This paper presents a study investigating the performance of functionally graded material (FGM) annular fins in heat transfer applications. An annular fin is a circular or annular structure used to improve heat transfer in various systems such as heat exchangers, electronic cooling systems, and power generation equipment. The main objective of this study is to analyze the efficiency of the ring fin in terms of heat transfer and temperature distribution. The fin surfaces are exposed to convection and radiation to dissipate heat. A supervised machine learning method was used to study the heat transfer characteristics and temperature distribution in the annular fin. In particular, a feedback architecture with the BFGS Quasi-Newton training algorithm (trainbfg) was used to analyze the solutions of the mathematical model governing the problem. This approach allows an in-depth study of the performance of fins, taking into account various physical parameters that affect its performance. To ensure the accuracy of the obtained solutions, a comparative analysis was performed using guided machine learning. The results were compared with those obtained by conventional methods such as the homotopy perturbation method, the finite difference method, and the Runge–Kutta method. In addition, a thorough statistical analysis was performed to confirm the reliability of the solutions. The results of this study provide valuable information on the behavior and performance of annular fins made from functionally graded materials. These findings contribute to the design and optimization of heat transfer systems, enabling better heat management and efficient use of available space.

Biofiltration is a method of pollution management that utilizes a bioreactor containing live material to absorb and destroy pollutants biologically. In this paper, we investigate mathematical models of biofiltration for mixing volatile organic compounds (VOCs) for instance hydrophilic (methanol) and hydrophobic ( $$\alpha$$α -pinene). The system of nonlinear diffusion equations describes the Michaelis-Menten kinetics of the enzymic chemical reaction. These models represent the chemical oxidation in the gas phase and mass transmission within the air-biofilm junction. Furthermore, for the numerical study of the saturation of $$\alpha$$α -pinene and methanol in the biofilm and gas state, we have developed an efficient supervised machine learning algorithm based on the architecture of Elman neural networks (ENN). Moreover, the Levenberg-Marquardt (LM) optimization paradigm is used to find the parameters/ neurons involved in the ENN architecture. The approximation to a solutions found by the ENN-LM technique for methanol saturation and $$\alpha$$α -pinene under variations in different physical parameters are allegorized with the numerical results computed by state-of-the-art techniques. The graphical and statistical illustration of indications of performance relative to the terms of absolute errors, mean absolute deviations, computational complexity, and mean square error validates that our results perfectly describe the real-life situation and can further be used for problems arising in chemical engineering.

The inverse kinematics problem in serially manipulated upper limb rehabilitation robots implies the usage of the end-effector position to obtain the joint rotation angles. In contrast to the forward kinematics, there are no systematic approaches for solving the inverse kinematics problem. Furthermore, for some morphology of the upper limb rehabilitation robots, the inverse kinematics problem is particularly challenging to solve. Conventional methods to solve the inverse kinematics problem reported in the literature are computationally expensive. In the present work, we propose a deep learning-based model to acquire the joint angles for a given end-effector position. The proposed approach exhibits high efficacy in determining the joint angles for various target positions and can accurately predict the end-effector positions once trained, improving the ability of the upper limb rehabilitation robot to adapt to varying patient needs. Due to its improved capability and effectiveness to track positions, the proposed algorithm lays the foundation for the development of efficient controllers in future.

The remaining useful life (RUL) of complex mechanical systems is the primary aspect of prognostics and health management, which is critical for ensuring reliability and safety. Recent developments have shifted towards a data-driven approach, emphasizing empirical insights over expert opinions. The similarity-based data-driven approach operates on the premise that systems with similar historical behaviors will likely exhibit similar future behaviors, making it suitable for RUL estimation. Conventionally, most similarity-based approaches utilize all historical data to identify reference systems for RUL estimations. However, not all historical events within a system hold equal significance for RUL. Certain events have a substantial impact on the remaining lifespan of a system. These significant and impactful events are called degradation events (DEs) in this study. Based on the hypothesis that systems undergoing similar DEs may share the same RUL, this study presents an innovative framework for RUL estimation that leverages only the DEs of a test system to identify reference systems that have experienced similar DEs. Furthermore, the model incorporates novel strategies for adjusting the RUL of the reference system based on the initial wear and degradation rates, thereby improving estimation accuracy. The effectiveness of the proposed model, in comparison with similar state-of-the-art models, is demonstrated through experiments on widely recognized jet engine datasets provided by NASA and bearing degradation data from the XJTU-SY.