Purpose The purpose of this study is to investigate the free vibration behavior of stepped sandwich cylinders with auxetic honeycomb cores using semi-analytical and numerical approaches. The study aims to develop efficient formulations based on the first-order shear deformation theory and evaluate the effects of key geometric parameters, including inclination angle, thickness ratio, relative thickness and length ratio, on the natural frequencies and dynamic characteristics of the structure. Design/methodology/approach The formulation is based on the first-order shear deformation theory to model the free vibration behavior of stepped sandwich cylinders with auxetic honeycomb cores. The governing equations are derived using energy principles, including kinetic and potential energy expressions. The problem is solved using both semi-analytical and numerical approaches. In the semi-analytical framework, the Rayleigh–Ritz method is applied with trigonometric basis functions, and an extended formulation employs Legendre polynomials with Lagrange multipliers to enforce boundary conditions. In addition, a one-dimensional ring finite element is developed, and its mass and stiffness matrices are obtained via the energy method. The resulting eigenvalue problems are solved to determine natural frequencies. Findings The results show that the proposed semi-analytical and finite element formulations are in excellent agreement with available literature, confirming their accuracy and reliability. It is observed that increasing the inclination angle and relative thickness, as well as decreasing the length ratio, leads to a reduction in the natural frequencies of the stepped sandwich cylinder. A higher core-to-face sheet thickness ratio also generally lowers the frequencies. Furthermore, increasing the length ratio reduces the natural frequencies for all thickness configurations. At low length ratios, the effect of the auxiliary–cylinder thickness ratio is non-monotonic, whereas at high length ratios, it leads to a consistent increase in frequencies. Originality/value This study presents a comprehensive vibration analysis of stepped sandwich cylinders with auxetic honeycomb cores using both semi-analytical and numerical frameworks. The originality lies in the integration of Rayleigh–Ritz formulations with trigonometric and Legendre basis functions alongside a Lagrange multiplier approach, enabling flexible enforcement of boundary conditions. In addition, a dedicated one-dimensional ring finite element is developed for efficient numerical modeling. The combined methodology provides a robust and accurate tool for analyzing complex stepped cylindrical structures. The findings offer valuable insights into how geometric parameters and core configurations influence dynamic behavior, supporting improved design of lightweight, high-performance sandwich cylindrical structures.
Purpose This study was aimed at investigating the mechanical responses and failure characteristics of soft–hard interbedded rock samples under uniaxial compression and Brazilian splitting tests with varying strength ratios between the hard and soft layers (i.e. anisotropy degrees, λ). How the degree of anisotropy influences the safety factors, failure mechanisms, and failure modes of soft–hard interbedded antidip slopes (SHIADSs) was also examined. Design/methodology/approach By setting different anisotropy degrees (λ = 1.5, 2, 4, 6, 8 and 10) and layer dip angles (θ = 0°, 15°, 30°, 45°, 60 and 75°), the finite-discrete element method (FDEM) was adopted to determine the strength characteristics and failure behaviours of soft–hard interbedded rock samples under uniaxial compression and Brazilian splitting. In addition, different combinations of the anisotropy degree (λ = 1.5, 2, 4, 6, 8 and 10), layer dip angle (θ = 0°, 15°, 30°, 45°, 60 and 75°) and slope angle (β = 70°, 75°, 80°, 85°, 90°, 95° and 100°) were designed to investigate the effects of the degree of anisotropy on the stability of SHIADSs. Findings With increasing degree of anisotropy, the compressive strength of soft–hard interbedded rock samples may either increase exponentially (when θ = 0°, 15 and 75°) or change slightly (when θ = 30°, 45 and 60°). The tensile strength increases exponentially with increasing λ, independent of the layer dip angle. At the same slope angle (β = 80°), the safety factors of SHIADSs may either increase exponentially (when θ = 0–30°) with an increase in the value of λ or change slightly (when θ ≥ 45°). However, at the same layer dip angle (θ = 30°), the safety factor increases exponentially with increasing λ, independent of the slope angle. Originality/value The results indicate that the influence of the degree of anisotropy should be considered when investigating the stability and failure mechanisms of SHIADSs. In addition, the findings provide meaningful guidance for controlling the stability of SHIADSs; for example, reducing the slope angle is the preferred stability control measure.
