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).     

柴达木盆地三湖坳陷横波勘探中的低幅异常消除技术

近年来,在柴达木盆地三湖坳陷开展了横波地震勘探,但是由于该区低幅度构造发育,横波静校正引起的"低幅"异常与上述低幅度构造相互混杂,难以区分。为此,针对该区横波表层调查难以控制表层横波速度模型的变化、横波近偏移距初至污染严重、横波折射层发育导致高速界面难以确定等问题,首先采用曲线拟合技术预测污染区横波初至时间确保初至完整性,然后采用面波模型与多层折射分层联合约束反演横波表层速度,最后通过基于速度谱分析的层位匹配建模技术确定合理的横波速度界面,形成了横波表层"低幅"异常消除技术,并进行了现场应用及效果评价。研究结果表明:①曲线拟合技术可以弥补近道污染区横波初至空白,保证层析反演模型的完整性;②基于瑞雷波的频散特性反演建模可以为确定该区浅层横波速度提供可靠的资料,提高浅层模型精度;③面波模型与多层折射分层联合约束反演能够更准确的反演该区表层横波速度场,较好地建立横波速度模型,消除横波剖面上"低幅"异常现象。结论认为,所形成的横波地震勘探低幅异常消除技术消除了横波静校正引起的"低幅"异常现象,提高了横波地震资料的成像品质。     

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.     

Prebiotic Pathway from Ribose to RNA Formation

At the focus of abiotic chemical reactions is the synthesis of ribose. No satisfactory explanation was provided as to the missing link between the prebiotic synthesis of ribose and prebiotic RNA (preRNA). Hydrogen cyanide (HCN) is assumed to have been the principal precursor in the prebiotic formation of aldopentoses in the formose reaction and in the synthesis of ribose. Ribose as the best fitting aldopentose became the exclusive sugar component of RNA. The elevated yield of ribose synthesis at higher temperatures and its protection from decomposition could have driven the polymerization of the ribose-phosphate backbone and the coupling of nucleobases to the backbone. RNA could have come into being without the involvement of nucleotide precursors. The first nucleoside monophosphate is likely to have appeared upon the hydrolysis of preRNA contributed by the presence of reactive 2′-OH moieties in the preRNA chain. As a result of phosphorylation, nucleoside monophosphates became nucleoside triphosphates, substrates for the selective synthesis of genRNA.     

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。     

Multilayer thermal object identification in frequency domain using IR thermography and vector fitting

This paper deals with the identification of the thermal parameters of multilayer objects using the concept of thermal impedance. In order to perform such identification, temperature evolution in time is obtained by an infrared camera after power excitation is applied in the investigated structure. Infrared thermography offers the advantage of being a noncontact temperature detection and measurement method. In many practical cases, it is impossible to use contact temperature measurements. Typically, the power in the form of a step function is applied. In order to calculate the thermal impedance of an object, temperature and power are converted into the frequency domain using the Laplace transform for s = jω. Then, the poles of the thermal impedance are identified using vector fitting, which allows calculating the thermal impedance as a sum of partial fractions. This corresponds directly to the Foster network of a thermal object. In addition, the vector fitting method offers much better convergence in comparison with other methods using the polynomial rational approximation of thermal impedance. A considerable improvement of the numerical Laplace transform in high frequency range is proposed. In this approach, the variable s = jω is replaced by , and then, the integration result is corrected by the Taylor series. It leads to a kind of filtering of the temperature signal.