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The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools.

Technology: general issues --- History of engineering & technology --- fractional order IMC --- first order plus dead-time processes --- event-based implementation --- numerical simulations --- comparative closed loop results --- nonlinear wave phenomen --- RBF --- local RBF-FD --- stability --- unmanned aerial vehicle (UAV) --- quaternion-based estimator --- low-cost design --- automatic optical inspection --- kinetic theory --- parallel robots --- robust control --- sliding mode control --- basinI --- basinII --- mean pressure head --- pressure head with different probabilities of occurrence --- standard deviation of the pressure fluctuations --- statistical modeling --- USBR --- desalination --- humidification-dehumidification --- waste heat recovery --- mathematical model --- yearly analysis --- thermo-economics --- multi-objective optimization --- cruise altitude --- fuel consumption --- time to climb --- Hermite-Simpson method --- trajectory optimization --- terminal residual analysis (TRA) --- m-σ terminal residual analysis (m-σ TRA) --- power transformer --- stray losses --- analytical methods --- finite element method --- gridshell structures --- shape ratio --- length ratio --- regularity --- particle swarm optimization --- genetic algorithm --- hybrid nanofluid --- dual solutions --- mixed convection --- stagnation point --- radiation --- stability analysis --- machine learning --- eXterme Gradient Boosting --- Computation Fluid Dynamics --- blade vibration --- unsteady aerodynamic model --- active disturbance rejection control (ADRC) --- multiobjective optimization --- time delay systems --- tuning rules --- soft robotics --- fractional calculus --- CACSD toolbox --- operating point linearization --- automatic uncertainty bound computation --- Model-in-the-Loop simulation --- hybrid simulation --- ℋ∞ control --- μ synthesis --- DC-to-DC power converters --- buck --- boost --- SEPIC --- rainfall-runoff model --- curve number --- inferential statistics --- 3D runoff difference model --- model calibration --- PAT model --- modified affinity laws --- hydraulic simulation tool --- μ-synthesis --- fractional-order control --- swarm optimization --- artificial bee colony optimization --- CNC machine --- mixed sensitivity --- D–K iteration --- Linear Matrix Inequality --- biotechnology --- fermentation process --- batch bioreactors --- modeling --- control system design and synthesis --- linear control --- adaptive control --- model reference adaptive control --- control system realization --- mixed-sensitivity --- FO-PID --- twin rotor aerodynamic system --- fractional order IMC --- first order plus dead-time processes --- event-based implementation --- numerical simulations --- comparative closed loop results --- nonlinear wave phenomen --- RBF --- local RBF-FD --- stability --- unmanned aerial vehicle (UAV) --- quaternion-based estimator --- low-cost design --- automatic optical inspection --- kinetic theory --- parallel robots --- robust control --- sliding mode control --- basinI --- basinII --- mean pressure head --- pressure head with different probabilities of occurrence --- standard deviation of the pressure fluctuations --- statistical modeling --- USBR --- desalination --- humidification-dehumidification --- waste heat recovery --- mathematical model --- yearly analysis --- thermo-economics --- multi-objective optimization --- cruise altitude --- fuel consumption --- time to climb --- Hermite-Simpson method --- trajectory optimization --- terminal residual analysis (TRA) --- m-σ terminal residual analysis (m-σ TRA) --- power transformer --- stray losses --- analytical methods --- finite element method --- gridshell structures --- shape ratio --- length ratio --- regularity --- particle swarm optimization --- genetic algorithm --- hybrid nanofluid --- dual solutions --- mixed convection --- stagnation point --- radiation --- stability analysis --- machine learning --- eXterme Gradient Boosting --- Computation Fluid Dynamics --- blade vibration --- unsteady aerodynamic model --- active disturbance rejection control (ADRC) --- multiobjective optimization --- time delay systems --- tuning rules --- soft robotics --- fractional calculus --- CACSD toolbox --- operating point linearization --- automatic uncertainty bound computation --- Model-in-the-Loop simulation --- hybrid simulation --- ℋ∞ control --- μ synthesis --- DC-to-DC power converters --- buck --- boost --- SEPIC --- rainfall-runoff model --- curve number --- inferential statistics --- 3D runoff difference model --- model calibration --- PAT model --- modified affinity laws --- hydraulic simulation tool --- μ-synthesis --- fractional-order control --- swarm optimization --- artificial bee colony optimization --- CNC machine --- mixed sensitivity --- D–K iteration --- Linear Matrix Inequality --- biotechnology --- fermentation process --- batch bioreactors --- modeling --- control system design and synthesis --- linear control --- adaptive control --- model reference adaptive control --- control system realization --- mixed-sensitivity --- FO-PID --- twin rotor aerodynamic system

