A dimension-wise method for the static analysis of structures with interval parameters

A novel method for the static analysis of structures with interval parameters under uncertain loads is proposed, which overcomes the inherent conservatism introduced by the conventional interval analysis due to ignoring the dependency phenomenon. Instead of capturing the extremum of the structural static responses in the entire space spanned by uncertain parameters, their lower and upper bounds are calculated at the minimal and maximal point vectors obtained dimension by dimension with respect to uncertain parameters based on the Legend orthogonal polynomial approximation, overcoming the potential engineering insignificance caused by the optimization strategy. After performing its theoretical analysis, both the accuracy and applicability of the proposed method are verified.     

Uncertainty propagation in SEA for structural–acoustic coupled systems with non-deterministic parameters

Considering limited available information on uncertainties in structural - acoustic coupled systems, two methods namely the vertex method and the Legendre orthogonal polynomial based method for predicting their dynamic behavior are developed based on the Statistical Energy Analysis (SEA) approach. For the vertex method, an efficient program for determining coordinates of all vertices of the rectangular spanned by entries of the involved interval input vector is coded, which is well suited for an interval input vector in arbitrary dimension. Instead of calculating the extremum of the response of interest, a method for determining its minimal and maximal point vectors dimension by dimension with respect to uncertain parameters is proposed based on the Legendre orthogonal polynomial approximation. Following the theoretical analysis of the accuracy and efficiency of the proposed methods, their validation is performed by one numerical example and two applications.     

Interval design point method for calculating the reliability of structural systems

The evaluation of reliability for structural system is important in engineering practices.In this paper,by combining the design point method,JC method,interval analysis theory,and increment load method,we propose a new interval design point method for the reliability of structural systems in which the distribution parameters of random variables are described as interval variables.The proposed method may provide exact probabilistic interval reliability of structures whose random variables can have either a normal or abnormal distribution form.At last,we show the feasibility of the proposed approach through a typical example.     

模糊随机参数二维声场数值计算

解决声场参数同时具有模糊性和随机性的问题,实现模糊随机声场声压响应的预测,引入了信息熵理论,利用信息熵的等效转换,将模糊随机声场转化为纯随机声场或者纯模糊声场进行求解,推导了基于摄动法的二维随机声场和模糊声场的有限元计算公式。以模糊随机参数下的二维管道声场模型和某轿车二维声腔模型为例进行了数值计算,所得结果与蒙特卡洛法(Monte Carlo Method)所预测声压变化范围基本一致,同时,转化为纯随机声场和纯模糊声场所求得声压响应变化范围也基本一致,说明了本文方法计算结果的准确性。因此本文方法能很好地应用于模糊随机参数下二维声场的预测,具有重要的工程应用价值。      

Stochastic collocation method for secondary bifurcation of a nonlinear aeroelastic system

A stochastic collocation method is proposed to investigate the secondary bifurcation of a two-dimensional aeroelastic system with structural nonlinearity represented by cubic restoring forces, and uncertainties expressed by random parameters in the cubic stiffness coefficient and in the initial pitch angle. The accuracy of the stochastic collocation method is improved by incorporating higher order schemes, such as piecewise cubic interpolation and piecewise cubic spline interpolation, instead of a piecewise linear interpolation formula. For an aeroelastic problem with the uncertainty expressed by a time dependent combination of five random variables, an efficient collocation method is developed using a sparse grid approach with a dimension adaptive strategy. Numerical simulations are carried out to demonstrate the effectiveness of the proposed method for long term computation and discontinuous problems.     

P-adic coverage method in fractal analysis of showers

Self-similarity in multiple processes at high energies is considered. It is assumed that a parton cascade transforms into a hadron shower with a fractal structure. The box counting (BC) method used to calculate the fractal dimension is analyzed. The parton shower with permissible 1/3 parts of pseudorapidity space, which corresponds to a triadic Cantor set, was used as a test fractal. It was found that there is an optimal set of bins (a parameter of the BC method) that allows one to find the fractal dimension with maximal accuracy. The optimal set of bins is shown to depend on the fractal generation law. The P-adic coverage (PaC) method is proposed and used in the fractal analysis. This method makes it possible to determine the fractal dimension of a shower as accurately as possible, the number of fractal levels and partons at each branching point during the parton shower evolution, the type of cascade (either random or regular), and its structure. It is shown to be applicable to an analysis of the regular and random N-ary cascades with permissible 1/k parts of the space studied.     

