Applied Mathematical Modelling最新文献

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Adjoint-based optimization for non-linear inverse problems with high-order discretization of the compressible RANS equations

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-31 DOI: 10.1016/j.apm.2025.115984

Bartolomeo Fanizza , Pedro Stefanin Volpiani , Florent Renac , Emeric Martin , Denis Sipp

This work presents an adjoint-based strategy to solve non-linear inverse problems discretized with high-order numerical methods. The inverse problem is defined here based on the optimization of a control parameter to minimize a cost-functional subject to the compressible RANS equations discretized with the modal discontinuous Galerkin (DG) method. The distributed control parameter is searched in the DG function space and the discrete adjoint approach, consistent with the formal problem, is used to compute the derivative of the cost function in the optimization process. The linearization of the cost-functional and of the governing equations, the expression of the gradient, as well as the numerical strategy to efficiently solve the adjoint system with flexible inner-outer GMRES solvers have been detailed. In the case of a strongly under-determined problem, regularization techniques based on the penalization of the norm of the control parameter have been introduced. The methodology is illustrated on the case of a data-assimilation (DA) problem, which aims at minimizing the discrepancy of (sparse) high-fidelity measurements with the solution of the RANS equations corrected by four different control parameters. The optimization strategy is tested progressively with measurements on the full computational domain (abundant measurements) and solid wall boundaries (sparse measurements). First, a laminar flow around a cylinder is used to validate the inverse problem resolution with a DG discretization of different approximation orders. Subsequently, results regarding a turbulent flow around a square cylinder allow to compare the optimization convergence of each corrective parameters with abundant measurements. Finally, a shock-wave/turbulent boundary-layer interaction configuration is considered. Great correction of the velocity field is obtained with one of the proposed corrective term. In the case of abundant measurements it is also possible to get accurate correction of wall variables such as the skin-friction and pressure coefficient. Regularization of the optimal space, in case of sparse measurements, is attempt through penalization techniques.

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引用次数: 0

Oxygen-assisted cracking behavior model based on phase-field fracture framework

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-31 DOI: 10.1016/j.apm.2025.115988

Xin Huang , Qikun Xie , Shaolin Li , Hongyu Qi , Xiaoguang Yang , Duoqi Shi

Oxidation can have a major effect on the crack growth behavior of components working at high temperatures. However, phase-field (PF) fracture models considering oxidation are lacking. This study proposes a PF framework specifically designed for oxygen-assisted cracking. The model builds on the dynamic embrittlement behavior caused by oxygen, and an oxygen-related fracture-toughness degradation function is established. Then, this model is extended to fatigue, creep, and creep-fatigue cracks by employing the corresponding PF model. The model is validated using several examples. Specifically, (i) fatigue cracks for compact tension specimens, (ii) creep cracks for compact tension specimens, and (iii) creep-fatigue cracks for compact tension and shear specimens are simulated. The simulation results are consistent with the experimental results, proving the predictive ability of the proposed framework.

引用次数: 0

A semi-analytical dosimetry model for inspiratory flow of reactive gases in the lung

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-31 DOI: 10.1016/j.apm.2025.115989

Pouria Motevalian, María Antonieta Sánchez-Farrán, James S. Ultman, Ali Borhan

A semi-analytical dosimetry model for steady flow and mass transfer in cylindrical tubes is developed for reactive gas transport and uptake in proximal airways of the lung during quasi-steady inspiratory flow. The model is used to predict the longitudinal concentration distribution of inhaled ozone along selected airway pathways in the lung of a two-month-old rhesus monkey. Two ideal airway structures are considered; a symmetrically-branched model based on computer tomography (CT) scan measurements and an asymmetric one informed by airway measurements from magnetic resonance imaging (MRI) data. The model is validated by comparison with predictions of computational fluid dynamics (CFD) simulations of ozone transport and uptake in an anatomically-accurate airway structure reconstructed from MRI data. The relative error between the CFD results and model predictions for the asymmetrically-branched airway structure is less than 1.5% along all airway paths, rendering the dosimetry model a computationally efficient tool for capturing longitudinal variations of reactive species concentration within the lung airways.

