Properness and Inversion of Rational Parametrizations of Surfaces

 In this paper we characterize the properness of rational parametrizations of hypersurfaces by means of the existence of intersection points of some additional algebraic hypersurfaces directly generated from the parametrization over a field of rational functions. More precisely, if V is a hypersurface over an algebraically closed field ? of characteristic zero and is a rational parametrization of V, then the characterization is given in terms of the intersection points of the hypersurfaces defined by x _i q _i (tˉ)−p _i (tˉ), i=1,...,n over the algebraic closure of ?(V). In addition, for the case of surfaces we show how these results can be stated algorithmically. As a consequence we present an algorithmic criteria to decide whether a given rational parametrization is proper. Furthermore, if the parametrization is proper, the algorithm also computes the inverse of the parametrization. Moreover, for surfaces the auxiliary hypersurfaces turn to be plane curves over ?(V), and hence the algorithm is essentially based on resultants. We have implemented these ideas, and we have empirically compared our method with the method based on Gr?bner basis. Received: November 20, 2000; revised version: November 20, 2001     

A turbulence model based on principal components

Literature on turbulence is very wide, providing several models for the power spectral density function of the single-point turbulence components, for the two-point coherence function of the same turbulence component and for the single-point coherence function of different turbulence components. On the other hand, no suitable and simple model seems to be available for representing the two-point coherence function of different turbulence components, in particular of the longitudinal and vertical turbulence components, which would be useful for modelling buffeting actions on bridges. The Proper Orthogonal Decomposition provides efficient tools to formulate a new model of the turbulence field based on principal components. Furthermore, it suggests physical principles and defines mathematical rules to establish an appropriate model of the two-point coherence function of the longitudinal and vertical components, completing the statistical model of turbulence. Embedded in a Monte Carlo framework, this new representation can be used to simulate multi-dimensional and multi-variate random turbulence fields.     

An efficient space–time based simulation approach of wind velocity field with embedded conditional interpolation for unevenly spaced locations

The classical spectral representation method (SRM) has been extensively used in the simulation of multivariate stationary Gaussian random processes. Due to the application of fast Fourier transform (FFT), the simulation is usually efficient. However, for processes with a large number of simulation points, it becomes necessary to enhance the simulation efficiency. One example is the wind velocity field along a large-span bridge, where hundreds of wind velocity fluctuations are required. In the case of bridges built over a homogeneous terrain such as coastal area or flat plain, the wind velocity field can be modeled as a multivariate homogeneous random process i.e., the auto power spectral densities (PSDs) at evenly-spaced simulation points are same and the cross PSD is a function of separation distance between two simulation points. Furthermore, in some applications, additional simulation points need to be included to a set of uniformly distributed points in order to make the wind velocity field consistent to the structural dynamic analysis requirement.In this paper, a hybrid approach of space–time random-field based SRM and proper orthogonal decomposition (POD)-based interpolation is developed for simulating the above wind velocity process. In this approach, the random-field based SRM is used to simulate the multivariate homogeneous random process composed of a set of uniformly distributed simulation locations while POD-based interpolation is used to conditionally generate the wind velocities at a few unevenly distributed points using the previously simulated wind velocities. The idea of the former is based on transforming the simulation of the homogeneous random process into that of the corresponding space–time random field where the phase angle is assumed to be zero and the coherence function must be an even function in terms of separation distance. Through this procedure, customary requirement for spectral matrix decomposition is eliminated and application of two dimensional FFT can improve the simulation efficiency dramatically. The shortcomings of this method include a slight approximation regarding the simulated sample and the non-ergodicity for the correlation function. The numerical example of a homogeneous wind velocity field along a bridge deck shows that the proposed random field-based method is very efficient in terms of accuracy and efficiency when the number of simulation locations is large and the POD-based interpolation also has good performance.     

