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The combined effects of several complex phenomena cause the deterioration of elements in steel hydraulic structures (SHSs) within the US lock system: corrosion, cracking and fatigue, impact and overloads. Predicting the future condition state of these structures by the use of current condition state inspection data can be achieved through the probabilistic chain deterioration model. The purpose of this study is to derive the transition probability matrix using final elements modeling of a miter gate.

If predicted accurately, this information would yield benefits in determining the need for rehabilitation or replacement of SHS. However, because of the complexity and difficulties on obtaining sufficient inspection data, there is a lack of available condition states needed to formulate proper transition probability matrices for each deterioration case.

This study focuses on using a three-dimensional explicit finite element analysis (FEM) of a miter gate that has been fully validated with experimental data to derive the transition probability matrix when the loss of flexural capacity in a corroded member is simulated.

New methodology using computational mechanics to derive the transition probability matrices of navigation steel structures has been presented.

The difficulty of deriving the transition probability matrix to perform a Markovian analysis increases when limited amount of inspection data is available. The used state of practice FEM to derive the transition probability matrix is not just necessary but also essential when the need for proper maintenance is required but limited amount of the condition of the structural system is unknown.

This study aims to reduce the redundant weight of the anti-roll torsion bar brought by the traditional empirical design and improving its strength and stiffness.

Based on the finite element approach coupled with the improved beluga whale optimization (IBWO) algorithm, a collaborative optimization method is suggested to optimize the design of the anti-roll torsion bar structure and weight. The dimensions and material properties of the torsion bar were defined as random variables, and the torsion bar's mass and strength were investigated using finite elements. Then, chaotic mapping and differential evolution (DE) operators are introduced to improve the beluga whale optimization (BWO) algorithm and run case studies.

The findings demonstrate that the IBWO has superior solution set distribution uniformity, convergence speed, solution correctness and stability than the BWO. The IBWO algorithm is used to optimize the anti-roll torsion bar design. The error between the optimization and finite element simulation results was less than 1%. The weight of the optimized anti-roll torsion bar was lessened by 4%, the maximum stress was reduced by 35% and the stiffness was increased by 1.9%.

The study provides a methodological reference for the simulation optimization process of the lateral anti-roll torsion bar.

The “chiralisation” of Euclidean polygonal tessellations is a novel, recent method which has been used to design new auxetic metamaterials with complex topologies and improved geometric versatility over traditional chiral honeycombs. This paper aims to design and manufacture chiral honeycombs representative of four distinct classes of 2D Euclidean tessellations with hexagonal rotational symmetry using fused-deposition additive manufacturing and experimentally analysed the mechanical properties and failure modes of these metamaterials.

Finite Element simulations were also used to study the high-strain compressive performance of these systems under both periodic boundary conditions and realistic, finite conditions. Experimental uniaxial compressive loading tests were applied to additively manufactured prototypes and digital image correlation was used to measure the Poisson’s ratio and analyse the deformation behaviour of these systems.

The results obtained demonstrate that these systems have the ability to exhibit a wide range of Poisson’s ratios (positive, quasi-zero and negative values) and stiffnesses as well as unusual failure modes characterised by a sequential layer-by-layer collapse of specific, non-adjacent ligaments. These findings provide useful insights on the mechanical properties and deformation behaviours of this new class of metamaterials and indicate that these chiral honeycombs could potentially possess anomalous characteristics which are not commonly found in traditional chiral metamaterials based on regular monohedral tilings.

To the best of the authors’ knowledge, the authors have analysed for the first time the high strain behaviour and failure modes of chiral metamaterials based on Euclidean multi-polygonal tessellations.

The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

The purpose of this paper is to propose a framework for data analytics where everything is grey in nature and the associated uncertainty is considered as an essential part in data collection, profiling, imputation, analysis and decision making.

A comparative study is conducted between the available uncertainty models and the feasibility of grey systems is highlighted. Furthermore, a general framework for the integration of grey systems and grey sets into data analytics is proposed.

Grey systems and grey sets are useful not only for small data, but also big data as well. It is complementary to other models and can play a significant role in data analytics.

The proposed framework brings a radical change in data analytics. It may bring a fundamental change in our way to deal with uncertainties.

The proposed model has the potential to avoid the mistake from a misleading data imputation.

The proposed model takes the philosophy of grey systems in recognising the limitation of our knowledge which has significant implications in our way to deal with our social life and relations.

This is the first time that the whole data analytics is considered from the point of view of grey systems.

The smoothness of the high-speed railway (HSR) on the bridge may exceed the allowable standard when an earthquake causes vibrations for HSR bridges, which may threaten the safety of running trains. Indeed, few studies have evaluated the exceeding probability of rail displacement exceeding the allowable standard. The purposes of this article are to provide a method for investigating the exceeding probability of the rail displacement of HSRs under seismic excitation and to calculate the exceeding probability.