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引用次数: 0

LS-SVM-based nonlinear multi-physical steady-state field coupled problems computing method

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-30 DOI: 10.1016/j.apm.2025.115987

Xiaoming Han , Xin Zhao , Zhengwei Qu , Yecheng Wu , Guofeng Li

Multi-physical steady-state field coupled problems are addressed using mesh-based methods, including finite element and finite volume methods, along with their enhancements. To streamline computational complexity, this paper employs a least squares support vector machine (LS-SVM) for tackling the multi-physical steady-state field coupled problems. First, LS-SVM lowers computational complexity by eliminating mesh dependency. Second, it effectively solves multi-physical steady-state field coupled problems with high adaptability. Finally, it can restrain the complex boundary conditions. This paper validates the approach with two case studies: a one-dimensional nonlinear electro-mechanical coupled problem and a two-dimensional nonlinear thermoelectric coupled problem. The LS-SVM method achieved calculation accuracy comparable to the finite element method while offering greater precision and faster computation than both the radial basis function (RBF) interpolation and physics-informed neural network (PINN) methods.

引用次数: 0

Quantification of uncertainty information in remaining useful life estimation

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-30 DOI: 10.1016/j.apm.2025.115992

Changdong Zhao , Shihu Xiang , Songhua Hao , Feng Niu , Kui Li

Accurate remaining useful life prediction is crucial for prognostics and health management of products. Model uncertainty is an important factor negatively affecting prediction performance. Existing methods fail to evaluate the predictive ability of a degradation model without the actual remaining useful life, and typically require adequate degradation data or prior information. They may be unable to ensure a reliable prediction performance in practical engineering scenarios with limited degradation data and mechanism knowledge. To address these issues, a model fusion based method is proposed using the uncertainty theory. Specifically, a comprehensive model performance evaluation method is proposed by simultaneously considering complexity, fitting ability, and predictive ability. The evolution process of the comprehensive model performance index is modelled by proposing a generalized arithmetic Liu process model that can flexibly depict characteristics of an uncertain process. A model fusion method is proposed by quantifying the similarity between a candidate model and the actual degradation process based on the predictive evolution analysis of the performance index. Then, a random initial solutions based algorithm is proposed to estimate remaining useful life from the fused model. Finally, three real cases and a numerical case are utilized to demonstrate the effectiveness and versatility of the proposed method by comparing it with existing methods.

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引用次数: 0

Modeling of temperature dependent graded vibration in a piezoelectric microbeam composite plates with a sliding contact

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-30 DOI: 10.1016/j.apm.2025.115983

Mohd Sadab, Santimoy Kundu

The present study introduces a novel framework for analyzing shear wave propagation in piezoelectric microbeam-dielectric elastic composite plates, emphasizing the temperature-dependent graded factors that influence key material properties. Unlike previous works, which often assume constant material coefficients, this model considers quadratic variations of elastic, piezoelectric, and dielectric coefficients with respect to the temperature graded. The mathematical modeling employs the separation of variables and asymptotic expansions of Bessel functions to derive comprehensive analytical solutions. A sliding contact interface with a sliding parameter is considered, enabling a more realistic simulation of composite structures. The dynamic governing equation, transverse deflection, and Maxwell's equation for electric potential are solved simultaneously across domains, yielding a system of linear homogeneous equations via admissible boundary conditions. The dispersion relations for shear waves are derived for electrically open and short-circuit cases and validated through comparison with existing studies. This study highlights the significant influence of temperature grade, temperature ratio, micro-length parameters in the piezoelectric microbeam, and the sliding parameter on shear wave propagation. The findings provide a theoretical basis for designing and optimizing piezotronic devices, offering enhanced control over elastic wave propagation in composite structures.

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引用次数: 0

Latent model-free adaptive control of nonlinear multivariable processes via virtual dynamic data modeling

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-30 DOI: 10.1016/j.apm.2025.115977

Mingming Lin, Ronghu Chi

Model free adaptive control has become an excellent method for complex processes with no model information available. However, the increasing scale of production in modern industries makes it difficult to model and control these processes. Therefore, a novel latent model-free adaptive control is proposed to deal with the high-dimension and collinearity problem of process variables in real-world industries. First, a nonlinear autoregressive moving average with exogenous input model is designed as a dynamical partial least squares inner relationship in the latent space to formulate the system input and output dynamics in a most common way. Then, a latent full-form dynamic linearization is developed to make the nonlinear model linearly parametric and a latent full-form dynamic linearization based virtual dynamical partial least squares data model is proposed consequently. An estimation algorithm is developed for identifying the unknown parameters of the virtual dynamical data model. By means of the virtual dynamical data model, the latent model-free adaptive control method is proposed by designing and optimizing a quadratic objective function. Theoretical analysis and simulation study confirm the efficiency of the latent model-free adaptive control.

