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• A Goal Programming model to optimize a waste paper recycling network was elaborated. • The model considers objectives related to sustainability, multiple products and periods. • Vehicle routing, different-capacity vehicles and multiple trips are highlights. • The possibility of storing material at the collection points is considered. • The formulation provides relevant solutions to assist decision-makers. Organization and planning of reverse logistics networks make sustainable processes more efficient. Thus, an important sector for connecting the collection and waste paper recycling echelons is the intermediate center. In this study, a Mixed Integer Linear Programming model, which is multi-objective, multi-product, multi-level and multi-period, was developed to optimize the waste paper logistics processes of intermediate centers. The formulation includes the following echelons: collection, considering vehicle routing with different capacities; inventory of non-baling materials; baling sorted waste and inventory of bales; selling bales; disposal of non-recyclable waste. The aims of the model include: maximizing the collected waste; minimizing distances; maximizing both the production and sale of bales, and minimizing costs. According to research carried out in the literature, the developed model is a new proposal and to implement it, the Weighted Goal Programming and Revised Multi-Choice Goal Programming approaches were used to deal with multiple objectives and incorporate uncertainty into the quantity of waste available for collection. To analyze the proposed model, computational tests were executed with instances based on real data from a Brazilian company in the sector. For all performed tests, General Algebraic Modeling System 23.6.5 modeling language and CPLEX 12.2.0.2 solver were used for modeling and optimization. The results show that this study presents formulation and technological approaches that represent real situations and provide competitive solutions to the problem. [ABSTRACT FROM AUTHOR]

In this short communication the solution of a steady state model of a sextuple evaporator system used in a paper industry has been presented. With the help of the residual values of model equations (a set of 12 nonlinear algebraic equations) it has been shown that the presently obtained results are superior to the previously published results. The importance of the number of significant digits in calculation are also briefly discussed. [ABSTRACT FROM AUTHOR]

• This research proposes a new formulation for the integrated lot-sizing and cutting-stock problem. • It is also presented analytical and numerical comparisons of the proposed model against the model from the literature. • A column generation approach and a relax-and-fix heuristic were applied to solve the proposed model. The integrated lot-sizing and cutting-stock problem has become a trend in the last decades for its applicability and advantage. Consequently, different approaches and formulations have been developed. One of them, which is widespread and related to the production and cutting process of paper, is the research subject of this paper. Fundamental considerations about the literature model are discussed and an alternative formulation is proposed, which consists of a simplified version that can provide better solutions. The upgrade modifications are proved analytically and an instance is analyzed to exemplify the discussed improvement. Moreover, computational tests are performed to compare both formulations. The novelty of the proposed formulation is the possibility of finding better solutions through the reduction of a constraint set, which guarantees the flexibility given by item and object inventories in meeting demand and it also enables a reduction in the total amount of produced paper. The proposed formulation has a significant impact on future research since the addressed model is the target of many scientific researches and practical applications. [ABSTRACT FROM AUTHOR]

We investigate the one-dimensional cutting-stock problem integrated with the lot-sizing problem in the context of paper industries. The production process in paper mill industries consists of producing raw materials characterized by rolls of paper and cutting them into smaller rolls according to customer requirements. Typically, both problems are dealt with in sequence, but if the decisions concerning the cutting patterns and the production of rolls are made together, it can result in better resource management. We investigate Dantzig–Wolfe decompositions and develop column generation techniques to obtain upper and lower bounds for the integrated problem. First, we analyze the classical column generation method for the cutting-stock problem embedded in the integrated problem. Second, we propose the machine decomposition that is compared with the classical period decomposition for the lot-sizing problem. The machine decomposition model and the period decomposition model provide the same lower bound, which is recognized as being better than the linear relaxation of the classical lot-sizing model. To obtain feasible solutions, a rounding heuristic is applied after the column generation method. In addition, we propose a method that combines an adaptive large neighborhood search and column generation method, which is performed on the machine decomposition model. We carried out computational experiments on instances from the literature and on instances adapted from real-world data. The rounding heuristic applied to the first column generation method and the adaptive large neighborhood search combined with the column generation method are efficient and competitive. [ABSTRACT FROM AUTHOR]

We propose a new concept which is a generalization of fuzzy soft subset and fuzzy soft equal. Using such notions, we will be able to consider the distributive law of fuzzy soft sets. Using the distributive law of fuzzy soft sets, we point out that the distributive law of trapezoidal fuzzy soft sets as proposed by Xiao et al. (2012) is not true. The correction will further improve further extensions of the results of Xiao et al. (2012). We will also establish the generalized distributive law of trapezoidal fuzzy soft sets along with illustrative examples. [ABSTRACT FROM AUTHOR]

This Special Issue of Applied Mathematical Modelling journal consists of selected quality papers originally presented at 15th International Conference "Dynamical Systems - Theory and Applications" (DSTA) which took place on December 2-5, 2019 in Lodz, Poland. B Dzyubak et al. b analysed a non-linear multi-scale diffusion cancer invasion model that describes the interactions of the tumour cells, matrix-metalloproteinases, matrix-degradative enzymes and oxygen. Chaotic cancer attractors are quantified and multi-parametric evolution of conditions leading to cancer invasion is defined. [Extracted from the article]

The paper deals with modification and minor correction of the presentation and results of paper ( http://dx.doi.org/10.1016/j.apm.2015.09.103 ). The current paper demonstrates that the solution obtained in the paper (doi.org/10.1016/j.apm.2015.09.103) for the thin cylindrical shell problem holds well near the cylindrical edge surfaces but may deviate near the mid-cylindrical surface. The reason behind it, is the observation of the paper (doi.org/10.1016/j.apm.2015.09.103) that different asymptotic modes are uncoupled, can be justified near edge surfaces but not near the mid-surface. In this paper an attempt is made to predict the vibration near mid-surface of the shell with a prior knowledge of the solution near edge surfaces, which has already been discussed in (doi.org/10.1016/j.apm.2015.09.103). [ABSTRACT FROM AUTHOR]

• Semi-analytical solution of damping fluid-conveying pipe systems are obtained. • The concepts of the original system and the adjoint system are introduced for research. • The eigenvalues and eigenfunctions of the original system and the adjoint system are obtained. • The orthogonality condition of damped gyroscopic system is obtained in state space. • It is proved that the original system and the adjoint system of the system with free boundary are not orthogonal. In this paper, the response solutions of the damped fluid-conveying pipe system with elastic torsion constraints at both ends are analyzed. The pipe system considering gyroscopic effect induced by internal flow and damping effect is a typical damped gyroscopic system. This system cannot be decoupled in the modal space by the traditional modal analysis, and then the semi-analytical response solutions cannot be obtained by the classical modal superposition method. In order to remedy this problem, this paper proposes a new method based on complex modal superposition method and state-space method to give the semi-analytical response solutions of the damped fluid-conveying pipe system. The adjoint system is introduced through the concept of adjoint operator, and the orthogonality conditions of the damped fluid-conveying pipe system are derived in the state-space by using the eigenvalue relationship between the original system and the adjoint system. The Laplace transformation method is used to solve the eigenvalue problems of the original system and the adjoint system, and the implicit function equations about the eigenvalues and analytical eigenfunctions are obtained. According to the obtained orthogonality conditions, the semi-analytical response solutions of the system under arbitrary initial conditions and excitations are given, and the obtained solutions include transient and steady-state response solutions. In the numerical discussion part, the reliability and accuracy of the present method are verified. This research has positive significance for the dynamic analysis of fluid-conveying pipe systems, and the obtained orthogonality conditions have potential value for the nonlinear dynamics research. [ABSTRACT FROM AUTHOR]