Purpose The purpose of this paper is to develop an efficient spectral-Galerkin method for solving the "Good" Boussinesq (GB) equation with homogeneous boundary conditions. The study aims to overcome the computational challenges associated with unbounded domains while preserving high-order accuracy and computational efficiency.Design/methodology/approach A spectral-Galerkin framework based on generalized Jacobi polynomials (GJPs) is proposed for the spatial discretization of the GB equation. Exploiting the localized structure of solitary-wave solutions, the original problem posed on an unbounded domain is truncated to a finite interval. The resulting semi-discrete system is advanced in time using an explicit fourth-order Runge-Kutta scheme. Theoretical properties of the method, including boundedness, generalized stability, and convergence, are established through an energy-based analysis. Detailed implementation procedures are provided to facilitate practical computation.Findings The proposed method yields a sparse algebraic system due to the use of GJP basis functions, thereby significantly reducing computational cost and memory requirements. The selected GJP basis functions inherently satisfy the homogeneous Neumann boundary conditions, simplifying both the formulation and theoretical analysis. Rigorous analysis confirms the boundedness, generalized stability and convergence of the scheme. Numerical results confirm the theoretical findings and demonstrate spectral accuracy in space.Originality/value The proposed method combines domain truncation and GJP-based spectral approximation to efficiently solve the GB equation. The approach effectively transforms an unbounded-domain problem into a bounded-domain formulation, avoiding difficulties associated with unboundedness while maintaining high accuracy. The use of GJP basis functions naturally accommodates the homogeneous boundary conditions and leads to sparse discrete systems that are computationally attractive. The developed framework provides a rigorous theoretical foundation and can be extended to a broader class of nonlinear wave propagation problems.
Purpose The paper surveys the evolution of sliding surface design in variable-structure control with sliding modes. It contrasts linear and nonlinear approaches, outlining how the choice of sliding surface fundamentally shapes closed-loop dynamics. The purpose is to provide researchers and practitioners with a consolidated roadmap to select sliding surfaces that balance simplicity, robustness, and performance for modern control applications. Design/methodology/approach This work systematically reviews classical linear surfaces including proportional, PI/PD, integral, and dynamic extensions and modern nonlinear variants such as terminal, nonsingular terminal, fast terminal, integral terminal, and higher-order surfaces. The methodology involves comparing their convergence properties, robustness to uncertainties, sensitivity to disturbances, and practical implementation challenges such as noise amplification, parameter tuning, and chattering. Findings Linear sliding surfaces deliver predictable exponential convergence and strong disturbance rejection but face limitations under severe uncertainties, noise, and actuator constraints. Nonlinear designs achieve finite-time or prescribed-time convergence, improve robustness against friction and modeling errors, and reduce tracking errors. However, they often introduce greater noise sensitivity and tuning complexity. By contrasting these trade-offs, the survey highlights that no single design is universally optimal, and emphasizes the importance of tailoring surface selection to application-specific demands. Originality/value This survey uniquely bridges the gap between classical linear and emerging nonlinear sliding surface designs by presenting a comparative perspective that emphasizes their trade-offs and complementary strengths. Unlike prior works that focus narrowly on either theory or a specific class of surfaces, this study integrates diverse approaches into a coherent framework. It provides actionable insights for selecting and tailoring sliding surfaces to contemporary control challenges, thereby serving as a practical reference for both academic researchers and practicing engineers.
