A study on mechanical behavior of functionally-graded carbon nanotube-reinforced nanocomposites

In this study, we are focusing on the investigation of the effects of gradient patterns on mechanical behavior of functionally-graded carbon nanotube-reinforced nanocomposites and considering typical beams made of such nanocomposites. Both analytic and finite element-based numerical models were developed. Analytic model was developed based on the first-order shear deformation and Timoshenko beam theories meanwhile finite element models were developed using Abaqus in conjunction with user-defined subroutines for defining the continuously gradient material properties for different gradient patterns. Position-dependent elastic modulus equations for four continuously graded patterns were studied. A nongraded pattern was used for benchmarking with the same geometry and total carbon nanotube (CNT) contents. For validation and verification, the results on both deflection and stress of these nanocomposite beams were analyzed, which clearly showed high influence from gradient patterns on these mechanical behaviors of such beams.

Microstructure modeling and prediction of the mechanical properties of advanced high strength steels

Dual phase (DP) steels were modeled using 2D and 3D representative volume elements (RVE). Both the 2D and 3D models were generated using the Monte-Carlo-Potts method to represent the realistic microstructural details. In the 2D model, a balance between computational efficiency and required accuracy in truly representing heterogeneous microstructure was achieved. In the 3D model, a stochastic template was used to generate a model with high spatial fidelity. The 2D model proved to be efficient for characterization of the mechanical properties of a DP steel where the effect of phase distribution, morphology and strain partitioning was studied. In contrast, the current 3D modeling technique was inefficient and impractical due to significant time cost. It is shown that the newly proposed 2D model generation technique is versatile and sufficiently accurate to capture mechanical properties of steels with heterogeneous microstructure.

Discrete Wirtinger-based inequality and its application

In this paper, we derive a new inequality, which encompasses the discrete Jensen inequality. The new inequality is applied to analyze stability of linear discrete systems with an interval time-varying delay and a less conservative stability condition is obtained. Two numerical examples are given to show the effectiveness of the obtained stability condition.

New tools for understanding the local asymptotic power of panel unit root tests

Abstract Motivated by the previously documented discrepancy between actual and predicted power, the present paper provides new tools for analyzing the local asymptotic power of panel unit root tests. These tools are appropriate in general when considering panel data with a dominant autoregressive root of the form ^ρi=1+^ciN-^κT-^τ, where i=1,...,N indexes the cross-sectional units, T is the number of time periods and ^ci is a random local-to-unity parameter. A limit theory for the sample moments of such panel data is developed and is shown to involve infinite-order series expansions in the moments of ^ci, in which existing theories can be seen as mere first-order approximations. The new theory is applied to study the asymptotic local power functions of some known test statistics for a unit root. These functions can be expressed in terms of the expansions in the moments of ^ci, and include existing local power functions as special cases. Monte Carlo evidence is provided to suggest that the new results go a long way toward bridging the gap between actual and predicted power.

Cross-sectional averages versus principal components

In spite of the increased use of factor-augmented regressions in recent years, little is known regarding the relative merits of the two main approaches to estimation and inference, namely, the cross-sectional average and principal component estimators. By providing a formal comparison of the approaches, the current paper fills this gap in the literature.

Nonparametric rank tests for non-stationary panels

We develop a set of nonparametric rank tests for non-stationary panels based on multivariate variance ratios which use untruncated kernels. As such, the tests do not require the choice of tuning parameters associated with bandwidth or lag length and also do not require choices with respect to numbers of common factors. The tests allow for unrestricted cross-sectional dependence and dynamic heterogeneity among the units of the panel, provided simply that a joint functional central limit theorem holds for the panel of differenced series. We provide a discussion of the relationships between our setting and the settings for which first- and second generation panel unit root tests are designed. In Monte Carlo simulations we illustrate the small-sample performance of our tests when they are used as panel unit root tests under the more restrictive DGPs for which panel unit root tests are typically designed, and for more general DGPs we also compare the small-sample performance of our nonparametric tests to parametric rank tests. Finally, we provide an empirical illustration by testing for income convergence among countries.

The effect of recursive detrending on panel unit root tests

This paper analyzes the properties of panel unit root tests based on recursively detrended data. The analysis is conducted while allowing for a (potentially) non-linear trend function, which represents a more general consideration than the current state of affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial trend and iid errors are shown to be surprisingly simple. Indeed, the test statistic is not only asymptotically independent of the true trend polynomial, but also is in fact unique in that it is independent also of the degree of the fitted polynomial. However, this invariance property does not carry over to the local alternative, under which it is shown that local power is a decreasing function of the trend degree. But while power does decrease, the rate of shrinking of the local alternative is generally constant in the trend degree, which goes against the common belief that the rate of shrinking should be decreasing in the trend degree. The above results are based on simplifying assumptions. To compensate for this lack of generality, a second, robust, test statistic is proposed, whose validity does not require that the trend function is a polynomial or that the errors are iid.