• Improved lorenz chaotic systems with higher complexity. • Pixel permutation method based on the image pyramid structure. • Secure and efficient image encryption method. • Galois field multiplication for efficient diffusion of pixels. This paper proposes an improved Lorenz chaotic system and a secure and efficient image encryption method to enhance encryption effectiveness in encrypted images. The proposed improved Lorenz chaotic system addresses the problem of applying the Lorenz chaotic system to image encryption, resulting in weak chaotic characteristics and susceptibility to reconstruction. Dynamic analysis, sensitivity analysis, and randomness testing demonstrate that the improved Lorenz chaotic system exhibits hyperchaotic characteristics, with a maximum Lyapunov exponent of 2.9897. Based on the improved Lorenz chaotic system, this paper proposes an image encryption method that combines image pyramid structure permutation and Galois field diffusion. Unlike most of the current permutation methods limited to a single image layer, this paper proposes a multilayer permutation method based on the image pyramid structure to enhance the permutation effect of image encryption. Although diffusion based on Galois field multiplication operation is efficient and secure, it is less effective in encrypting pixel points with a pixel value of '0′. To address this issue, this paper incorporates DNA computing into diffusion based on Galois field operations, enabling even pure black images to achieve better encryption effectiveness. Experimental results demonstrate that the encryption method proposed in this paper effectively conceals information contained in the plain image. The global Shannon entropy of the encrypted Lena image can reach 7.9975, indicating a high level of randomness and complexity. Notably, even a slight alteration, such as changing a single pixel, results in a significant divergence, with 99.6307 % of the cipher image's pixels being distinct. Moreover, it effectively withstands analysis from various attacks. Therefore, the encryption method proposed in this paper can be effectively applied to grayscale image encryption scenarios requiring relatively high security and encryption efficiency, such as remote sensing image encryption and personal privacy image encryption. [ABSTRACT FROM AUTHOR]

• The elastic instability phenomenon in hyperelastic layered materials with the phases exhibiting stiffening behavior is studied • A closed-form expression for the critical stretch of macroscopic instability is derived • An analytical prediction based on Bloch-Floquet analysis for the microscopic instability is exhibited • The critical parameters and transition of instability modes are found to be highly tunable with phase stiffening This paper investigates the elastic instability behavior in soft periodic laminates subjected to finite strains, with a focus on both macroscopic and microscopic instabilities. Considering the deformation-induced phase stiffening, the Gent model with a high bulk-to-shear modulus ratio describes the behavior of incompressible phases. This non-Gaussian statistics-based model captures the non-linear constitutive results from the limited extensibility of polymeric molecular chains. This paper derives an analytical prediction for the onset of macroscopic (or longwave) instability and microscopic instability as functions of material parameters. Moreover, a numerical Bloch-Floquet analysis is imposed on identifying the instability behavior under compression. We consider a wide range of phase combinations and find that the relatively rapid stiffening of the matrix compared to the stiff layer increases the stability of laminates by decreasing the critical stretch ratio. Essentially, properly manipulating the stiffening parameters can produce an absolutely stable region without observed instability. This paper also systematically illustrates the changes in instability and the transition between macro and micro instability in fully Gent laminates, which show higher stability than fully neo-Hookean laminates with larger critical stretch ratios. The critical characteristics of instabilities, such as critical stretch ratios and critical wavenumbers, can be controlled by the choice of stiffening parameters and other material properties, enlarging the tuning of soft laminates for desired buckling patterns in practical applications. [ABSTRACT FROM AUTHOR]

The dynamic behaviour of wildfires is mainly influenced by weather, fuel, and topography. Based on fundamental conservation laws involving numerous physical processes and large scales, atmospheric models require substantial computational resources. Therefore, coupling wildfire and atmospheric models is impractical for high resolutions. Instead, a static atmospheric wind field is typically input into the wildfire model, either as boundary conditions on the control surface or distributed over the control volume. Wildfire propagation models may be (i) data-driven ; (i i) theoretical ; or (i i i) mechanistic surrogates. Data-driven models are beyond the scope of this paper. Theoretical models are based on conservation laws (species, energy, mass, momentum) and are, therefore, computationally intensive; e.g. the Fire Dynamics Simulator (FDS). Mechanistic surrogate models do not closely follow fire dynamics laws, but related laws observed to make predictions more efficiently with sufficient accuracy; e.g. FARSITE, and FDS with the Level Set model (FDS-LS). Whether theoretical or mechanistic surrogate, these wildfire models may be coupled with or decoupled from wind models (e.g. Navier-Stokes equations). Only coupled models account for the effect of the fire on the wind field. In this paper, a series of simulations of wildfire propagation on grassland are performed using FDS-LS to study the impact of the fire-induced wind on the fire propagation dynamics. Results show that coupling leads to higher Rates of Spread (RoS), closer to those reported from field experiments, with increasing wind speeds and higher terrain slopes strengthening this trend. Aiming to capture the fire–wind interaction without the hefty cost of solving Navier-Stokes equations, a conceptual framework is proposed: 1) a swarm of unmanned aerial vehicles measure wind velocities at flight height; 2) the wind field is constructed with the acquired data; 3) the high-altitude wind field is mapped to near-surface, and 4) the near-surface wind field is fed into the wildfire model periodically. A series of simulations are performed using an in-house decoupled physics-based reduced-order fire propagation model (FireProM-F) enhanced by wind field "measurements". In this proof of concept, wind velocities are not measured but extracted from physics-based Large Eddy Simulations taken as ground truth. Unsurprisingly, higher measurement frequencies lead to more accurate and realistic predictions of the propagating fire front. An initial attempt is made to study the effect of wind measurement uncertainty on the model predictions by adding Gaussian noise. Preliminary results show that higher noise leads to the fire front displaying more irregular shapes and slower propagation. • Higher wildfire model prediction accuracy normally achieved by coupling it with wind model such as Navier-Stokes equations. • Coupled fire-wind models often too computationally expensive for real-time use in operational contexts. • Prediction accuracy of wildfire model uncoupled from wind model enhanced by periodic inputs of updated wind field. • Wind field to be constructed from UAV swarm measurements, surrogated here to velocities obtained from full CFD simulations. • Proposed method to enhance wildfire model predictions robust to Gaussian noise added to represent measurement uncertainty. [ABSTRACT FROM AUTHOR]

A new enhanced multi-strategy bottlenose dolphin optimizer is proposed. • The superiority of the proposed algorithm is verified by comparing with efficient intelligent algorithms. • A three-dimensional path planning model for unmanned aerial vehicles with time, threat, height and smooth cost is studied. • The proposed algorithm is applied to solve the three-dimensional path planning problem for unmanned aerial vehicles. • The quality of the proposed algorithm based path planning results is better than other approaches. The path planning of unmanned aerial vehicle is a complex practical optimization problem, which is an important part of unmanned aerial vehicle technology. For constrained path planning problem, the traditional path planning methods can not deal with the complex constraint conditions well, and the classical nature-inspired algorithms will find the local optimal solution due to the lack of optimization ability. In this paper, an enhanced multi-strategy bottlenose dolphin optimizer is proposed to solve the unmanned aerial vehicle path planning problem under threat environments. Firstly, the introduction of fish aggregating device strategy that simulates the living habits of sharks enriches the behavioral diversity of the population. Secondly, random mixed mutation strategy and chaotic opposition-based learning strategy expand the exploration range of the algorithm in the solution space by disturbing the positions of some individuals and generating the opposite population respectively. Finally, after balancing the exploration and exploitation ability of the algorithm more reasonably through the mutation factor and energy factor, this paper proposes a new swarm intelligence algorithm. After verifying the adaptability and efficiency of the proposed algorithm through different types of test functions, this paper further highlights the advantages of the proposed algorithm in finding the optimal feasible path in the unmanned aerial vehicle path planning model based on four constraints. [ABSTRACT FROM AUTHOR]