Purpose The blast-resistant performance of a real reinforced concrete petrochemical control room retrofitted with an aluminum foam Sandwich panel is analyzed. Design/methodology/approach Considering different levels of blast loads and the thickness of the control room's shearing wall, the deformation and energy absorption of each member of the control room are taken as the performance indices to determine the optimal positioning and thickness of the foam aluminum Sandwich panel. Findings It is found that, without the aluminum foam Sandwich panel, the energy absorption of the shear wall facing the blast accounts for 45.1% and 76.4% of the total structural energy absorption for 1t and 2t Trinitrotoluene (TNT) respectively. The optimal thickness of aluminum foam is about 57.1% of the shearing wall thickness of the petrochemical control room which results in a reduction in the original shearing wall thickness by 29%. Originality/value Using only the reinforced concrete shearing wall is difficult to meet the blast-resistant performance requirement of the petrochemical control room. As the Aluminum foam material is an ideal lightweight material with excellent energy absorption ability, in this paper, the blast-resistant performance of a real reinforced concrete petrochemical control room retrofitted with an aluminum foam Sandwich panel is analyzed.
Purpose The purpose of this study is to develop and evaluate the effectiveness of Radial Basis Function (RBF) collocation and quintic B-spline methods for solving the fractionally differentiable Good Boussinesq equation in the Caputo sense. By comparing numerical results with the exact solution and analyzing error norms, the study aims to demonstrate the accuracy and computational efficiency of the proposed methods for solving complex fractional differential equations (FDEs). Design/methodology/approach This study employs RBF collocation and quintic B-spline methods as numerical techniques to solve the Good Boussinesq equation with fractional derivatives defined in the Caputo sense. The accuracy and efficiency of these methods are systematically evaluated using $L_2$ and $L_\infty$ error norms. Numerical solutions are computed and compared against the exact solution, with results presented through detailed tables and graphical illustrations to validate the methods' performance. Findings The study finds that both the RBF collocation and quintic B-spline methods deliver highly accurate solutions for the fractionally differentiable Good Boussinesq equation. Error analyses using $L_2$ and $L_\infty$ norms confirm their precision. Additionally, the methods demonstrate strong computational efficiency, making them practical for solving complex FDEs. Comparative results show close agreement with the exact solution, validating the reliability of both approaches. Overall, these methods offer robust and effective numerical tools for fractional PDE problems. Originality/value This study is the first to apply both the RBF collocation and quintic B-spline methods specifically to the fractionally differentiable Good Boussinesq equation in the Caputo sense. By introducing these novel numerical approaches to this class of FDEs, the research expands the available toolkit for solving such complex problems. The demonstrated accuracy and computational efficiency highlight the value of these methods as reliable and practical solutions, contributing original insights and techniques to the field of fractional partial differential equations.
Purpose This study aims to analyze the dynamic stability of non-prismatic beams resting on a Winkler-Pasternak foundation under axial harmonic loading. The objective is to evaluate the influence of geometric tapering and foundation stiffness parameters on the buckling behavior in both static and dynamic conditions. Design/methodology/approach The governing equations are derived using Hamilton's principle. The Rayleigh-Ritz numerical method with Chebyshev polynomials is applied to approximate the displacement function. The weak form is used to extract stiffness and mass matrices. Dynamic responses are analyzed using the Bolotin method and solved via MATLAB programming. Findings An increase in the tapering ratio reduces the beam's flexural rigidity, lowering the resonance frequency. Meanwhile, higher Winkler and Pasternak coefficients raise the system's stiffness and shift the resonance frequency. Pasternak shear modulus has a stronger influence on dynamic stability due to its second-order derivative dependence. Research limitations/implications The model assumes linear elasticity and does not consider thermal effects or material nonlinearity. Future research may include viscoelastic behavior and temperature-dependent properties for enhanced accuracy. Practical implications The findings provide a reliable analytical tool for engineers to predict and enhance the stability performance of tapered beams in civil and mechanical structures, particularly under dynamic loads. Social implications Improving the structural resilience of dynamically loaded beams enhances public safety in infrastructures such as bridges, towers, and pipelines, reducing risks during seismic or variable load events. Originality/value This research offers a novel application of the Rayleigh-Ritz and Bolotin methods for dynamic buckling analysis of non-prismatic beams on elastic foundations. The approach enables high computational efficiency and accuracy validated against existing studies.
