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.

A grouting simulation method for quick-setting slurry in karst conduit:The sequential flow and solidification method

It is difficult to temporally and spatially track and characterize the slurry viscosity in flowing water during grouting simulation.In this study,a sequential flow and solidification(SFS)method considering the spatial-temporal evolution of slurry viscosity in flowing water in karst conduit is proposed.First,a time-dependent model for the threshold function of slurry viscosity is established.During the grouting process,the spatial-temporal evolution of slurry viscosity is revealed by tracking the diffusion behavior of the slurry injected at different times.This method is capable of describing the gradual solidification process of the slurry during grouting.Furthermore,a physical model of grouting in a karst conduit is developed.Second,the effectiveness of the SFS method in grouting simulation is verified by the experiment of grouting conduit in flowing water.The SFS method enables real-time monitoring of fluid velocity and pressure during grouting in flowing water and provides a feasible calculation method for revealing the grouting plugging mechanism in complex karst conduits at different engineering scales.In addition,it can be used to guide the design of grouting tests in flowing water,improve cost efficiency,and provide theoretical basis for optimizing grouting design and slurry selection.

Sequential Monte Carlo Method Toward Online RUL Assessment with Applications

Online assessment of remaining useful life(RUL) of a system or device has been widely studied for performance reliability, production safety, system conditional maintenance, and decision in remanufacturing engineering. However,there is no consistency framework to solve the RUL recursive estimation for the complex degenerate systems/device.In this paper, state space model(SSM) with Bayesian online estimation expounded from Markov chain Monte Carlo(MCMC) to Sequential Monte Carlo(SMC) algorithm is presented in order to derive the optimal Bayesian estimation.In the context of nonlinear & non-Gaussian dynamic systems, SMC(also named particle filter, PF) is quite capable of performing filtering and RUL assessment recursively. The underlying deterioration of a system/device is seen as a stochastic process with continuous, nonreversible degrading. The state of the deterioration tendency is filtered and predicted with updating observations through the SMC procedure. The corresponding remaining useful life of the system/device is estimated based on the state degradation and a predefined threshold of the failure with two-sided criterion. The paper presents an application on a milling machine for cutter tool RUL assessment by applying the above proposed methodology. The example shows the promising results and the effectiveness of SSM and SMC online assessment of RUL.

Plotting the Sequential Rock Remote Sensing Information by Optimization Dichotomy Method

The sequential rock remote sensing information is a group of rocks that are correlative in space or in space and time. For the sake of plottiug them, someone had brought forward the optimization segn.entotion metkod. We have ased this method to plot the sequential rock remote sensing information at tbe remote sensing hyperspetral test field of Daqing mountain, Inner Mongolia Autonomous Region, China, and found some disadvantages of this method. Therefore, we put forward the optimization dichotomy to plot them, and get better results. Finally we make a conclusion.

A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION

This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.

An Adaptive Sequential Replacement Method for Variable Selection in Linear Regression Analysis

With the rapid development of DNA technologies, high throughput genomic data have become a powerful leverage to locate desirable genetic loci associated with traits of importance in various crop species. However, current genetic association mapping analyses are focused on identifying individual QTLs. This study aimed to identify a set of QTLs or genetic markers, which can capture genetic variability for marker-assisted selection. Selecting a set with k loci that can maximize genetic variation out of high throughput genomic data is a challenging issue. In this study, we proposed an adaptive sequential replacement (ASR) method, which is considered a variant of the sequential replacement (SR) method. Through Monte Carlo simulation and comparing with four other selection methods: exhaustive, SR method, forward, and backward methods we found that the ASR method sustains consistent and repeatable results comparable to the exhaustive method with much reduced computational intensity.

