An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

2D multi-scale hybrid optimization method for geophysical inversion and its application

Local and global optimization methods are widely used in geophysical inversion but each has its own advantages and disadvantages. The combination of the two methods will make it possible to overcome their weaknesses. Based on the simulated annealing genetic algorithm （SAGA） and the simplex algorithm, an efficient and robust 2-D nonlinear method for seismic travel-time inversion is presented in this paper. First we do a global search over a large range by SAGA and then do a rapid local search using the simplex method. A multi-scale tomography method is adopted in order to reduce non-uniqueness. The velocity field is divided into different spatial scales and velocities at the grid nodes are taken as unknown parameters. The model is parameterized by a bi-cubic spline function. The finite-difference method is used to solve the forward problem while the hybrid method combining multi-scale SAGA and simplex algorithms is applied to the inverse problem. The algorithm has been applied to a numerical test and a travel-time perturbation test using an anomalous low-velocity body. For a practical example, it is used in the study of upper crustal velocity structure of the A＇nyemaqen suture zone at the north-east edge of the Qinghai-Tibet Plateau. The model test and practical application both prove that the method is effective and robust.

Establishment and Application of Agricultural Landscape Pattern Spatial Optimization Model Based on GIS-MATLAB-CA

Reasonable degree of the landscape pattern spatial distribution directly influences the sustainable use of regional land resources. Aiming at the unreasonable distribution of agricultural ecological landscape pattern, the deterioration of ecological environment, the Cellular Automaton (CA) principles were used to establish the optimized rules, such as landscape suitability rules, landscape prior rules and restraint conditions; and the standardization of the spatial data was realized by the competence of GIS spatial data handling and data spatial analysis, and finally, landscape pattern spatial optimization model was established with the support of MATLAB platform, i.e. LPSO Model. The spatial pattern optimization of agricultural landscape in west Jilin Province has been realized, which also laid a theoretical foundation for the proper spatial distribution of landscape pattern in west Jilin Province and realizing the sustainable agricultural development.

PARETO FRONT CAPTURE USING DETERMINISTIC OPTIMIZATION METHODS IN MULTI-CRITERION AERODYNAMIC DESIGN

Deterministic optimization methods are combined with the Pareto front concept to solve multi-criterion design problems. The algorithm and the numerical implementation are applied to aerodynamic designs. Evolutionary algorithms （EAs） and the Pareto front concept are used to solve practical design problems in industry for its robustness in capturing convex, concave, discrete or discontinuous Pareto fronts of multi-objective optimization problems. However, the process is time-consuming. Therefore, deterministic optimization methods are introduced to capture the Pareto front, and the types of the captured Pareto front are explained. Numerical experiments show that the deterministic optimization method is a good alternative to EAs for capturing any convex and some concave Pareto fronts in multi-criterion aerodynamic optimization problems due to its efficiency.

基于MATLAB的导向轮结构参数优化设计

基于TVR型双轮缘单轮导向系统,研究以质量轻为目标的导向轮在直线和曲线两种工况下均满足强度要求的最优结构。以导向轮的质量轻为优化目标建立目标函数,以其强度及刚度充足作为约束条件来建立数学模型。在MATLAB软件中编写代码并采用SQP和Interior Point算法对所建立的数学模型进行求解。将不同寻优算法得到的导向轮结构参数建立有限元分析模型,并在有限元分析软件Workbench中进行所述工况下的静力学仿真。结果表明,应用Interior Point求解得到的优化参数的导向轮刚度及强度均满足要求,验证了所选取的结构优化参数对导向轮的结构优化是有效的,达到了导向轮轻量化的设计要求。

A NEW DERIVATIVE FREE OPTIMIZATION METHOD BASED ON CONIC INTERPOLATION MODEL

In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.