This paper presents a case study on condition monitoring of power generators at offshore wind turbines. Two fault detection models are proposed for detecting sudden changes in the sensed value of metallic debris at the generator. The first model uses an exponentially weighted moving average, while the second monitors first-order derivatives using a fixed threshold. This is expected to improve the maintenance activities by avoiding late or early part replacement. The economic impact of the proposed approach is also provided with a realistic depiction of the cost structure associated with the corresponding maintenance plan. While the specifics of the case study are supported by real-life data, considering the prevalence of the use of generators not only in offshore wind turbines but also in other production environments, we believe the case study covered in this paper can be used as a blueprint for similar studies in other applications. • Large scale condition monitoring demonstrates economic benefits. • Case study from real wind turbine population with economic impact assessment. • Sensor for monitoring fault mode results in lead time for maintenance planning. • Sensitivity analysis assesses results despite downtime and power price uncertainty. [ABSTRACT FROM AUTHOR]

• A model to explore the multiphysics characteristic of semiconductors is presented. • The model determines the thermal and mechanical properties of complex patterns. • Results show a strong correlation between thermal and mechanical properties. • Dielectric bands asymmetrically affect thermal and mechanical behavior. • Machine learning can predict one property from another. As semiconductor performance improves through advanced package designs, it becomes important to consider both thermal and mechanical properties. Better understanding their relationship enhances system design and optimization. This study has introduced a numerical method that takes into account both thermal and mechanical fluxes to construct thermal and mechanical property maps for practical application in semiconductor engineering. Furthermore, this paper investigated the relationship between the two properties using the constructed property maps in commercially available semiconductor packages. Owing to the complexity of packaging design patterns, a coupled isoparametric mapping and machine learning (ML) method was introduced to investigate their effects. The model then determines and investigates the anisotropic equivalent thermal and mechanical properties of the commercialized semiconductor packages with complex pattern designs, according to the package materials, volume fractions of each material, and design patterns. This approach pursues more sophistication and practicality compared to simplified composite structure property evaluation models. Additionally, all processes in the algorithm are automated based on ML methods, making them practically applicable in the semiconductor industry. The study shows that there is a strong correlation between the thermal and mechanical characteristics in the complex package patterns. This relationship was able to form a fairly clear category based on the shape of the dielectric band because the dielectric band had significantly different effects on the thermal and mechanical fluxes. The study discussed the physical implications of the similarities and differences between the two behaviors and validated the results of the equivalent properties through finite element (FE) analysis. Finally, the study cross-validates the relationship by showing that information from one flux behavior can be used to predict the other based on the ML method. Based on the results, this paper can provide a better understanding of thermal and mechanical fluxes in semiconductor package patterns for package design and optimization. [ABSTRACT FROM AUTHOR]

• A dynamic model of L-shaped fluid-conveying pipes based on ANCF method is established. • Effects of the radius of the arc section and the fluid velocity on the natural frequency are discovered. • Results of the ANCF method are verified by results obtained by the experiment and simulation. In this study of fluid-conveying pipe dynamics, it is usually assumed that the shape of the pipe is straight. This paper establishes a flow-induced vibration model of an L-shaped pipe based on the absolute nodal coordinate formulation (ANCF), and mainly studies the effects of fluid velocity, structural parameters, and boundary conditions on the vibration characteristics of the pipe. The results show that the fluid velocity will reduce the natural frequency and affect the modal shapes on the basis of causing static deformation of the pipe. After reaching the critical fluid velocity, the modal combination will occur when the fluid velocity continues to increase. Notably, alterations in pipe length, arc radius, wall thickness, eccentricity and boundary conditions exert diverse effects on the natural frequencies of the pipe. In particular, the arc radius is not involved in the previous study of straight and curved pipe dynamics, so it is analyzed emphatically. Among these variables, the fluid velocity is always a key factor affecting the dynamic characteristics. Finally, experiments and finite element software were used to compare the ANCF method, verifying the effectiveness of the method. Therefore, this paper has developed an effective analytical method to study the flow-induced vibration of complex shaped conveying fluid pipes. [ABSTRACT FROM AUTHOR]

Urbanization and the release of carbon emission are two significant features of contemporary economic and social progress in China. However, there are few studies that consider how urbanization policy goals affect carbon emission. This paper aims to study the nonlinear effects of urbanization policy goals on carbon emission in 13 cities of the Beijing-Tianjin-Hebei region. In this paper, a multi-dimensional spatial disturbance grey model is proposed. Based on matrix perturbation theory, this paper explores the spatial perturbation bounds of the novel model and verifies that the spatial property of the model is consistent with the viewpoint of the First Law of Geography. Then, the novel model is used to predict the urban carbon emission under different urbanization policy goal scenarios. The results showed that the novel model has spatial regional correlation in spatial region prediction. With the development of urbanization level, carbon emissions show a downward trend in more than 50% of cities from 2022 to 2025. In addition, the improvement of urbanization policy goals will promote the carbon peak time of most cities. The carbon emission intensity will exhibit an inverted U-shaped trend distribution in space. The research results are conducive to providing scientific guidance for the formulation of new-type urbanization policies and helping to achieve the dual carbon goals. • A multi-dimensional spatial disturbance grey model is proposed. • The novel grey model is consistent with the viewpoint of the First Law of Geography. • The spatial distribution of carbon intensity showed an inverted U-shaped pattern. [ABSTRACT FROM AUTHOR]

We present a general methodology to evaluate the mass moments of two-dimensional domains and axisymmetric solids made of functionally graded materials. The approach developed in the paper is based on the sequence of two steps. First, the original domain integrals are converted to integrals extended to the relevant boundary by exploiting Gauss theorem. Second, for domains having a polygonal or circular shape, the boundary integrals are evaluated analytically by providing algebraic expressions that depend upon the parameters defining the density distribution, the position vectors of the vertices of the polygonal domain or the initial and ending points of an arbitrary circular sector, respectively. While the first step refers to moments of arbitrary order, the second step is limited to the most useful quantities for engineering applications, i.e. generalised mass, static moment and inertia tensor. The formulas derived in the paper are validated by means of examples retrieved from the specialised literature for which analytical results are available or have been specifically derived by the authors. Finally, in order to ascertain the computational savings entailed by the use of the proposed analytical formulas with respect to numerical techniques, the mass moments of a longitudinal section of a human femure, made of a functionally graded material and characterised by a linear density distribution, have been computed. • Mass moments for functionally graded domains expressed by boundary integrals. • Polynomial, exponential and polynomial quadratic density distributions. • General methodology for computing mass moments of order greater than 2. • Analytical evaluation of mass moments for polygonal or circular domains. • Accuracy and computational efficiency of the analytical formulas. [ABSTRACT FROM AUTHOR]

• Exact geometrical shape of tool is involved in the mathematical model. • Friction force comprises the sliding friction force and the rolling friction force. • Plough force is involved in the cutting force model due to the cutting edge radius. Variations in cutting forces significantly influence the tool wear and part quality in machining high-volume SiC-particle-reinforced aluminum matrix (SiCp/Al) composites. Properties of the reinforcement SiC particles, such as size and volume fraction, contribute to the change in the cutting forces. This paper presents a cutting force model based on the geometrical and mechanical nature of the tool and workpiece, considering the effect of the SiC reinforcement particles. The cutting force is predicted as three components (F z , F x , and F y) and the resultant cutting force F τ s. The cutting force was considered to generate three deformed zones: (a) shear deformed zone, (b) friction deformed zone on the chip–tool interface, (c) plow deformed zone. The effect of SiC reinforcement particles on friction deformed zone is analyzed emphatically. The friction force from friction deformed zone was obtained by calculating the sliding friction force and rolling friction force. To verify the feasibility and validity of the predicted model of cutting force, cutting experiments were performed with different combinations of cutting speed, feed rate, depth of cut, and tool nose radius. The predicted cutting force values demonstrate good agreement with the measured experimental cutting force values in most cutting conditions. The average percentages of the prediction error were 1.93%, 6.20%, and 10.48% for the F z , F x , and F y components, respectively, thus proving the validity and accuracy of the predicted model of cutting forces. [ABSTRACT FROM AUTHOR]

