Mathematical and Computational Applications

23 pages, 49612 KiB

Open AccessArticle

Evaluation of Physics-Informed Neural Network Solution Accuracy and Efficiency for Modeling Aortic Transvalvular Blood Flow

by Jacques Francois Du Toit and Ryno Laubscher

Math. Comput. Appl. 2023, 28(2), 62; https://doi.org/10.3390/mca28020062 - 14 Apr 2023

Viewed by 3476

Abstract

Physics-Informed Neural Networks (PINNs) are a new class of machine learning algorithms that are capable of accurately solving complex partial differential equations (PDEs) without training data. By introducing a new methodology for fluid simulation, PINNs provide the opportunity to address challenges that were [...] Read more.

Physics-Informed Neural Networks (PINNs) are a new class of machine learning algorithms that are capable of accurately solving complex partial differential equations (PDEs) without training data. By introducing a new methodology for fluid simulation, PINNs provide the opportunity to address challenges that were previously intractable, such as PDE problems that are ill-posed. PINNs can also solve parameterized problems in a parallel manner, which results in favorable scaling of the associated computational cost. The full potential of the application of PINNs to solving fluid dynamics problems is still unknown, as the method is still in early development: many issues remain to be addressed, such as the numerical stiffness of the training dynamics, the shortage of methods for simulating turbulent flows and the uncertainty surrounding what model hyperparameters perform best. In this paper, we investigated the accuracy and efficiency of PINNs for modeling aortic transvalvular blood flow in the laminar and turbulent regimes, using various techniques from the literature to improve the simulation accuracy of PINNs. Almost no work has been published, to date, on solving turbulent flows using PINNs without training data, as this regime has proved difficult. This paper aims to address this gap in the literature, by providing an illustrative example of such an application. The simulation results are discussed, and compared to results from the Finite Volume Method (FVM). It is shown that PINNs can closely match the FVM solution for laminar flow, with normalized maximum velocity and normalized maximum pressure errors as low as

5.74 %

and

9.29 %

, respectively. The simulation of turbulent flow is shown to be a greater challenge, with normalized maximum velocity and normalized maximum pressure errors only as low as

41.8 %

and

113 %

, respectively. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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19 pages, 1098 KiB

Open AccessReview

An Overview of the Vision-Based Human Action Recognition Field

by Fernando Camarena, Miguel Gonzalez-Mendoza, Leonardo Chang and Ricardo Cuevas-Ascencio

Math. Comput. Appl. 2023, 28(2), 61; https://doi.org/10.3390/mca28020061 - 13 Apr 2023

Cited by 6 | Viewed by 4616

Abstract

Artificial intelligence’s rapid advancement has enabled various applications, including intelligent video surveillance systems, assisted living, and human–computer interaction. These applications often require one core task: video-based human action recognition. Research in human video-based human action recognition is vast and ongoing, making it difficult [...] Read more.

Artificial intelligence’s rapid advancement has enabled various applications, including intelligent video surveillance systems, assisted living, and human–computer interaction. These applications often require one core task: video-based human action recognition. Research in human video-based human action recognition is vast and ongoing, making it difficult to assess the full scope of available methods and current trends. This survey concisely explores the vision-based human action recognition field and defines core concepts, including definitions and explanations of the common challenges and most used datasets. Additionally, we provide in an easy-to-understand manner the literature approaches and their evolution over time, emphasizing intuitive notions. Finally, we explore current research directions and potential future paths. The core goal of this work is to provide future works with a shared understanding of fundamental ideas and clear intuitions about current works and find new research opportunities. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2022)

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14 pages, 7716 KiB

Open AccessArticle

A Computational Magnetohydrodynamic Modelling Study on Plasma Arc Behaviour in Gasification Applications

by Quinn G. Reynolds, Thokozile P. Kekana and Buhle S. Xakalashe

Math. Comput. Appl. 2023, 28(2), 60; https://doi.org/10.3390/mca28020060 - 12 Apr 2023

Viewed by 1991

Abstract

The application of direct-current plasma arc furnace technology to the problem of coal gasification is investigated using computational multiphysics models of the plasma arc inside such units. An integrated modelling workflow for the study of DC plasma arc discharges in synthesis gas atmospheres [...] Read more.

The application of direct-current plasma arc furnace technology to the problem of coal gasification is investigated using computational multiphysics models of the plasma arc inside such units. An integrated modelling workflow for the study of DC plasma arc discharges in synthesis gas atmospheres is presented. The thermodynamic and transport properties of the plasma are estimated using statistical mechanics calculations and are shown to have highly non-linear dependencies on the gas composition and temperature. A computational magnetohydrodynamic solver for electromagnetically coupled flows is developed and implemented in the OpenFOAM^® framework, and the behaviour of three-dimensional transient simulations of arc formation and dynamics is studied in response to different plasma gas compositions and furnace operating conditions. To demonstrate the utility of the methods presented, practical engineering results are obtained from an ensemble of simulation results for a pilot-scale furnace design. These include the stability of the arc under different operating conditions and the dependence of voltage–current relationships on the arc length, which are relevant in understanding the industrial operability of plasma arc furnaces used for waste coal gasification. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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13 pages, 1202 KiB

Open AccessEditor’s ChoiceArticle

A Parallel Solver for FSI Problems with Fictitious Domain Approach

by Daniele Boffi, Fabio Credali, Lucia Gastaldi and Simone Scacchi

Math. Comput. Appl. 2023, 28(2), 59; https://doi.org/10.3390/mca28020059 - 10 Apr 2023

Cited by 1 | Viewed by 1843

Abstract

We present and analyze a parallel solver for the solution of fluid structure interaction problems described by a fictitious domain approach. In particular, the fluid is modeled by the non-stationary incompressible Navier–Stokes equations, while the solid evolution is represented by the elasticity equations. [...] Read more.