Purpose The purpose of the current research work is to study the frequency responses of the FGM-sandwich structure with and without damage. The study has been stretched to investigate the influence of damage and various geometrical input parameters. Design/methodology/approach A higher-order kinematics is used to derive the mathematical model based on the isoparametric finite element (FE) technique. The crack is also modelled mathematically to obtain the desired numerical responses. Findings The uniformity and exactness of the numerical model are established by solving and equating a few numerical illustrations from the previously published results. Further, the effects of damage and geometrical characteristics on the structural final strength caused by static loading are provided in detail. Originality/value The analysis underscores the necessity of the developed mathematical model for evaluating the effect of damage and multiple geometrical input parameters.
Purpose In this study, we investigate the optimum model for a virtual material test of wood by comparing finite element method (FEM) analysis using the representative volume element (RVE) of wood cells and experiments.Design/methodology/approach The influence of the annual ring tilt angle theta on compression properties was investigated in the experiment and FEM analysis. Japanese cypress was used in this study. The RVE is a one-year annual ring comprising earlywood and latewood cells, and the cell shape was based on observations of the wood that was used for the experiment. The number of cells was optimized by comparing the FEM and experimental results.Findings Young's modulus E and proportional limit stress sigma p varied depending on the annual ring tilt angle theta in the experiment. In the analysis, E and sigma p varied depending on the latewood volume fraction Vl, which was determined by the number of cells of the earlywood and the latewood, and the FEM results agreed with the experimental results using RVE, whose Vl was the same as that of the specimen in the experiment.Originality/value The anisotropy of deformation in FEM with RVE based on wood observations were compared to those in the experiment using the wood observed to create the RVE. The FEM results agreed with the experimental results using the RVE, whose latewood volume fraction Vl was the same as that in the experiment.
Purpose This study aims to investigate the stochastic Nizhnik-Novikov-Veselov (SNNV) system; incorporating local fractional derivatives, to enhance the understanding of its dynamics.Design/methodology/approach We utilize the semi-inverse method to formulate the variational principle, which serves as the foundation for deriving the Hamiltonian. To find various exact solutions of the fractional stochastic system, we propose a novel variable coefficient sub-equation method, which differs from traditional sub-equation methods that employ constant coefficients.Findings The proposed technique provides new analytical solutions, thereby enhancing our understanding of the system's dynamics. It establishes a robust framework for exploring similar fractional stochastic models in mathematical physics. Additionally, graphical simulations are presented to illustrate the physical relevance and behavior of the obtained solutions.Originality/value This study introduces a novel approach to solving fractional stochastic systems, contributing significant analytical tools and insights that advance the field of mathematical physics. Furthermore, we present a fractional and stochastic formulation of the SNNV system.
Purpose The purpose of this paper is to propose a comprehensive model that skillfully interpolates missing values without introducing potential bias, and performs high-precision prediction of the remaining useful life (RUL) of an engine using an improved transformer model. Design/methodology/approach This paper proposes a method that integrates Bayesian temporal factorization with improved transformer architecture. By integrating low-rank matrix factorization and vector autoregressive (VAR) processes into a unified probabilistic graphical model, which enables the framework to capture both global and local consistency within large-scale time series data, is essential for robust RUL prediction. Additionally, a tailored Gibbs sampling algorithm is developed to impute missing spatiotemporal engine data effectively. Following the estimation of missing values, an improved transformer model is employed for RUL prediction, which leverages gated convolutional units to enhance its ability to fuse local contextual information at each time step, and harnesses bespoke gated attention units further to improve the computational efficiency of transformer models. Findings Extensive experimentation on a turbofan engine dataset validates the efficacy of the proposed method. Results demonstrate that our approach either outperforms or is comparable to the best existing approaches in RUL estimation. Originality/value The method proposed in this study addresses the problem of poor RUL prediction capability of traditional deep learning (DL) models when engine data are partially missing.