The power of PANIC

The current paper considers the asymptotic local power of second-generation panel unit root tests that are robust to the presence of cross-section dependence in the form of common factors. As a basis for our analysis, we take the PANIC approach of Bai and Ng (2004, 2010), which is one of the single most popular and general second-generation approaches around.

New improved tests for cointegration with structural breaks

This article proposes Lagrange multiplier-based tests for the null hypothesis of no cointegration. The tests are general enough to allow for heteroskedastic and serially correlated errors, deterministic trends, and a structural break of unknown timing in both the intercept and slope. The limiting distributions of the test statistics are derived, and are found to be invariant not only with respect to the trend and structural break, but also with respect to the regressors. A small Monte Carlo study is also conducted to investigate the small-sample properties of the tests. The results reveal that the tests have small size distortions and good power relative to other tests. © 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

New simple tests for panel cointegration

In this paper, two new simple residual-based panel data tests are proposed for the null of no cointegration. The tests are simple because they do not require any correction for the temporal dependencies of the data. Yet they are able to accommodate individual specific short-run dynamics, individual specific intercept and trend terms, and individual specific slope parameters. The limiting distributions of the tests are derived and are shown to be free of nuisance parameters. The Monte Carlo results in this paper suggest that the asymptotic results are borne out well even in very small samples. Copyright © Taylor & Francis, Inc.

Partial state estimation of LTI systems with multiple constant time-delays

Functional observer design for Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 - delay-dependent, and 2 - internal-delay independent. The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of Linear Matrix Inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen's inequality, and improved Park's inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.

Mathematical modelling of linear motion error for Hexarot parallel manipulators

Hexarot is a robotic manipulator that belongs to the family of axis symmetric parallel mechanisms. The robot is able to move the robot platform or tool center point in six degrees of freedom (DOF). This paper presents the kinematics model of the robot including the inverse and forward kinematics, and its time derivatives. Then using the kinematics formulations, investigation of the nonlinear motion of the Hexarot robot for a desired linear motion path is performed. For this purpose, the concept of curvature of the robot path is used for measuring the nonlinearity of the actual motion of the robot. The nonlinear motion error of the robot is analyzed for the scenario where the platform moves on a linear path between two arbitrary points of the robot workspace. The effects of different parameters on the nonlinear motion error of the mechanism are demonstrated and strategies for motions with low error values are proposed.

An LMI-based functional estimation scheme of large-scale time-delay systems with strong interconnections

In this paper, the problem of distributed functional state observer design for a class of large-scale interconnected systems in the presence of heterogeneous time-varying delays in the interconnections and the local state vectors is considered. The resulting observer scheme is suitable for strongly coupled subsystems with multiple time-varying delays, and is shown to give better results for systems with very strong interconnections while only some mild existence conditions are imposed. A set of existence conditions are derived along with a computationally simple observer constructive procedure. Based on the Lyapunov-Krasovskii functional method (LKF) in the framework of linear matrix inequalities (LMIs), delay-dependent conditions are derived to obtain the observer parameters ensuring the exponential convergence of the observer error dynamics. The effectiveness of the obtained results is illustrated and tested through a numerical example of a three-area interconnected system.

Minimal-order functional observer-based residual generators for fault detection and isolation of dynamical systems

This paper examines the design of minimal-order residual generators for the purpose of detecting and isolating actuator and/or component faults in dynamical systems. We first derive existence conditions and design residual generators using only first-order observers to detect and identify the faults. When the first-order functional observers do not exist, then based on a parametric approach to the solution of a generalized Sylvester matrix equation, we develop systematic procedures for designing residual generators utilizing minimal-order functional observers. Our design approach gives lower-order residual generators than existing results in the literature. The advantages for having such lower-order residual generators are obvious from the economical and practical points of view as cost saving and simplicity in implementation can be achieved, particularly when dealing with high-order complex systems. Numerical examples are given to illustrate the proposed fault detection and isolation schemes. In all of the numerical examples, we design minimum-order residual generators to effectively detect and isolate actuator and/or component faults in the system.

A common functional observer scheme for three systems with unknown inputs

This paper presents a novel common functional observer scheme for three systems with unknown inputs. The scheme uses three observers in cascade with two logic switches. The existence conditions of the scheme are investigated and presented in terms of the original system matrices. Significantly, the conditions allow the observers to be designed independently of each other which greatly simplify the design process, and also serve as a basis of comparison for future development of common functional observer schemes. A numerical example is given to illustrate the effectiveness of the proposed scheme.