We present and analyze a parallel solver for the solution of fluid structure interaction problems described by a fictitious domain approach. In particular, the fluid is modeled by the non-stationary incompressible Navier–Stokes equations, while the solid evolution is represented by the elasticity equations. The parallel implementation is based on the PETSc library and the solver has been tested in terms of robustness with respect to mesh refinement and weak scalability by running simulations on a Linux cluster. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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14 pages, 2817 KiB

Open AccessArticle

Digital Twin Hybrid Modeling for Enhancing Guided Wave Ultrasound Inspection Signals in Welded Rails

by Dineo A. Ramatlo, Daniel N. Wilke and Philip W. Loveday

Math. Comput. Appl. 2023, 28(2), 58; https://doi.org/10.3390/mca28020058 - 10 Apr 2023

Cited by 2 | Viewed by 2202

Abstract

Guided wave ultrasound (GWU) systems have been widely used for monitoring structures such as rails, pipelines, and plates. In railway tracks, the monitoring process involves the complicated propagation of waves over several hundred meters. The propagating waves are multi-modal and interact with discontinuities [...] Read more.

Guided wave ultrasound (GWU) systems have been widely used for monitoring structures such as rails, pipelines, and plates. In railway tracks, the monitoring process involves the complicated propagation of waves over several hundred meters. The propagating waves are multi-modal and interact with discontinuities differently, increasing complexity and leading to different response signals. When the researcher wants to gain insight into the behavior of guided waves, predicting response signals for different combinations of modes becomes necessary. However, the task can become computationally costly when physics-based models are used. Digital twins can enable a practitioner to deal systematically with the complexities of guided wave monitoring in practical or user-specified settings. This paper investigates the use of a hybrid digital model of an operational rail track to predict response signals for varying user-specified settings, specifically, the prediction of response signals for various combinations of modes of propagation in the rail. The digital twin hybrid model employs a physics-based model and a data-driven model. The physics-based model simulates the wave propagation response using techniques developed from the traditional 3D finite element method and the 2D semi-analytical finite element method (FEM). The physics-based model is used to generate virtual experimental signals containing different combinations of modes of propagation. These response signals are used to train the data-driven model based on a variational auto-encoder (VAE). Given an input baseline signal containing only the most dominant mode excited by a transducer, the VAE is trained to predict an inspection signal with increased complexity according to the specified combination of modes. The results show that, once the VAE has been trained, it can be used to predict inspection signals for different combinations of propagating modes, thus replacing the physics-based model, which is computationally costly. In the future, the VAE architecture will be adapted to predict response signals for varying environmental and operational conditions. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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15 pages, 4951 KiB

Open AccessArticle

Spatio-Temporal Gradient Enhanced Surrogate Modeling Strategies

by Johann M. Bouwer, Daniel N. Wilke and Schalk Kok

Math. Comput. Appl. 2023, 28(2), 57; https://doi.org/10.3390/mca28020057 - 8 Apr 2023

Cited by 1 | Viewed by 1836

Abstract

This research compares the performance of space-time surrogate models (STSMs) and network surrogate models (NSMs). Specifically, when the system response varies over time (or pseudo-time), the surrogates must predict the system response. A surrogate model is used to approximate the response of computationally [...] Read more.

This research compares the performance of space-time surrogate models (STSMs) and network surrogate models (NSMs). Specifically, when the system response varies over time (or pseudo-time), the surrogates must predict the system response. A surrogate model is used to approximate the response of computationally expensive spatial and temporal fields resulting from some computational mechanics simulations. Within a design context, a surrogate takes a vector of design variables that describe a current design and returns an approximation of the design’s response through a pseudo-time variable. To compare various radial basis function (RBF) surrogate modeling approaches, the prediction of a load displacement path of a snap-through structure is used as an example numerical problem. This work specifically considers the scenario where analytical sensitivities are available directly from the computational mechanics’ solver and therefore gradient enhanced surrogates are constructed. In addition, the gradients are used to perform a domain transformation preprocessing step to construct surrogate models in a more isotropic domain, which is conducive to RBFs. This work demonstrates that although the gradient-based domain transformation scheme offers a significant improvement to the performance of the space-time surrogate models (STSMs), the network surrogate model (NSM) is far more robust. This research offers explanations for the improved performance of NSMs over STSMs and recommends future research to improve the performance of STSMs. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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13 pages, 1031 KiB

Open AccessArticle

A Computational Method with Maple for Finding the Maximum Curvature of a Bézier-Spline Curve

by Henk Pijls and Le Phuong Quan

Math. Comput. Appl. 2023, 28(2), 56; https://doi.org/10.3390/mca28020056 - 8 Apr 2023

Cited by 2 | Viewed by 2014

Abstract

In this paper, we propose two Maple procedures and some related utilities to determine the maximum curvature of a cubic Bézier-spline curve that interpolates an ordered set of points in

R^{2}

or

R^{3}

. The procedures are designed from closed-form formulas [...] Read more.

In this paper, we propose two Maple procedures and some related utilities to determine the maximum curvature of a cubic Bézier-spline curve that interpolates an ordered set of points in

R^{2}

or

R^{3}

. The procedures are designed from closed-form formulas for such open and closed curves. Full article

(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications 2023)

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20 pages, 5672 KiB

Open AccessArticle

Fourier Image Analysis of Multiphase Interfaces to Quantify Primary Atomization

by Johannes C. Joubert, Daniel N. Wilke and Patrick Pizette

Math. Comput. Appl. 2023, 28(2), 55; https://doi.org/10.3390/mca28020055 - 3 Apr 2023

Cited by 1 | Viewed by 1637

Abstract

This work describes a post-processing scheme for multiphase flow systems to characterize primary atomization. The scheme relies on the 2D fast Fourier transform (FFT) to separate the inherently multi-scale features present in the flow results. Emphasis is put on the robust quantitative analysis [...] Read more.

