Fuzzy stochastic generalized reliability studies on embankment systems based on first-order approximation theorem

In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.

Determining Hubbard U of VO_(2) by the quasi-harmonic approximation

Vanadium dioxide VO_(2) is a strongly correlated material that undergoes a metal-to-insulator transition around 340 K.In order to describe the electron correlation effects in VO_(2), the DFT+U method is commonly employed in calculations.However, the choice of the Hubbard U parameter has been a subject of debate and its value has been reported over a wide range. In this paper, taking focus on the phase transition behavior of VO_(2), the Hubbard U parameter for vanadium oxide is determined by using the quasi-harmonic approximation(QHA). First-principles calculations demonstrate that the phase transition temperature can be modulated by varying the U values. The phase transition temperature can be well reproduced by the calculations using the Perdew–Burke–Ernzerhof functional combined with the U parameter of 1.5eV. Additionally,the calculated band structure, insulating or metallic properties, and phonon dispersion with this U value are in line with experimental observations. By employing the QHA to determine the Hubbard U parameter, this study provides valuable insights into the phase transition behavior of VO_(2). The findings highlight the importance of electron correlation effects in accurately describing the properties of this material. The agreement between the calculated results and experimental observations further validates the chosen U value and supports the use of the DFT+U method in studying VO_(2).

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process

Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Integrating a novel irrigation approximation method with a process-based remote sensing model to estimate multi-years'winter wheat yield over the North China Plain

Accurate estimation of regional winter wheat yields is essential for understanding the food production status and ensuring national food security.However,using the existing remote sensing-based crop yield models to accurately reproduce the inter-annual and spatial variations in winter wheat yields remains challenging due to the limited ability to acquire irrigation information in water-limited regions.Thus,we proposed a new approach to approximating irrigations of winter wheat over the North China Plain(NCP),where irrigation occurs extensively during the winter wheat growing season.This approach used irrigation pattern parameters(IPPs)to define the irrigation frequency and timing.Then,they were incorporated into a newly-developed process-based and remote sensing-driven crop yield model for winter wheat(PRYM–Wheat),to improve the regional estimates of winter wheat over the NCP.The IPPs were determined using statistical yield data of reference years(2010–2015)over the NCP.Our findings showed that PRYM–Wheat with the optimal IPPs could improve the regional estimate of winter wheat yield,with an increase and decrease in the correlation coefficient(R)and root mean square error(RMSE)of 0.15(about 37%)and 0.90 t ha–1(about 41%),respectively.The data in validation years(2001–2009 and 2016–2019)were used to validate PRYM–Wheat.In addition,our findings also showed R(RMSE)of 0.80(0.62 t ha–1)on a site level,0.61(0.91 t ha–1)for Hebei Province on a county level,0.73(0.97 t ha–1)for Henan Province on a county level,and 0.55(0.75 t ha–1)for Shandong Province on a city level.Overall,PRYM–Wheat can offer a stable and robust approach to estimating regional winter wheat yield across multiple years,providing a scientific basis for ensuring regional food security.

Visualizing and witnessing first-order coherence,Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame

A quantum steering ellipsoid(QSE)is a visual characterization for bipartite qubit systems,and it is also a novel avenue for describing and detecting quantum correlations.Herein,by using a QSE,we visualize and witness the first-order coherence(FOC),Bell nonlocality(BN)and purity under non-inertial frames.Also,the collective influences of the depolarizing channel and the non-coherence-generating channel(NCGC)on the FOC,BN and purity are investigated in the QSE formalism.The results reveal that the distance from the center of the QSE to the center of the Bloch sphere visualizes the FOC of a bipartite system,the lengths of the QSE semiaxis visualize the BN,and the QSE's shape and position dominate the purity of the system.One can capture the FOC,BN and purity via the shape and position of the QSE in the non-inertial frame.The depolarizing channel(the NCGC)gives rise to the shrinking and degradation(the periodical oscillation)of the QSE.One can use these traits to visually characterize and detect the FOC,BN and purity under the influence of external noise.Of particular note is that the condition for the QSE to achieve the center of the Bloch sphere cannot be influenced by the depolarizing channel and the NCGC.The characterization shows that the conditions for the disappearance of the FOC are invariant under the additional influences of the depolarizing channel and NCGC.