Numerical analysis of the 2D acoustic field with fuzzy-random parameters

Regard for the fuzziness and the randomness in some acoustic fields,a method for the numerical analysis of the 2D acoustic field with Fuzzy-Random parameters was proposed based on the equivalent conversion of information entropy.In the proposed method,a fuzzyrandom acoustic field was treated as a pure fuzzy acoustic field or a pure random acoustic field by transforming all the variables into fuzzy variables or random variables.Perturbation finite element methods for analyzing the two-dimensional acoustic fuzzy and random field are deduced.The sound pressure response of a 2D acoustic tube and the 2D acoustic cavity of a car with fuzzy-random parameters were analyzed by the proposed method and the Monte Carlo method,the results show that the proposed method can be well applied to the numerical analysis of the 2D acoustic field with fuzzy-random parameters,and has good prospect of engineering application.     

Adaptive fuzzy nonlinear inversion-based control for uncertain chaotic systems

<正>This paper presents a robust output feedback control method for uncertain chaotic systems,which comprises a nonlinear inversion-based controller with a fuzzy robust compensator.The proposed controller eliminates the unknown nonlinear function by using a fuzzy system,whose inputs are not the state variables but feedback error signals.The underlying stability analysis as well as parameter update law design are carried out by using the Lyapunov-based technique.The proposed method indicates that the nonlinear inversion-based control approach can also be applied to uncertain chaotic systems.Theoretical results are illustrated through two simulation examples.     

A method for predicting psychological response to meaningless random noise based on fuzzy system model

By examining the memory effect and the fuzziness of human subjective judgment, the fuzzy relation between physical meaningless random noise stimuli and the psychological response is clarified quantitatively based on bivariate membership functions. Two variables describing the sound pressure level of the random noise stimulus and the temporal change in the level are employed as the fundamental variables for the bivariate membership functions. A method for predicting the psychological response to such stimuli is proposed, introducing the concept of fuzzy probability. The validity and usefulness of the proposed method is confirmed experimentally by applying the method to observed data. The theoretical calculations are in good agreement with the experimental results.     

The extremal independence problem

Consider a finite sequence of independent-though not, necessarily, identically distributed-real-valued random scores. If the scores are absolutely continuous random variables, the sequence possesses a unique maximum (minimum). We say that “maximal (minimal) independence” holds if the value and the identity of the sequence’s unique maximal (minimal) score are independent random variables. In this research we study the class of statistics for which maximal (minimal) independence holds, and: (i) establish explicit characterizations of this class; (ii) connect this class with the class of Lévy processes; (iii) unveil the underlying spatial Poissonian structure of this class.     

一种识别关联维数无标度区间的新方法

在计算关联维数过程中, 为了减少人为因素识别无标度区间带来的误差, 提出一种基于模拟退火遗传模糊C均值聚类识别无标度区间的新方法. 该方法根据无标度区间对应曲线的二阶导数在零附近波动的变化特征, 利用分类算法进行识别. 首先对双对数关联积分的离散数据进行二阶差分; 然后利用模拟退火遗传模糊C均值聚类方法对该数据进行分类, 选出在零附近波动的数据; 再剔除粗大误差保留有效数据; 最后进行统计分析识别出线性度最好的作为无标度区间. 应用新方法对两个著名的混沌系统Lorenz 和Henon 进行了仿真, 计算结果与理论值非常符合. 实验表明, 所提出的新方法与主观识别、K-means和2-means方法比较, 可以有效自动识别无标度区间, 减少误差, 计算结果更加精确.     

High dimensional model representation method for fuzzy structural dynamics

Uncertainty propagation in multi-parameter complex structures possess significant computational challenges. This paper investigates the possibility of using the High Dimensional Model Representation (HDMR) approach when uncertain system parameters are modeled using fuzzy variables. In particular, the application of HDMR is proposed for fuzzy finite element analysis of linear dynamical systems. The HDMR expansion is an efficient formulation for high-dimensional mapping in complex systems if the higher order variable correlations are weak, thereby permitting the input-output relationship behavior to be captured by the terms of low-order. The computational effort to determine the expansion functions using the α-cut method scales polynomically with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is first illustrated for multi-parameter nonlinear mathematical test functions with fuzzy variables. The method is then integrated with a commercial finite element software (ADINA). Modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations. It is shown that using the proposed HDMR approach, the number of finite element function calls can be reduced without significantly compromising the accuracy.     