This work describes a post-processing scheme for multiphase flow systems to characterize primary atomization. The scheme relies on the 2D fast Fourier transform (FFT) to separate the inherently multi-scale features present in the flow results. Emphasis is put on the robust quantitative analysis enabled by this scheme, with this work specifically focusing on comparing atomizer nozzle designs. The generalized finite difference (GFD) method is used to simulate a high pressure gas injected into a viscous liquid stream. The proposed scheme is applied to time-averaged results exclusively. The scheme is used to evaluate both the surface and volume features of the fluid system. Due to the better recovery of small-scale features using the proposed scheme, the benefits of post-processing multiphase surface information rather than fluid volume information was shown. While the volume information lacks the fine-scale details of the surface information, the duality between interfaces and fluid volumes leads to similar trends related to the large-scale spatial structure recovered from both surface- and volume-based data sets. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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18 pages, 4298 KiB

Open AccessArticle

Applicability of Extreme Vertices Design in the Compositional Optimization of 3D-Printed Lightweight High-Entropy-Alloy/B₄C/ZrO₂/Titanium Trihybrid Aero-Composite

by Abayomi Adewale Akinwande, Dimitry Moskovskikh, Elena Romanovskaia, Oluwatosin Abiodun Balogun, J. Pradeep Kumar and Valentin Romanovski

Math. Comput. Appl. 2023, 28(2), 54; https://doi.org/10.3390/mca28020054 - 3 Apr 2023

Cited by 5 | Viewed by 2342

Abstract

Recent studies have shown the benefits of utilizing ceramic particles as reinforcement in metal alloys; nevertheless, certain drawbacks, including loss of ductility, embrittlement, and decreases in toughness, have been noted. For the objective of obtaining balanced performance, experts have suggested the addition of [...] Read more.

Recent studies have shown the benefits of utilizing ceramic particles as reinforcement in metal alloys; nevertheless, certain drawbacks, including loss of ductility, embrittlement, and decreases in toughness, have been noted. For the objective of obtaining balanced performance, experts have suggested the addition of metal particles as supplement to the ceramic reinforcement. Consequently, high-performance metal hybrid composites have been developed. However, achieving the optimal mix for the reinforcement combination with regards to the optimal performance of developed composite remains a challenge. This research aimed to determine the optimal mixture of Al₅₀Cu₁₀Sn₅Mg₂₀Zn₁₀Ti₅ lightweight high-entropy alloy (LHEA), B4C, and ZrO₂ for the fabrication of trihybrid titanium composites via direct laser deposition. A mixture design was involved in the experimental design, and experimental data were modeled and optimized to achieve the optimal performance of the trihybrid composite. The ANOVA, response surface plots, and ternary maps analyses of the experimental results revealed that various combinations of reinforcement particles displayed a variety of response trends. Moreover, the analysis showed that these reinforcements significantly contributed to the magnitudes and trends of the responses. The generated models were competent for predicting response, and the best formulation consisted of 8.4% LHEA, 1.2% B4C, and 2.4% ZrO₂. Full article

(This article belongs to the Special Issue Computational Applications in Engineering, Experimental Optimization, and Sustainable Manufacturing)

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17 pages, 10213 KiB

Open AccessArticle

Generative Design of Soft Robot Actuators Using ESP

by Martin Philip Venter and Izak Johannes Joubert

Math. Comput. Appl. 2023, 28(2), 53; https://doi.org/10.3390/mca28020053 - 3 Apr 2023

Cited by 3 | Viewed by 2284

Abstract

Soft robotics is an emerging field that leverages the compliant nature of materials to control shape and behaviour. However, designing soft robots presents a challenge, as they do not have discrete points of articulation and instead articulate through deformation in whole regions of [...] Read more.

Soft robotics is an emerging field that leverages the compliant nature of materials to control shape and behaviour. However, designing soft robots presents a challenge, as they do not have discrete points of articulation and instead articulate through deformation in whole regions of the robot. This results in a vast, unexplored design space with few established design methods. This paper presents a practical generative design process that combines the Encapsulation, Syllabus, and Pandamonium method with a reduced-order model to produce results comparable to the existing state-of-the-art in reduced design time while including the human designer meaningfully in the design process and facilitating the inclusion of other numerical techniques such as Markov chain Monte Carlo methods. Using a combination of reduced-order models, L-systems, MCMC, curve matching, and optimisation, we demonstrate that our method can produce functional 2D articulating soft robot designs in less than 1 s, a significant reduction in design time compared to monolithic methods, which can take several days. Additionally, we qualitatively show how to extend our approach to produce more complex 3D robots, such as an articulating tentacle with multiple grippers. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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17 pages, 3766 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A PINN Surrogate Modeling Methodology for Steady-State Integrated Thermofluid Systems Modeling

by Kristina Laugksch, Pieter Rousseau and Ryno Laubscher

Math. Comput. Appl. 2023, 28(2), 52; https://doi.org/10.3390/mca28020052 - 27 Mar 2023

Cited by 1 | Viewed by 2596

Abstract

Physics-informed neural networks (PINNs) were developed to overcome the limitations associated with the acquisition of large training data sets that are commonly encountered when using purely data-driven machine learning methods. This paper proposes a PINN surrogate modeling methodology for steady-state integrated thermofluid systems [...] Read more.

Physics-informed neural networks (PINNs) were developed to overcome the limitations associated with the acquisition of large training data sets that are commonly encountered when using purely data-driven machine learning methods. This paper proposes a PINN surrogate modeling methodology for steady-state integrated thermofluid systems modeling based on the mass, energy, and momentum balance equations, combined with the relevant component characteristics and fluid property relationships. The methodology is applied to two thermofluid systems that encapsulate the important phenomena typically encountered, namely: (i) a heat exchanger network with two different fluid streams and components linked in series and parallel; and (ii) a recuperated closed Brayton cycle with various turbomachines and heat exchangers. The results generated with the PINN models were compared to benchmark solutions generated via conventional, physics-based thermofluid process models. The largest average relative errors are 0.17% and 0.93% for the heat exchanger network and Brayton cycle, respectively. It was shown that the use of a hybrid Adam-TNC optimizer requires between 180 and 690 fewer iterations during the training process, thus providing a significant computational advantage over a pure Adam optimization approach. The resulting PINN models can make predictions 75 to 88 times faster than their respective conventional process models. This highlights the potential for PINN surrogate models as a valuable engineering tool in component and system design and optimization, as well as in real-time simulation for anomaly detection, diagnosis, and forecasting. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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22 pages, 3475 KiB

Open AccessArticle

A Generalized Finite Difference Scheme for Multiphase Flow

by Johannes C. Joubert, Daniel N. Wilke and Patrick Pizette

Math. Comput. Appl. 2023, 28(2), 51; https://doi.org/10.3390/mca28020051 - 26 Mar 2023

Cited by 1 | Viewed by 2133

Abstract

This paper presents a GPU-based, incompressible, multiphase generalized finite difference solver for simulating multiphase flow. The method includes a dampening scheme that allows for large density ratio cases to be simulated. Two verification studies are performed by simulating the relaxation of a square [...] Read more.

