A time-varying identification method for mixed response measurements

The proper orthogonal decomposition is a method that may be applied to linear and nonlinear structures for extracting important information from a measured structural response. This method is often applied for model reduction of linear and nonlinear systems and has been applied recently for time-varying system identification. Although methods have previously been developed to identify time-varying models for simple linear and nonlinear structures using the proper orthogonal decomposition of a measured structural response, the application of these methods has been limited to cases where the excitation is either an initial condition or an applied load but not a combination of the two. This paper presents a method for combining previously published proper orthogonal decomposition-based identification techniques for strictly free or strictly forced systems to identify predictive models for a system when only mixed response data are available, i.e. response data resulting from initial conditions and loads that are applied together. This method extends the applicability of the previous proper orthogonal decomposition-based identification techniques to operational data acquired outside of a controlled laboratory setting. The method is applied to response data generated by finite element models of simple linear time-invariant, time-varying, and nonlinear beams and the strengths and weaknesses of the method are discussed.     

基于GLS模型的光照鲁棒性人脸的识别

针对线性子空间模型在处理具有阴影的人脸图像时出现的不足之处,提出了GLS模型,并将其用于不同光照下的人脸识别。按照测试图像与正确模型间距离尽可能小的原则构造了一个确定最优分组数和子空间维数的标准;采用SVD方法和K平均聚类法将像素分组,并确定每个分组的线性子空间模型;计算测试图像到每个GLS模型中所有分组的线性子空间模型的距离之和,进而识别人脸图像。经假设检验统计表明,基于该模型的方法在处理不同光照下的人脸图像时,效果明显优于其他方法。     

Critical statics of elastic phase transitions

The critical behaviour of elastic phase transitions of second order, where the order parameter is a strain component and the soft mode is an acoustic mode, is studied by the RNG method. A classification of the different types of elastic phase transitions in three-dimensional crystals is given and two general models are introduced for these transitions which are suitable for an investigation by the RNG method. Critical exponents of thesed-dimensional models with anm-dimensional subspace of soft directions are calculated by the-expansion as a function ofd andm. The critical dimensionality is shifted to lower values in comparison to spin models. In systems where softening occurs only in a one-dimensional subspace the critical behaviour is classical in three dimensions, for those where softening occurs in a two-dimensional subspace logarithmic corrections to the classical behaviour are found.Work supported by the Fonds zur Förderung der wissenschaftlichen ForschungA short account of the present work was reported (by F.S.) at the MECO-Seminar of Phase Transitions, 1976, University of Ljubljana, Yugoslavia     

Multisubject activation detection in fMRI by testing correlation of data with a signal subspace

In this article, a generalized likelihood ratio test is proposed to assess the correlation between multisubject functional MRI (fMRI) time series and bases of a signal subspace for detecting the existence of group activation in each voxel of the brain. The signal subspace is generated by a design matrix using the time series of the desired effects. The proposed method leads to testing the product of eigenvalues of a specific matrix. The eigenvector corresponding to the largest eigenvalue is the weighting vector for the linear combination of time series of various subjects that has the maximum correlation with the signal subspace. In another method, namely, canonical correlation analysis, the largest eigenvalue of the above matrix is tested for activation detection. Surrogate data on resting state (no activation) are generated by randomization and used to estimate the statistical distribution of these parameters under the null hypothesis condition. A postprocessing step is applied to prevent false detection of voxels that are not sufficiently active (among subjects) by defining a minimum ratio for the active population. The proposed methods are applied on simulated and experimental fMRI data, and the results are compared with those of the general linear model (GLM; using the SPM and FMRISTAT toolboxes). The proposed methods showed higher detection sensitivity as compared with the GLM for activation detection in simulated data. Similarly, they detected more activated regions than did the GLM from multisubject experimental fMRI data on a visual (sensorimotor) event-related task.     