An approximate solution scheme for the algebraic random eigenvalue problem

A reduced basis formulation is presented for the efficient solution of large-scale algebraic random eigenvalue problems. This formulation aims to improve the accuracy of the first order perturbation method, and also allow the efficient computation of higher order statistical moments of the eigenparameters. In the present method, the two terms of the first order perturbation approximation for the eigenvector are used as basis vectors for Ritz analysis of the governing random eigenvalue problem. This leads to a sequence of reduced order random eigenvalue problems to be solved for each eigenmode of interest. Since, only two basis vectors are used to represent each eigenvector, explicit expressions for the random eigenvalues and eigenvectors can readily be derived. This enables the statistics of the random eigenparameters and the forced response to be efficiently computed. Numerical studies are presented for free and forced vibration analysis of a linear stochastic structural system. It is demonstrated that the reduced basis method gives better results as compared to the first order perturbation method.     

基于UMAP辅助的模糊C聚类方法进行太赫兹光谱识别

太赫兹(THz)具有低能性、瞬态性、波谱分析能力强的优点,在物质鉴别方面具有广阔的应用前景。现有的基于THz的物质鉴别方法,虽然取得了一定的效果,但是存在容易陷入局部最优的问题,从而导致识别精度不高。均匀流形逼近与投影(UMAP)作为一种非线性降维方法,其假设数据均匀分布在黎曼流形上,可以对具有模糊拓扑结构的流形进行建模。UMAP降维的过程是通过最小化两个拓扑表示之间的交叉熵,从而实现低维空间中数据表示的布局优化。传统的模糊C聚类方法(FCM)在聚类时,初始聚类中心往往随机给定,当初始聚类中心选择不恰当时,容易导致错误的聚类。为此,提出一种基于UMAP辅助的模糊C聚类算法,首先运用UMAP对输入的THz样本矩阵进行降维;再根据类与类之间距离最大化的原则,选择合适的初始聚类中心;最后利用模糊C均值聚类的方法进行聚类。所提出的方法不仅能够解决聚类过程中类与类之间过度拥挤的现象,而且能够反映出类别间的距离信息以便于给样本选择合适的初始聚类中心。为了验证提出的聚类方法的可靠性,运用太赫兹时域光谱技术对鲁棉研28、鲁棉研29、鲁棉研36、中棉28四种不同类型的转基因棉花种子进行了探测,利用基于U...     

向后迭代区间选择算法及其在近红外光谱模型转移中的应用

近红外光谱（NIR）具有快速、无损、操作方便的特点,故广泛用于食品分析。作为一种间接的分析技术,NIR需要建立光谱与待测浓度之间的统计模型来实现检测。故模型的维护有助于保证NIR的预测准确性。在外界条件发生变化的情况下,诸如样品性状的改变、仪器对理化指标函数关系的变化、湿度和温度等环境因素的改变,会导致相同样品的光谱信号发生偏移,进而使得原有模型的预测精度下降。此时,如果重新建模,虽然可以解决光谱偏移对建模的影响,但是重新建模将耗费大量的人力物力。对此,模型转移可以在避免重新建模的情况下,校正光谱的偏移,进而提高模型预测精度。通常模型转移算法多用全光谱进行模型转移,这种方法计算量较大,且不能找到合适的有化学意义的波段。故提出一种基于模型转移中的变量选择方法：向后迭代区间选择法（IIBS）,通过计算主光谱（用于建模的那组光谱）和从光谱（发生偏移,需要通过模型转移算法将其校正的光谱）中,变量区间的重要性信息（回归系数（β）、残差向量（Res）以及变量重要性投影（VIP））。进而通过计算该区间变量重要性信息的几何平均数,并以此作为该区间的区间重要性指标。接着根据区间的重要性,删除重要性信息较小的变量区间。然后对主光谱和从光谱重复迭代上述过程：计算变量的重要性信息,计算区间的重要性信息,删除重要性信息较小的区间。最后,比较不同的主光谱和从光谱区间组合的验证均方根误差（RMSEV）,选择RMSEV最小的主光谱和从光谱区间作为最优区间。玉米、小麦两套NIR数据测试了该算法。结果显示,与全波段相比,β,Res以及VIP均可以从主光谱和从光谱中选择较少的,有化学意义的区间,提高模型转移的精度。在比较不同变量重要性向量方面,基于β的变量选择算法,模型转移的计算误差较小。     

