In this study, an adaptive linear neuron (ADALINE) network is employed to adjust the parameters of a conventional proportional-integral (PI) controller. The proposed adaptive neuron controller (NEURON-PI) has been used here instead of the conventional power system stabilizer (PSS) to control the rotor speed deviation of the single-machine infinite-bus (SMIB) system. The rotor speed deviation is used as a control error fed to the neural network in order to adjust the PI controller gains. This strategy achieves an optimal response of the power system against a wide range of operational conditions. The linearized Heffron-Phillips model of the SMIB system with the proposed NEURON-PI controller is simulated using MATLAB R2025a/Simulink software. The simulation results have shown that the power system using the proposed control technique becomes more reliable for a wide range of operating conditions as the speed deviation and power angle deviation become less oscillatory compared to the conventional PSS controller tuned by the equilibrium optimizer algorithm (EOA) reported in a previous study.

Accurate buckling prediction of functionally graded porous (FGP) nanobeams requires the simultaneous consideration of material gradation, porosity distribution, transverse shear deformation, and small-scale effects. Conventional analytical models provide a sound mechanical basis; however, they become less convenient when repeated evaluations and multi-objective design decisions are required. This study develops a hybrid analytical-machine-learning framework for predicting and interpreting the buckling behavior of FGP nanobeams. An analytical model was formulated using exponential shear deformation theory and Eringen’s nonlocal elasticity theory. The governing equations were derived from the minimum total potential energy principle and solved by Navier’s method for simply supported boundary conditions. The formulation was verified against published benchmark results and was subsequently used to generate 540 configurations covering different slenderness ratios, nonlocal parameters, porosity coefficients, and porosity distributions. A residual-learning surrogate was then constructed by combining a regularized Ridge baseline with nonlinear machine learning (ML) models. Nested cross-validation (CV) showed that the hybrid support vector regression model with a radial basis function produced the lowest prediction errors, with a root mean square error (RMSE) of 0.00729, a mean absolute error (MAE) of 0.00309, and an $R^2$ of 0.999900. The analytical and surrogate results showed that the buckling load decreases with increasing slenderness ratio, nonlocal parameter, and porosity coefficient, while the functionally graded X-pattern (FGX) distribution retains the highest buckling resistance. The conformal prediction intervals achieved 97.04% empirical coverage. SHapley Additive exPlanations (SHAP) analysis identified the slenderness ratio as the dominant input, and Nondominated Sorting Genetic Algorithm II (NSGA-II) yielded a Pareto-based compromise between porosity and buckling resistance. The proposed framework demonstrates how analytical mechanics, residual learning, uncertainty quantification, model interpretation, and multi-objective optimization can be coordinated within a unified engineering design procedure.

Reliable monitoring of chip formation and tool degradation is essential for machining quality, process stability, and condition-based maintenance in intelligent manufacturing systems. However, individual sensing modalities and isolated learning models provide incomplete representations of the heterogeneous and time-dependent interactions that characterize computer numerical control (CNC) milling. This study investigates a hybrid multimodal modelling framework that integrates heterogeneous sensing, complementary feature-learning mechanisms, and joint classification–regression tasks for chip morphology and progressive flank-wear monitoring. Vibration, acoustic emission (AE), cutting force, spindle current, and temperature signals were synchronized and fused within a unified modelling architecture. A convolutional neural network (CNN) was used to extract local signal characteristics, a bidirectional long short-term memory (BiLSTM) network modelled temporal dependencies, and Transformer-based self-attention captured long-range interactions within the fused representation. The resulting features were used jointly to classify continuous, segmented, discontinuous, and serrated chip morphologies and to estimate progressive flank wear. The framework was evaluated under variations in spindle speed, feed rate, and wet and dry machining conditions, together with sensor-fusion comparisons and architectural ablation experiments. The full multimodal configuration achieved approximately 97.2% chip-classification accuracy, while the complete hybrid architecture reached approximately 98% in the ablation analysis and maintained prediction accuracy above 94% across the investigated cutting conditions. Tool-wear estimates also showed close agreement with the experimentally measured values. These results indicate that coordinated integration of heterogeneous sensing with complementary local, sequential, and attention-based modelling mechanisms improves predictive stability and robustness under variable machining conditions. The proposed framework provides a structured hybrid-modelling approach for intelligent machining-process monitoring and offers a basis for predictive maintenance and adaptive CNC manufacturing systems.