This paper presents a GPU-based, incompressible, multiphase generalized finite difference solver for simulating multiphase flow. The method includes a dampening scheme that allows for large density ratio cases to be simulated. Two verification studies are performed by simulating the relaxation of a square droplet surrounded by a light fluid and a bubble rising in a denser fluid. The scheme is also used to simulate the collision of binary droplets at moderate Reynolds numbers (250–550). The effects of the surface tension and density ratio are explored in this work by considering cases with Weber numbers of 8 and 180 and density ratios of 2:1 and 1000:1. The robustness of the multiphase scheme is highlighted when resolving thin fluid structures arising in both high and low density ratio cases at We = 180. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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14 pages, 3663 KiB

Open AccessArticle

Numerical Analysis of the Effect of the Vortex Finder on the Hydrocyclone’s Split Water Ratio and Separation Performance

by Vuyo T. Hashe and Thokozani J. Kunene

Math. Comput. Appl. 2023, 28(2), 50; https://doi.org/10.3390/mca28020050 - 22 Mar 2023

Viewed by 1955

Abstract

Hydrocyclones are devices used in numerous areas of the chemical, food, and mineral industries to separate fine particles. A hydrocyclone with a diameter of d50 mm was modeled using the commercial Simcenter STAR-CCM+13 computational fluid dynamics (CFD) simulation package. The numerical methods [...] Read more.

Hydrocyclones are devices used in numerous areas of the chemical, food, and mineral industries to separate fine particles. A hydrocyclone with a diameter of d50 mm was modeled using the commercial Simcenter STAR-CCM+13 computational fluid dynamics (CFD) simulation package. The numerical methods confirmed the results of the different parameters, such as the properties of the volume fraction, based on CFD simulations. Reynolds Stress Model (RSM) and the combined technique of volume of fluid (VOF) and discrete element model (DEM) for water and air models were selected to evaluate semi-implicit pressure-linked equations and combine the momentum with continuity laws to obtain derivatives of the pressure. The targeted particle sizes were in a range of 8–100 microns for a dewatering application. The depth of the vortex finder was varied to 20 mm, 30 mm, and 35 mm to observe the effects of pressure drop and separation efficiency. The split water ratio increased toward a 50% split of overflow and underflow rates as the length of the vortex finder increased. It results in better particle separation when there is a high injection rate at the inlet. The tangential and axial velocities increased as the vortex finder length increased. As the depth of the vortex finder length increased, the time for particle re-entrainment into the underflow stream increased, and the separation efficiency improved. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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12 pages, 310 KiB

Open AccessFeature PaperArticle

A Survey on the Hausdorff Dimension of Intersections

by Pertti Mattila

Math. Comput. Appl. 2023, 28(2), 49; https://doi.org/10.3390/mca28020049 - 22 Mar 2023

Cited by 1 | Viewed by 1612

Abstract

Let A and B be Borel subsets of the Euclidean n-space with

dim A + dim B > n

. This is a survey on the following question: what can we say about the Hausdorff dimension of the intersections [...] Read more.

Let A and B be Borel subsets of the Euclidean n-space with

dim A + dim B > n

. This is a survey on the following question: what can we say about the Hausdorff dimension of the intersections

A \cap (g (B) + z)

for generic orthogonal transformations g and translations by z? Full article

(This article belongs to the Special Issue Geometry of Deterministic and Random Fractals)

17 pages, 2186 KiB

Open AccessArticle

An Efficient Optimal Derivative-Free Fourth-Order Method and Its Memory Variant for Non-Linear Models and Their Dynamics

by Himani Sharma, Munish Kansal and Ramandeep Behl

Math. Comput. Appl. 2023, 28(2), 48; https://doi.org/10.3390/mca28020048 - 22 Mar 2023

Cited by 1 | Viewed by 1488

Abstract

We propose a new optimal iterative scheme without memory free from derivatives for solving non-linear equations. There are many iterative schemes existing in the literature which either diverge or fail to work when

f^{'} (x) = 0

. However, our [...] Read more.

We propose a new optimal iterative scheme without memory free from derivatives for solving non-linear equations. There are many iterative schemes existing in the literature which either diverge or fail to work when

f^{'} (x) = 0

. However, our proposed scheme works even in these cases. In addition, we extended the same idea for iterative methods with memory with the help of self-accelerating parameters estimated from the current and previous approximations. As a result, the order of convergence increased from four to seven without the addition of any further functional evaluation. To confirm the theoretical results, numerical examples and comparisons with some of the existing methods are included which reveal that our scheme is more efficient than the existing schemes. Furthermore, basins of attraction are also included to describe a clear picture of the convergence of the proposed method as well as some of the existing methods. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)

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12 pages, 1763 KiB

Open AccessArticle

A Hierarchical Design Framework for the Design of Soft Robots

by Philip Frederik Ligthart and Martin Philip Venter

Math. Comput. Appl. 2023, 28(2), 47; https://doi.org/10.3390/mca28020047 - 21 Mar 2023

Cited by 1 | Viewed by 2314

Abstract

This paper demonstrates the effectiveness of a hierarchical design framework in developing environment-specific behaviour for fluid-actuated soft robots. Our proposed framework employs multi-step optimisation and reduced-order modelling to reduce the computational expense associated with simulating non-linear materials used in the design process. Specifically, [...] Read more.

