Adaptive neuro-fuzzy capsule network optimised by Salp Swarm Algorithm for simultaneous prediction of strength and durability indices in sustainable PET–RHA concrete

Concrete is a sustainable alternative to conventional concrete, which incorporates recycled polyethylene terephthalate (PET) and rice husk ash (RHA). Also, the complexity of nonlinear interactions between all mix constituents makes accurately predicting their mechanical and durability properties difficult. In addition, knowledge in engineering is mainly expressed in qualitative form and not in a strictly numerical relation. So, conventional regression techniques or standard deep learning models may not work effectively. The objective of the research is to put forth an Adaptive Neuro-Fuzzy Capsule Network optimised by Salp Swarm Algorithm (ANFCapsNet-SSA) capable of predicting and assessing simultaneously the compressive strength (CS), splitting tensile strength (STS), flexural strength (FS), water absorption (WA), modulus of elasticity (MoE) and rapid chloride permeability (RCPT) of concrete. A merged framework proposed which the ANFIS (Adaptive Neuro-Fuzzy Inference system) and capsule network (CapsNet) to capture fuzzy linguistic knowledge of expert and a complex non-linear relationship within the experimental dataset. The ANFIS module converts the input that are typically mix-design variables into fuzzy feature forms that is intePretable, while the CapsNet learns hierarchical statistical patterns on the input via dynamic routing by agreement. The learned relationships, which are inherently data-driven and designed for predictive modelling, do not explicitly represent the underlying physics or chemistry of concrete behaviour. For improved model performance, Salp Swarm Algorithm (SSA) will optimise the hyper parameters of integrated ANFIS-CapsNet architecture. The Conditional Generative Adversarial Network with Gradient Penalty (CGAN-GP) generates statistically consistent synthetic training samples to mitigate the limitation of the experimental dataset while Gradient-weighted Relevance Propagation (GRP) supplies post hoc interpretation of the contribution of each input variable to predicted outputs. The analysis of the suggested scheme is based on a 90-day experimental dataset. Of all the models that were investigated, the ANFCapsNet-SSA showed the best predictive performance with R² = 0.9993, MAE = 0.0007, RMSE = 0.0019, MAPE = 0.006%, EVS = 0.9941, RSR = 0.000171, CPI = 0.9968. The proposed framework can thus be quite useful as a decision-support tool in designing and evaluating the performance of sustainable PET-RHA concrete as evidenced by the strong predictive power of the framework for the considered dataset.