H基于模糊观测器参数摄动的耦合时空混沌H跟踪控制

由于子系统的时空耦合作用及参数的摄动性，实现参数摄动的耦合时空混沌的跟踪控制非常困难。然而模型未知的耦合时空混沌的每个子系统可由一系列模糊逻辑模型逼近，每个模糊逻辑模型代表子系统在特定运行点的局部线性化模型，同时考虑子系统状态的不可测性，采用模糊观测器来估计子系统的状态。基于模糊模型及状态观测器，计及混沌参数的摄动性，提出一种模糊跟踪控制方案，实现了参数摄动的耦合时空混沌的鲁棒跟踪控制，并将模糊跟踪控制表征为线性矩阵不等式问题，用线性矩阵不等式的凸优化方法求解控制器参数，确保系统的全局渐近稳定性。仿真验证了方案的有效性。     

Ensemble Linear Subspace Analysis of High-Dimensional Data

Regression models provide prediction frameworks for multivariate mutual information analysis that uses information concepts when choosing covariates (also called features) that are important for analysis and prediction. We consider a high dimensional regression framework where the number of covariates (p) exceed the sample size (n). Recent work in high dimensional regression analysis has embraced an ensemble subspace approach that consists of selecting random subsets of covariates with fewer than p covariates, doing statistical analysis on each subset, and then merging the results from the subsets. We examine conditions under which penalty methods such as Lasso perform better when used in the ensemble approach by computing mean squared prediction errors for simulations and a real data example. Linear models with both random and fixed designs are considered. We examine two versions of penalty methods: one where the tuning parameter is selected by cross-validation; and one where the final predictor is a trimmed average of individual predictors corresponding to the members of a set of fixed tuning parameters. We find that the ensemble approach improves on penalty methods for several important real data and model scenarios. The improvement occurs when covariates are strongly associated with the response, when the complexity of the model is high. In such cases, the trimmed average version of ensemble Lasso is often the best predictor.     

基于子空间分析的人脸识别方法研究

人脸识别技术是模式识别和机器视觉领域的一个重要研究方向,在众多人脸识别的算法中,基于子空间分析的特征提取方法以其稳定可靠的识别效果成为了人脸识别中特征提取的主流方法之一。本文对目前应用较多的子空间分析方法进行了研究,具体介绍了线性子空间分析方法：主成分分析（PCA）、线性鉴别分析（LDA）、独立主成分分析（ICA）、快速主成分分析（FastICA）等及非线性子空间分析方法：基于核的PCA （KPCA）等的基本思想及其在人脸识别中的研究进展,包括一些新的研究成果。此外,还应用orl及Yale B人脸库对几个基础的子空间方法进行了验证实验。实验结果表明,在几个子空间分析方法中,FastICA算法取得了最高的识别率。最后结合实验结果对各算法的优缺点进行了分析总结。     

A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics

In structural dynamics, a predictive model is constructed by developing a mathematical-mechanical model of a designed system in order to predict the response of the real system which is the manufactured system realized from the designed system. The mathematical-mechanical modelling process of the designed system introduces two fundamental types of uncertainties: the data uncertainties and the model uncertainties. Uncertainties have to be taken into account for improving the predictability of the model. Model uncertainties cannot be modelled by using the usual parametric probabilistic approach. Recently, a general non-parametric probabilistic approach of model uncertainties for dynamical systems has been proposed using the random matrix theory. This paper gives a comprehensive overview of this approach in developing its foundations in simple terms and in illustrating all the concepts and the tools introduced in the general theory, by using a simple example. This paper deals with (1) notions of designed systems, real systems, mean models as predictive models, errors and uncertainties; (2) the definition of a simple example in linear elastodynamics; (3) a comprehensive overview of the non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics; (4) a summary of the random matrix ensembles which are necessary for the non-parametric modelling of random uncertainties; (5) the estimation of the dispersion parameters of the non-parametric probabilistic model using experimental data; (6) the method to solve the stochastic equation of the dynamical system with non-parametric probabilistic model of random uncertainties; (7) a numerical simulation and the validation for the simple example.     

