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Fuzzy Reliability and Availability of System under a Calendar-based Inspection Involving Multiple Failures and Its Application to Wind Turbine System

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Journal of Systems Science and Systems Engineering 2024年第2期33卷 187-206页

作者： Mintu Kumar Himani Pant S.B.Singh department of Mathematics statistics and Computer Science G.B.Pant University of AgricultureTechnologyPantnagarUttarakhandIndia

Uncertainty is an important factor that needs to be considered while analyzing the performance of any engineering system.In order to quantify uncertainty,fuzzy set theory is frequently used by most of researchers,including energy system experts.According to the classical reliability theory,component lifetimes have crisp parameters,but due to uncertainty and inaccuracy in data,it is sometimes very difficult to determine the exact values of these parameters in real-world systems.To overcome this difficulty in the current research,failure and repair rates were taken as triangular fuzzy numbers to determine the fuzzy availability of a system undergoing calendar-based periodic inspection subject to multiple failure modes(FMs).It was assumed that each component in the system had an exponential failure rate and repair rate with fuzzy parameters.System FMs were explicitly taken into account when a functional state of the system was considered.Each FM had a random failure time.On the occurrence of any failure,a random time was selected for the relevant corrective repair work.The proposed research was studied for one of the major sources of green energy,namely a wind turbine system wherein all the derived propositions have been implemented on it.

关键词： Fuzzy reliability fuzzy availability wind turbine system multiple failure modes triangular fuzzy number

A Local Macroscopic Conservative(LoMaC)Low Rank Tensor Method with the Discontinuous Galerkin Method for the Vlasov Dynamics

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Communications on Applied Mathematics and Computation 2024年第1期6卷 550-575页

作者： Wei Guo Jannatul Ferdous Ema Jing-Mei Qiu department of Mathematics and statistics Texas Tech UniversityLubbockTX70409USA department of Mathematical Sciences University of DelawareNewarkDE19716USA

In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)system.The LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete level.The recently developed LoMaC low rank tensor algorithm(arXiv:2207.00518)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables.This paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long term.The algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal fashion.With the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid points.The algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection algorithm.In a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity direction.Extensive numerical results are performed to showcase the efficacy of the method.

关键词： Hierarchical Tucker(HT)decomposition Conservative SVD Energy conservation Discontinuous Galerkin(DG)method

Sequential good lattice point sets for computer experiments

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Science China Mathematics 2024年

作者： Xue-Ru Zhang Yong-Dao Zhou Min-Qian Liu Dennis K.J.Lin NITFID LPMC & KLMDASR School of Statistics and Data Science Nankai University department of statistics Purdue University

Sequential Latin hypercube designs (SLHDs) have recently received great attention for computer experiments, with much of the research restricted to invariant spaces. The related systematic construction methods are inflexible, and algorithmic methods are ineffective for large designs. For designs in contracting spaces, systematic construction methods have not been investigated yet. This paper proposes a new method for constructing SLHDs via good lattice point sets in various experimental spaces. These designs are called sequential good lattice point (SGLP) sets. Moreover, we provide efficient approaches for identifying the (nearly)optimal SGLP sets under a given criterion. Combining the linear level permutation technique, we obtain a class of asymptotically optimal SLHDs in invariant spaces, where the L1-distance in each stage is either optimal or asymptotically optimal. Numerical results demonstrate that the SGLP set has a better space-filling property than the existing SLHDs in invariant spaces. It is also shown that SGLP sets have less computational complexity and more adaptability.

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Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fin exposed to magnetic field in the presence of a shape-dependent trihybrid nanofluid

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Applied Mathematics and Mechanics(English Edition) 2024年第1期45卷 197-216页

作者： C.G.PAVITHRA B.J.GIREESHA M.L.KEERTHI department of PG Studies and Research in Mathematics Kuvempu UniversityShankaraghatta 577451India department of Mathematics and statistics M.S.Ramaiah University of Applied SciencesBengaluru 560058India

The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical(Fe_3O_4), cylindrical(Au), and platelet(Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method(ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.

