Robust Combustion Prediction for Alternative-Fuel Engines Using an Equilibrium Optimizer-Based Echo State Network with ϵ-Insensitive SVR Readout

Alternative-fuel engines, such as diesel–compressed natural gas (CNG) dual fuel systems, exhibit increased cycle-to-cycle combustion variability, placing demanding requirements on the accuracy and robustness of prediction models for key combustion parameters. Echo state networks (ESNs), owing to their reservoir computing architecture, can capture nonlinear temporal dynamics, yet their performance is sensitive to reservoir hyperparameters, and the conventional linear readout trained by minimizing mean squared error is susceptible to outliers in noisy observations. This paper proposes a robust ESN framework based on the equilibrium optimizer (EO), termed EO-Robust-ESN, that automatically searches for key model hyperparameters and replaces the conventional squared loss with the ϵ-insensitive loss by adopting linear support vector regression (SVR) to train the readout weights, thereby enhancing prediction robustness under noisy conditions. Results on the Mackey–Glass chaotic time series benchmark and a peak in-cylinder pressure series from a diesel–CNG dual fuel engine demonstrate that EO significantly outperforms the genetic algorithm and manual tuning on the Mackey–Glass benchmark, reducing the mean RMSE by approximately 5.6% relative to GA, and achieves comparable accuracy with higher search stability on the Pmax series. The ϵ-insensitive SVR readout further reduces prediction errors, with the MSE on the noisy Pmax series reduced by approximately 42% compared with the ridge regression readout, suggesting that the proposed framework provides an effective data-driven tool for robust combustion prediction in alternative-fuel engines.