This paper demonstrates the effectiveness of a hierarchical design framework in developing environment-specific behaviour for fluid-actuated soft robots. Our proposed framework employs multi-step optimisation and reduced-order modelling to reduce the computational expense associated with simulating non-linear materials used in the design process. Specifically, our framework requires the designer to make high-level decisions to simplify the optimisations, targeting simple objectives in earlier steps and more complex objectives in later steps. We present a case study, where our proposed framework is compared to a conventional direct design approach for a simple 2D design. A soft pneumatic bending actuator was designed that is able to perform asymmetrical motion when actuated cyclically. Our results show that the hierarchical framework can find almost 2.5 times better solutions in less than 3% of the time when compared to a direct design approach. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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19 pages, 2211 KiB

Open AccessArticle

An Analysis of Numerical Homogenisation Methods Applied on Corrugated Paperboard

by Rhoda Ngira Aduke, Martin P. Venter and Corné J. Coetzee

Math. Comput. Appl. 2023, 28(2), 46; https://doi.org/10.3390/mca28020046 - 20 Mar 2023

Cited by 2 | Viewed by 2254

Abstract

Corrugated paperboard is a sandwich structure composed of wavy paper (fluting) bonded between two flat paper sheets (liners). The analysis of an entire package using three-dimensional numerical finite element models is computationally expensive due to the waved geometry of the board that requires [...] Read more.

Corrugated paperboard is a sandwich structure composed of wavy paper (fluting) bonded between two flat paper sheets (liners). The analysis of an entire package using three-dimensional numerical finite element models is computationally expensive due to the waved geometry of the board that requires the use of a relatively large number of elements in a simulation. Because of this, homogenisation approaches are used to evaluate equivalent homogenous models with similar material properties. These techniques have been successfully implemented by various researchers to evaluate the strength of corrugated paperboard. However, studies analysing the various homogenisation techniques and their ranges of applicability are limited. This study analyses the application of three homogenisation techniques: classical laminate plate theory, first-order shear deformation theory and deformation energy equivalence method in the evaluation of effective elastic material properties. In addition, inverse analysis has been applied to determine the effective properties of the board. Finite element models have been used to evaluate the accuracy of the three homogenisation techniques in comparison to the inverse method in modelling four-point bending tests and the results reported. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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20 pages, 352 KiB

Open AccessArticle

On Some Fixed Point Iterative Schemes with Strong Convergence and Their Applications

by Anku, Mona Narang and Vinay Kanwar

Math. Comput. Appl. 2023, 28(2), 45; https://doi.org/10.3390/mca28020045 - 20 Mar 2023

Viewed by 1995

Abstract

In this paper, a new one-parameter class of fixed point iterative method is proposed to approximate the fixed points of contractive type mappings. The presence of an arbitrary parameter in the proposed family increases its interval of convergence. Further, we also propose new [...] Read more.

In this paper, a new one-parameter class of fixed point iterative method is proposed to approximate the fixed points of contractive type mappings. The presence of an arbitrary parameter in the proposed family increases its interval of convergence. Further, we also propose new two-step and three-step fixed point iterative schemes. We also discuss the stability, strong convergence and fastness of the proposed methods. Furthermore, numerical experiments are performed to check the applicability of the new methods, and these have been compared with well-known similar existing methods in the literature. Full article

(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)

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13 pages, 10586 KiB

Open AccessArticle

Experimental Study of Coupled Torsional and Lateral Vibration of Vertical Rotor-to-Stator Contact in an Inviscid Fluid

by Desejo Filipeson Sozinando, Bernard Xavier Tchomeni and Alfayo Anyika Alugongo

Math. Comput. Appl. 2023, 28(2), 44; https://doi.org/10.3390/mca28020044 - 20 Mar 2023

Cited by 1 | Viewed by 2222

Abstract

Diagnosis of faults in a rotor system operating in a fluid is a complex task in the field of rotating machinery. In an ideal scenario, a forced shutdown due to rotor-stator contact failure would necessitate the replacement of the rotor or stator. However, [...] Read more.

Diagnosis of faults in a rotor system operating in a fluid is a complex task in the field of rotating machinery. In an ideal scenario, a forced shutdown due to rotor-stator contact failure would necessitate the replacement of the rotor or stator. However, factors such as time constraints, economic considerations, and the aging of infrastructure make it imprudent to abruptly shut down machinery that can still be safe to operate. The purpose of this paper is to present an experimental study that validates the theoretical results of the dynamic behavior and friction detection using the wavelet synchrosqueezing transformation (WSST) method for recurrent rotor-stator contacts in a fluid environment, as presented in a previous study. The investigation focused on the analysis of whirl orbits, shaft deflection, and fluctuation frequency during passage through critical speeds. The WSST method was used to decompose the dynamic responses of the rotor in the supercritical speed zone into several supercomponents. The variation of the high-frequency component was studied based on the fluctuation of the instantaneous frequency (IF) technique. Additionally, the fast Fourier transform (FFT) method, in conjunction with the WSST technique, was used to calculate the variation in the amplitude of high-order frequencies in the vibration signal spectrum. The experimental study revealed that the split in resonance caused by rubbing effects is reduced when the rotor and stator interact with an inviscid fluid. However, despite the effects of elasticity and fluid boundaries generating self-excitation at low frequencies and uneven motion due to stator clearance, the experimental results were consistent with the theoretical analysis, demonstrating the effectiveness of the contact detection method based on WSST. Full article

(This article belongs to the Special Issue Computational Applications in Engineering, Experimental Optimization, and Sustainable Manufacturing)

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17 pages, 6288 KiB

Open AccessArticle

CFD Modelling of Gas-Solid Reactions: Analysis of Iron and Manganese Oxides Reduction with Hydrogen

by Mopeli Khama and Quinn Reynolds

Math. Comput. Appl. 2023, 28(2), 43; https://doi.org/10.3390/mca28020043 - 18 Mar 2023

Viewed by 2317

Abstract

Metallurgical processes are characterized by a complex interplay of heat and mass transfer, momentum transfer, and reaction kinetics, and these interactions play a crucial role in reactor performance. Integrating chemistry and transport results in stiff and non-linear equations and longer time and length [...] Read more.