In order to investigate the exceeding probability of the rail displacement under different seismic excitations, the workflow of analyzing the smoothness of the rail based on incremental dynamic analysis (IDA) is proposed, and the intensity measure and limit state for the exceeding probability analysis of HSRs are defined. Then a finite element model (FEM) of an assumed HSR track-bridge system is constructed, which comprises a five-span simply-supported girder bridge supporting a finite length CRTS II ballastless track. Under different seismic excitations, the seismic displacement response of the rail is calculated; the character of the rail displacement is analyzed; and the exceeding probability of the rail vertical displacement exceeding the allowable standard (2mm) is investigated.

The results show that: (1) The bridge-abutment joint position may form a step-like under seismic excitation, threatening the running safety of high-speed trains under seismic excitations, and the rail displacements at mid-span positions are bigger than that at other positions on the bridge. (2) The exceeding probability of rail displacement is up to about 44% when PGA = 0.01g, which is the level-five risk probability and can be described as 'very likely to happen'. (3) The exceeding probability of the rail at the mid-span positions is bigger than that above other positions of the bridge, and the mid-span positions of the track-bridge system above the bridge may be the most hazardous area for the running safety of trains under seismic excitation when high-speed trains run on bridges.

The work extends the seismic hazardous analysis of HSRs and would lead to a better understanding of the exceeding probability for the rail of HSRs under seismic excitations and better references for the alert of the HSR operation.

This paper aims to offer a tutorial/introduction to new statistics arising from the theory of optimal transport to empirical researchers in econometrics and machine learning.

Presenting in a tutorial/survey lecture style to help practitioners with the theoretical material.

The tutorial survey of some main statistical tools (arising from optimal transport theory) should help practitioners to understand the theoretical background in order to conduct empirical research meaningfully.

This study is an original presentation useful for new comers to the field.

Let X⊂ℙr be an integral and non-degenerate complex variety. For any q∈ℙr let rX(q) be its X-rank and S(X,q) the set of all finite subsets of X such that |S|=rX(q) and q   ∈  〈S〉, where 〈〉 denotes the linear span. We consider the case |S(X,q)|>1 (i.e. when q is not X -identifiable) and study the set W(X)q:=∩ S∈S(X,q)〈S〉, which we call the non-uniqueness set of q. We study the case dimX=1 and the case X a Veronese embedding of ℙn. We conclude the paper with a few remarks concerning this problem over the reals.

This paper aims to develop a geometry of moral systems. Existing social choice mechanisms predominantly employ simple structures, such as rankings. A mathematical metric among moral systems allows us to represent complex sets of views in a multidimensional geometry. Such a metric can serve to diagnose structural issues, test existing mechanisms of social choice or engender new mechanisms. It also may be used to replace active social choice mechanisms with information-based passive ones, shifting the operational burden.

Under reasonable assumptions, moral systems correspond to computational black boxes, which can be represented by conditional probability distributions of responses to situations. In the presence of a probability distribution over situations and a metric among responses, codifying our intuition, we can derive a sensible metric among moral systems.

Within the developed framework, the author offers a set of well-behaved candidate metrics that may be employed in real applications. The author also proposes a variety of practical applications to social choice, both diagnostic and generative.

The proffered framework, derived metrics and proposed applications to social choice represent a new paradigm and offer potential improvements and alternatives to existing social choice mechanisms. They also can serve as the staging point for research in a number of directions.

Molecular dynamics is an emerging simulation technique in the field of machining in recent years. Many researchers have tried to simulate different processing methods of various materials with the theory of molecular dynamics (MD), and some preliminary conclusions have been obtained. However, the application of MD simulation is more limited compared with traditional finite element model (FEM) simulation technique due to the complex modeling approach and long computation time. Therefore, more studies on the MD simulations are required to provide a reliable theoretical basis for the nanoscale interpretation of grinding process. This study investigates the crystal structures, dislocations, force, temperature and subsurface damage (SSD) in the grinding of iron-nickel alloy using MD analysis.

In this study the simulation model is established on the basis of the workpiece and single cubic boron nitride (CBN) grit with embedded atom method and Morse potentials describing the forces and energies between different atoms. The effects of grinding parameters on the material microstructure are studied based on the simulation results.

When CBN grit goes through one of the grains, the arrangement of atoms within the grain will be disordered, but other grains will not be easily deformed due to the protection of the grain boundaries. Higher grinding speed and larger cutting depth can cause greater impact of grit on the atoms, and more body-centered cubic (BCC) structures will be destroyed. The dislocations will appear in grain boundaries due to the rearrangement of atoms in grinding. The increase of grinding speed results in the more transformation from BCC to amorphous structures.

This study is aimed to study the grinding of Fe-Ni alloy (maraging steel) with single grit through MD simulation method, and to reveal the microstructure evolution within the affected range of SSD layer in the workpiece. The simulation model of polycrystalline structure of Fe-Ni maraging steel and grinding process of single CBN grit is constructed based on the Voronoi algorithm. The atomic accumulation, transformation of crystal structures, evolution of dislocations as well as the generation of SSD are discussed according to the simulation results.