An important property of brain signals is their nonstationarity. How to adapt a brain-computer interface (BCI) to the changing brain states is one of the challenges faced by BCI researchers, especially in real application where the subject's real intent is unknown to the system. Gaussian mixture model (GMM) has been used for the unsupervised adaptation of the classifier in BCI. In this paper, a method of initializing the model parameters is proposed for expectation maximization-based GMM parameter estimation. This improved GMM method and other two existing unsupervised adaptation methods are applied to groups of constructed artificial data with different data properties. Performances of these methods in different situations are analyzed. Compared with the other two unsupervised adaptation methods, this method shows a better ability of adapting to changes and discovering class information from unlabelled data. The methods are also applied to real EEG data recorded in 19 experiments. For real data, the proposed method achieves an error rate significantly lower than the other two unsupervised methods. Results of the real data agree with the analysis based on the artificial data, which confirms not only the effectiveness of our method but also the validity of the constructed data. Copyright © 2009 John Wiley & Sons, Ltd.
martes, 1 de diciembre de 2009
Improved GMM with parameter initialization for unsupervised adaptation of Brain-Computer interface
An important property of brain signals is their nonstationarity. How to adapt a brain-computer interface (BCI) to the changing brain states is one of the challenges faced by BCI researchers, especially in real application where the subject's real intent is unknown to the system. Gaussian mixture model (GMM) has been used for the unsupervised adaptation of the classifier in BCI. In this paper, a method of initializing the model parameters is proposed for expectation maximization-based GMM parameter estimation. This improved GMM method and other two existing unsupervised adaptation methods are applied to groups of constructed artificial data with different data properties. Performances of these methods in different situations are analyzed. Compared with the other two unsupervised adaptation methods, this method shows a better ability of adapting to changes and discovering class information from unlabelled data. The methods are also applied to real EEG data recorded in 19 experiments. For real data, the proposed method achieves an error rate significantly lower than the other two unsupervised methods. Results of the real data agree with the analysis based on the artificial data, which confirms not only the effectiveness of our method but also the validity of the constructed data. Copyright © 2009 John Wiley & Sons, Ltd.
Identification of damage parameters for discontinuous rock mass
This paper presents an identification method for a discontinuous rock mass employing damage mechanics theory and wavelet analysis. Parameter identification methods based on deterministic approaches are classified into inverse and direct approaches. The proposed method combines the inverse approach and the direct approach and by applying the discrete wavelet transform to the system matrix of the iteration equation, we estimate unknown damage tensors for the case in which the number of unknown parameters exceeds the observed data. The validity of this method is examined for geotechnical engineering problems. Copyright © 2009 John Wiley & Sons, Ltd.
Integral estimation with the ordinary Kriging method using the Gaussian semivariogram function
This paper describes a detailed procedure for integral estimation of an unknown function using the ordinary Kriging method. This method estimates the definite integral of an approximated surface generated using the ordinary Kriging method. The integral of an approximated surface can be computed directly using a set of sampling data for a function value. One of the merits of the proposed method is that the integral can be estimated without iterative summation generally used in a conventional numerical integration technique. In addition to a continuous function, the proposed method enables to estimate the integral using a set of discrete sampling data.In this paper, a basic formulation for an integral estimation using the Kriging method, especially with the Gaussian-type semivariogram model, is introduced. An explicit form of the integral of the Gaussian function is approximated by Williams' method.As test problems, definite integrals of some elementary functions are estimated using the proposed method. In addition, as an engineering example, a flow in a pipe is estimated using the proposed method with less samples of the velocity of fluid. The numerical results illustrate the accuracy and efficiency of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.
High-order finite difference schemes for the solution of the generalized Burgers-Fisher equation
Up to tenth-order finite difference (FD) schemes are proposed in this paper to solve the generalized Burgers-Fisher equation. The schemes based on high-order differences are presented using Taylor series expansion. To obtain the solutions, up to tenth-order FD schemes in space and fourth-order Runge-Kutta scheme in time have been combined. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of the present methods. The produced results are also seen to be more accurate than some available results given in the literature. Comparisons showed that there is very good agreement between the numerical solutions and the exact solutions in terms of accuracy. The present methods are seen to be very good alternatives to some existing techniques for such realistic problems. Copyright © 2009 John Wiley & Sons, Ltd.
A constrained non-linear system approach for the solution of an extended limit analysis problem
A number of recent papers (see, e.g. (Int. J. Mech. Sci. 2007; 49:454-465; Eur. J. Mech. A/Solids 2008; 27:859-881; Eng. Struct. 2008; 30:664-674; Int. J. Mech. Sci. 2009; 51:179-191)) have shown that classical limit analysis can be extended to incorporate such important features as geometric non-linearity, softening and various so-called ductility constraints. The generic formulation takes the form of a challenging (nonconvex and nonsmooth) optimization problem referred to in the mathematical programming literature as a mathematical program with equilibrium constraints (MPEC). Similar to a classical limit analysis, the aim is to compute in a single step a bound (upper bound, in the case of the extended problem) to the maximum load. The solution algorithm so far proposed to solve the MPEC is to convert it into an iterative non-linear programming problem and attempts to process this using a standard non-linear optimizer. Motivated by the fact that no method is guaranteed to solve such MPECs and by the need to avoid the use of an optimization approach, which is unfamiliar to most practising engineers, we propose, in the present paper, a novel numerical scheme to solve the MPEC as a constrained non-linear system of equations. We illustrate the application of this approach using the simple class of elastoplastic softening skeletal structures for which certain ductility conditions are prescribed. Copyright © 2009 John Wiley & Sons, Ltd.
On the optimum support size in meshfree methods: A variational adaptivity approach with maximum-entropy approximants
We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle. The method is based on a variational approach, and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters, here those defining the support size of each basis function. We consider local maximum-entropy approximation schemes, which exhibit smooth basis functions with respect to both space and the discretization parameters (the node location and the locality parameters). We illustrate by the Poisson, linear and non-linear elasticity problems the effectivity of the method, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions. Copyright © 2009 John Wiley & Sons, Ltd.
Proper generalized decomposition of multiscale models
In this paper the coupling of a parabolic model with a system of local kinetic equations is analyzed. A space-time separated representation is proposed for the global model (this is simply the radial approximation proposed by Pierre Ladeveze in the LATIN framework (Non-linear Computational Structural Mechanics. Springer: New York, 1999)). The originality of the present work concerns the treatment of the local problem, that is first globalized (in space and time) and then fully globalized by introducing a new coordinate related to the different species involved in the kinetic model. Thanks to the non-incremental nature of both discrete descriptions (the local and the global one) the coupling is quite simple and no special difficulties are encountered by using heterogeneous time integrations. Copyright © 2009 John Wiley & Sons, Ltd.
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