Soil compression is the phenomenon in which the volume of soil decreases under pressure, accompanied by the drainage of pore water. This leads to changes in soil properties such as the arrangement of soil particles, porosity, and water drainage. Therefore, it is important to determine the compressibility of fine-grained soils with low permeability, such as clays. Soil compressibility is a key factor in assessing the settlement of soil layers beneath structures, making it crucial to estimate this parameter accurately.
The compressibility of soil is represented by the compressibility coefficient (Cc), which is widely used in the design of various civil engineering projects, including pavements, dams, foundations, and retaining walls. This coefficient is usually obtained through an Oedometer test, performed in a laboratory setting. However, this test can be time-consuming and requires skilled technicians to operate the equipment.
To address these limitations, researchers have developed data-driven models. Machine learning models have been shown to be reliable and capable of effectively simulating complex geotechnical processes. Artificial Neural Networks (ANN) have gained popularity among researchers for modelling various aspects of geotechnical engineering, such as estimating the compression characteristics of artificially mixed soil and predicting compressibility parameters of different soils.
Several studies have combined artificial neural networks (ANN) with metaheuristic approaches, including differential evolution, particle swarm optimization, dynamic group optimization, cuckoo search, ant colony optimization, and symbiotic organism search. These combinations enhance the construction of ANN models, enabling them to address complex problems across various engineering disciplines.
Before 2018, there have been no studies conducted to estimate the compressibility coefficient (Cc) of soil. However, a notable research article published in 2018 in Advanced Engineering Informatics details a study carried out by a team of researchers from Vietnam. This study employed a machine learning approach using a combination of Multi-Layer Perceptron Neural Network (MLPNN) and Particle Swarm Optimization (PSO) to predict the soil compression coefficient. The structure of MLP Neural Networks is adept at modelling nonlinear and complex real-world processes and consists of three interconnected layers: input, hidden, and output. The integration of the PSO algorithm serves to optimize the MLPNN model, enhancing its predictive capabilities.
The hybrid Particle Swarm Optimization (PSO) and Multilayer Perceptron (MLP) Neural Networks model has been meticulously implemented within the MATLAB environment. This model’s development can be broken down into six distinct and detailed steps:
1. MLP Neural Network Initialization: It includes choosing the activation function, number of layers and number of neurons in each layer.
2. Generating Model parameters: Initial values for the network’s weight and biases are generated.
3 .PSO parameter adaptation: It involves setting up a swarm of particles, where each particle represents a potential solution or set of weights for the neural network.
4. Fitness calculation: After adjusting the parameters, a fitness function is calculated to evaluate the MLP model’s performance by comparing its outputs to known target values. This step is crucial for determining the model’s predictive accuracy.
5. Stopping condition verification: After calculating fitness, the model checks if it meets stopping conditions, such as achieving a target fitness level, reaching a maximum number of iterations, or showing
minimal improvement. Timely stopping is crucial to prevent overfitting and reduce unnecessary computational effort.
6. Prediction of Cc: After verifying the stopping conditions, the final tuned model is established and ready to predict the target variable, Cc. At this stage, the model can be tested on new data to evaluate its performance and generate predictions, showcasing the effectiveness of the hybrid approach combining PSO and MLP neural networks.
The data was collected from the Royal City project located in Hanoi City, Vietnam, which encompasses an area of 120945 m². The dataset comprises a total of 154 samples, featuring 12 input variables, which include the following: Depth of sample (m), Sand percentage (%), Loam percentage (%), Clay percentage (%), Moisture content percentage (%), Wet density (g/cm³), Dry density (g/cm³), Void Ratio, Liquid limit (%), Plastic limit (%), Plastic Index (%), and Liquidity index. For analytical purposes, the dataset was partitioned into 70% for training and 30% for testing.
The parameters for the Particle Swarm Optimization (PSO) were determined through a systematic trial and error process, resulting in the following specifications: IterMax is set to 3000, PopSize to 100, VarMin to −1.5, and VarMax to 1.5. Additionally, the inertia weight and the inertia weight damping ratio are established at 0.98 and 0.75, respectively. The personal learning coefficient (c1) and the global learning coefficient (c2) are assigned values of 1 and 2, respectively. Furthermore, the hyperparameters for the Multilayer Perceptron Neural Network (MLPNN) have been identified, with the number of neurons in the hidden layer set to 8 and the activation function chosen as tan-sigmoid.
Based on the evaluation metric of R-squared, the PSO-MLPNN model has demonstrated a value of 0.957. Furthermore, the performance of PSO-MLPNN was compared against a variety of models, including conventional backpropagation MLP (BP-MLP), radial basis function neural network (RBF-Neural Nets), support vector regression (SVReg), random forest (RF), and Gaussian Process regression (GP). The comparative results indicate that PSO-MLPNN achieved the highest accuracy with an R-squared value of 0.884. This was followed by BP-MLPNN with an R-squared value of 0.862, RBF-Neural Nets at 0.678, SVReg at 0.777, RF at 0.804, and GP at 0.797. Given that PSO-MLPNN significantly outperformed BP-MLPNN, it can be concluded that the application of the PSO metaheuristic effectively enhances the construction of the MLP Neural Nets model used for Cc estimation.
The PSO-MLP Neural Nets model represents an innovative and effective tool that can significantly assist geotechnical engineers in the intricate process of foundation design. This hybrid approach combines Particle Swarm Optimization (PSO) with Multi-Layer Perceptron (MLP) Neural Networks, enhancing the predictive capabilities and efficiency of the design process. Looking ahead, the current study opens up exciting avenues for future research. One potential direction could involve expanding the application of this hybrid framework beyond foundation design, targeting a range of other engineering challenges. By leveraging the strengths of PSO and MLP Neural Nets, researchers may explore how this model can address complex problems in various fields, such as structural integrity assessments, soil-structure interaction analysis, or even environmental engineering projects. The versatility of the PSO-MLP model has the potential to revolutionize the way engineering problems are approached and solved.
Reference
Bui, D. T., Nhu, V. H., & Hoang, N. D. (2018). Prediction of soil compression coefficient for urban housing project using novel integration machine learning approach of swarm intelligence and multi-layer perceptron neural network. Advanced Engineering Informatics, 38, 593-604.