (2022), “Optimization and prediction of a geofoam-filled trench in homogeneous and layered soil”, PhD thesis, RWTH Aachen University.

Naghizadehrokni, M. and Ziegler, M. (2020), “Effect of different configurations of the geofoam filled barrier in vibration scattering and its optimization by genetic algorithm”, XI International Conference on Structural Dynamics, Athens, Greece, pp.4069-4084.

Naghizadehrokni, M., Ziegler, M. and Sprengel, J. (2020), “A full experimental and numerical modelling of the practicability of thin foam barrier as vibration reduction measure”, Soil Dynamics and Earthquake Engineering, Vol. 139, p. 106416.

Oliveira, G.G.D., Iano, Y., Vaz, G.C., Chuma, E.L. and Arthur, R. (2022), “Intelligent transportation: Application of deep learning techniques in the search for a sustainable environment”, Proceedings of the 2022 5th International Conference on Big Data and Internet of Things, pp. 7-12.

Reed, R. and Marks, R.J. II. (1999), Neural Smithing: supervised Learning in Feedforward Artificial Neural Networks, MIT Press, London.

Rezania, M. (2008), “Evolutionary polynomial regression based constitutive modelling and incorporation in finite element analysis”, Doctoral dissertation, University of Exeter.

Shahin, M.A., Jaksa, M.B. and Maier, H.R. (2001), “Artificial neural network applications in geotechnical engineering”, Australian Geomechanics, Vol. 36 No. 1, pp. 49-62.

Sreekantan, P.G., Pant, A. and Ramana, G.V. (2024), “Parametric evaluation and prediction of design parameters of geofoam using artificial neural network and extreme gradient boosting models”, Innovative Infrastructure Solutions, Vol. 9 No. 7, pp. 282.

Ulgen, D. and Toygar, O. (2015), “Screening effectiveness of open and in-filled wave barriers: a full-scale experimental study”, Construction and Building Materials, Vol. 86, pp. 12-20.

Woods, R.D. (1968), “Screening of surface wave in soils”, Journal of the Soil Mechanics and Foundations Division, Vol. 94 No. 4, pp. 951-979.

Corresponding author

Mehran Naghizadeh can be contacted at: Naghizadehrokni@geotechnik.rwth-aachen.de

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