A Fully-Self-Adaptive Harmony Search GMDH-Type Neural Network Algorithm to Estimate Shear-Wave Velocity in Porous Media

Shear wave velocity (VS) is one of the most important parameters in deep and surface studies and the estimation of geotechnical design parameters. This parameter is widely utilized to determine permeability and porosity, lithology, rock mechanical parameters, and fracture assessment. However, measuring this important parameter is either impossible or difficult due to the challenges related to horizontal and deviation wells or the difficulty in reaching cores. Artificial Intelligence (AI) techniques, especially Machine Learning (ML), have emerged as efficient approaches for dealing with such challenges. Therefore, considering the advantage of the ML, the current research proposes a novel Fully-Self-Adaptive Harmony Search—Group Method of Data Handling (GMDH)-type neural network, named FSHS-GMDH, to estimate the VS parameter. In this way, the Harmony Memory Consideration Rate (HMCR) and Pitch Adjustment Rate (PAR) parameters are calculated automatically. A novel method is also introduced to adjust the value of the Bandwidth (BW) parameter based on the cosine wave and each decision variable values. In addition, a variable-size harmony memory is proposed to enhance both the diversification and intensification. Our proposed FSHS-GMDH algorithm quickly explores the problem space and exploits the best regions at the late iterations. This algorithm allows for the training of the prediction model based on the P-wave velocity (VP) and the bulk density of rock (RHOB). Applying the proposed algorithm to a carbonate petroleum reservoir in the Persian Gulf demonstrates that it is capable of accurately estimating the VS parameter better than state-of-the-art machine learning methods in terms of the coefficient of determination (R2), Mean Square Error (MSE), and Root Mean Square Error (RMSE).