基于MATLAB矢量化物质点法的车身防撞梁碰撞分析

基于MATLAB矢量化的物质点法(material point method,MPM)框架,分析车身前防撞梁的碰撞冲击问题。MPM在每一迭代步将物理参数在物质点和背景网格间相互映射,使用MATLAB矢量化框架可以使用户在快速入门的同时保证求解效率,其应力更新采用车身结构材料的弹塑性本构模型。前防撞梁碰撞冲击数值算例结果表明,MPM可以保证求解精度,同时矢量化技术可以大幅提高求解效率。

Development of hybrid optimization algorithm for structures furnished with seismic damper devices using the particle swarm optimization method and gravitational search algorithm

Previous studies about optimizing earthquake structural energy dissipation systems indicated that most existing techniques employ merely one or a few parameters as design variables in the optimization process,and thereby are only applicable only to simple,single,or multiple degree-of-freedom structures.The current approaches to optimization procedures take a specific damper with its properties and observe the effect of applying time history data to the building;however,there are many different dampers and isolators that can be used.Furthermore,there is a lack of studies regarding the optimum location for various viscous and wall dampers.The main aim of this study is hybridization of the particle swarm optimization(PSO) and gravitational search algorithm(GSA) to optimize the performance of earthquake energy dissipation systems(i.e.,damper devices) simultaneously with optimizing the characteristics of the structure.Four types of structural dampers device are considered in this study:(ⅰ) variable stiffness bracing(VSB) system,(ⅱ) rubber wall damper(RWD),(ⅲ) nonlinear conical spring bracing(NCSB) device,(iv) and multi-action stiffener(MAS) device.Since many parameters may affect the design of seismic resistant structures,this study proposes a hybrid of PSO and GSA to develop a hybrid,multi-objective optimization method to resolve the aforementioned problems.The characteristics of the above-mentioned damper devices as well as the section size for structural beams and columns are considered as variables for development of the PSO-GSA optimization algorithm to minimize structural seismic response in terms of nodal displacement(in three directions) as well as plastic hinge formation in structural members simultaneously with the weight of the structure.After that,the optimization algorithm is implemented to identify the best position of the damper device in the structural frame to have the maximum effect and minimize the seismic structure response.To examine the performance of the proposed PSO-GSA optimization method,it has been applied to a three-story reinforced structure equipped with a seismic damper device.The results revealed that the method successfully optimized the earthquake energy dissipation systems and reduced the effects of earthquakes on structures,which significantly increase the building’s stability and safety during seismic excitation.The analysis results showed a reduction in the seismic response of the structure regarding the formation of plastic hinges in structural members as well as the displacement of each story to approximately 99.63%,60.5%,79.13% and 57.42% for the VSB device,RWD,NCSB device,and MAS device,respectively.This shows that using the PSO-GSA optimization algorithm and optimized damper devices in the structure resulted in no structural damage due to earthquake vibration.

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.

Design of small-scale gradient coils in magnetic resonance imaging by using the topology optimization method

A topology optimization method based on the solid isotropic material with penalization interpolation scheme is utilized for designing gradient coils for use in magnetic resonance microscopy.Unlike the popular stream function method,the proposed method has design variables that are the distribution of conductive material.A voltage-driven transverse gradient coil is proposed to be used as micro-scale magnetic resonance imaging(MRI)gradient coils,thus avoiding introducing a coil-winding pattern and simplifying the coil configuration.The proposed method avoids post-processing errors that occur when the continuous current density is approximated by discrete wires in the stream function approach.The feasibility and accuracy of the method are verified through designing the z-gradient and y-gradient coils on a cylindrical surface.Numerical design results show that the proposed method can provide a new coil layout in a compact design space.

Matlab Methods for Roots of Characteristic Equation of Cylindrical Bessel Equation Eigenvalue Problems on General Interval

Root of characteristic equation for cylindrical Bessel equation eigenvalue problems on general interval is of great real physical importance at engineering and physical. First, the characteristic equation of cylindrical Bessel equation eigenvalue problem on general interval is given, second, by mean of compared method, we obtaining roots of characteristic equation with Matlab program is discussed.

基于MATLAB编程的碎屑岩粒度计算对比:以江西省会昌盆地上白垩统周田组为例

计算机强大的图像分析和统计功能在碎屑岩粒度测量过程中能够有效解决计算结果精度不足以及工作负荷大等问题。通过MATLAB编程语言对会昌盆地上白垩统周田组样品进行灰度化、二值化、自适应中值滤波、彩色标注等图像处理方式,准确测量出其粒度参数。结果显示:①MATLAB直接计算法与图解法所求得平均粒径分别为4.008φ和3.103φ(φ为粒级);标准偏差分别为0.8φ和0.803φ;偏度分别为-0.195φ和-0.041φ;峰度分别为0.911φ和0.916φ。两种计算方式中标准偏差和峰度误差较小,可以互相替代,而标准偏差和偏度误差程度较大,不可互相替代;②MATLAB直接计算方法与镜下岩矿鉴定均显示周田组整体磨圆度较差,碎屑颗粒呈棱角状-次棱角状,通过沉积环境判别公式反映周田组形成于河流相沉积环境中;③通过MATLAB编程语言,能够精准识别碎屑岩中颗粒轮廓及统计各项参数,对沉积物粒度研究提供了极大的便利,避免了人为主观因素干扰,提高了工作效率。