Antibacterial activity of sequentially extracted organic solvent extracts of fruits,flowers and leaves of Lawsonia inermis L.from Jaffna

Objective:To reveal the antibacterial activity of sequentially extracted different cold organic solvent extracts of fruits,flowers and leaves of Lawsonia inermis(L against)some pathogenic bacteria.Methods:Powders of fruits,flowers and leaves of L inermis were continuously extracted with dichloromethane(DCM),ethyl acetate and ethanol at ambient temperature.The dried extracts were prepared into different concentrations and tested for antibacterial activity by agar well diffusion method,and also the extracts were tested to detennine the available phytochemicals.Results:Except DCM extract of flower all other test extracts revealed inhibitory effect on all tested bacteria and their inhibitory effect differed significantly(P<0.05).The highest inhibitory effect was showed by ethyl acetate extract of flower against Staphylococcus aureus(S.aureus)and Pseudomonas aeruginosa(P.aeruginosa),and ethyl acetate extract of fruit on Escherichia coli(E.coli)and Bacillus subtilis(6.subtilis).The ethyl acetate and ethanol extracts of flower,fruit and leaf expressed inhibition even at 1 mg/100μl against all test bacteria.Among the tested phytochemicals flavonoids were detected in all test extracts except DCM extract of flower.Conclusions:The study demonstrated that the ethyl acetate and ethanol extracts of fruit and flower of L inermis are potentially better source of antibacterial agents compared to leaf extracts of respective solvents.

Bayesian sequential testing for exponential life system with reliability growth

A Bayesian sequential testing method is proposed to evaluate system reliability index with reliability growth during development.The method develops a reliability growth model of repairable systems for failure censored test,and figures out the approach to determine the prior distribution of the system failure rate by applying the reliability growth model to incorporate the multistage test data collected from system development.Furthermore,the procedure for the Bayesian sequential testing is derived for the failure rate of the exponential life system,which enables the decision to terminate or continue development test.Finally,a numerical example is given to illustrate the efficiency of the proposed model and procedure.

ZnO micro-nano composite hydrophobic film prepared by the three-step method

The hydrophobicity of the lotus leaf is mainly due to its surface micro-nano composite structure. In order to mimic the lotus structure, ZnO micro-nano composite hydrophobic films were prepared via the three-step method. On thin buffer films of SiO2, which were first fabricated on glass substrates by the so,gel dip-coating method, a ZnO seed layer was deposited via RF magnetron sputtering. Then two different ZnO films, micro-nano and micro-only flowerlike structures, were grown by the hydrothermal method. The prepared films have different hydrophobic properties after surface modification. The structures of the obtained ZnO films were characterized using x-ray diffraction and field-emission scanning electron microscopy. A conclusion that a micro-nano composite structure is more beneficial to hydrophobicity than a micro-only structure was obtained through research into the effect of structure on hydrophobic properties.

General Convergence Analysis for Three-step Projection Methods and Applications to Variational Problems

First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.

Theoretical study on non-sequential double ionization of carbon disulfide with different bond lengths in linearly polarizedlaser fields

By using a two-dimensional Monte-Carlo classical ensemble method, we investigate the double ionization（DI） process of the CS_2 molecule with different bond lengths in an 800-nm intense laser field. The double ionization probability presents a ＂knee＂ structure with equilibrium internuclear distance R = 2.9245 a.u.（a.u. is short for atomic unit）. As the bond length of CS increases, the DI probability is enhanced and the ＂knee＂ structure becomes less obvious. In addition,the momentum distribution of double ionized electrons is also investigated, which shows the momentum mostly distributed in the first and third quadrants with equilibrium internuclear distance R = 2.9245 a.u. As the bond length of CS increases,the electron momentum becomes evenly distributed in the four quadrants. Furthermore, the energy distributions and the corresponding trajectories of the double-ionized electrons versus time are also demonstrated, which show that the bond length of CS in the CS_2 molecule plays a key role in the DI process.

