Symmetry

Accurate prediction of the internal corrosion rate is crucial for the safety management and maintenance planning of oil and gas pipelines. However, this task is challenging due to the complex, multi-factor nature of corrosion and the scarcity of available inspection data. To address this, we propose a novel hybrid prediction model, GM-Markov-PSO, which integrates a gray prediction model with a Markov chain and a particle swarm optimization algorithm. A key innovation of our approach is the systematic incorporation of symmetry principles—observed in the spatial distribution of corrosion factors, the temporal evolution of the corrosion process, and the statistical fluctuations of monitoring data—to enhance model stability and accuracy. The proposed model effectively overcomes the limitations of individual components, providing superior handling of small-sample, non-linear datasets and demonstrating strong robustness against stochastic disturbances. In a case study, the GM-Markov-PSO model achieved prediction accuracy improvements ranging from 0.93% to 13.34%, with an average improvement of 4.51% over benchmark models, confirming its practical value for informing pipeline maintenance strategies. This work not only presents a reliable predictive tool but also enriches the application of symmetry theory in engineering forecasting by elucidating the inherent order within complex corrosion systems.

Industrial environments still rely heavily on analog instruments for process supervision, as their robustness and low cost make them suitable for harsh conditions. However, these devices require manual readings, which limit automation and digital integration within Industry 4.0 frameworks. To address this gap, this study proposes an intelligent and cost-effective system for non-invasive acquisition of measurement data from analog industrial instruments, leveraging machine vision and Artificial Neural Networks (ANNs). The proposed framework exploits the geometric symmetry inherent in circular and linear scales to interpret pointer positions under varying lighting and perspective conditions. A dedicated image-processing pipeline is combined with lightweight ANN architectures optimized for embedded platforms, ensuring real-time inference without the need for high-end hardware. The processed data are wirelessly transmitted to a Human–Machine Interface (HMI) and web-based dashboard for real-time visualization. Experimental validation on pressure and flow instruments demonstrated an average Mean Absolute Error (MAE) of 0.589 PSI and 0.085 GPM, Root Mean Square Error (RMSE) values of 0.731 PSI and 0.097 GPM, and coefficients of determination (R²) of 0.985 and 0.978, respectively. The system achieved an average processing time of 3.74 ms per cycle on a Raspberry Pi 3 platform, outperforming Optical Character Recognition (OCR) and Convolutional Neural Network (CNN)-based methods in terms of computational efficiency and latency. The results confirm the feasibility of a symmetry-driven vision framework for real-time industrial supervision, providing a practical pathway to digitalize legacy analog instruments and promote low-cost, intelligent Industry 4.0 implementations.

Generalized censoring, combined with a power-based distribution, improves inferential efficiency by capturing more detailed failure-time information in complex testing scenarios. Conventional censoring schemes may discard substantial failure-time information, leading to inefficiencies in parameter estimation and reliability prediction. To address this limitation, we develop a comprehensive inferential framework for the alpha-power Weibull (APW) distribution under a generalized progressive hybrid Type-II censoring scheme, a flexible design that unifies classical, hybrid, and progressive censoring while guaranteeing test completion within preassigned limits. Both maximum likelihood and Bayesian estimation procedures are derived for the model parameters, reliability function, and hazard rate. Associated uncertainty quantification is provided through asymptotic confidence intervals (normal and log-normal approximations) and Bayesian credible intervals obtained via Markov chain Monte Carlo (MCMC) methods with independent gamma priors. In addition, we propose optimal censoring designs based on trace, determinant, and quantile-variance criteria to maximize inferential efficiency at the design stage. Extensive Monte Carlo simulations, assessed using four precision measures, demonstrate that the Bayesian MCMC estimators consistently outperform their frequentist counterparts in terms of bias, mean squared error, robustness, and interval coverage across a wide range of censoring levels and prior settings. Finally, the proposed methodology is validated using real-life datasets from engineering (electronic devices), clinical (organ transplant), and physical (rare metals) studies, demonstrating the APW model’s superior goodness-of-fit, reliability prediction, and inferential stability. Overall, this study demonstrates that combining generalized censoring with the APW distribution substantially enhances inferential efficiency and predictive performance, offering a robust and versatile tool for complex life-testing experiments across multiple scientific domains.

This study looks at the stability and stabilization issues concerning the nonlinear timedelay systems specified by conformable derivatives. These requirements can be used for many useful applications. Through the construction of appropriate Lyapunov–Krasovskii functionals, we develop novel linear matrix inequality (LMI) conditions for the exponential stability of autonomous systems and practical exponential stability for systems subject to bounded perturbations. Furthermore, we propose state-feedback stabilization strategies that transform the controller design problem into a convex optimization framework solvable via efficient LMI techniques. The theoretical developments are comprehensively validated through numerical examples that demonstrate the effectiveness of the proposed stability and stabilization criteria. The results establish a rigorous framework for analyzing and controlling conformable fractional-order systems with time delays, bridging theoretical advances with practical implementation considerations.