关键词： convection radiation moving longitudinal fin Adomian decomposition Sumudu transform method(ADSTM) trihybrid nanofluid magnetic field

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Optimal investment and consumption with forward preferences and uncertain parameters

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Probability, Uncertainty and Quantitative Risk 2024年第1期9卷 65-84页

作者： Wing Fung Chong Gechun Liang Marwell Institute for Mathematical Sciences and department of Actuarial Mathematics and statistics Heriot-Watt UniversityEdinburgh EH144ASUK department of statistics The University of WarwickCoventry CV47ALUK

We introduce and analyze a class of forward performance criteria in incomplete markets in the presence of model ambiguity.Incompleteness stems from general investment constraints,while model uncertainty is represented by a convex and compact set of plausible model parameter processes.Following the max-min criteria in traditional(backward)robust control,we formulate similar criteria for the robust forward performance processes and focus on the rich class of time-monotone processes.We provide a novel PDE characterization and a semi-explicit saddle-point construction of the robust forward performance criteria and their optimal policies.Furthermore,we present additional results within the class of homothetic constant relative risk aversion(CRRA)processes.Within this class,we investigate the relationship between forward performance processes on wealth and those on consumption,establishing an interesting dominance through time.

关键词： Robust forward performance criteria Portfolio constraints Consumption Saddle points Constant relative risk aversion

Bound-Preserving Discontinuous Galerkin Methods with Modified Patankar Time Integrations for Chemical Reacting Flows

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Communications on Applied Mathematics and Computation 2024年第1期6卷 190-217页

作者： Fangyao Zhu Juntao Huang Yang Yang department of Mathematical Sciences Michigan Technological UniversityHoughtonMI49931USA department of Mathematics and statistics Texas Tech UniversityLubbockTX79409USA

In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive flows.There are several difficulties in constructing suitable numerical schemes.First of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and 1.Second,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step sizes.To obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG methods.Though traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1 of the mass fractions.To solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is preserved.With the above two conditions,the positive mass fractions have summation 1,and then,they are all between 0 and 1.For time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the source.Such methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be 1.Finally,it is not straightforward to combine the bound-preserving DG methods and the Patankar time integrations.The positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target variables.To match the degree of freedom,we use polynomials on rectangular meshes for problems in two space dimensions.To evolve in time,we first read the polynomials at the Gaussian points.Then,suitable slope limiters can be applied to enforce the positivity

关键词： Compressible Euler equations Chemical reacting flows Bound-preserving Discontinuous Galerkin(DG)method Modified Patankar method

Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation

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Communications on Applied Mathematics and Computation 2024年第1期6卷 311-324页

作者： Bo Dong Wei Wang department of Mathematics University of Massachusetts DartmouthNorth DartmouthMA02747USA department of Mathematics and statistics Florida International UniversityMiamiFL33199USA

In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.

关键词： Discontinuous Galerkin(DG)method Multiscale method Resonance errors One-dimensional Schrödinger equation

Non-static plane symmetric perfect fluid solutions and Killing symmetries in f(R,T)gravity

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Communications in Theoretical Physics 2024年第2期76卷 145-150页

作者： Preeti Dalal Karanjeet Singh Sachin Kumar department of Mathematics and statistics Central University of PunjabBathinda151401PunjabIndia department of Mathematics Jaypee University of Information TechnologySolan173234Himachal PradeshIndia

In this paper,the non-static solutions for perfect fluid distribution with plane symmetry in f(R,T)gravitational theory are obtained.Firstly,using the Lie symmetries,symmetry reductions are performed for considered vector fields to reduce the number of independent variables.Then,corresponding to each reduction,exact solutions are obtained.Killing vectors lead to different conserved quantities.Therefore,we figure out the Killing vector fields corresponding to all derived solutions.The derived solutions are further studied and it is observed that all of the obtained spacetimes,at least admit to the minimal symmetry group which consists of δ_(y),δ_(z) and -zδ_(y)+yδ_(z).The obtained metrics,admit to 3,4,6,and 10,Killing vector fields.Conservation of linear momentum in the direction of y and z,and angular momentum along the x axis is provided by all derived solutions.

关键词： Einstein field equations perfect fluid solutions f(R T)gravity killing symmetries

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New Upper Bounds for the Inverse of H-Matrices Including S-SDD Matrices and Linear Complementarity Problems

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Journal of Mathematical Research with Applications 2024年第2期44卷 170-186页

作者： Yebo XIONG department of Mathematics and statistics Hunan First Normal University

A partition reduction method is used to obtain new upper bounds for the inverses of H-matrices and S-strictly diagonally dominant(S-SDD) matrices. The estimates are expressed via the determinants of third order matrices. Numerical experiments with various random matrices show that they are stable and better than the estimates presented in literatures. We use these upper bounds to improve known error estimates for linear complementarity problems with H-matrices and S-SDD matrices.

关键词： linear complementarity problem error bound upper bound S-SDD matrices H-matrice