Stochastic polynomial optimization

ABSTRACT

This paper studies stochastic optimization problems with polynomials. We propose an optimization model with sample averages and perturbations. The Lasserre-type Moment-SOS relaxations are used to solve the sample average optimization. Properties of the optimization and its relaxations are studied. Numerical experiments are presented.     

Stochastic collocation-based nonlinear analysis of concrete bridges with uncertain parameters

This paper focuses on the stochastic response of concrete bridges considering uncertainty in bearing and abutment stiffness. A multi-span simply supported bridge with concrete girders is selected. A 3D-dimensional model is prepared, and nonlinear response history analyses are performed. For the numerical dynamic simulation, the non-sampling stochastic method based on generalized polynomial chaos (gPC) expansion is utilised. The uncertain parameters include the vertical and shear stiffness of bearings and the lateral stiffness of abutments are presented by the truncated gPC expansions. Furthermore, the system response such as base shear, acceleration, velocity and displacement in different columns is presented by gPC expansion with unknown deterministic coefficients. The stochastic Galerkin projection is employed to calculate a set of deterministic equations. A non-intrusive solution, as a set of collocation points, determines the unknown gPC coefficients of the system response and the results are compared with Monte Carlo simulations. The key advantage of spectral discretization is the combination of the mentioned method with the spatial discretization, e.g. finite element model. This study also emphasises the accuracy in results and time efficiency of the proposed non-sampling method for uncertainty quantification of stochastic systems comparing to sampling procedure (e.g. Monte Carlo simulation).     

Rhombellation: a builder for multi-shell clusters

Rhombellanes are mathematical structures, proposed by us in 2017; they may appear both in periodic crystals or in finite structures. The simplest rhombellane is rbl.5 or K_2.3, the complete bipartite graph. In this paper, rhombellation operation is iteratively applied on three classes of structures: cube, tori and cubic pcu-network, respectively. The structural topological parameters are detailed.     

Improved error bound for multivariate Chebyshev polynomial interpolation

ABSTRACT

Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties which provides tremendous application potential in mathematical finance. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For efficiency, a sharp error bound is essential, in particular for high-dimensional applications. For tensorized Chebyshev interpolation, we present an error bound that improves existing results significantly.     

An enhanced data-driven polynomial chaos method for uncertainty propagation

As a novel type of polynomial chaos expansion (PCE), the data-driven PCE (DD-PCE) approach has been developed to have a wide range of potential applications for uncertainty propagation. While the research on DD-PCE is still ongoing, its merits compared with the existing PCE approaches have yet to be understood and explored, and its limitations also need to be addressed. In this article, the Galerkin projection technique in conjunction with the moment-matching equations is employed in DD-PCE for higher-dimensional uncertainty propagation. The enhanced DD-PCE method is then compared with current PCE methods to fully investigate its relative merits through four numerical examples considering different cases of information for random inputs. It is found that the proposed method could improve the accuracy, or in some cases leads to comparable results, demonstrating its effectiveness and advantages. Its application in dealing with a Mars entry trajectory optimization problem further verifies its effectiveness.     

Design and analysis adaptivity in multiresolution topology optimization

Multiresolution topology optimization (MTO) methods involve decoupling of the design and analysis discretizations, such that a high-resolution design can be obtained at relatively low analysis costs. Recent studies have shown that the MTO method can be approximately 3 and 30 times faster than the traditional topology optimization method for two-dimensional (2D) and three-dimensional (3D) problems, respectively. To further exploit the potential of decoupling analysis and design, we propose a dp-adaptive MTO method, which involves locally increasing/decreasing the polynomial degree of the shape functions (p) and the design resolution (d). The adaptive refinement/coarsening is performed using a composite refinement indicator that includes criteria based on analysis error, presence of intermediate densities, as well as the occurrence of design artifacts referred to as QR-patterns. While standard MTO must rely on filtering to suppress QR-patterns, the proposed adaptive method ensures efficiently that these artifacts are suppressed in the final design, without sacrificing the design resolution. The applicability of the dp-adaptive MTO method is demonstrated on several 2D mechanical design problems. For all the cases, significant speedups in computational time are obtained. In particular for design problems involving low material volume fractions, speedups of up to a factor of 10 can be obtained over the conventional MTO method.     

采用磁流变阻尼器的人体座椅悬架系统模糊ANFIS-PID复合控制技术研究

对座椅悬架用单出杆式磁流变阻尼器进行阻尼特性试验,并借助MATLAB多项式拟合工具箱对改进多项式模型中未知参数进行辨识。分析人体振动特性,建立五自由度人体座椅悬架模型。综合模糊控制器与自适应模糊神经推理系统(Adaptive Neuro-Fuzzy Inference System,ANFIS)整定PID控制器的优点,提出一种模糊ANFIS-PID复合控制策略。采用正弦信号作为外界激励,分别对被动悬架、传统模糊控制、ANFIS-PID控制及模糊ANFIS-PID复合控制人体座椅悬架系统进行仿真分析。结果表明,辨识得出的参数和建立的改进多项式模型均可满足后续仿真要求;采用模糊ANFIS-PID复合控制策略的隔振效果明显优于传统模糊控制及ANFIS-PID控制,能有效改善人体座椅悬架系统的行驶平顺性及驾乘人员乘坐舒适性。     

平板集热器(倾角)变化工况数值模拟

运用FLUENT数值模拟软件分析了平板集热器(倾角)变化对集热器传热特性的影响,保证其结构参数不变,通过对5组不同倾角(0°、30°、45°、60°、75°)的数值模型进行非稳态模拟,对模拟数据进行分析,得出了平板集热器不同倾角对集热器传热性能变化的影响。     

基于地表温度和植被指数的黑龙江省旱情遥感动态监测

干旱灾害是一种影响范围广、时间跨度大的自然灾害,对社会经济发展尤其是给农业生产造成重大损失。遥感技术具有观测空间尺度大、实时性强的特点,有利于大范围、实时、动态的旱情监测。利用MODIS的LST和NDVI遥感数据,依托站点实测土壤含水率数据,分析土壤含水率与地表温度和植被指数之间的关系,考虑土壤类型,构建温度植被多项式模型,进行表层土壤水分反演,基于此开展2018年3~7月黑龙江省旱情遥感监测应用研究。监测结果显示,监测期内黑龙江省经历了两次规模较大的干旱过程,干旱的核心区域为黑龙江省西南部区域,与实际情况相吻合。研究表明,考虑土壤类型的温度植被多项式模型对旱情遥感监测具有良好的应用效果。