Purpose The study mainly focuses on the incorporation of fibers in concrete, such as steel, glass, carbon fibers, etc., which reduces the propagation of cracks in concrete. The paper also emphasizes the addition of supplementary cementitious material in concrete, such as metakaolin, Silica fume, Ground Granulated Blast-Furnace Slag, Fly ash, etc., which are added in concrete to make the concrete high in strength. It also aims to bridge the research gap between the innovation of materials and their practical implementation in fiber-reinforced concrete in present construction scenarios. The findings presented throughout this review underscore the importance of integrating advanced materials like high strength fiber-reinforced concrete (HSFRC) in modern construction practices, paving the way for innovative designs and sustainable building solutions. Design/methodology/approach In the process, dry components like coarse aggregate, fine aggregate, OPC 53 grade cement and supplementary cementitious materials are initially placed into the concrete mixer. Following this, the necessary amount of water and superplasticizer is added. The fiber is then evenly distributed and fed into the concrete mixture, ensuring thorough mixing to achieve a consistent blend. The freshly prepared concrete is subsequently poured into steel molds, removed from the molds the following day and cured for the specified duration before being subjected to testing. Findings The implementation of artificial intelligence-based prediction techniques in concrete, which is capable of predicting the strength of concrete without the use of technical assistance and sophisticated equipment, is also discussed. The present work is a comprehensive four-part review of the HSFRC. The first part of the review focuses on the Fiber-Reinforced Concrete and various fibers used in FRC. Originality/value This review uniquely connects the world of FRC with the rapidly evolving field of AI-based prediction techniques. While most studies treat them separately, we bring them together to show how advanced algorithms can predict the performance of FRC with greater accuracy and efficiency. By combining insights from experimental research with modern AI models, we highlight not only current capabilities but also future possibilities. This human-centred approach aims to guide engineers, researchers and practitioners toward smarter, faster and more sustainable decisions in designing and evaluating fiber-reinforced concrete.
Purpose This article proposes a novel numerical method, the Chebyshev Ensemble Extreme Learning Machine (CH-EN-ELM), to solve variable-order (VO) fractional partial differential equations (FPDEs). The study aims to provide accurate and robust solutions for important VO fractional models in fluid dynamics, including the Burger's, wave and diffusion equations. It seeks to improve solution accuracy and overcome the generalization and stability issues associated with conventional extreme learning machines (ELMs). Design/methodology/approach The study develops a feedforward neural network (FNN) scheme that integrates Chebyshev polynomials with an ensemble of ELMs, in which the network outputs of two or more independently trained ELM-based single-layer FNNs (SLFNN-ELMs) are aggregated to obtain a single output of the scheme. The method enhances network efficiency by using Chebyshev polynomials for input feature expansion and a radial basis function as the hidden-layer activation function of each SLFNN-ELM in the ensemble network. Findings The numerical results demonstrate that the proposed CH-EN-ELM method produces highly accurate solutions and exhibits a good convergence rate. The approach shows superior performance with strong error minimization capabilities when compared to other techniques in the literature. The method's effectiveness is confirmed across various examples, including the nonlinear time-fractional Burger's equation and diffusion-wave equations, outperforming methods presented in other studies. Research limitations/implications The authors suggest future work could extend the approach to more complex models, such as VO fractal-fractional PDEs, coupled systems of VO FPDEs and higher-order problems. There is also potential to combine the CH-EN-ELM method with data-driven frameworks like physics-informed neural networks (PINNs) to enhance its application to real-world problems. Practical implications The article provides a robust, efficient, and easily implemented method for solving a wide range of VO FPDEs that model complex phenomena in physics, mechanics and fluid dynamics. The method is a promising alternative for tackling large-scale, multidimensional problems where traditional numerical methods often face difficulties. Originality/value This study is the first to propose an ensemble ELM technique that uses Chebyshev-augmented input patterns to solve VO FPDEs. The novel combination of ensemble learning with specific feature expansion provides a powerful and efficient framework for accurately solving complex fractional differential equations, demonstrating versatility across different types of fractional operators.