论风景名胜区的“合理开发”

风景名胜区问题的实质在于：如何正确对待和处理好风景名胜区在旅游开发中的保护与开发的辩证关系。风景名胜区“合理开发”应包括原真性、生态性、适度性、协调性、系统性、按规划建设、旅游宿分离等原则。     

鞍形索网等效静力风荷载研究

针对大跨度屋盖结构多振型参与振动的特点,提出了一套确定该类结构等效静力风荷载的精细化方法。该方法的流程包括风振响应分析和静力等效两个阶段,每个阶段又分为平均分量、背景分量和共振分量等3个部分分别进行研究。风振响应分析时,背景响应分析采用准静力方法;共振响应分析综合运用本征正交分解法(POD法)和Ritz向量直接叠加法。静力等效时,等效静力风荷载的背景分量采用荷载响应相关系数法分析,其共振分量表示为多个主要参与振型惯性力的组合。基于本文的分析方法,对一鞍形索网结构的风振响应和等效静力风荷载进行了研究,探讨了不同风向下、针对不同响应的等效静力风荷载分布情况。结果表明本文方法能够有效地分析大跨度屋盖结构的风振响应和等效静力风荷载,能够解决大跨度屋盖结构中多振型参与振动这一主要问题。     

基于图神经网络的铅铋快堆上腔室三维热分层现象非线性降阶分析

铅铋快堆上腔室的热分层现象对堆内构件的结构安全性和系统余热排出能力具有重要影响,需重点分析。本文首先基于计算流体动力学（CFD）程序FLUENT得到铅铋快堆上腔室热分层现象的高精度全阶快照,然后利用图神经网络（GNN）构建的图自编码器（GAE）对快照进行非线性降阶,并将非线性降阶后的重构结果与本征正交分解（POD）的线性降阶结果进行对比分析,最后通过结合多层感知机对热分层快照开展在线状态识别与预测分析。结果表明,由于GNN具有高度的非线性,使其在大规模CFD数据的非线性降阶方面具备独特优势,其1阶模态重构精度与POD的30~50阶基函数的重构精度相当;在在线阶段,以472 ms的时长即可完成对热分层快照的特征识别和预测,且预测精度与直接重构精度相近。相关研究成果可为铅铋快堆热分层现象演化机理分析及后果预测提供新的分析方法支撑。     

Model reduction for multidisciplinary optimization - application to a 2D wing

Multidisciplinary optimization (MDO) is a growing field in engineering, with various applications in aerospace, aeronautics, car industry, etc. However, the presence of multiple disciplines leads to specific issues, which prevent MDO to be fully integrated in industrial design methodology. In practice, the key issues in MDO lie in the management of the interconnections between disciplines, along with the high number of simulations required to find a feasible multidisciplinary (optimal) solution. Therefore, in this paper, a novel approach is proposed, combining proper orthogonal decomposition to decrease the amount of data exchanged between disciplines, with surrogate models based on moving least squares to reduce disciplines. This method is applied to an original 2D wing demonstrator involving two disciplines (fluid and structure). The numerical results obtained for an optimization task show its benefits in diminishing both the interfaces between disciplines and the overall computational time.     

Off-line model reduction for on-line linear MPC of nonlinear large-scale distributed systems

Model predictive control (MPC) is an efficient method for the controller design of a large number of processes. However, linear MPC is often inappropriate for controlling nonlinear large-scale systems, while non-linear MPC can be computationally costly. The resulting optimization-based procedure can lead to local minima due to the, non-convexities that non-linear systems can exhibit. To overcome the excessive computational cost of MPC application for large-scale nonlinear systems, model reduction methodology in conjunction with efficient system linearizations have been exploited to enable the efficient application of linear MPC for nonlinear distributed parameter systems (DPS). An off-line model reduction technique, the proper orthogonal decomposition (POD) method, combined with a finite element Galerkin projection is first used to extract accurate non-linear low-order models from the large-scale ones. Trajectory Piecewise-Linear (TPWL) methodologies are subsequently developed to construct a piecewise linear representation of the reduced nonlinear model, both in a static and in a dynamic fashion. Linear MPC, based on quadratic programming, can then be efficiently performed on the resulting low-order, piece-wise affine system. Our combined methodology is readily applicable in combination with advanced MPC methodologies such as multi-parametric MPC (MP-MPC) (Pistikopoulos, 2009). The stabilisation of the oscillatory behaviour of a tubular reactor with recycle is used as an illustrative example to demonstrate our methodology.