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools.

fractional order IMC --- first order plus dead-time processes --- event-based implementation --- numerical simulations --- comparative closed loop results --- nonlinear wave phenomen --- RBF --- local RBF-FD --- stability --- unmanned aerial vehicle (UAV) --- quaternion-based estimator --- low-cost design --- automatic optical inspection --- kinetic theory --- parallel robots --- robust control --- sliding mode control --- basinI --- basinII --- mean pressure head --- pressure head with different probabilities of occurrence --- standard deviation of the pressure fluctuations --- statistical modeling --- USBR --- desalination --- humidification-dehumidification --- waste heat recovery --- mathematical model --- yearly analysis --- thermo-economics --- multi-objective optimization --- cruise altitude --- fuel consumption --- time to climb --- Hermite-Simpson method --- trajectory optimization --- terminal residual analysis (TRA) --- m-σ terminal residual analysis (m-σ TRA) --- power transformer --- stray losses --- analytical methods --- finite element method --- gridshell structures --- shape ratio --- length ratio --- regularity --- particle swarm optimization --- genetic algorithm --- hybrid nanofluid --- dual solutions --- mixed convection --- stagnation point --- radiation --- stability analysis --- machine learning --- eXterme Gradient Boosting --- Computation Fluid Dynamics --- blade vibration --- unsteady aerodynamic model --- active disturbance rejection control (ADRC) --- multiobjective optimization --- time delay systems --- tuning rules --- soft robotics --- fractional calculus --- CACSD toolbox --- operating point linearization --- automatic uncertainty bound computation --- Model-in-the-Loop simulation --- hybrid simulation --- ℋ∞ control --- μ synthesis --- DC-to-DC power converters --- buck --- boost --- SEPIC --- rainfall-runoff model --- curve number --- inferential statistics --- 3D runoff difference model --- model calibration --- PAT model --- modified affinity laws --- hydraulic simulation tool --- μ-synthesis --- fractional-order control --- swarm optimization --- artificial bee colony optimization --- CNC machine --- mixed sensitivity --- D–K iteration --- Linear Matrix Inequality --- biotechnology --- fermentation process --- batch bioreactors --- modeling --- control system design and synthesis --- linear control --- adaptive control --- model reference adaptive control --- control system realization --- mixed-sensitivity --- FO-PID --- twin rotor aerodynamic system

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In this Special Issue on symmetry, we mainly discuss the application of symmetry in various structural health monitoring. For example, considering the health monitoring of a known structure, by obtaining the static or dynamic response of the structure, using different signal processing methods, including some advanced filtering methods, to remove the influence of environmental noise, and extract structural feature parameters to determine the safety of the structure. These damage diagnosis methods can also be effectively applied to various types of infrastructure and mechanical equipment. For this reason, the vibration control of various structures and the knowledge of random structure dynamics should be considered, which will promote the rapid development of the structural health monitoring. Among them, signal extraction and evaluation methods are also worthy of study. The improvement of signal acquisition instruments and acquisition methods improves the accuracy of data. A good evaluation method will help to correctly understand the performance with different types of infrastructure and mechanical equipment.

Technology: general issues --- History of engineering & technology --- real-time hybrid simulation --- H∞ control --- time delay --- mixed sensitivity --- structural health monitoring --- deep learning --- data anomaly detection --- convolutional neural network --- time–frequency extraction --- micro inertial measurement unit (MIMU) --- variational mode decomposition (VMD) --- Hilbert–Huang transform (HHT) --- frequency-domain integration approach (FDIA) --- torsion angle calculation --- offshore oil platform --- self-anchored suspension bridge --- cable clamp --- slippage --- force analysis --- high formwork --- ARMA --- BPNN --- stress trend prediction --- crack detection --- improved YOLOv4 --- concrete surface --- substructure shake table testing --- integration algorithm --- finite element method --- damper --- digital twin --- prestressed steel structure --- construction process --- safety assessment --- intelligent construction --- structural health monitoring (SHM) --- vibration --- frequency domain --- time domain --- time-frequency domain --- technical codes --- multiple square loops (MSL)-string --- seismic excitation --- dynamic response --- seismic pulse --- near and far field --- three-dimensional laser scanning --- surface flatness of initial support of tunnel --- curved surface fitting --- flatness calculation datum --- curvedcontinuous girder bridge --- collision response --- seismic mitigation --- pounding mitigation and unseating prevention --- heavy-duty vehicle --- road --- coupling model --- terrestrial laser scanning --- RGB --- genetic algorithm --- artificial neutral network