基于RF-GABPSO混合选择算法的黑土有机质含量估测研究

针对土壤有机质含量高光谱估测研究中变量维数过高与特征谱段筛选问题,提出了一种结合随机森林和自适应搜索算法的混合特征选择方法。首先依据随机森林变量重要性原理获取初始优化集,然后利用遗传二进制粒子群封装算法对初始优化集进一步自适应筛选。对于土壤有机质含量估测建模问题,选择稳健性强且能有效处理高维变量的随机森林算法。以典型黑土区采集的土壤样品为研究对象,将ASD光谱仪获取的可见光-近红外区间光谱数据和经化学分析得到的土壤有机质含量为数据源,对原始光谱进行光谱变换和重采样处理后,采用随机森林-遗传二进制粒子群混合选择方法提取特征光谱区间,构建有机质含量随机森林估测模型。与利用全光谱、随机森林方法筛选的光谱和自适应搜索算法筛选的光谱构建随机森林模型得到的预测精度进行比较。结果表明,利用随机森林-遗传二进制粒子群混合特征选择算法筛选的波谱变量参与随机森林建模,预测决定系数,均方根误差和相对分析误差分别为0.838,0.54%,2.534。该方案应用最少的变量个数获得最高的预测精度,能够较高效地估测黑土有机质含量,也能为其他类型土壤在有机质含量估测研究的变量筛选与建模问题上提供参考。     

Fractional calculus approach to the statistical characterization of random variables and vectors

Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has inverse power-law tails and, consequently, it lacks integer order moments. In this paper, starting from the Mellin transform of the characteristic function and by fractional calculus method we present a new perspective on the statistics of random variables. Introducing the class of complex moments, that include both integer and fractional moments, we show that every random variable can be represented within this approach, even if its integer moments diverge. Applications to the statistical characterization of raw data and in the representation of both random variables and vectors are provided, showing that the good numerical convergence makes the proposed approach a good and reliable tool also for practical data analysis.     

一种基于关键帧的人体行为识别方法

为了提高人体动作识别的准确率和实时性,提出了一种基于关键帧的人体行为识别新方法。用Kinect提取人体骨架信息(各关节点的3D坐标),将中心点(人体基准参考点)分别与其他各关节点作结构向量,根据空间不变性选取中心向量,计算各个结构向量和中心向量之间的夹角,并将夹角的角速度作为一种新的姿态描述特征,利用AP(Affinity Propagation)聚类算法提取关键帧,利用SVM将得到的关键帧进行动作序列的分类。在Cornell Activity Dataset-60(CAD-60)数据库实验结果表明,新方法具有良好的识别能力。     

Discontinuity detection in multivariate space for stochastic simulations

Edge detection has traditionally been associated with detecting physical space jump discontinuities in one dimension, e.g. seismic signals, and two dimensions, e.g. digital images. Hence most of the research on edge detection algorithms is restricted to these contexts. High dimension edge detection can be of significant importance, however. For instance, stochastic variants of classical differential equations not only have variables in space/time dimensions, but additional dimensions are often introduced to the problem by the nature of the random inputs. The stochastic solutions to such problems sometimes contain discontinuities in the corresponding random space and a prior knowledge of jump locations can be very helpful in increasing the accuracy of the final solution. Traditional edge detection methods typically require uniform grid point distribution. They also often involve the computation of gradients and/or Laplacians, which can become very complicated to compute as the number of dimensions increases. The polynomial annihilation edge detection method, on the other hand, is more flexible in terms of its geometric specifications and is furthermore relatively easy to apply. This paper discusses the numerical implementation of the polynomial annihilation edge detection method to high dimensional functions that arise when solving stochastic partial differential equations.     

STOCHASTIC PERTURBATION APPROACH TO ENGINEERING STRUCTURE VIBRATIONS BY THE FINITE DIFFERENCE METHOD

The main idea of the paper is to introduce the second order perturbation second probabilistic moment analysis in the context of the finite difference method (FDM) modelling of vibrations. The approach can be successfully applied in all those engineering analyses where FDM modelling of engineering structures vibrations is still useful and, at the same time, some structural parameters are random variables or fields. The general advantage of the stochastic finite difference method (SFDM) proposed is the relatively easy extension of the existing deterministic results of the classical elastodynamics on the random or stochastic case. However, similarly to stochastic boundary or finite element methods, the approach proposed has its limitations on the second order random uncertainties measures of input random variables.