A novel PID controller tuning method based on optimization technique

An approach for parameter estimation of proportional-integral-derivative(PID) control system using a new nonlinear programming(NLP) algorithm was proposed.SQP/IIPM algorithm is a sequential quadratic programming(SQP) based algorithm that derives its search directions by solving quadratic programming(QP) subproblems via an infeasible interior point method(IIPM) and evaluates step length adaptively via a simple line search and/or a quadratic search algorithm depending on the termination of the IIPM solver.The task of tuning PI/PID parameters for the first-and second-order systems was modeled as constrained NLP problem. SQP/IIPM algorithm was applied to determining the optimum parameters for the PI/PID control systems.To assess the performance of the proposed method,a Matlab simulation of PID controller tuning was conducted to compare the proposed SQP/IIPM algorithm with the gain and phase margin(GPM) method and Ziegler-Nichols(ZN) method.The results reveal that,for both step and impulse response tests,the PI/PID controller using SQP/IIPM optimization algorithm consistently reduce rise time,settling-time and remarkably lower overshoot compared to GPM and ZN methods,and the proposed method improves the robustness and effectiveness of numerical optimization of PID control systems.

Feasibility evaluation for excavation of Naghshe Jahan Square subway station by underground methods

In recent years, in reaction to the increasing usage of urban areas, the excavation of underground spaces has been developed. One of the most challenging issues encountered by engineers is the construction of subway stations as large underground spaces at shallow depth with soft surrounding soils. In this paper, Naghshe Jahan Square subway station located in Isfahan, Iran, has been simulated by geomechanical fnite difference method(FDM). This station is located under important historical structures. Therefore, the ground displacement and surface settlement induced by the excavation of the subway station should be strictly controlled. Many of such problems are affected by selected excavation method. For these reasons, different underground excavation methods associated with construction have been studied. In this study, sequential excavation method and large-diameter curved pipe roofng method are used and the numerical results of the two methods are compared. The presence of groundwater table obliges us to choose special techniques for the stability of the ground around the subway station during construction; hence compressed air and ground freezing techniques are utilized in the simulations of the subway station. Finally, after choosing appropriate support systems, the large-diameter curved pipe roofng method with 1.5 m spacing between curved pipes is proposed.

Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings

Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.

Numerical method for optimum motion of undulatory swimmingplate in fluid flow

A numerical method for the optimum motion of an undulatory swimming plate is presented. The optimum problem is stated as minimizing the power input under the condition of fixed thrust. The problem is singular for the invisible modes, and therefore the commonly used Lagrange multiplier method cannot predict an optimum solution but just a saddle point. To eliminate the singularity, an additional amplitude inequality constraint is added to the problem. A numerical optimization code with a sequential quadratic programming method is used to solve the problem. The method is applied to several cases of the motion of two-dimensional and three-dimensional undulatory plates, and the optimum results are obtained.

Study on the wind field and pollutant dispersion in street canyons using a stable numerical method

A stable finite element method for the time dependent Navier-Stokes equations was used for studying the wind flow and pollutant dispersion within street canyons. A three-step fractional method was used to solve the velocity field and the pressure field separately from the governing equations. The Streamline Upwind Petrov-Galerkin(SUPG) method was used to get stable numerical results. Numerical oscillation was minimized and satisfactory results can be obtained for flows at high Reynolds numbers. Simulating the flow over a square cylinder within a wide range of Reynolds numbers validates the wind field model. The Strouhal numbers obtained from the numerical simulation had a good agreement with those obtained from experiment. The wind field model developed in the present study is applied to simulate more complex flow phenomena in street canyons with two different building configurations. The results indicated that the flow at rooftop of buildings might not be assumed parallel to the ground as some numerical modelers did. A counter-clockwise rotating vortex may be found in street canyons with an inflow from the left to right. In addition, increasing building height can increase velocity fluctuations in the street canyon under certain circumstances, which facilitate pollutant dispersion. At high Reynolds numbers, the flow regimes in street canyons do not change with inflow velocity.