In this paper, we develop a method for the estimation of airgap spatial variation from the harmonics that appear in the stator's current under static eccentricity conditions. We move beyond the detection of the eccentricity fault and endeavour to quantify the severity of this fault. To achieve this, we formulate the problem as a mathematical inverse problem and attempt to solve it in the Bayesian framework using the so-called Bayesian approximation error approach. The solution takes the form of an algorithm capable of estimating the parameter(s) that characterize the spatial variation of the airgap length from noisy and limited data. Furthermore, it can quantify the uncertainty associated with the results as a byproduct of the Bayesian analysis approach employed in this paper. The results demonstrate that with each iteration of the algorithm, estimation accuracy improves, and the uncertainty of the estimated results reduces. • Bayesian approximation error analysis shows promise in monitoring electrical machines with eccentric rotors. • The paper applies Bayesian inversion for online estimation of airgap length in induction machines with eccentric rotors. • The study estimates static eccentricity ratio from limited data on harmonics of the machine line currents. • This paper gives an analytical method for calculating all inductances of induction machines under static eccentricity. [ABSTRACT FROM AUTHOR]

This paper discusses the challenging issues that reliability practitioners face in conducting destructive tests that lead to completely censored lifetimes, especially in estimating the defect rate of products. Manufacturers need to measure the defect rate for quality control purposes, but obtaining enough defective devices for accurate estimation is not easy when the defect rate is relatively low. To address the issues, a Bayesian approach for estimating the defect rate is proposed in this paper. The proposed method is devised to make up for the heavy computational burdens of the Metropolis-Hastings algorithm. To quantify the uncertainty in the Bayesian estimation, a nonparametric bootstrap technique is employed to construct a credible interval for the defect rate. The performance of the proposed method is evaluated through a variety of Monte Carlo simulation studies. The efficiency of the proposed Bayesian estimation procedure is validated using a real-world dataset of return-springs in DC motor systems under an accelerated destructive degradation test. • Estimate the defect rate of products in conducting destructive tests with completely censored lifetime data. • Propose a computationally efficient Bayesian estimator of an analytical form for the defect rate with masking. • Propose a nonparametric bootstrap technique to construct a credible interval for the defect rate. • The proposed method is validated using accelerated destructive degradation testing data of return-springs. [ABSTRACT FROM AUTHOR]

• Proposing and establishing a dynamic model for the combined rotor that accounts for rub-impact. • Increasing the stiffness of the stator advances the speed at which the system enters the quasi-periodic period. • The Stribeck friction model reduces the speed range of the system's period three motion compared to Coulomb friction. • The magnitude and phase angle of the imbalance significantly alters the state of motion of the system. • Analyzing the basic mechanism that governs the variation of friction and its impact on the stability of the system. This paper aims to analyze the dynamic behavior of the rod-fastening combined rotor(RFCR) system in a rub-impact state and proposes a rod-fastening rotor dynamics model based on the Stribeck friction model. This model offers advantages such as generating frictional forces based on relative velocities and considering the coupling effects of rub-impact under complex excitations, providing greater flexibility in studying rotor systems. The Lagrange equation is utilized to deduce the RFCR formula, and the balance equation of the combined rotor is presented under friction, oil-film, and unbalanced conditions. This paper investigates the dynamic response of the RFCR system under rub-impact using the 4th-order Runge–Kutta method. The effects of parameter variations on the nonlinear dynamics of the combined rotor are systematically analyzed by means of bifurcation diagrams, motion trajectory, time domain waveform, frequency spectrum, and Poincaré maps. The results show that the dynamic characteristics of the rotor system show a regular variation with the variation of the system parameters. Different forms of periodic motions, namely Periodic 1 motion (P1), Periodic 2 motion (P2), and Periodic 3 motion (P3) motions, along with quasi-periodic motions, are observed in response to varying system parameters. The results show that the higher the stator stiffness, the earlier the rotor enters the quasi-periodic speed. The velocity effect of friction reduces the speed range of the P3 motion of the rotor system and enhances the nonlinearity of the system. The magnitude and phase of the unbalance force change the frequency component of the system, which has a more substantial effect on the rotor system. These findings can help engineers and researchers in comprehending system behavior and designing more dependable and effective gas turbine rotor systems. [ABSTRACT FROM AUTHOR]

· This paper presents a multi-stage mechanical deformation mode with complex loading surfaces. · All multi-stage contact mechanical models involved in the actual loading deformation process are established. · APSD can describe and analyze the characteristics of fractal surfaces. The contact mechanical behavior of rough surfaces is related to the friction and wear of mechanical components, and also has an important impact on the dynamic performance and force transfer characteristics of assembly surfaces. This paper aims to solve the complex multi-stage mechanical deformation mode of the loading surface, and establishes all multi-stage contact mechanical models involved in the actual loading deformation process from the perspective of the actual deformation and critical deformation of the asperity. Firstly, based on the three-dimensional fractal contact theory, the force deformation relationship of a single asperity during the full deformation stage of loading is constructed. Then, six critical contact areas and four critical deformation quantities of a multi scale asperity are derived. Finally, the complex multi-stage deformation contact mechanical models of three-dimensional fractal surfaces under actual loading are established. The area power spectral density (APSD) function spectrum of rough surface under different fractal parameters, as well as the variation of contact load, contact stiffness, and contact area are analyzed numerically. Compared with several classical models, the rationality of the proposed model is verified. This study can be used as the basis for constructing the overall dynamic model of an assembly system [Display omitted] [ABSTRACT FROM AUTHOR]

• Eringen's nonlocal and strain gradient theories are used for wave propagation. • Symmetric wave propagation and scattering are modelled using the two theories. • The study is carried out for layered piezoelectric media at nanoscale. • Length scale effect on the propagation of polarized guided waves is investig. • Changes in mechanical displacement and electrical potential are plotted and analyzed. This paper investigates the dynamic propagation behavior of guided waves in nanoscale media composed of alternating layers of piezoelectric phases. The study employs Eringen's nonlocal and strain gradient theories to derive equations for symmetric wave propagation and the scattering relations of guided waves perpendicular to these structures. Dispersion curves are calculated and plotted to compare these theories, considering the influence of nanoscale size-effect, volume ratio of constituent layers, and material length scale. Using the strain gradient theory, the paper explores the impact of length scale parameters on the propagation behavior of horizontally polarized guided waves in an alternating layer structure of nanoscale piezoelectric material, specifically nanoscale piezoelectric laminates. The analysis involves calculating localization factors and dispersion curves to analyze the effects of size-effect and length scale parameters on wave propagation and band structures. Additionally, the study plots and analyzes changes in mechanical displacement and electrical potential, followed by an investigation and discussion of nanoscale size effects and the effects of the material's length scale parameter on dispersion curves and conversion modes within specific regions. The results highlight that the length scale effect parameter significantly impacts the mode conversion zones and band gap structures, more so than the NLPE continuum theory suggests. As the strain gradient parameter increases, these zones shift towards higher wavenumbers and to the right. Furthermore, introducing the length scale factor results in a substantial decrease in both the formation of conversion zones and the density of dispersion curves. [ABSTRACT FROM AUTHOR]