The role of sensitivity and uncertainty analysis in combustion modelling

Models play an important role in improving our understanding of combustion processes and more and more are able to assist in the design of advanced energy conversion devices. Due to constant improvements in computing power and techniques such as automatic kinetic mechanism generation, we have the ability to represent combustion processes with increasing levels of detail. This is particularly true for kinetic processes where complex mechanisms are being developed which describe the oxidation of both conventional and alternative fuels. These mechanisms may comprise of up to hundreds of species and thousands of reactions with thermo-kinetic data derived from a wide variety of sources including direct measurements, global combustion experiments, and theoretical calculations. However, significant uncertainties in the data used to parametrise combustion models still exist. These input uncertainties propagate through models of combustion devices leading to uncertainties in the prediction of key combustion properties. In order to improve confidence in these models to the extent where they can successfully be used in design, input uncertainties need to be reduced as far as possible. This requires focussing efforts on those parameters which drive predictive uncertainty, which may be identified through sensitivity analysis. The paper will describe the methodologies available for the sensitivity and uncertainty analysis of combustion models with examples focussed on chemical kinetics. It will then discuss how such techniques can be incorporated into strategies for model improvement and will try to provide some future perspectives on how we can proceed in this direction as a research community.     

A signal subspace dimension estimator based on F-norm with application to subspace-based multi-channel speech enhancement

Although the signal subspace approach has been studied extensively for speech enhancement,no good solution has been found to identify signal subspace dimension in multichannel situation.This paper presents a signal subspace dimension estimator based on F-norm of correlation matrix,with which subspace-based multi-channel speech enhancement is robust to adverse acoustic environments such as room reverberation and low input signal to noise ratio (SNR).Experiments demonstrate the presented method leads to more noise reduction and less speech distortion comparing with traditional methods.     

Bilinear modal representations for reduced-order modeling of localized piecewise-linear oscillators

A novel reduced-order modeling method for vibration problems of elastic structures with localized piecewise-linearity is proposed. The focus is placed upon solving nonlinear forced response problems of elastic media with contact nonlinearity, such as cracked structures and delaminated plates. The modeling framework is based on observations of the proper orthogonal modes computed from nonlinear forced responses and their approximation by a truncated set of linear normal modes with special boundary conditions. First, it is shown that a set of proper orthogonal modes can form a good basis for constructing a reduced-order model that can well capture the nonlinear normal modes. Next, it is shown that the subspace spanned by the set of dominant proper orthogonal modes can be well approximated by a slightly larger set of linear normal modes with special boundary conditions. These linear modes are referred to as bi-linear modes, and are selected by an elaborate methodology which utilizes certain similarities between the bi-linear modes and approximations for the dominant proper orthogonal modes. These approximations are obtained using interpolated proper orthogonal modes of smaller dimensional models. The proposed method is compared with traditional reduced-order modeling methods such as component mode synthesis, and its advantages are discussed. Forced response analyses of cracked structures and delaminated plates are provided for demonstrating the accuracy and efficiency of the proposed methodology.     

不确定海洋环境中的模态子空间重构稳健定位方法

实际的海洋是一个不确定的声传播环境,常规的匹配场方法在进行目标定位时会遇到环境失配的问题,导致定位性能下降.在不确定的海洋环境中,声场传播中的一部分简正波模态受到声场不确定性的影响较小.基于此,本文提出了一种模态子空间重构的稳健定位方法.该方法使用稳定的模态来重构拷贝场向量,相比于常规匹配场定位方法中使用全阶模态来构造拷贝场向量,其定位结果更加稳健.利用计算机仿真数据和海试数据进行了定位性能分析,并给出了常规匹配场定位方法和稳健最大似然定位方法作为对比.研究结果表明:1)不确定海洋环境中,常规匹配场定位方法即使在较高的信噪比条件下其定位性能也较差.2)模态子空间重构定位方法的性能优于常规匹配场定位方法和稳健最大似然方法.     

Evaluation of a liquid ionization chamber for relative dosimetry in small and large fields of radiotherapy photon beams

Commissioning and quality assurance of radiotherapy linear accelerators require measurement of the absorbed dose to water, and a wide range of detectors are available for absolute and relative dosimetry in megavoltage beams.In this paper, the PTW microLion isooctane-filled ionization chamber has been tested to perform relative measurements in a 6 MV photon beam from a linear accelerator. Output factors, percent depth dose and dose profiles have been obtained for small and large fields. These quantities have been compared with those from usual detectors in the routine practice. In order to carry out a more realistic comparison, an uncertainty analysis has been developed, taking type A and B uncertainties into account.The results present microLion as a good option when high spatial resolution is needed, thanks to its reduced sensitive volume. The liquid filling also provides a high signal compared to other detectors, like that based on air filling. Furthermore, the relative response of microLion when field size is varied suggests that this detector has energy dependence, since it is appreciated an over-response for small fields and an under-response for the large ones. This effect is more obvious for field sizes wider than 20 × 20 cm², where the differences in percent depth dose at great depths exceed the uncertainties estimated in this study.     