Purpose To study short-time fractional series solutions of nonlinear time–fractional KdV-type systems and to determine, through the equation residual, where a truncated series remains usable. Design/methodology/approach The modified Riemann–Liouville derivative is used. Applying FRDT gives recurrence relations for the coefficients of powers tkα. These recurrences are written out for the generalized fractional Ito's system, the generalized fractional Drinfeld–Sokolov system and the fractional Kaup–Kupershmidt equation. The truncated series are then substituted back into the original equations to compute residual norms. Findings Explicit coefficient recurrences are obtained for the three models. In the Banachspace setting used in the paper, with bounded spatial operators and a locally Lipschitz nonlinear part, the coefficients satisfy a majorant estimate and the series converges locally in time. For an N-term truncation, the residual has order O(t(N+1)α) 1 near t = 0. The computations show that the useful time interval depends on both N and α, and is shortest for the Kaup–Kupershmidt case. Originality/value The paper gives explicit FRDT coefficient recurrences for three fractional KdV-type models and uses the residual of the original equation to mark the interval on which a truncated fractional series should still be regarded as a valid approximation.
Purpose This study develops a computationally oriented framework to obtain exact coherent structures for a stochastic coupled Klein–Gordon–Schrödinger (KGS) system driven by multiplicative amplitude noise in the Stratonovich sense. Design/methodology/approach A traveling-wave reduction, combined with a mean-field representation of the stochastic exponential modulation, converts the stochastic PDE model into a deterministic nonlinear ODE system. Two algorithmic solvers are then implemented: the Enhanced Direct Algebraic Method and the New Projective Riccati Equation Method, which systematically generate closed-form solutions together with their parameter admissibility constraints. Findings The procedure yields families of bright, dark, kink-type, singular, straddled, and periodic waves expressed via hyperbolic and elliptic functions. Explicit parameter regimes are derived to guarantee real-valuedness and boundedness, and to quantify how free parameters control amplitude, width, and propagation speed under noise modulation. Originality/value The paper contributes reproducible solution algorithms and a benchmark catalogue of exact waveforms for validating numerical solvers and computer-aided engineering workflows involving stochastic coupled-wave dynamics in nonlinear dispersive media.
Purpose This study aims to introduce a novel boundary element method (BEM) formulation for two-dimensional elastic contact problems in anisotropic materials subjected to centrifugal loads. Design/methodology/approach The formulation enforces displacement compatibility and force equilibrium to model evolving contact regions. Its performance is demonstrated through four numerical studies: (1) flat contact between orthotropic bodies, showing excellent agreement with published results; (2) an isotropic fretting problem, validating the method for incremental loading against analytical and finite element solutions; (3) a rotating disc segment, confirming the correct treatment of centrifugal loads, and (4) a dovetail joint with inclined contact surfaces and varying friction coefficients, illustrating robustness and low sensitivity to mesh refinement. Findings The proposed BEM approach provides accurate and computationally efficient solutions to frictional contact problems. Its key contribution is the direct inclusion of centrifugal body forces through radial integration, eliminating the need for domain discretization, internal points or radial basis function interpolation. Originality/value To the best of the authors' knowledge, this is the first work applying BEM to contact problems with centrifugal loads in orthotropic materials. By incorporating body forces through radial integration without radial basis functions, the method offers a simpler yet effective framework. The dovetail joint application highlights both its engineering relevance and novelty.