Rainstorm is one of the most severe and frequent meteorological disasters. The rainstorm event brings considerable risks to the natural ecosystem and human life. There is a limited body of research on applying the grey prediction model for predicting rainstorm-related data. Based on the extreme precipitation index defined by the Expert Team on Climate Change Detection and Indices, this paper uses the data of rainstorm days from 493 weather stations in the middle and lower reaches of the Yangtze River to establish a prediction model. Improving the accuracy of rainstorm days prediction can bring valuable results to decision-makers in a specific region. The annual rainstorm days series exhibits randomness, irregular nonlinearity, fluctuations, etc.; however, the traditional grey prediction model can only identify the trend of a series but not its fluctuations, making its prediction extremely challenging. Therefore, this paper introduces a new dynamic grey action quantity based on the traditional grey model, and the parameters are solved by the hybrid technique of the genetic algorithm and the constrained fmincon function. The prediction results of the new model are compared with those of the traditional grey model, the seasonal grey model, the neural network, and the seasonal autoregressive integrated moving average. In terms of prediction accuracy and similarity of fluctuations, the results demonstrate that the new model outperforms these models. • A fluctuation data grey model is proposed to predict the rainstorm days. • A novel dynamic grey action quantity is introduced into the traditional grey model. • The nonlinear parameters are determined based on hybrid optimization algorithm. • The new model has better simulation and prediction accuracy than the traditional models. [ABSTRACT FROM AUTHOR]

• A model-based approach is proposed for the design synthesis of autonomous articulated vehicles. • The dynamically coupled subsystems of an autonomous vehicle are devised and evaluated simultaneously. • A prediction vehicle model for articulated vehicles is developed. • The effectiveness of the proposed approached is demonstrated by numerical simulations. • The results presented in the paper may be used as guidelines for devising autonomous articulated vehicles. In conventional autonomous vehicle designs, the mechanical system is first devised, and the automated driving systems are subsequently added. The conventional method can be categorized as a sequential design approach. An autonomous vehicle consists of the subsystems of mechanical assembles, automated driving, etc. There exist dynamic couplings among these subsystems, and the sequential design method may not be the most effective. This observation initiates the motivation of this research, and the objective of this paper is thus to explore a more effective design method for autonomous vehicles and, in particular, autonomous articulated vehicles. To this end, this paper proposes a model-based design synthesis method, i.e., a concurrent design method, for autonomous articulated vehicles. The autonomous articulated vehicle assumes to be composed of the subsystems of a mechanical unit, a trajectory tracking-controller based on a model predictive control technique, and a motion-planner. The design synthesis of the autonomous articulated vehicle is constructed as a bi-level optimization problem. With the proposed concurrent design approach, the subsystems are optimally devised simultaneously. To examine the proposed approach, it is applied to the design of a car-trailer combination with automated steering. The insightful findings attained from the study may be used as guidelines for developing autonomous articulated vehicles. [ABSTRACT FROM AUTHOR]

• A learning algorithm for human-robot skill transfer based on dynamic movement primitive was proposed. • The impedance control system was investigated to improve the compliance and robustness. • Two-dimensional writing tasks were extended to three-dimensions space. • Constraints on the inverse solutions of redundant robots were ensured by adding constraint equations. • The proposed algorithm had been validated on a ROKAE xMate robot platform. This paper proposed a learning algorithm for human-robot skill transfer based on dynamic movement primitive. Through the establishment of Transmission Control Protocol communication, the position trajectory and force characteristic of the human demonstrator while demonstrating the robot were recorded as the training data of the dynamic movement primitive model. The demonstrated skill/motion reproduction and generalization were successfully achieved through adjusting the parameters of the dynamic movement primitive model. The impedance control system investigated in this paper improved the compliance of the robot trajectory reproduction and skill generalization, and improved the robustness of robot control system in different environments. In addition, for the problem of inverse solution of redundant robots, this paper improved the dimension of constraint equations in the inverse solution of robots by training multiple dynamic movement primitive models, which guaranteed the constraints of inverse solutions of redundant robots. The proposed algorithm had been validated on a simulated robot platform using MATLAB and a ROKAE xMate robot platform, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear switched dynamical system (NSDS) with unknown system parameters in the context of uncertain experimental data. This system is employed to model the continuous fermentation for the production of 1,3-propanediol through glycerol bioconversion. The uncertain experimental data points are regarded as stochastic variables and only their first-order moment information of the probability distributions is available. The target of this paper is to optimize these system parameters under the environment of uncertain experimental data. Taking these factors into account, we propose a distributionally robust system identification (DRSI) problem (i.e., a bi-level system identification problem) governed by the NSDS. The objective functional comprises two level objectives: (i) the inner-level objective aims to maximize the expectation of the relative error between the solution of the NSDS and the uncertain experimental data with respect to their probability distributions at approximately stable time; and (ii) the outer-level objective is to minimize the expectation with respect to these system parameters. The DRSI problem is equivalently transformed into a single-level system identification (SLSI) problem with non-smooth term through the application of the duality theory in the probability space. A smoothing technique is employed to approximate the non-smooth term in the SLSI problem. Subsequently, an error analysis of the employed smoothing technique is derived. The gradients of the objective functional in the SLSI with respect to these system parameters are obtained. An optimization algorithm is designed to solve the SLSI problem. Finally, the paper concludes with simulation results. • The DRSI problem lies between RSI problem and SSI problem. • An optimization algorithm with the duality theory is proposed to solve the DRSI problem. • A smoothing technique is employed to approximate the non-smooth term in the objective functional. [ABSTRACT FROM AUTHOR]

• Small scale analysis of functionally graded triply periodic minimal surface (FG-TPMS) nanoplates. • The generalized weak form formulation for the FG-TPMS nanoplate is proposed. • A fitting technique based on a two-phase piece-wise function for porous structures of TPMS. • The length scale parameters can high-efficiently predict size effects. • Novel benchmark numerical results are illustrated and introduced. In recent years, the triply periodic minimal surface (TPMS) has emerged as a remarkable solution for constructing structures, drawing inspiration from natural architectures. TPMS offers several outstanding features, including porous architectures with high interconnectivity, smooth surfaces and the ability to achieve mathematically controllable geometry features. However, it is evident that the current research has not fully harnessed the extensive potential and benefits of TPMS structures. In this paper, a groundbreaking approach for analyzing functionally graded triply periodic minimal surface (FG-TPMS) nanoplate, which is utilized a novel nonlocal strain gradient isogeometric analysis, is provided. Three patterns of the FG-TPMS nanoplate, namely Primitive (P), Gyroid (G) and I-gragh and Wrapped Package-graph (IWP), are utilized in this study. The primary focus is to investigate size dependent problems with two types of density distributions. The proposed model successfully incorporates both nonlocal effects and strain gradient effects into nanoplate structures. The paper demonstrates how the mechanisms responsible for both reducing and enhancing stiffness in the nanoplate can be understood by fine-tuning the nonlocal and strain gradient parameters. The findings of this study offer promising prospects for future design and optimization as they provide a robust approach to address the complex mechanical behavior observed in the FG-TPMS nanoplate. The proposed model not only captures the behavior accurately but also opens up new avenues for exploring the capabilities of FG-TPMS structures. [ABSTRACT FROM AUTHOR]