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引用次数: 0

Grey relational analysis in the metric space of continuous functions: Foundations, extensions, and applications

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-29 DOI: 10.1016/j.apm.2025.115978

Baolei Wei , Yuwen Li

This paper derives a piecewise linear interpolation representation of grey relational analysis from its algebraic form, laying the mathematical foundation in the metric space of continuous functions. By introducing cubic spline interpolation, a novel functional-type model is proposed, and its geometric invariant properties are thoroughly analyzed. Furthermore, physics-informed high-order and high-dimensional extensions are developed and validated through two real-world applications: analyzing erosion and wear of gun barrels and clustering polluted cities in China's Yangtze River Delta region. The results demonstrate the usability and superiority, particularly in terms of accuracy and interpretability.

引用次数: 0

Control switch layout-design for active structural acoustic control of piezoelectric curved shell structures in shallow sea

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-28 DOI: 10.1016/j.apm.2025.115985

Linyuan Shang, Jingjuan Zhai

Existing acoustic topology optimization methods integrate the traditional finite element method-boundary element method (FEM-BEM) to optimize the layout of piezoelectric structure in free space, thereby improving the performance of active structural acoustic control (ASAC). Unfortunately, the inability of the traditional finite element method-boundary element method to deal with the reflected sound from waveguide boundaries limits their application in the optimization design of piezoelectric structures submerged in shallow seas. In addition, previous piezoelectric structure layouts designed for specific working conditions cannot realize online control of acoustic radiation for diverse working conditions in engineering practice. Therefore, a novel topological layout-design scheme for control switches of piezoelectric curved shell structures to bring down acoustic radiation in a shallow sea is proposed based on the velocity feedback control scheme and the combined method of the FEM, the added mass method (AM) and the image method-based boundary element method (I-BEM), which can handle the fluid-structure interaction and boundary sound reflection problems. A finite element formulation for the piezoelectric curved shell element is presented. In this context, the sensitivity analysis equation for sound pressure level is derived. The optimization problem is formulated in the framework of an artificial active damping model with penalization. The volumetric densities describing the control switch distribution are assigned as the design variables. Numerical examples demonstrate the validity of the proposed optimization approach and its potential applications in practical designs.

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引用次数: 0

Flat elliptical matrix crack impact on bending, stresses and stability of beam-like aerospace structures

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling

Pub Date : 2025-01-27 DOI: 10.1016/j.apm.2025.115963

Piotr Jankowski, Krzysztof Kamil Żur

For the first time, the present investigation comprehensively examines the effect of elliptical crack parameters and positions in individual or system layers on stress distributions, bifurcation buckling points, and bending under different loads of beam-like aerospace structural members. It also constitutes an effort to develop a model of graphene nanoplatelets reinforced multilayer composite beams with an elliptical matrix crack. Mechanical properties of the beam are obtained based on the modified Halpin–Tsai micromechanical model that is well-established experimentally and presented in the literature. Variational Euler–Lagrange equations of motion were derived based on assumptions of Reddy's shear deformation theory and linear Green–Lagrange strain tensor. Moreover, physical neutral surface properties were used to formulate the boundary value problem for unsymmetric nanocomposite laminates correctly. In addition, graphene platelet and crack distribution move neutral surface position in nanocomposite layers. Numerical results are obtained via the Fourier series method and by solving nonlinear multi-parametric characteristic equations. Before a complete numerical investigation, an example validation study of the obtained solution was performed. The results addressed how several layers, diverse elliptical matrix crack patterns, density, graphene nanoplatelets distribution, and weight fraction influence bending and shear stress distribution, critical axial forces, and beam bending under diverse loads. One exception where results for the first and last three layers with cracks do not overlap is FG-V distribution with nonsymmetric material properties for the midplane. Based on the study, in the case of nanofiller-reinforced nanocomposite with 21 layers, three cracked layers hardly influence bending behaviour and stress distribution. Finally, it is shown that the neutral surface position is insignificantly shifted compared to the beam's middle surface for diverse crack combinations and functionally graded graphene platelet distributions.

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