Purpose To aid the design of empty, open-top, unstiffened, ground-supported, steel cylindrical-tanks against wind-induced buckling, this study proposes a fast and innovative artificial neural network (ANN) to predict buckling load-multiplier, assessing the protective effects of geometric aspect ratios of tank and fill level, based on stability analysis. Design/methodology/approach A multiphysics system coupling has been utilized to perform finite element methodology-based one-way wind-structure interaction analysis by joining computational fluid dynamics and structural mechanics (eigenvalue buckling) solvers. The accuracy of the numerical model is ensured through experimental and theoretical validations. Basic wind speed (Vb), tank diameter (D), filling height to tank height (HF/H), tank height to diameter (H/D) and tank radius to wall thickness (r/t) ratios have been varied as inputs for studying the wind-induced buckling through buckling load multiplier (λ). Findings Four different stability conditions, namely safe stability (λ>2), low stability (1<λ ≤ 2), critical stability (λ≈1) and instability (λ<1) are observed based on load-multiplier values. An economically safe buckling capacity is observed for H/D ratios of 0.5 and ≥ 0.75 up to 1.0 in 75% filled tanks with diameters of 15m and 20m with r/t ratios of 1,000 and 750, respectively. An empty tank with H/D ≤ 0.25 is completely safe against wind-induced buckling when r/t ratio 750 and 1,000 are ensured, respectively for tank diameter ≤ 15m and 20m. Originality/value ANN has been trained efficiently with ≥ 60% data from the multiphysics analyses, which showcased 97.03% accuracy for assessing the buckling load multiplier of unstiffened, open-top, steel tank against wind-induced buckling. The developed ANN model can predict the required fluid level inside the unstiffened tank to maintain its stability against wind-induced buckling, based on the velocity of an impending storm and the tank’s geometrical features.
Purpose This paper aims to enhance the effectiveness of emergency response in the event of infectious disease outbreaks, reduce the population infection rate, contain the scope of epidemic spread and minimise losses from casualties. Design/methodology/approach This study pioneers the examination of emergency supply allocation in epidemic regions amid public health crises, formulating a multi-objective optimisation model. The model addresses two types of locations – demand points and distribution centres – and three categories of emergency supplies: food, daily necessities and medical supplies. To address the issue of uncertainty in demand for emergency materials, this paper compares evaluation indicators and performs an error analysis based on emergency material demand forecasts using long short-term memory (LSTM) and susceptible–exposed–infectious–recovered–susceptible (SEIRS) models. Findings The empirical results demonstrate that the LSTM model significantly outperforms the SEIRS model in terms of forecast accuracy. Given this, the study employs LSTM networks to extract time-series features from real-time epidemic information, enabling dynamic assessment of emergency material demand and real-time prediction of demand in each epidemic area. We develop a novel Particle Swarm Optimization–Gravitational Search Algorithm (PSO-GSA), integrating particle swarm optimisation and gravitational search algorithms, to solve this complex model. Using Hubei Province's 202 epidemic data as a case study, we aim to minimise distribution time, unmet demand and total distribution cost. Originality/value This paper establishes a dynamic demand prediction model of LSTM, and applies LSTM to emergency material demand prediction in public health emergencies for the first time. This paper improves the algorithm and optimises the parameters, and proposes a new hybrid algorithm, PSO-GSA. Through comparative analysis, it is proven that LSTM prediction and the PSO-GSA algorithm have significant advantages in practical scenarios, which provide a feasible decision support for the dynamic deployment of emergency supplies during public health emergencies. Graphical abstract Figure 12 A diagram illustrating a multi-objective optimization model for emergency materials distribution during public health emergencies. A diagram of a multi-objective optimization model for emergency materials distribution. The diagram features a central distribution center depicted as a warehouse with a truck, surrounded by four requirement points represented by clusters of buildings with red virus icons. Arrows indicate the flow of materials from the distribution center to the requirement points. The top section of the diagram includes text boxes describing different algorithms and their applications. The left text box mentions LSTM and SEIRS, highlighting the reduction in prediction errors. The middle text box introduces a hybrid PSO-GSA algorithm combined with LSTM for forecasting demand during public health emergencies. The right text box compares the hybrid PSO-GSA algorithm with traditional PSO algorithm and GA. The overall structure emphasizes the dynamic extraction of real-time epidemic information to optimize the distribution of emergency materials.