• A fractional-order viscoelastic model is used to simulate soil. • The time variation of engineering load is considered. • The layered property of soil is considered. • The influence of the bottom rock on the soil is considered. • The recovery of settlement after unloading is analyzed. Time-varying loading is a frequently encountered loading type in geotechnical engineering. As the deformation of viscoelastic soil is related to its loading history, studying the viscoelastic problems under time-varying loads has important practical engineering significance. In this paper, the stress and displacement of a layered soil with fractional-order viscoelastic model under time-varying loads were solved using the complex variable method and the corresponding principle. Under the assumption of quasi-static and linear elasticity, this paper derives the quasi-static elastic solutions of a layered soil under time-varying strip loads. By introducing the fractional-order viscoelastic model and using the corresponding principle, the Laplace-domain analytical solutions are obtained. Finally, numerical methods are utilized to perform the Laplace inverse transform and obtain the solutions in the physical domain. The correctness of this paper is validated by comparing the numerical results with the ANSYS software, as well as by comparison with previous literature. Based on the experimental data, the material parameters of frozen soil at two temperatures are fitted. The settlement patterns of soil under two engineering loads were analyzed through case studies. By controlling variables, the influence of parameters of the fractional viscoelastic model on elastic aftereffect was investigated. [ABSTRACT FROM AUTHOR]

This paper proposes a novel nature-inspired meta-heuristic algorithm, named Snow Geese Algorithm. It is inspired by the migratory behavior of snow geese and emulates the distinctive "Herringbone" and "Straight Line" shaped flight patterns observed during their migration. The algorithm is structured into three main phases for benchmark testing. In the first phase, the Snow Geese Algorithm's numerical results are compared with those of several classical meta-heuristic algorithms using the same test functions and original data from these algorithms. In the second phase, in order to minimize potential variations during the comparison, all algorithms undergo evaluation on a standardized testing platform. In the third phase, this paper applies the Snow Geese Algorithm to solve four widely recognized engineering optimization problems: the tubular column design, piston lever optimization design, reinforced concrete beam design and car side impact design. These real-world engineering problems serve as test cases to assess Snow Geese Algorithm problem-solving capabilities. The primary objective of the Snow Geese Algorithm is to provide an alternative perspective for tackling complex optimization problems. Please note that the complete source code for the Snow Geese Algorithm is publicly available at https://github.com/stones3421/SGA-project. • Snow Geese Algorithm: A novel meta-heuristic approach inspired by snow geese flight behavior, tackling optimization problems. • Two-stage Strategy: Mimics snow geese exploration and exploitation patterns, setting it apart from traditional methods. • Performance Evaluation: Multiple algorithms are assessed on different problems. • Algorithm Features: Experimental results validate the effectiveness of the Snow Geese Algorithm. • Practical Applications: Snow Geese Algorithm shows potential in engineering optimization, aiding accurate decision-making. [ABSTRACT FROM AUTHOR]

• Treat a problem of predicting the demand for staple food and feed grain. • A novel fractional discrete dynamic multivariate grey model is proposed. • The model considers the effects of linear correction term & random disturbance term. • Sailfish optimizer is used to optimize the fractional order accumulation parameter. • Empirical analysis shows the proposed method performs better than similar methods. Increasing geopolitical conflicts, extreme weather and other emergencies are continuously affecting global agriculture and food systems, threatening national and regional food security. Therefore, it is particularly important to accurately predict national or regional grain demand. In this paper, a novel fractional discrete dynamic multivariate grey model is proposed to predict grain demand. Based on the discrete modeling idea, the model considers the impacts of the change trend of the related factor sequences, adds the linear correction term and the random disturbance term, and applies the fractional order accumulation strategy, which improves the accuracy and robustness. An algorithm based on sailfish optimizer is introduced to optimize the fractional order accumulation parameter of the model. Taking the Yangtze River Economic Belt as an example, the fitting and prediction results of the novel and the existing three models are compared. The novel model can better fit and predict the demand for staple and feed grain, which is superior compared to other models. The predictions show that demand for staple food and urban feed grain in the Yangtze River Economic Belt will increase to varying degrees, while rural feed grain demand will remain stable overall. This paper will help the government to better grasp the changes in the structure and quantity of staple food and feed grain demand in the Yangtze River Economic Belt and formulate efforts to ensure food security. [ABSTRACT FROM AUTHOR]

• The mathematical model of the 2-DOF manipulator attitude system is established. • The relationships between yaw and lifting motion and the gyroscopic effect are analyzed. • This is the first time to conduct a nonlinear dynamic analysis of the 2-DOF aerial manipulator. • The nonlinear dynamics of the non-autonomous 2-DOF aerial manipulator under dynamic conditions are analyzed. • The energy consumption of open-loop control is analyzed when the system is at different dynamic behaviors. This paper establishes the dynamic model of the angular velocity system of the 2-DOF (degree of freedom) aerial manipulator, describes the coupling relationship between the quadrotor aircraft and the manipulator, and provides the rotational speed relationship of each propeller during open-loop control. On this basis, the dynamic parameters, the nonlinear dynamics under static and dynamic conditions, and the Casimir energy of the system are studied in four parts. In the part of system dynamics parameters, the influence of manipulator configurations and postures on system moment of inertia, yaw motion, and lifting motion are analyzed, and their influence on gyroscopic effect is discussed. In the nonlinear dynamics of the system under static conditions, this paper analyzes the nonlinear dynamics of a typical aerial manipulator by the nonlinear dynamics methods. It reveals for the first time that the angular velocity of the system can produce dynamic behaviors such as sinks, chaotic oscillations, and period-doubling oscillations. The system is a non-autonomous system when it is under dynamic conditions. In this part, this paper considers the dynamic behaviors of the aerial manipulator in three situations: grasping operation, presence of external interference, and presence of time-varying yaw control quantity. It can be seen from the analysis that the dynamic conditions make the nonlinear dynamic behaviors of the system more complicated, which is worthy of further study. In the energy analysis, the Casimir energy of the three cases in this paper is calculated respectively when the sink, chaotic oscillation, and periodic oscillation are generated, and their mean, variance, and standard deviation are calculated. When the system is a sink, the three indexes are the smallest, the energy consumption is the least, and it is easier to control. [ABSTRACT FROM AUTHOR]

• The magneto-elastoplastic behavior is investigated for functionally graded cylinder. • Critical pressures between different elastoplastic deformation states are given analytically. • Exact solutions of stress and displacement are obtained for different deformation states. • The residual stress caused by unloading internal pressure is solved analytically. With the development of composite material technology, the multi-field coupling analysis of functionally graded (FG) structures has attracted extensive attention. For FG cylindrical pressure vessels, due to the non-uniform distribution of stresses filed in the structure, plastic deformation occurs irreversibly under external load, and Lorentz's force under static magnetic field is also one of the key factors affecting the elastoplastic state. Assuming that the elastic modulus of FG cylinder changes as a power function along the thickness and Poisson's ratio is constant, the hollow cylinder under the combined action of applied magnetic field and internal pressure may have four deformation states containing pure elastic deformation, partial plastic deformation yielding from the inner surface, partial plastic deformation yielding from the outer surface, and full plasticity. In this paper, analytical solutions of stress and displacement fields of the FG cylinder under these four different elastoplastic states are given, and the critical load conditions corresponding to the transition between these four different states are proposed. The correctness of the present analytical solution in this paper is verified by comparing it with the existing results of related simplified problems. In addition, the analytical solution of residual stress distribution caused by unloading internal pressure is discussed for self-reinforcing processing. Based on the analytical solution in this paper, the influence of FG parameter, applied magnetic field and internal pressure on the elastoplastic state, plastic zone size, stresses and displacements distribution of FG cylinder is analyzed in detail. This study shows that for this magneto-elastoplastic problem of FG cylinder, plastic deformation may appear from the inner surface or outer surfaces. With the increase of FG parameter, the first yielding position of FG cylinder changes from the inner surface to the outer surface. In addition, the existence of an applied magnetic field reduces the critical internal pressure required for FG cylinders to yield, making the FG hollow cylinder more prone to plastic deformation. [ABSTRACT FROM AUTHOR]