Application of CLEAR-VOF method to wave and flow simulations

A two-dimensional numerical model based on the Navier-Stokes equations and computational Lagrangian-Eulerian advection remap-volume of fluid （CLEAR-VOF） method was developed to simulate wave and flow problems. The Navier-Stokes equations were discretized with a three-step finite element method that has a third-order accuracy. In the CLEAR-VOF method, the VOF function F was calculated in the Lagrangian manner and allowed the complicated free surface to be accurately captured. The propagation of regular waves and solitary waves over a flat bottom, and shoaling and breaking of solitary waves on two different slopes were simulated with this model, and the numerical results agreed with experimental data and theoretical solutions. A benchmark test of dam-collapse flow was also simulated with an unstructured mesh, and the capability of the present model for wave and flow simulations with unstructured meshes, was verified. The results show that the model is effective for numerical simulation of wave and flow problems with both structured and unstructured meshes.

A Study of Sediments and Radioactive Particles of the Yenisei River Using a Variety of Analytical Methods

The Yenisei River, one of the largest rivers in the world, is contaminated with artificial radionuclides released by a Russian nuclear facility producing weapon-grade plutonium, which has been in operation for many years. Examination of Yenisei River sediment samples revealed the presence of artificial radionuclides typical of radioactive discharge from the Mining-and-Chemical- Combine (MCC) nuclear facility: isotopes of europium (152Eu, 154Eu, and 155Eu), cesium (137Cs and 134Cs), 60Co, 90Sr, and transuranium elements. The MCC is also a source of radioactive particles in the Yenisei. New data on radionuclide concentrations in sediments and radioactive particles in the Yenisei River were obtained using a wide range of analytical methods. Sequential extraction performed on samples of sediment cores showed different degrees of potential environmental availability of artificial radionuclides and uranium. In a few samples, 241Am was present in the unextractable form, which may be accounted for by the presence of microparticles of the reactor fuel. These microparticles were investigated using scanning electron microscopy, and their reactor origin was confirmed.

The Method for Optimum Estimation of COVID-19 Variant Type Virus Infection Status Analysis by the Multivariate Analysis Considering the Environmental Variability Impact in Japan

Currently, the estimated value of the effective reproduction number (ERN), which is an index for grasping the COVID-19 infection status, is used for important planning and evaluation of infection prevention measures. Since ERN in the Sequential SIR model fluctuates in multiple dimensions due to changes in the surrounding environment, it is difficult to set the appropriate accuracy of the uncertainty region of the estimated data. The challenge in this study is to build a mathematical model of infectious disease according to the characteristics and data characteristics of the infectious disease and select an appropriate estimation method. Highly accurate quantitative research that analyzes the validity of “how infectious diseases prevail” from an academic point of view is the key to prediction and estimation in appropriate infection situation analysis. In this study, we adopted a statistical multivariate analysis method (T method) that enables evaluation and prediction of important factors related to ERN estimation and analysis of phenomena that change in real time (time series analysis). It was clarified that it is possible to estimate with higher accuracy by applying the T method to the estimated value of ERN by the current SIR mathematical model.

Development an Adaptive Environmental Assessment Method for Buildings

The idea behind this work is developing an adaptive method for the environmental assessment of buildings, to configure different versions according to the variables affecting them (spatial, temporal and associated with building characteristics) to suit different evaluated projects. This method may be applied using an electronic tool, which is in a development stage. Amending different assessment versions of the adaptive method is done by including the variables effect, according to set of steps, such as modifying the formulation of the assessment items, adjusting their estimation weights, and amending their achievement evaluation levels and their returned scores. When using the adaptive method, the assessment result of a building using a certain version differs from the results using other versions, even in the same country, so configuring an appropriate version due to the variables affecting the assessment helps getting more accurate results than the ones currently provided. The main goal of that research is to introduce the adaptive method that is proposed to ensure a fairer assessment results from the perspective of Green Architecture, and allow a more credible and accuracy of results comparison according to the environmental performance of buildings. The researcher analyzed the different main features she used in developing the adaptive method, the Comparative aspects between it and the current assessment methods, and the expected reached advantages from its usage. The paper arrived to the importance of adapting the environmental assessment of buildings according to the different affecting variables, and recommended developing the adaptive method and its tool to the stage of application to benefit its advantages.