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.

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）.

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.

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.

小净距多线隧道掘进方案对围岩稳定性的影响研究

目的小净距多线隧道在轨道交通工程中应用广泛,但由于施工步骤繁多且掘进过程中影响因素较多,需设计合理的小净距多线隧道并行掘进方案。方法采用2种不同开挖顺序的并行掘进方案,通过建立三维有限元数值仿真模型,比较2种方案的隧道围岩应力与位移发展规律,分析现场监测数据,对比模型的准确性,确定掘进方案的可行性。结果结果表明,开挖顺序对围岩间相互作用影响明显,中隧应力和变形受影响最大。中隧先挖法可以较好地避免应力较为集中现象,2种开挖方式的变形值均在安全范围内;依次开挖法和中隧先挖法拱腰处水平应力的变化规律基本一致,依次开挖法的拱顶处垂直应力比中隧先挖法的大40%左右;中隧先挖法的拱腰水平变形和拱顶沉降值分别比依次开挖法的增大23%,26%,但中隧先挖法开挖初期的沉降值较少;中隧先挖进度较快,应力和沉降控制能力优于依次开挖法,数值模拟方法能较好反映真实施工情况,现场监测结果也表明中隧先挖法适用于小净距隧道进口段施工。结论综合考虑衬砌结构应力、变形和施工工期,现场可采用中隧先挖法进行施工。研究结果可为类似小净距多线并行隧道工程设计与施工提供理论参考。

基于序贯贝叶斯方法的核素快速检测方法研究

适当的放射性核素快速检测方法对于具有流量大和计数率水平低特征的海关放射性安检等场景是必要的。相较于传统不确定性分析方法,贝叶斯方法和序贯概率比检验可充分利用测量物理量的全部信息而所需的样本量较少,基于此提出了一种新型序贯贝叶斯核素快速检测方法,分别在低辐射本底环境和自然辐射本底环境,使用一套LaBr3(Ce)探测系统和一组标准点源对该方法的可行性、检测性能和普适性开展了实验研究,并探究了方法的关键参数中第一类错误概率α、第二类错误概率β和时间间隔下限τmin对检测性能的影响。在本底计数率分别为59.3 s^(-1)和165.9 s^(-1)的两类本底环境中,α和β分别不超过0.1和0.01的条件下,实验结果显示:在无源情况下,该方法对本底辐射的平均检出时间分别为24.08 s和10.54 s,平均检出样本量分别为1427和1742,且发生误报后均可快速自适应消除并做出有效判决;在有源情况下,实验测量检测灵敏度下限分别约为8.2%和6.1%,对应的平均检出时间分别为8.59 s和6.61 s,实验测量漏报率均为0,平均检出时间只与全谱净计数率有关,平均检出样本量只与放射源信号的计数率信噪比有关,检测灵敏度下限可理论计算且与实验结果相吻合;参数τ_(min)的减小会增大检测灵敏度下限和减小检出时间,参数α和β可决定实验测量误报率和漏报率。研究表明本方法非常适用于低水平放射性核素的快速检测。

基于剩余碰撞时间的线控制动分层控制策略

针对不同制动工况需求的制动策略存在差异的情况,提出一种线控制动分层控制策略.在该分层策略的上层,利用二阶TTC安全碰撞时间模型计算出车辆与前车的剩余碰撞时间,以此作为依据进行制动策略的选取,并建立了汽车二自由度模型、车身法向受力模型和Burckhardt轮胎模型;在该分层策略的下层,进行了制动力在轮间的分配,使用序列二次规划(SQP)方法,分别在一般制动、紧急制动、失稳制动3种工况下,以轮胎滑移率为对象建立优化函数,对车辆制动力进行了优化分配.使用MATLAB/Simulink和Carsim进行了联合仿真,对所提出3种工况下的制动分配策略进行了有效性验证.结果表明:在一般制动工况下,采用该策略时相比对照工况制动距离减少18.08%,制动时间减少25.12%;在紧急制动工况下,采用该策略时相比对照工况制动距离减少19.17%,制动时间减少12.79%;在失稳制动工况下,该策略可通过轮胎差扭来提升车辆的横向稳定性.采用文中制动策略显著提升了车辆的制动效能.

序贯服法对2型糖尿病合并稳定型心绞痛患者的疗效观察

目的探讨中药常规服法与序贯服法对气虚血瘀型2型糖尿病合并稳定型心绞痛在临床效果上的差异。方法选择2型糖尿病合并稳定型心绞痛患者,随机分成对照组、整方组和序贯组,对照组80例,整方组和序贯组各40例,维持现有的化药治疗方式不变,对照组服用安慰剂,整方组与序贯组每日服用中药一致,序贯组早上用补阳还五汤加减,中午用泽泻汤加味,晚上用四妙勇安汤加减,疗程24周,比较治疗前后以及停药后的心绞痛1周发作次数、心绞痛单次发作持续时间和硝酸甘油1周消耗量,中医证候积分,FPG、HbA1c以及100 g和200 g馒头餐负荷后2 h-PG变化。结果治疗前后,心绞痛相关指标、中医证候积分和血糖相关指标,整方组和序贯组明显优于对照组(P<0.05),治疗后序贯组馒头餐负荷后2 h-PG波动幅度较整方组更小,差异无统计学意义(P>0.05);停药后回访,整方组相关数值反弹明显,与对照组比较差异无统计学意义(P>0.05),序贯组则较为稳定(P>0.05),与对照组和整方组比较差异有显著性意义(P<0.05)。结论中药整方服法和序贯服法均能有效改善T2DM-SAP患者心绞痛相关指标、中医证候积分和血糖相关指标,序贯服法在停药后的疾病稳定上效果更优。

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.

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.

SEQUENTIAL CONVEX PROGRAMMING METHODS FOR SOLVING LARGE TOPOLOGY OPTIMIZATION PROBLEMS： IMPLEMENTATION AND COMPUTATIONAL RESULTS

In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming （SCP）. A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.

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.