纤维增强复合材料裂纹动态起始行为的研究

本论文主要研究线弹性纤维增强复合材料在冲击载荷作用下裂纹的动态起裂行为。全文共分六章。第一章对裂纹动态起始问题的研究方法和纤维增强复合材料中裂纹动态起始问题的国内外研究现状进行了综述，确定了本论文的主要研究内容和研究方法。第二章用有限元方法研究有限尺度含裂纹纤维增强复合材料板在阶跃冲击载荷作用下的动力响应，分析了裂尖附近的应力分布、应力波在板中的传播和应力强度因子时间历程。第三章根据第二章的计算结果用线弹性简单梁理论和拉格朗日运动方程研究了各向同性材料和纤维增强复合材料中裂纹在阶跃冲击载荷作用下的动力响应和起裂行为，得到了应力强度因子初始上升阶段的数学表达式和裂纹起裂的临界载荷面。第四章提出了用于单向和层合纤维增强复合材料裂纹静态和动态起始预测的拟应力强度因子比准则。该准则将裂纹的起裂和起裂方向的预测合二为一，只需测定材料的四个基本动态断裂韧性，就可据此准则对任意角度单向板中裂纹的起裂和起裂方向进行预测，用于层合板时，还可以对铺层裂纹的起裂顺序进行预测。第五章用SHTB（分离式Hopkinson拉杆）技术对纤维增强复合材料裂纹动态起始问题进行了实验研究。测量了碳纤维增强环氧树脂复合材料板裂纹起裂的I型动态断裂韧性，并首次验证了拟应力强度因子比准则在裂纹动态起裂预测中的合理性。第六章对全文进行了总结，归纳了本论文的主要结论，并展望了今后的研究工作。

Classifier selection using sequential error ratio criterion for multi-instance and multi-sample fusion

Classifier selection is a problem encountered by multi-biometric systems that aim to improve performance through fusion of decisions. A particular decision fusion architecture that combines multiple instances (n classifiers) and multiple samples (m attempts at each classifier) has been proposed in previous work to achieve controlled trade-off between false alarms and false rejects. Although analysis on text-dependent speaker verification has demonstrated better performance for fusion of decisions with favourable dependence compared to statistically independent decisions, the performance is not always optimal. Given a pool of instances, best performance with this architecture is obtained for certain combination of instances. Heuristic rules and diversity measures have been commonly used for classifier selection but it is shown that optimal performance is achieved for the `best combination performance' rule. As the search complexity for this rule increases exponentially with the addition of classifiers, a measure - the sequential error ratio (SER) - is proposed in this work that is specifically adapted to the characteristics of sequential fusion architecture. The proposed measure can be used to select a classifier that is most likely to produce a correct decision at each stage. Error rates for fusion of text-dependent HMM based speaker models using SER are compared with other classifier selection methodologies. SER is shown to achieve near optimal performance for sequential fusion of multiple instances with or without the use of multiple samples. The methodology applies to multiple speech utterances for telephone or internet based access control and to other systems such as multiple finger print and multiple handwriting sample based identity verification systems.

Channel estimation relying on the minimum bit-error-ratio criterion for BPSK and QPSK signals

The authors consider the channel estimation problem in the context of a linear equaliser designed for a frequency selective channel, which relies on the minimum bit-error-ratio (MBER) optimisation framework. Previous literature has shown that the MBER-based signal detection may outperform its minimum-mean-square-error (MMSE) counterpart in the bit-error-ratio performance sense. In this study, they develop a framework for channel estimation by first discretising the parameter space and then posing it as a detection problem. Explicitly, the MBER cost function (CF) is derived and its performance studied, when transmitting binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) signals. It is demonstrated that the MBER based CF aided scheme is capable of outperforming existing MMSE, least square-based solutions.

Strain-energy density ratio criterion for failure of composite-materials

n the authors' previous paper, the Strain Energy Density Ratio (SEDR) criterion was proposed. As an example of applications, it was used to predict cracking direction of mixed-mode fracture in a random short fibre laminated composite.

Modeling strategies in longitudinal data analysis: Covariate, variance function and correlation structure selection

A modeling paradigm is proposed for covariate, variance and working correlation structure selection for longitudinal data analysis. Appropriate selection of covariates is pertinent to correct variance modeling and selecting the appropriate covariates and variance function is vital to correlation structure selection. This leads to a stepwise model selection procedure that deploys a combination of different model selection criteria. Although these criteria find a common theoretical root based on approximating the Kullback-Leibler distance, they are designed to address different aspects of model selection and have different merits and limitations. For example, the extended quasi-likelihood information criterion (EQIC) with a covariance penalty performs well for covariate selection even when the working variance function is misspecified, but EQIC contains little information on correlation structures. The proposed model selection strategies are outlined and a Monte Carlo assessment of their finite sample properties is reported. Two longitudinal studies are used for illustration.