• To solve the forecasting problems of time-lead and nonlinearity in a system, a novel grey multivariable model is proposed. • To reduce the morbidity of the model, the solution of the proposed model is deduced through a derivation method. • The grey prediction evolution algorithm is employed to find the optimal value of parameters. • The validity of the new model was verified by three examples and applied to house price forecasting. Time lags or leads and non-linearity of complex systems are critical to address in accurate scientific prediction. However, few studies have focused on time-lead and nonlinear models with limited information. Therefore, this paper aims to develop a novel grey multivariate model with time-lead operator τ and nonlinear factor r from the perspective of this problem. Next, the solution of the proposed model is deduced through a derivation method to reduce the morbidity of the model. Then, the parameter identification of the model is given on the basis of the least-squares method. The grey prediction evolution algorithm is employed to find the optimal value of parameters τ and r to meet the minimum errors. Finally, house prices of Wuhan, Beijing and Shanghai in China are performed to verify the validity and reliability of the new model. The results demonstrate the model we proposed has satisfactory prediction precision, demonstrating that time-lead and nonlinear factor in the model is reasonable. At the end of the paper, the house prices of these three cities from 2022 to 2028 are also predicted. The average annual growth rate in the three regions is 2.49%, 3.57% and 2.97%, respectively. These results are useful to policy analysis regarding house price correlations. They provide insights for market investors and policy makers. [ABSTRACT FROM AUTHOR]

• Proposing physics-informed DCNN for HFI-SCB temperature field reconstruction. • Proposing Deep MC-QR method to quantify data uncertainty caused by noise. • Proposing HFI-SCB reliability analysis method based on interval multilevel BN. Temperature field reconstruction is essential for analyzing the reliability of a high-density functionally integrated satellite circuit board (HFI-SCB). As a representative deep learning model, the deep convolutional neural network (DCNN) is a powerful tool for reconstructing the HFI-SCB temperature field. However, DCNN needs a lot of labeled data to learn its parameters, which is contrary to the fact that actual satellite engineering can only acquire noisy unlabeled data. Thus, this paper proposes an unsupervised method, i.e., the physics-informed deep Monte Carlo quantile regression method, for reconstructing the HFI-SCB temperature field and quantifying the data uncertainty caused by sensor noise. The proposed method combines a DCNN with known physics knowledge to reconstruct an accurate HFI-SCB temperature field using only monitoring point temperatures. Besides, the proposed method can quantify the data uncertainty by the Monte Carlo quantile regression. Based on the reconstructed temperature field and the quantified data uncertainty, this paper builds an interval multilevel Bayesian Network to analyze the HFI-SCB reliability. Two case studies are used to validate the proposed method. [ABSTRACT FROM AUTHOR]

• A novel combined interval prediction algorithm is proposed in this paper. • Hybrid feature selection strategy is designed in the proposed system. • Multi-objective optimization mechanism reflects strong search capabilities. • Four interval prediction models cover the inherent modes of sequence. Traditional point prediction approaches can not reflect the uncertainty, which brings greater risks to decision-makers. To fill this gap, this paper extends a feature selection strategy that relies solely on correlation and redundant feature judgment, proposes a novel combined interval prediction algorithm, 3-Mcip (Combined Interval Prediction Based on Maximize Relevancy, Minimize Redundancy and Maximize Synergy) system, and solves the tradeoff between prediction accuracy and interval width. This system first designs a hybrid feature selection strategy to optimally select candidate variables and reduce model input redundancy. Secondly, the structure of the four ANN models is improved to accommodate the results of feature selection, and an optimization mechanism is introduced to search for the Pareto optimal solution set. In order to measure the comprehensive performance of the 3-Mcip system, hourly power load data and related candidate variables from Pittsburgh and Washington, D.C are considered. The numerical results show that the 3-Mcip system has coverage rates of 53.3333, 90.1667, and 99.4479 for Site 1 at different levels of interval width coefficients, which not only achieves perfect prediction of power load but also analyzes uncertainty. It is also helpful for power system managers to better capture the fluctuation range of future load and improve the flexibility of smart grid dispatching. [ABSTRACT FROM AUTHOR]

• A new damage quantification based on peridynamic theory has been established. • This new approach tackles the complex crack initiation plane, which is unsolved. • The new technique has been validated by experimental case studies. • The predictions exhibit very good agreements with experiments. • Crack propagation patterns can be accurately predicted using this new approach. This paper proposes a novel approach to evaluate the damage in Peridynamic simulations to identify the crack initiation and propagation, based on the physical meaning of the bond network. The most commonly used criterion to assess the damage in Peridynamic simulations is the nodal damage value, a ratio of the broken bonds to number of unbroken bonds for each point. There is no consensus on the magnitude of nodal damage value within the literature. In most cases, the assessment is conducted visually via damage contours. Rarely, researchers calculate nodal damage value by counting the bonds that pass through a crack plane and must be broken to initiate a crack. Despite being widely-used, the application of nodal damage value is questionable since it neglects the likelihood of broken bonds that are irrelevant to a crack. In other words, the applied value of the nodal damage value might not give the information about the crack whether it emerges or not. This paper shows the influence of the nodal damage value on damage assessments and compares the proposed method with the nodal damage value in different scenarios. The results exhibit that the proposed method is robust, effective, and more importantly provides a single outcome for Peridynamic simulations. [ABSTRACT FROM AUTHOR]

• This paper investigated uncertainty propagation in several problems using a new interval field formulation BIFD. • The BIFD method facilitates accurate and efficient prediction of output bounds through an intrusive approach. • B-spline based collocation method is favourable in solving BVPs when using the BIFD method. • A new interval field FEM is proposed based on the BIFD method and the Neumann expansion method. In this paper, uncertainty propagation problems are addressed by modelling the non-deterministic parameters as an interval field to account for spatial dependency. The interval field is constructed using a recently proposed B-spline based interval field decomposition method, which is related to an explicit formulation composed of B-spline basis functions and corresponding interval field coordinates, which can be incorporated directly into the governing equation of the boundary value problems. The solution to the governing equation can be approximated by a B-spline basis expansion using the collocation method taking advantage of high-degree continuity of B-spline basis functions. In this way, the crisp bounds of the output can be effectively accounted for. Numerical cases are provided to illustrate the effectiveness of the proposed method. The impact of the influence radius, the results obtained using an interval variable model and the combined impact of multiple uncertain parameters are also studied. Furthermore, for discretised problems, the interval field finite element formulation is presented and the resulting bounds of the output are determined by the Neumann expansion method, by which the extreme values can be effectively approximated. [ABSTRACT FROM AUTHOR]

• This paper investigates the finite-time and fixed-time input-to-state stability of impulsive nonlinear systems. • Both cases of stable/unstable continuous dynamics and impulses are studied by unified ADT conditions. • The Lyapunov functions with time-varying linear/nonlinear rates are utilized to handle the twofold effect of impulses. • It determines that the stable nonlinear systems are robust against hybrid impulses with multiple jump maps. In this paper, we investigate the finite-time and fixed-time input-to-state stability of impulsive nonlinear systems involving hybrid impulses which have time-dependent multiple jump maps. Under unified average dwell-time conditions, several criteria for finite-time and fixed-time input-to-state stability are established by virtue of the Lyapunov function with linear rate and nonlinear rate of jump maps. It shows that, when the finite/fixed-time input-to-state stable continuous systems are subject to hybrid impulses, the finite-time and fixed-time input-to-state stability can be ascertained under the requirement that the accumulative effect of hybrid impulses is non-destabilizing or the accumulative effect of hybrid impulses is destabilizing and the impulses are not activated too frequently. Finally, the effectiveness of theoretical results is verified by two numerical examples and an application example about an axisymmetric circular spacecraft. [ABSTRACT FROM AUTHOR]