Discriminant Analysis under f-Divergence Measures

In statistical inference, the information-theoretic performance limits can often be expressed in terms of a statistical divergence between the underlying statistical models (e.g., in binary hypothesis testing, the error probability is related to the total variation distance between the statistical models). As the data dimension grows, computing the statistics involved in decision-making and the attendant performance limits (divergence measures) face complexity and stability challenges. Dimensionality reduction addresses these challenges at the expense of compromising the performance (the divergence reduces by the data-processing inequality). This paper considers linear dimensionality reduction such that the divergence between the models is maximally preserved. Specifically, this paper focuses on Gaussian models where we investigate discriminant analysis under five f-divergence measures (Kullback–Leibler, symmetrized Kullback–Leibler, Hellinger, total variation, and χ2). We characterize the optimal design of the linear transformation of the data onto a lower-dimensional subspace for zero-mean Gaussian models and employ numerical algorithms to find the design for general Gaussian models with non-zero means. There are two key observations for zero-mean Gaussian models. First, projections are not necessarily along the largest modes of the covariance matrix of the data, and, in some situations, they can even be along the smallest modes. Secondly, under specific regimes, the optimal design of subspace projection is identical under all the f-divergence measures considered, rendering a degree of universality to the design, independent of the inference problem of interest.     

A signal subspace approach for modeling the hemodynamic response function in fMRI

Many fMRI analysis methods use a model for the hemodynamic response function (HRF). Common models of the HRF, such as the Gaussian or Gamma functions, have parameters that are usually selected a priori by the data analyst. A new method is presented that characterizes the HRF over a wide range of parameters via three basis signals derived using principal component analysis (PCA). Covering the HRF variability, these three basis signals together with the stimulation pattern define signal subspaces which are applicable to both linear and nonlinear modeling and identification of the HRF and for various activation detection strategies. Analysis of simulated fMRI data using the proposed signal subspace showed increased detection sensitivity compared to the case of using a previously proposed trigonometric subspace. The methodology was also applied to activation detection in both event-related and block design experimental fMRI data using both linear and nonlinear modeling of the HRF. The activated regions were consistent with previous studies, indicating the ability of the proposed approach in detecting brain activation without a priori assumptions about the shape parameters of the HRF. The utility of the proposed basis functions in identifying the HRF is demonstrated by estimating the HRF in different activated regions.     

Robust H_∞ control for uncertain systems with heterogeneous time-varying delays via static output feedback

This paper is concerned with the problem of robust H∞ control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties.The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ performance level for all admissible uncertainties.By constructing an appropriate Lyapunov-Krasvskii functional,a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality.From the derived criterion,the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically.A simulation example is given to illustrate the effectiveness of the proposed design method.     

地球外核热对流运动的区域分解多重网格并行数值模拟

旋转球层中热对流运动的数值模拟是地球发电机模型的重要组成部分,对研究地球发电机作用机理具有重要意义.本文设计一个基于国产超级计算平台并行性能良好的地球外核热对流运动并行数值模型.时间积分方案采用与Crank-Nicolson格式和二阶Adams-Bashford公式相结合的近似分解分步法,空间离散基于立方球网格的二阶精度有限体积格式.所得到的两个大规模稀疏线性代数方程组采用带预处理的Krylov子空间迭代法进行求解.为加速迭代求解过程及提高并行性能,迭代过程采用区域分解多重网格的多层限制型加法Schwarz预处理子,减少了求解程序的计算时间,提高了数值模型的并行性能,模型被很好地扩展到上万处理器核数.数值模拟结果与基准模型算例0的参考值吻合得很好.