Metallurgical processes are characterized by a complex interplay of heat and mass transfer, momentum transfer, and reaction kinetics, and these interactions play a crucial role in reactor performance. Integrating chemistry and transport results in stiff and non-linear equations and longer time and length scales, which ultimately leads to a high computational expense. The current study employs the OpenFOAM solver based on a fictitious domain method to analyze gas-solid reactions in a porous medium using hydrogen as a reducing agent. The reduction of oxides with hydrogen involves the hierarchical phenomena that influence the reaction rates at various temporal and spatial scales; thus, multi-scale models are needed to bridge the length scale from micro-scale to macro-scale accurately. As a first step towards developing such capabilities, the current study analyses OpenFOAM reacting flow methods in cases related to hydrogen reduction of iron and manganese oxides. Since reduction of the oxides of interest with hydrogen requires significant modifications to the current industrial processes, this model can aid in the design and optimization. The model was verified against experimental data and the dynamic features of the porous medium observed as the reaction progresses is well captured by the model. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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15 pages, 6200 KiB

Open AccessArticle

Numerical Modeling of Cavitation Rates and Noise Acoustics of Marine Propellers

by Kwanda Mercury Dlamini, Vuyo Terrence Hashe and Thokozani Justin Kunene

Math. Comput. Appl. 2023, 28(2), 42; https://doi.org/10.3390/mca28020042 - 15 Mar 2023

Cited by 1 | Viewed by 2579

Abstract

The study numerically investigated the noise dissipation, cavitation, output power, and energy produced by marine propellers. A Ffowcs Williams–Hawkings (FW–H) model was used to determine the effects of three different marine propellers with three to five blades and a fixed advancing ratio. The [...] Read more.

The study numerically investigated the noise dissipation, cavitation, output power, and energy produced by marine propellers. A Ffowcs Williams–Hawkings (FW–H) model was used to determine the effects of three different marine propellers with three to five blades and a fixed advancing ratio. The large-eddy Simulations model best predicted the turbulent structures’ spatial and temporal variation, which would better illustrate the flow physics. It was found that a high angle of incidence between the blade’s leading edge and the water flow direction typically causes the hub vortex to cavitate. The roll-up of the cavitating tip vortex was closely related to propeller noise. The five-blade propeller was quieter under the same dynamic conditions, such as the advancing ratio, compared to three- or four-blade propellers. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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19 pages, 12377 KiB

Open AccessArticle

Effect of Adhesive Materials in Re-Attachment of Crown and Crown–Root Fractures of Permanent Maxillary Anterior Tooth: A Computational Study

by Anshika Garg, Shubham Gupta, Nitesh Tewari, Sukeshana Srivastav and Arnab Chanda

Math. Comput. Appl. 2023, 28(2), 41; https://doi.org/10.3390/mca28020041 - 10 Mar 2023

Cited by 3 | Viewed by 2492

Abstract

Traumatic dental injuries (TDI) are frequent among individuals of all ages, with a prevalence ranging from 12–22%, with crown and crown–root fractures being the most common. Fragment reattachment using light-cured nanocomposites is the recommended method for the management of these fractures. Though there [...] Read more.

Traumatic dental injuries (TDI) are frequent among individuals of all ages, with a prevalence ranging from 12–22%, with crown and crown–root fractures being the most common. Fragment reattachment using light-cured nanocomposites is the recommended method for the management of these fractures. Though there are several clinical studies that have assessed the efficacy of such materials, an in-silico characterization of the effects of traumatic forces on the re-attached fragments has never been performed. Hence, this study aimed to evaluate the efficacy of various adhesive materials in crown and crown–root reattachments through computational modelling. A full-scale permanent maxillary anterior tooth model was developed by segmenting 3D scanned cone beam computed tomography (CBCT) images of the pulp, root, and enamel precisely. The full-scale 3D tooth model was then subjected to a novel numerical cutting operation to describe the crown and crown–root fractures. The fractured tooth models were then filled computationally with three commonly used filler (or adhesive) materials, namely flowable composite, resin cement, and resin adhesive, and subjected to masticatory and traumatic loading conditions. The flowable composite demonstrated a statistically significant difference and the lowest produced stresses when subjected to masticatory loading. Resin cement demonstrated reduced stress values for crown–root fractures that were masticatory loaded after being reattached using adhesive materials. During traumatic loading, resin cement demonstrated lower displacements and stress values across both fractures. The novel findings reported in this study are anticipated to assist dentists in selecting the most appropriate adhesive materials that induce the least stress on the reattached tooth when subjected to second trauma, for both crown and crown–root fractures. Full article

(This article belongs to the Special Issue Mathematical and Computational Modelling in Mechanics of Materials and Structures)

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18 pages, 11533 KiB

Open AccessArticle

A Strain-Gauge-Based Method for the Compensation of Out-of-Plane Motions in 2D Digital Image Correlation

by Carl-Hein Visser, Gerhard Venter and Melody Neaves

Math. Comput. Appl. 2023, 28(2), 40; https://doi.org/10.3390/mca28020040 - 10 Mar 2023

Cited by 1 | Viewed by 1952

Abstract

When performing a digital image correlation (DIC) measurement, multi-camera stereo-DIC is generally preferred over single-camera 2D-DIC. Unlike 2D-DIC, stereo-DIC is able to minimise the in-plane strain error that results from out-of-plane motion. This makes 2D-DIC a less viable alternative for strain measurements than [...] Read more.

