Journal of Applied Mathematical Models in Engineering

Hybrid AI-Mathematical Modeling Approach for Predictive Maintenance in Rotating Machinery Systems

M. Kavitha — 2025-05-12

Industrial and industrial environments place increasing pressures on rotating machine systems to be operational efficient and reliable — which drives increasing focus on predictive maintenance (PdM) strategic utilization. The motor, turbine, pump, and compressor systems are subjected to continuous mechanical stresses and are subject to similar wear and performance degradation and failures. In this paper a novel hybrid form works synergistically blending physics based mathematical modeling with the most advanced artificial intelligence (AI) for optimizing prediction maintenance. First a coupled second order differential equations that describe vibration dynamics and torque transmission as well as thermal interactions are developed for a comprehensive dynamic model of the rotating machinery under different operational loads. The physical model answers to what the system will behave like and how it should show up based on our baseline. At the same time, an AI module based on data, which employs a bidirectional long short term memory (BiLSTM) network to learn temporal pattern from real time vibration and temperature sensor data, is developed in parallel. A co-simulation strategy is used to achieve the hybrid model, wherein the outputs from the physical model are used as residual inputs for the AI network so that it can detect early anomalies and predict failures. The approach proposed is validated through the simulation studies and on an industrial real world employment in the thermal power plant with the systems of centrifugal pump. Experimental results indicate that with substantial improvement in fault detection accuracy, remaining useful life prediction and early warning capabilities to conventional physics (only) or AI (only) methods. The results of this research not only show the superiority of hybrid model for predicting the failures of rotating systems for predictive maintenance, but this also lays the groundwork for future developments of next generation digital twin frameworks for intelligent industrial asset management

Nonlinear Dynamic Modeling and Vibration Analysis of Smart Composite Structures Using Multiscale Techniques

Dahlan Abdullah — 2025-03-19

Engineered smart composite structures are being utilized in the fields of aerospace, automotive and civil engineering due to adaptive capabilities that would be obtained through incorporation of functional materials such as piezoelectric fibrous or shape memory alloy materials within a heterogeneous matrix. As such, these materials lead to complex nonlinear dynamic responses as a result of the coupling of mechanical, electrical and thermal fields at a range of scales. A complete nonlinear dynamic modeling framework which uses the multiscale techniques to accurately model the interaction between microstructural constituents and their effect on the macroscopic vibration characteristics is developed in this paper. The proposed approach combines asymptotic homogenization theory and nonlinear finite element methods to incorporate both material nonlinearity (e.g. strain dependent stiffness) that results from a nonlinear relationship between the variables of a stress strain law and the associated geometric nonlinearity that arises due to large deformations. Finally, the dynamic response is studied under harmonic and transient excitations through the use of advanced analysis method including the nonlinear modal decomposition, Hilbert-Huang Transform (HHT), and continuous wavelet transform (CWT). The framework is applied to piezoelectric fibre reinforced laminates and it is found that microscale phase distribution variation significantly affects both damping capacity, modulated stiffness and intermodal energy transfer. Nonlinear phenomena including the resonance frequency shifts and internal resonances are predicted by the model, and these phenomena are often overlooked in single scale or linear models. Studies conducted in comparison confirm that the multiscale nonlinear approach improves the fidelity of vibration analysis, and revealed design and optimization important for the smart composite structures in dynamic environment.

Mathematical Model-Based Optimization of Thermal Performance in Heat Exchangers Using PDE-Constrained Methods

Robbi Rahim — 2025-03-24

Heat exchangers are an important element seen inNULL power generation, chemical processing and HVAC lines, wherein the efficient thermal management concludes directly on the energy consumption, system life and the operational cost. One of the common traditional design approaches is empirical correlations with iterative experimentation, which is time consuming and suboptimal for complex geometries or changing operating condition. This article reports on a comprehensive and mathematically rigorus optimization framework for heat exchanger thermal performance using partial differential equation (PDE) constrained optimization. The model couples the incompressible Navier–Stokes equations for fluid flow with the convection–diffusion energy equation for heat transfer, which allows details in coupling of the thermal and fluid domains of the heat exchanger. A physical and geometric constrained approach is then used to formulate the objective functional that minimizes temperature non uniformity, pressure losses and thermodynamics irreversibility. Finite element discretization with a Galerkin formulation is used for numerical implementation while adjoint based sensitivity analysis is used for efficient gradient computation which make gradient based optimization algorithms scalable. The proposed method is shown to effectively improve the heat transfer rate, reduce pressure drop post heat transfer, and minimize entropy in a shell and tube heat exchanger using a case study. Predictions from this modeling agree with experimental data, hence verifying the applicability of PDE-constrained optimization to enable them to become the next generation of thermal systems through high fidelity, physics informed and computationally efficient pathway.