Criteria for working-correlation-structure selection in GEE: Assessment via simulation

Efficiency of analysis using generalized estimation equations is enhanced when intracluster correlation structure is accurately modeled. We compare two existing criteria (a quasi-likelihood information criterion, and the Rotnitzky-Jewell criterion) to identify the true correlation structure via simulations with Gaussian or binomial response, covariates varying at cluster or observation level, and exchangeable or AR(l) intracluster correlation structure. Rotnitzky and Jewell's approach performs better when the true intracluster correlation structure is exchangeable, while the quasi-likelihood criteria performs better for an AR(l) structure.

On the stability of a nonlinear system with periodic coefficients

A quasi-geometric stability criterion for feedback systems with a linear time invariant forward block and a periodically time varying nonlinear gain in the feedback loop is developed.

纤维复合材料复合型断裂正应力强度因子比准则

对纤维增强复合材料的裂纹起裂及开裂方向准则进行了研究，提出了复合型断裂的正应力强度因子比准则（Normal Stress Intensity Factor Raito Criterion).此准则是一种综合考虑了正应力强度因子和剪应力强度因子对裂纹起裂的推动的准则，并且不需要预先确定材料的特征尺度，使用较方便，且预测结果是很好的。

复合材料的比应变能密度破坏准则

<正> 在文献中,提出了一个预测复合材料中裂纹扩展方向的比应变能密度准则(Strain energy density ratio criterion)。用一个短纤维复合材料层合板中Ⅰ-Ⅱ型复合型裂纹扩展方向的预测为例子与实验结果进行了对比。结果表明,该准则对预测复合材料中裂纹扩展方向是成功的。那么,这个准则可否用来预测复合材料的破坏强度呢,本文将研究这个问题。

Two-Stage Orthogonal Least Squares Methods for Neural Network Construction

A number of neural networks can be formulated as the linear-in-the-parameters models. Training such networks can be transformed to a model selection problem where a compact model is selected from all the candidates using subset selection algorithms. Forward selection methods are popular fast subset selection approaches. However, they may only produce suboptimal models and can be trapped into a local minimum. More recently, a two-stage fast recursive algorithm (TSFRA) combining forward selection and backward model refinement has been proposed to improve the compactness and generalization performance of the model. This paper proposes unified two-stage orthogonal least squares methods instead of the fast recursive-based methods. In contrast to the TSFRA, this paper derives a new simplified relationship between the forward and the backward stages to avoid repetitive computations using the inherent orthogonal properties of the least squares methods. Furthermore, a new term exchanging scheme for backward model refinement is introduced to reduce computational demand. Finally, given the error reduction ratio criterion, effective and efficient forward and backward subset selection procedures are proposed. Extensive examples are presented to demonstrate the improved model compactness constructed by the proposed technique in comparison with some popular methods.

Coalescence of particles by differential sedimentation

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel. We obtain self-similar steady-state and time-dependent solutions to the kinetic equation, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.

Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors

This paper considers two-sided tests for the parameter of an endogenous variable in an instrumental variable (IV) model with heteroskedastic and autocorrelated errors. We develop the nite-sample theory of weighted-average power (WAP) tests with normal errors and a known long-run variance. We introduce two weights which are invariant to orthogonal transformations of the instruments; e.g., changing the order in which the instruments appear. While tests using the MM1 weight can be severely biased, optimal tests based on the MM2 weight are naturally two-sided when errors are homoskedastic. We propose two boundary conditions that yield two-sided tests whether errors are homoskedastic or not. The locally unbiased (LU) condition is related to the power around the null hypothesis and is a weaker requirement than unbiasedness. The strongly unbiased (SU) condition is more restrictive than LU, but the associated WAP tests are easier to implement. Several tests are SU in nite samples or asymptotically, including tests robust to weak IV (such as the Anderson-Rubin, score, conditional quasi-likelihood ratio, and I. Andrews' (2015) PI-CLC tests) and two-sided tests which are optimal when the sample size is large and instruments are strong. We refer to the WAP-SU tests based on our weights as MM1-SU and MM2-SU tests. Dropping the restrictive assumptions of normality and known variance, the theory is shown to remain valid at the cost of asymptotic approximations. The MM2-SU test is optimal under the strong IV asymptotics, and outperforms other existing tests under the weak IV asymptotics.

A note on the local power of the LR, Wald, score and gradient tests

This paper examines the local power of the likelihood ratio, Wald, score and gradient tests under the presence of a scalar parameter, phi say, that is orthogonal to the remaining parameters. We show that some of the coefficients that define the local powers remain unchanged regardless of whether phi is known or needs to be estimated, where as the others can be written as the sum of two terms, the first of which being the corresponding term obtained as if phi were known, and the second, an additional term yielded by the fact that phi is unknown. The contribution of each set of parameters on the local powers of the tests can then be examined. Various implications of our main result are stated and discussed. Several examples are presented for illustrative purposes

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n(-1/2), n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.