When performing a digital image correlation (DIC) measurement, multi-camera stereo-DIC is generally preferred over single-camera 2D-DIC. Unlike 2D-DIC, stereo-DIC is able to minimise the in-plane strain error that results from out-of-plane motion. This makes 2D-DIC a less viable alternative for strain measurements than stereo-DIC, despite being less financially and computationally expensive. This work, therefore, proposes a strain-gauge-based method for the compensation of errors from out-of-plane motion in 2D-DIC strain measurements on planar specimens. The method was first developed using equations for the theoretical strain error from out-of-plane motions in 2D-DIC and was then applied experimentally in tensile tests to two different dog-bone specimen geometries. The compensation method resulted in a clear reduction in the strain error in 2D-DIC. The strain-gauge-based method thus improves the accuracy of a 2D-DIC measurement, making it a more viable option for performing full-field strain measurements and providing a possible alternative in cases where stereo-DIC is not practical or is unavailable. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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14 pages, 502 KiB

Open AccessArticle

Prediction Interval for Compound Conway–Maxwell–Poisson Regression Model with Application to Vehicle Insurance Claim Data

by Jahnavi Merupula, V. S. Vaidyanathan and Christophe Chesneau

Math. Comput. Appl. 2023, 28(2), 39; https://doi.org/10.3390/mca28020039 - 9 Mar 2023

Viewed by 1797

Abstract

Regression models in which the response variable has a compound distribution have applications in actuarial science. For example, the aggregate claim amount in a vehicle insurance portfolio can be modeled using a compound Poisson distribution. In this paper, we propose a regression model, [...] Read more.

Regression models in which the response variable has a compound distribution have applications in actuarial science. For example, the aggregate claim amount in a vehicle insurance portfolio can be modeled using a compound Poisson distribution. In this paper, we propose a regression model, wherein the response variable is assumed to have a compound Conway–Maxwell–Poisson (CMP) distribution. This distribution is a parsimonious two-parameter Poisson distribution that accounts for both over- and under-dispersed count data, making it more suitable for application in various fields. A two-part methodology in the framework of a generalized linear model is proposed to estimate the parameters. Additionally, a method to obtain the prediction interval of the response variable is developed. The workings of the proposed methodology are illustrated through simulated data. An application of the compound CMP regression model to real-life vehicle insurance claims data is presented. Full article

(This article belongs to the Special Issue Statistical Inference in Linear Models)

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21 pages, 7882 KiB

Open AccessArticle

Performance Analysis of Multi-Objective Simulated Annealing Based on Decomposition

by Manuel Vargas-Martínez, Nelson Rangel-Valdez, Eduardo Fernández, Claudia Gómez-Santillán and María Lucila Morales-Rodríguez

Math. Comput. Appl. 2023, 28(2), 38; https://doi.org/10.3390/mca28020038 - 8 Mar 2023

Cited by 2 | Viewed by 1796

Abstract

Simulated annealing is a metaheuristic that balances exploration and exploitation to solve global optimization problems. However, to deal with multi- and many-objective optimization problems, this balance needs to be improved due to diverse factors such as the number of objectives. To deal with [...] Read more.

Simulated annealing is a metaheuristic that balances exploration and exploitation to solve global optimization problems. However, to deal with multi- and many-objective optimization problems, this balance needs to be improved due to diverse factors such as the number of objectives. To deal with this issue, this work proposes MOSA/D, a hybrid framework for multi-objective simulated annealing based on decomposition and evolutionary perturbation functions. According to the literature, the decomposition strategy allows diversity in a population while evolutionary perturbations add convergence toward the Pareto front; however, a question should be asked: What is the effect of such components when included as part of a multi-objective simulated annealing design? Hence, this work studies the performance of the MOSA/D framework considering in its implementation two widely used perturbation operators: classical genetic operators and differential evolution. The proposed algorithms are MOSA/D-CGO, based on classical genetic operators, and MOSA/D-DE, based on differential evolution operators. The main contribution of this work is the performance analysis of MOSA/D using both perturbation operators and identifying the one most suitable for the framework. The approaches were tested using DTLZ on two and three objectives and CEC2009 benchmarks on two, three, five, and ten objectives; the performance analysis considered diversity and convergence measured through the hypervolume (HV) and inverted generational distance (IGD) indicators. The results pointed out that there is a promising improvement in performance in favor of MOSA/D-DE. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2022)

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12 pages, 1560 KiB

Open AccessArticle

Construction and Modification of Topological Tables for Digital Models of Linear Complexes

by Aleksandr N. Rozhkov and Vera V. Galishnikova

Math. Comput. Appl. 2023, 28(2), 37; https://doi.org/10.3390/mca28020037 - 7 Mar 2023

Viewed by 1434

Abstract

Building information systems use topological tables to implement the transition from two-dimensional line drawings of the geometry of buildings to digital three-dimensional models of linear complexes. The topological elements of the complex are named and the topological relations of the complex are described [...] Read more.

Building information systems use topological tables to implement the transition from two-dimensional line drawings of the geometry of buildings to digital three-dimensional models of linear complexes. The topological elements of the complex are named and the topological relations of the complex are described by arranging the element names in topological tables. The efficient construction and modification of topological tables for complete buildings is investigated. The topology of a linear complex with nodes, edges, faces, and cells is described with 12 tables. Three of the tables of a complex are independent of each other and form a basis for the construction of the other tables. A highly efficient construction algorithm with complexity O (number of cells) for typical buildings with an approximately constant number of edges per face and faces per cell of is presented. In practice, building designs and their digital models are frequently modified. A modification algorithm is presented, whose complexity equals that of the construction algorithm. Examples illustrate that the efficient algorithms permit the replacement of the conventional focus on the topology of building components by a focus on the topology of the entire building. A set of properties of the original, which are not explicitly described by the topological tables, for example, the orientation of surfaces and multiply connected domains, are analyzed in the paper. An overview of the research dealing with the topological attributes that are not contained in topological tables concludes the paper. Full article

(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)

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15 pages, 381 KiB

Open AccessCommunication

Estimation of the Equivalent Circuit Parameters in Transformers Using Evolutionary Algorithms

by Hector Ascencion-Mestiza, Serguei Maximov, Efrén Mezura-Montes, Juan Carlos Olivares-Galvan, Rodrigo Ocon-Valdez and Rafael Escarela-Perez

Math. Comput. Appl. 2023, 28(2), 36; https://doi.org/10.3390/mca28020036 - 3 Mar 2023

Cited by 5 | Viewed by 2648

Abstract

The conventional methods of parameter estimation in transformers, such as the open-circuit and short-circuit tests, are not always available, especially when the transformer is already in operation and its disconnection is impossible. Therefore, alternative (non-interruptive) methods of parameter estimation have become of great [...] Read more.

