A team of researchers from the Indian Institute of Technology, Roorkee, India, has developed an innovative hybrid model that combines Particle Swarm Optimization (PSO) with Artificial Neural Networks (ANN) specifically designed for the prediction of the Factor of Safety (FOS) in slope stability analysis. Artificial Neural Networks (ANN) function by mimicking the way human brains process information. They consist of interconnected processing units referred to as neurons. Each connection between neurons is associated with weights and biases, which are adjusted during the learning process through a method known as Back Propagation (BP). The goal of BP is to minimize the prediction error by iteratively updating the weights and biases. Traditional optimization algorithms frequently employed in conjunction with ANN include Gradient Descent, Gradient Descent with Momentum, and the Levenberg–Marquardt algorithm. However, these methods can be sensitive to the initial weights set and often struggle with limitations such as slow convergence rates and the potential to get stuck in local minima.
To overcome these limitations, the research team explored metaheuristic methods, which include Genetic
Algorithms (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO), and Ant Colony Optimization (ACO). These methods have been successfully applied in geotechnical engineering; for instance, GA has been utilized with ANN for assessing liquefaction potential, DE has been paired with ANN for evaluating slope stability, and ACO has been integrated with ANN to predict the outcomes of blast-induced rock disturbances.
For their study, the researchers focused on six critical input parameters that influence the Factor of Safety. These parameters included:
1. Unit weight of the slope material (γ)
2. Shear strength parameter (c, cohesion)
3. Angle of internal friction (ϕ)
4. Average angle of the slope (β)
5. Height of the slope (H)
6. Coefficient of pore water pressure (ru)
The structured workflow for the PSO-ANN model was carefully conceived as follows:
1. Data Collection: The first step involved reading
the datasets containing both input features and target outcomes.
2. Network Formation: A feed-forward neural network
with an adjustable size ‘n’ was constructed, parallelly setting the parameters
required for the PSO.
3. Particle Initialization: A population of particles
was randomly initialized, assigning initial positions and velocities to each.
4. Initial Fitness Evaluation: The fitness of each
particle was assessed, identifying the individual best position (Pbest) and the
global best position (Gbest).
5. Iteration Count Setup: The iteration counter was
initialized at k=1.
6. Velocity and Position Update: The velocity and
position of each particle were updated based on the global and individual best
positions.
7. Fitness Re-evaluation: The fitness of each
particle was recalculated, updating Pbest and Gbest as necessary.
8. Iteration Check: A loop was established to
continue the process (go back to step 6) until the maximum iteration count
(Maxite) was reached.
9. Optimum Values Output: Finally, the optimized
values of weights and biases for the ANN were printed.
The PSO-ANN hybrid model incorporates various parameters pertinent to both Particle Swarm Optimization and Artificial Neural Networks. Among the key PSO parameters are the size of the swarm (N), acceleration factors (c1 and c2), and the inertia weight (w). For ANN, the important configurations include the network architecture, specifically the number of neurons situated in the hidden layer (n). Rigorous sensitivity analyses were executed to fine-tune these parameters. Initially, the swarm size was evaluated while the acceleration factors and neuron count were maintained at fixed levels. Subsequently, the acceleration factors were optimized while preserving previously established values. A third phase of
analysis varied the number of neurons, integrating the now-optimized swarm size and acceleration factors. Past studies underscored the necessity for a more extensive testing methodology. Hence, the researchers adopted a comprehensive new approach involving multiple experimental runs, totaling 900 iterations, to
establish optimal combinations of parameters. This included testing six different values for the number of neurons and swarm sizes, as well as five variations for acceleration factors, all defined within targeted ranges.
A thorough investigation culminated in the establishment of the PSO-ANN hybrid model aimed at accurately forecasting the Factor of Safety for slope stability. This model leveraged a database comprising 83 distinct slope sections. The pivotal findings of this exhaustive study are summarized as follows:
1. The architecture of the most efficient artificial neural network was determined to contain nine neurons in the hidden layer, which proved to be the optimal arrangement.
2. Following 900 experimental runs, the best parameters for the PSO-ANN model emerged: a swarm size of 50, with acceleration factors set at 1.5 and 2.25, all achieved through a maximum of 2000 iterations.
3. The practical application of this model was demonstrated through a detailed case study focused on a slope in the Indian Himalayas, where the PSO-ANN model was assessed against traditional methods such as limit equilibrium and numerical analysis.
4. The PSO-ANN hybrid model’s predicted Factor of Safety was consistently found to be higher than those determined through conventional analytical methods; however, all models affirmed that the slope remained stable against the risk of rotational failure.
This work significantly contributes to the field of geotechnical engineering by providing a robust framework for predicting slope stability and enhancing the reliability of safety assessments in geotechnical systems.
Reference
Rukhaiyar, S., Alam, M. N., & Samadhiya, N. K. (2018). A PSO-ANN hybrid model for predicting factor of safety of slope. International Journal of Geotechnical Engineering, 12(6), 556-566.