First-order primal-dual algorithm for sparse-view neutron computed tomography-based three-dimensional image reconstruction

Neutron computed tomography(NCT)is widely used as a noninvasive measurement technique in nuclear engineering,thermal hydraulics,and cultural heritage.The neutron source intensity of NCT is usually low and the scan time is long,resulting in a projection image containing severe noise.To reduce the scanning time and increase the image reconstruction quality,an effective reconstruction algorithm must be selected.In CT image reconstruction,the reconstruction algorithms can be divided into three categories:analytical algorithms,iterative algorithms,and deep learning.Because the analytical algorithm requires complete projection data,it is not suitable for reconstruction in harsh environments,such as strong radia-tion,high temperature,and high pressure.Deep learning requires large amounts of data and complex models,which cannot be easily deployed,as well as has a high computational complexity and poor interpretability.Therefore,this paper proposes the OS-SART-PDTV iterative algorithm,which uses the ordered subset simultaneous algebraic reconstruction technique(OS-SART)algorithm to reconstruct the image and the first-order primal–dual algorithm to solve the total variation(PDTV),for sparse-view NCT three-dimensional reconstruction.The novel algorithm was compared with other algorithms(FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV)by simulating the experimental data and actual neutron projection experiments.The reconstruction results demonstrate that the proposed algorithm outperforms the FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV algorithms in terms of preserving edge structure,denoising,and suppressing artifacts.

Investigation of magnetization reversal and domain structures in perpendicular synthetic antiferromagnets by first-order reversal curves and magneto-optical Kerr effect

Perpendicular synthetic-antiferromagnet(p-SAF) has broad applications in spin-transfer-torque magnetic random access memory and magnetic sensors. In this study, the p-SAF films consisting of (Co/Ni)3]/Ir(tIr)/[(Ni/Co)3are fabricated by magnetron sputtering technology. We study the domain structure and switching field distribution in p-SAF by changing the thickness of the infrared space layer. The strongest exchange coupling field(Hex) is observed when the thickness of Ir layer(tIr) is 0.7 nm and becoming weak according to the Ruderman–Kittel–Kasuya–Yosida-type coupling at 1.05 nm,2.1 nm, 4.55 nm, and 4.9 nm in sequence. Furthermore, the domain switching process between the upper Co/Ni stack and the bottom Co/Ni stack is different because of the antiferromagnet coupling. Compared with ferromagnet coupling films, the antiferromagnet samples possess three irreversible reversal regions in the first-order reversal curve distribution.With tIrincreasing, these irreversible reversal regions become denser and smaller. The results from this study will help us understand the details of the magnetization reversal process in the p-SAF.

Formalism of rotating-wave approximation in high-spin system with quadrupole interaction

We investigate the rotating wave approximation applied in the high-spin quantum system driven by a linearly polarized alternating magnetic field in the presence of quadrupole interactions.The conventional way to apply the rotating wave approximation in a driven high-spin system is to assume the dynamics being restricted in the reduced Hilbert space.However,when the driving strength is relatively strong or the driving is off resonant,the leakage from the target resonance subspace cannot be neglected for a multi-level quantum system.We propose the correct formalism to apply the rotating wave approximation in the full Hilbert space by taking this leakage into account.By estimating the operator fidelity of the time propagator,our formalism applied in the full Hilbert space unambiguously manifests great advantages over the conventional method applied in the reduced Hilbert space.

Cyclic Solution and Optimal Approximation of the Quaternion Stein Equation

In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation’s solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method. .

First-order approximate analytical expressions of oblique incident elastic wave at an interface of porous media saturated with a nonviscous fluid

The analysis technology of Amplitude Variation with Offset(AVO)is one of the important methods for oil and gas reservoir prediction.Zoeppritz equation and its approximations are the theoretical basis of AVO analysis,which assumes that the upper and lower media of a horizontal interface are single-phase media.Limited by this assumption,AVO analysis has limited prediction and identification accuracy for complex porous reservoirs.In view of this,the first-order approximate analytical expressions of oblique elastic wave at an interface of porous media are derived.Firstly,the incident and scattering characteristics of various waves at the interface of porous media are analyzed,and the displacement vectors generated by these elastic waves are described by exponential function.Secondly,the kinematic and dynamic boundary conditions at the interface of porous media are discussed.Thirdly,by substituting the displacement vectors of incident and scattered waves into boundary conditions,the exact analytical equation is derived.Then,considering the symmetry of scattering matrix in the equation,the exact analytical expressions of each scattered wave are obtained.Furthermore,under the assumptions of small incident angle,weak elasticity at an interface of porous media,and ignoring the second-and higherorder terms,the first-order approximate analytical expressions are derived.Establishing a model of sandstone porous media with different porosity in upper and lower media,the correctness of the approximate analytical expressions is verified,and the elastic wave response characteristics of lithology and pore fluids are analyzed.

MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE

We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the upper half-plane by dilatations and eventually by analytic polynomials.

Radial Basis Approximations Based BEMD for Enhancement of Non-Uniform Illumination Images

An image can be degraded due to many environmental factors like foggy or hazy weather,low light conditions,extra light conditions etc.Image captured under the poor light conditions is generally known as non-uniform illumination image.Non-uniform illumination hides some important information present in an image during the image capture Also,it degrades the visual quality of image which generates the need for enhancement of such images.Various techniques have been present in literature for the enhancement of such type of images.In this paper,a novel architecture has been proposed for enhancement of poor illumination images which uses radial basis approximations based BEMD(Bi-dimensional Empirical Mode Decomposition).The enhancement algorithm is applied on intensity and saturation components of image.Firstly,intensity component has been decomposed into various bi-dimensional intrinsic mode function and residue by using sifting algorithm.Secondly,some linear transformations techniques have been applied on various bidimensional intrinsic modes obtained and residue and further on joining the transformed modes with residue,enhanced intensity component is obtained.Saturation part of an image is then enhanced in accordance to the enhanced intensity component.Final enhanced image can be obtained by joining the hue,enhanced intensity and enhanced saturation parts of the given image.The proposed algorithm will not only give the visual pleasant image but maintains the naturalness of image also.

Approximations by Ideal Minimal Structure with Chemical Application

The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information.It can be characterized by two crisp sets,named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset.This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space MSAS via ideal J.The novel approach(indicated by JMSAS)modifies the approximation space to diminish the bound-ary region and enhance the measure of accuracy.The suggested method is more accurate than Pawlak’s and EL-Sharkasy techniques.Via illustrated examples,several remarkable results using these notions are obtained and some of their properties are established.Several sorts of near open(resp.closed)sets based on JMSAS are studied.Furthermore,the connections between these assorted kinds of near-open sets in JMSAS are deduced.The advantages and disadvan-tages of the proposed approach compared to previous ones are examined.An algorithm using MATLAB and a framework for decision-making problems are verified.Finally,the chemical application for the classification of amino acids(AAs)is treated to highlight the significance of applying the suggested approximation.

THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.

A 5MS/s 12-Bit Successive Approximation Analog-to-Digital Converter

With the continuous development of science and technology, digital signal processing is more and more widely used in various fields. Among them, the analog-to-digital converter (ADC) is one of the key components to convert analog signals to digital signals. As a common type of ADC, 12-bit sequential approximation analog-to-digital converter (SAR ADC) has attracted extensive attention for its performance and application. This paper aims to conduct in-depth research and analysis of 12-bit SAR ADC to meet the growing demands of digital signal processing. This article designs a 12-bit, successive approximation analog-to-digital converter (SAR ADC) with a sampling rate of 5 MS/s. The overall circuit adopts a fully differential structure, with key modules including DAC capacitor array, comparator, and control logic. According to the DAC circuit in this paper, a fully differential capacitor DAC array structure is proposed to reduce the area of layout DAC. The comparator uses a digital dynamic comparator to improve the ADC conversion speed. The chip is designed based on the SMIC180 nm CMOS process. The simulation results show that when the sampling rate is 5 MS/s, the effective bit of SAR ADC is 11.92 bit, the SNR is 74.62 dB, and the SFDR is 89.24 dB.

Improved QoS-Secure Routing in MANET Using Real-Time Regional ME Feature Approximation

Mobile Ad-hoc Network(MANET)routing problems are thoroughly studied several approaches are identified in support of MANET.Improve the Quality of Service(QoS)performance of MANET is achieving higher performance.To reduce this drawback,this paper proposes a new secure routing algorithm based on real-time partial ME(Mobility,energy)approximation.The routing method RRME(Real-time Regional Mobility Energy)divides the whole network into several parts,and each node’s various characteristics like mobility and energy are randomly selected neighbors accordingly.It is done in the path discovery phase,estimated to identify and remove malicious nodes.In addition,Trusted Forwarding Factor(TFF)calculates the various nodes based on historical records and other characteristics of multiple nodes.Similarly,the calculated QoS Support Factor(QoSSF)calculating by the Data Forwarding Support(DFS),Throughput Support(TS),and Lifetime Maximization Support(LMS)to any given path.One route was found to implement the path of maximizing MANET QoS based on QoSSF value.Hence the proposed technique produces the QoS based on real-time regional ME feature approximation.The proposed simulation implementation is done by the Network Simulator version 2(NS2)tool to produce better performance than other methods.It achieved a throughput performance had 98.5%and a routing performance had 98.2%.