In this paper, the anti-plane dynamics of rare earth giant magnetostrictive material with a cylindrical magnetically conducting inclusion in right-angle domain under the incidence of SH waves are studied. The governing equation and constitutive equation of magneto-elastic coupling are established. The outward scattered wave and internal standing wave caused by the inclusion are given by combining the complex function method, the wave function expansion method and mirror method. At the same time, the magnetic potential caused by wave is given by solving the Laplace equation. On the basis of boundary conditions, the Fourier series expansion method and effective truncated series are introduced to establish and solve infinite linear algebraic integral equations. Finally, based on numerical calculation, the analysis of dynamic stress concentration factor and magnetic field intensity concentration factor under different parameter combinations is given. The purpose of this paper is to provide an effective analytical method for the research of fracture dynamics of giant magnetostrictive materials under multi-magnetic field coupling. [ABSTRACT FROM AUTHOR]

• Green's function of two-layer coating structure provides a theoretical basis for analysis of multicoating problem. • Analytical expressions, expressed as elementary functions, can be easily converted into numerical calculation codes. • Those solutions are the basis for analyzing the two-layer coating under distributed loading with numerical integration. The study of multi-layer coating structure is an important problem in the fields of machinery and materials. In this paper, a two-dimensional theoretical solution of the orthotropic double-coated substrate structure under the normal line force of the free surface is derived. The method in this paper is mainly aimed at orthotropic materials and falls within the scope of linear elasticity. Based on the general solution of two-dimensional orthotropic materials, the harmonic functions with undetermined constants corresponding to each region are constructed. With the equilibrium conditions, surface boundary conditions and interface continuity conditions, the full-field analytical solution (Green's function) expressed in elementary functions is determined with the method of mirror images, which is valuable to solve the full field analytical expression of layered structures for the linear elasticity problem. Compared with the existing theories, the effectiveness and accuracy of the method are verified. In the future, Green's function of the paper is the basis for the numerical integration of distributed loads, which can be used as the code basis for the development of special software to study ultra-precision coatings. [ABSTRACT FROM AUTHOR]

• An original centrality metric objective function for the LMRNP is introduced. • A new data-driven adaptive distributionally robust equilibrium programming method. • The DBSCAN algorithm is newly adopted to construct a data-driven ambiguity set. • The proposed model is theoretically derived into a computationally solvable form. • The performance of the deduced model is validated by two real data sets. This paper studies a variant of the two-stage last mile relief network problem by introducing a centrality metric objective including the distance centrality metric, the demand centrality value-at-risk and the residual supplies centrality metric. Under the scenario-based design, the demand in each scenario is described as a random fuzzy variable whose probability distribution is ambiguous. In order to characterize its ambiguousness, this paper designs a Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm based on sample data to construct a data-driven ambiguity set containing the support and mean, which not only realizes the visualization of the ambiguous probability distribution, but also provides a finite set of scenarios for the uncertain demand. Given the constructed data-driven ambiguity set, this paper proposes a data-driven adaptive distributionally robust equilibrium programming (DDADREP) method for the last mile relief network problem (LMRNP). In view of its computational difficulty, the safe approximation, duality technique and credibility measure theory are used to approximate it as a mixed integer second-order cone programming with significant computational advantages. Finally, the proposed model is validated with two real-world cases, and its effectiveness as well as advantages is demonstrated by comparison with the classical robust optimization and the nominal equilibrium optimization, respectively. [ABSTRACT FROM AUTHOR]

• Physics-Constrained Bayesian Neural Network. • Failure prognostics of lithium-ion batteries. • Comparative study of physics-based, data-driven, and physics-constrained models. In order to predict the remaining useful life (RUL) of lithium-ion batteries, a capacity degradation model may be developed using either simplified physical laws or machine learning-based methods. It is observed that even though degradation models based on simplified physical laws are easy to implement, they may result in large error in the application of failure prognostics. While data-driven prognostics models can provide more accurate degradation forecasting, they may require a large volume of training data and may invoke predictions inconsistent with physical laws. It is also very challenging for existing methods to predict the RUL at the early stages of battery life. In this paper, we propose a Bayesian physics-constrained neural network for battery RUL prediction by overcoming limitations of the current methods. In the proposed method, a neural differential operator is learned from the first 100 cycles of data. The neural differential operator is modeled with a Bayesian neural network architecture that separates the fixed history dependence from the time dependence to isolate epistemic uncertainty quantification. Using the battery dataset presented in the paper by Severson et al. as an example, we compare our proposed method with a simplified physics-based degradation forecasting model and two data-driven prognostics models. The results show that the proposed physics-constrained neural network can provide more accurate RUL estimation than the other methods with the same group of training data. Most importantly, the proposed method allows for RUL prediction at earlier stages of the battery life cycle. [ABSTRACT FROM AUTHOR]

• The paper gives a novel combination between sparse signal recovery and moving least squares in the field of outlier detection. • This paper proposes a new method to detect outliers in scattered data for approximation. • The idea of sparse signal recovery in the proposed method provides the theoretical guarantee for its effectiveness. • The proposed method can restore the true values corresponding to outliers in high accuracy while outliers are marked. In the scattered data used for function approximation, there may be some data that deviate greatly from their true values, which are called outliers. The existence of outliers significantly affects the accuracy of some approximation methods, such as moving least squares. How to quickly and accurately find these outliers and restore their true values has not been well resolved. In this paper, a new outlier detection and recovery method is proposed for data processing. The method uses the high accuracy of moving least squares quasi-interpolation scheme, its sensitivity to outliers and the sparse distribution of outliers to construct a ł 0 -minimization problem with an inequality constrain. Under certain assumptions, it is proved theoretically that the deviation vector corresponding to the outliers is a solution to the optimization problem. The classical orthogonal matching pursuit algorithm is introduced to solve the optimization problem efficiently. By solving the problem, the outliers are marked, and the deviations are also estimated approximately, which can restore the true values of outliers. The numerical experiments demonstrate that the proposed method has high computational efficiency, very high detection accuracy, and high recovery accuracy for the scattered data used for function approximation, so it is practical. [ABSTRACT FROM AUTHOR]

• We proposed a methodology to perform vibration analysis of rotor systems that exhibit localized nonlinearities. • The motion equation of the whole system uses hybrid coordinates. • The stability analysis of the obtained solutions is performed by the floquet theory. In this paper, the differential quadrature finite element method (DQFEM), component mode synthesis (CMS) method and incremental harmonic balance (IHB) method are combined to propose a methodology to perform vibration analysis and stability analysis of rotor systems supported on fluid-film bearings that exhibit localized nonlinearities such as squeeze-film damper (SFD). In multi-degree of freedom systems with SFD, a method for dynamic analysis of the system by reducing the degrees of freedom is first suggested in this paper. DQFEM are used to create the mass matrix, stiffness matrix, and gyroscopic matrix of the system. Then, the system is divided into linear system and nonlinear system, and the motion equation of the linear system reduces the degrees of freedom using the free interface CMS method, and the motion equation of the nonlinear system is written without reducing the degrees of freedom. By synthesizing the equations of motion of each component, the motion equation of the entire system is created. That is, the motion equation of the whole system uses hybrid coordinates. The motion equation of the system is solved using the modified IHB method. To evaluate the effectiveness of the suggested method, the computed solutions are compared with the results presented in the previous literature, and the results are very consistent. Also, stability analysis of the obtained solutions is performed by the Floquet theory. The method suggested in the paper can be effectively used to analyze the dynamic behavior of rotor systems exhibiting localized nonlinearities such as SFD. [ABSTRACT FROM AUTHOR]