基于Matlab免疫算法的畜禽屠宰中心选址方法研究

为了加快畜牧业产业化经营的进程,规范畜禽交易行为,合理布局建设畜禽屠宰中心,本研究基于免疫优化算法求解目标函数的方法,模拟了31个养殖区坐标,获取每个养殖区的需求度,使用Matlab软件工具箱来建模、求解,在31个养殖区中选取6个最优中心点为畜禽屠宰中心建设点。结果表明:采用免疫算法求解中心选址问题具有较好的收敛性,选址结果为(18,25,5,27,9,14),各养殖区需求量权重距离和为5.68×10^(5)。说明Matlab免疫算法适用于大量数据集的求解,模型及算法可行、有效。

AI-Enhanced Performance Evaluation of Python, MATLAB, and Scilab for Solving Nonlinear Systems of Equations: A Comparative Study Using the Broyden Method

This research extensively evaluates three leading mathematical software packages: Python, MATLAB, and Scilab, in the context of solving nonlinear systems of equations with five unknown variables. The study’s core objectives include comparing software performance using standardized benchmarks, employing key performance metrics for quantitative assessment, and examining the influence of varying hardware specifications on software efficiency across HP ProBook, HP EliteBook, Dell Inspiron, and Dell Latitude laptops. Results from this investigation reveal insights into the capabilities of these software tools in diverse computing environments. On the HP ProBook, Python consistently outperforms MATLAB in terms of computational time. Python also exhibits a lower robustness index for problems 3 and 5 but matches or surpasses MATLAB for problem 1, for some initial guess values. In contrast, on the HP EliteBook, MATLAB consistently exhibits shorter computational times than Python across all benchmark problems. However, Python maintains a lower robustness index for most problems, except for problem 3, where MATLAB performs better. A notable challenge is Python’s failure to converge for problem 4 with certain initial guess values, while MATLAB succeeds in producing results. Analysis on the Dell Inspiron reveals a split in strengths. Python demonstrates superior computational efficiency for some problems, while MATLAB excels in handling others. This pattern extends to the robustness index, with Python showing lower values for some problems, and MATLAB achieving the lowest indices for other problems. In conclusion, this research offers valuable insights into the comparative performance of Python, MATLAB, and Scilab in solving nonlinear systems of equations. It underscores the importance of considering both software and hardware specifications in real-world applications. The choice between Python and MATLAB can yield distinct advantages depending on the specific problem and computational environment, providing guidance for researchers and practitioners in selecting tools for their unique challenges.

基于MATLAB/GUI 的真空泵抽速曲线预测计算

从工程实际应用的角度出发,以螺杆真空泵转子的几何特性和螺杆真空泵内部的泄漏模型为基础,建立螺杆真空泵内部工作过程的数学模型,借助MATLAB软件,采用四阶龙格-库塔(Runge-Kutta)法将每次微分方程求解结果作为初始条件反复迭代求解,依据MATLAB/GUI界面设计了一款可以快速计算螺杆真空泵抽速曲线的应用程序。使用该程序对多种螺杆真空泵进行了抽速曲线的预测计算,并根据算例结果对程序进行了完善。

A MATLAB code for the material-field series-expansion topology optimization method

This paper presents a MATLAB implementation of the material-field series-expansion(MFSE)topology optimization method.The MFSE method uses a bounded material field with specified spatial correlation to represent the structural topology.With the series-expansion method for bounded fields,this material field is described with the characteristic base functions and the corresponding coefficients.Compared with the conventional density-based method,the MFSE method decouples the topological description and the finite element discretization,and greatly reduces the number of design variables after dimensionality reduction.Other features of this method include inherent control on structural topological complexity,crisp structural boundary description,mesh independence,and being free from the checkerboard pattern.With the focus on the implementation of the MFSE method,the present MATLAB code uses the maximum stiffness optimization problems solved with a gradientbased optimizer as examples.The MATLAB code consists of three parts,namely,the main program and two subroutines(one for aggregating the optimization constraints and the other about the method of moving asymptotes optimizer).The implementation of the code and its extensions to topology optimization problems with multiple load cases and passive elements are discussed in detail.The code is intended for researchers who are interested in this method and want to get started with it quickly.It can also be used as a basis for handling complex engineering optimization problems by combining the MFSE topology optimization method with non-gradient optimization algorithms without sensitivity information because only a few design variables are required to describe relatively complex structural topology and smooth structural boundaries using the MFSE method.