The conventional methods of parameter estimation in transformers, such as the open-circuit and short-circuit tests, are not always available, especially when the transformer is already in operation and its disconnection is impossible. Therefore, alternative (non-interruptive) methods of parameter estimation have become of great importance. In this work, no-interruption, transformer equivalent circuit parameter estimation is presented using the following metaheuristic optimization methods: the genetic algorithm (GA), particle swarm optimization (PSO) and the gravitational search algorithm (GSA). These algorithms provide a maximum average error of 12%, which is twice as better as results found in the literature for estimation of the equivalent circuit parameters in transformers at a frequency of 50 Hz. This demonstrates that the proposed GA, PSO and GSA metaheuristic optimization methods can be applied to estimate the equivalent circuit parameters of single-phase distribution and power transformers with a reasonable degree of accuracy. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2022)

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15 pages, 2253 KiB

Open AccessArticle

Comprehensive Analysis of Learning Cases in an Autonomous Navigation Task for the Evolution of General Controllers

by Enrique Naredo, Candelaria Sansores, Flaviano Godinez, Francisco López, Paulo Urbano, Leonardo Trujillo and Conor Ryan

Math. Comput. Appl. 2023, 28(2), 35; https://doi.org/10.3390/mca28020035 - 2 Mar 2023

Viewed by 1838

Abstract

Robotics technology has made significant advancements in various fields in industry and society. It is clear how robotics has transformed manufacturing processes and increased productivity. Additionally, navigation robotics has also been impacted by these advancements, with investors now investing in autonomous transportation for [...] Read more.

Robotics technology has made significant advancements in various fields in industry and society. It is clear how robotics has transformed manufacturing processes and increased productivity. Additionally, navigation robotics has also been impacted by these advancements, with investors now investing in autonomous transportation for both public and private use. This research aims to explore how training scenarios affect the learning process for autonomous navigation tasks. The primary objective is to address whether the initial conditions (learning cases) have a positive or negative impact on the ability to develop general controllers. By examining this research question, the study seeks to provide insights into how to optimize the training process for autonomous navigation tasks, ultimately improving the quality of the controllers that are developed. Through this investigation, the study aims to contribute to the broader goal of advancing the field of autonomous navigation and developing more sophisticated and effective autonomous systems. Specifically, we conducted a comprehensive analysis of a particular navigation environment using evolutionary computing to develop controllers for a robot starting from different locations and aiming to reach a specific target. The final controller was then tested on a large number of unseen test cases. Experimental results provide strong evidence that the initial selection of the learning cases plays a role in evolving general controllers. This work includes a preliminary analysis of a specific set of small learning cases chosen manually, provides an in-depth analysis of learning cases in a particular navigation task, and develops a tool that shows the impact of the selected learning cases on the overall behavior of a robot’s controller. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2022)

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10 pages, 198 KiB

Open AccessEditorial

Interview: Kalyanmoy Deb Talks about Formation, Development and Challenges of the EMO Community, Important Positions in His Career, and Issues Faced Getting His Works Published

by Carlos Coello, Erik Goodman, Kaisa Miettinen, Dhish Saxena, Oliver Schütze and Lothar Thiele

Math. Comput. Appl. 2023, 28(2), 34; https://doi.org/10.3390/mca28020034 - 1 Mar 2023

Viewed by 2125

Abstract

Kalyanmoy Deb was born in Udaipur, Tripura, the smallest state of India at the time, in 1963 [...] Full article

(This article belongs to the Special Issue Evolutionary Multi-objective Optimization: An Honorary Issue Dedicated to Professor Kalyanmoy Deb)

23 pages, 5849 KiB

Open AccessArticle

Structural-Health-Monitoring-Oriented Finite Element Model for a Specially Shaped Steel Arch Bridge and Its Application

by Li Dai, Mi-Da Cui and Xiao-Xiang Cheng

Math. Comput. Appl. 2023, 28(2), 33; https://doi.org/10.3390/mca28020033 - 28 Feb 2023

Cited by 3 | Viewed by 2007

Abstract

To rigorously evaluate the health of a steel bridge subjected to vehicle-induced fatigue, both a detailed numerical model and effective fatigue analysis methods are needed. In this paper, the process for establishing the structural health monitoring (SHM)-oriented finite element (FE) model and assessing [...] Read more.

To rigorously evaluate the health of a steel bridge subjected to vehicle-induced fatigue, both a detailed numerical model and effective fatigue analysis methods are needed. In this paper, the process for establishing the structural health monitoring (SHM)-oriented finite element (FE) model and assessing the vehicle-induced fatigue damage is presented for a large, specially shaped steel arch bridge. First, the bridge is meticulously modeled using multiple FEs to facilitate the exploration of the local structural behavior. Second, manual tuning and model updating are conducted according to the modal parameters measured at the bridge’s location. Since the numerical model comprises a large number of FEs, two surrogate-model-based methods are employed to update the model. Third, the established models are validated by using them to predict the structure’s mode shapes and the actual structural behavior for the case in which the whole bridge is subjected to static vehicle loads. Fourth, using the numerical model, a new fatigue analysis method based on the high-circle fatigue damage accumulation theory is employed to further analyze the vehicle-induced fatigue damage to the bridge. The results indicate that manual tuning and model updating are indispensable for SHM-oriented FE models with erroneous configurations, and one surrogate-model-based model updating method is effective. In addition, it is shown that the fatigue analysis method based on the high-circle fatigue damage accumulation theory is applicable to real-world engineering cases. Full article

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Math. Comput. Appl., Volume 28, Issue 2 (April 2023) – 35 articles

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