PurposeIn this paper, we use the higher-order Haar wavelet method (HOHWM) for the approximate solution of first-order integro-differential equations (IDEs) of the second-kind. HOHWM is an improvement of the most popular HWM and depends on a parameter $\lambda$. The method is applied to both Volterra and Fredholm types of IDEs. The advantages of this method include higher accuracy, ease of implementation and good computing efficiency. The method is applied to several problems available in the literature. In the case of HOHWM, second- and fourth-order convergence is observed, which is an improvement over the first-order convergence of the HWM. Design/methodology/approachAssume that the equation has the highest order $n$ derivative. Next \begin{equation}\label{2} \frac{dˆ{n+2\lambda}w(t)}{dtˆ{n+2\lambda}} = \sum_{i = 1}ˆ{\infty}a_ih_i(t), \end{equation} $\lambda = 1,2,\dots$ in this case, {$h_i$,s are Haar functions having three values $0$, $1$ and $-1$}. Because of symmetry and more precise results, we use the even increment $2\lambda$ \cite{majakcs2018}. Values for the unknown function and its derivatives are found by integrating the previous formula. Integrating $n+2\lambda$ times Eq. \eqref{2} {yields the following formula:}\begin{equation}\label{3} w(t) = \frac{a_1tˆ{n+2\lambda}}{(n+2\lambda)!}+\sum_{k = 0}ˆ{\infty}\sum_{l = 0}ˆ{2ˆk-1}a_{2ˆk + l+1}Q_{n+2\lambda,2ˆk + l+1}(t) + S(t) + H(t), \end{equation} \(t = 2ˆk\), \(l = 0, \dots, t-1\), and \(T = 2ˆK\). Here, $t$ denotes the Haar wavelet (HW) resolution and $T$ denotes the greatest degree of resolution. Definitions of \(S(t)\) and \(H(t)\) in Eq.\eqref{3} are: \begin{equation} S(t) = \sum_{r = 0}ˆ{n-1}c_r\frac{tˆr}{r!},\qquad H(t) = \sum_{r = n}ˆ{n+2\lambda-1}c_r\frac{tˆr}{r!}. \end{equation} FindingsThe aforementioned process involves the $n+2\lambda$ variables $c_r,r = 0,\dots,n+2\lambda-1$. The original equation can be used to determine the values of the remaining $2\lambda$ constants, but the BCs can be used to calculate the values of the $n$ integration constants. Specifically, we choose $2\lambda$ points from the domain and insert them into discretized equations to generate $2\lambda$ more equations. These $2\lambda$ points and the collocation points ought to be distinct. There are countless ways to determine the remaining $2\lambda$ constants since there are countless ways to take the $2\lambda$ constants. Originality/valueNumerical solutions of boundary-value problems of IDEs and differential equations are considered. The higher-order HW collocation method is applied. The method works equally well for linear as well as nonlinear problems. The method is applied to several test problems. Fourth-order convergence is obtained.
Purpose Under the “dual-carbon” goal, this study optimized the Two-echelon Vehicle Routing Problem with Time Windows and Simultaneous Delivery and Pickup (2E-VRPSPDTW) in automotive inbound logistics under a milk-run mode to minimize the total cost and carbon emissions while maximizing time-window satisfaction. Design/methodology/approach A novel multi-objective mixed-integer programming model was developed for a three-echelon network comprising suppliers, distribution centers and an original equipment manufacturer. The model incorporates industry-specific constraints, such as two-stage operations, differentiated volume constraints for nested empty and loaded containers and time-window satisfaction requirements. An improved non-dominated sorting genetic algorithm II (NSGA-II) with enhanced operators was designed. Findings Validation using real third-party logistics provider data shows that the algorithm outperforms benchmarks (MOEA/D, SPEA2 and Pareto-TS) in terms of solution quality, convergence and diversity, particularly for small-to-medium instances. Furthermore, sensitivity analysis confirmed that carbon tax and time-penalty costs significantly influence routing decisions and system performance. Originality/value This study clarifies the essential differences between the classical VRPSPDTW and the 2E-VRP by treating empty container flow as an active management variable. It incorporates the physical characteristics of nested empty containers and double-carbon constraints, thus providing a targeted modeling framework and an efficient algorithm for the synergistic optimization of economic, environmental and service benefits in automotive inbound logistics.