基于MATLAB的民航发动机涡轮叶片寿命建模

针对民航飞机维修工作中发动机涡轮叶片普遍存在故障率较高的问题,收集某型民用航空发动机涡轮叶片的可靠性数据,并运用三参数Weibull分布建立该型发动机涡轮叶片的可靠性寿命模型。在模型求解的数值计算过程中,为保证模型的计算精度,采用经典的牛顿迭代法及三参数相关系数优化法对涡轮叶片的寿命数据进行拟合分析及计算;同时为减少计算工作量及提高数值计算过程中人工智能的参与度,基于MATLAB软件对上述数值计算方法编写计算程序,最后对计算结果进行K-S假设检验。结果表明:对涡轮叶片寿命数据进行可靠性分析时,运用Weibull分布建立的数学模型符合客观规律;同时牛顿迭代法、三参数相关系数优化法及MATLAB计算程序的有效利用,保证了计算结果的精度。

Global Optimization Method Using SLE and Adaptive RBF Based on Fuzzy Clustering

High fidelity analysis models,which are beneficial to improving the design quality,have been more and more widely utilized in the modern engineering design optimization problems.However,the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable.In order to improve the efficiency of optimization involving high fidelity analysis models,the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models,which can greately reduce the computation time.An efficient heuristic global optimization method using adaptive radial basis function（RBF） based on fuzzy clustering（ARFC） is proposed.In this method,a novel algorithm of maximin Latin hypercube design using successive local enumeration（SLE） is employed to obtain sample points with good performance in both space-filling and projective uniformity properties,which does a great deal of good to metamodels accuracy.RBF method is adopted for constructing the metamodels,and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced.The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space.The numerical benchmark examples are used for validating the performance of ARFC.The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method（ARSM） proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum.This method improves the efficiency and global convergence of the optimization problems,and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.

Cavity noise sensitivity analysis of tire contour design factors and application of contour optimization methodology

Cavity resonance noise of passenger car tires is generated by interacting excitation between a tire structure and the fill gas (air), and generally lies in a frequency range of 200?250 Hz. As such, this noise is strongly perceived and may be a serious source of driver annoyance. Thus, many studies regarding the cavity noise mechanism and its reduction have already been conducted. In this work, a vibro-acoustic coupled analysis was conducted between a tire structure and air cavity. Using this analysis, we can more accurately simulate the tire noise performance in the region of the cavity resonance frequency. An analysis of the effects of variation of tire contour design factors was conducted, using design-of-experiments methods. Finally, a multi-objective optimization was performed using in-house codes to reduce the cavity noise level while minimizing the loss of other performances, such as diminished ride comfort and handling caused by the variations of contour. As a result of this optimization, an optimized contour shape was derived, which satisfied the multi-objective performances.

MoM-based topology optimization method for planar metallic antenna design

The metallic antenna design problem can be treated as a problem to find the optimal distribution of conductive material in a certain domain. Although this problem is well suited for topology optimization method, the volumetric distribution of conductive material based on 3D finite element method (FEM) has been known to cause numerical bottlenecks such as the skin depth issue, meshed 'air regions' and other numerical problems. In this paper a topology optimization method based on the method of moments (MoM) for configuration design of planar metallic antenna was proposed. The candidate structure of the planar metallic antenna was approximately considered as a resistance sheet with position-dependent impedance. In this way, the electromagnetic property of the antenna can be analyzed easily by using the MoM to solve the radiation problem of the resistance sheet in a finite domain. The topology of the antenna was depicted with the distribution of the impedance related to the design parameters or relative densities. The conductive material (metal) was assumed to have zero impedance, whereas the non-conductive material was simulated as a material with a finite but large enough impedance. The interpolation function of the impedance between conductive material and non-conductive material was taken as a tangential function. The design of planar metallic antenna was optimized for maximizing the efficiency at the target frequency. The results illustrated the effectiveness of the method.