Mathematical Analysis of Vibration Attenuation in Smart Structures Using Piezoelectric Layers

S. Sindhu — 2025-03-29

In order to address this issue, a complete mathematical model of the vibration attenuation in smart structures with embedded piezoelectric layers is developed in this study. The Euler–Bernoulli beam theory with linear piezoelectric constitutive relations is used to develop a coupled electromechanical model. Hamilton’s principle is used to find the governing partial differential equations and Galerkin method is used for solving them in (modal) analysis. Harmonic and impulse loading cases of piezoelectric damping are investigated. Results show significant vibration suppression prospects with the optimal piezoelectric placement and the proper control gain. A robust model is proposed for designing next generation adaptive vibration control systems in the areas of aerospace and civil engineering.

Mathematical Modeling of Rotor Dynamics in High-Speed Electric Motors for Aerospace Applications

S.Poornimadarshini — 2025-03-25

No aerospace system can function without high speed electric motors, which are compact form factor, high power density and very high dynamic response. These motors are operating at rotational speed of more than 50,000 rpm, while they are subjected to complicated dynamic phenomena, leading to structural integrity, low level of vibration and stable long term operation. Accurate modelling of the rotor dynamics in the high speed regime where gyroscopic precession, rotor stator electromagnetic interaction, bearing anisotropy and structural damping characteristics are present is a critical factor towards reliable motor operation. A comprehensive mathematical modeling framework for the rotor dynamics analysis especially in aerospace grade high speed electric motors is developed in this study. The modeling approach is based on Lagrangian mechanics, is distributed mass and stiffness, anisotropic bearing supports, and gyroscopic coupling effects. Discretization and numerical solutions of these resulting nonlinear coupled differential equations in time domain and frequency domain are performed. Comparisons are made to finite element simulation performed in COMSOL Multiphysics and experimental data from a 120 kW aerospace prototype motor running above 60,000 rpm at critical speed for critical speed identification, mode shape visualization, and damping behavior respectively. The dynamic response characteristics, vibrational modes, and stability thresholds, and these vary widely as functions of the design parameters, are predicted with fidelity. This study offers insights to be used towards improvement in the rotor design optimization, material selection and bearing configurations to help advance the next generation of more robust, efficient, and lightweight electric propulsion systems of the aerospace.

Finite Element-Based Modeling of Stress Distribution in 3D-Printed Lattice Structures

Saravanakumar Veerappan — 2025-03-31

Additive manufacturing, or AM in short, is sweeping the design and fabrication of lattice structures into a new era, yielding lightweight components with high mechanical performance tailored to specific aerospace, biomedical, and engineering applications. One of the most competent production processes within various AM technologies for manufacturing precise metallic lattices with a well defined microarchitecture is the Selective Laser Melting (SLM). However, their geometrical complexity and process induced anisotropy make the mechanical behavior of such structures, specifically, stress distribution under operational loads inadequately understood. In this work we develop a complete finite element method (FEM) based modeling framework to study stress distribution in 3D printed lattice structures that are based on Body-Centered Cubic (BCC), Face-Centered Cubic (FCC) and Triply Periodic Minimal Surface (TPMS) designs. Coupled FEM simulations were carried out in both axial compression and torsional loading conditions to reveal critical stress zones, to investigate deformation patterns, and to examine the effect of geometrical topology on structural response. Material properties for AlSi10Mg are considered, and realistic boundary conditions are assumed to ensure accuracy of results. To validate the proposed analytical fits, strain gauge instrumentation and uniaxial compression tests were performed on SLM fabricated samples, and the results exhibit good agreement with FEM predictions and a maximum deviation less than 8.5%. These show that the TPMS-based structures have a better capacity for both stress distribution and load sharing over traditional strut based geometries. The developed methodology provides a robust means of mechanical evaluation and design optimization of lattice structures, which is beneficial to the development of next generation of lightweight and load bearing components in critical engineering disciplines.