Wavelet neural network (WNN) has been widely used in the field of civil engineering. However, WNN can only effectively handle problems of small dimensions as the computational cost for constructing wavelets of large dimensions is prohibitive. To expand the application of WNN to higher dimensions, this article develops a new wavelet support vector machine (SVM)based neural network metamodel for reliability analysis. The method first develops an autocorrelation wavelet kernel SVM and then uses a set of wavelet SVMs with different resolution as the activation function of WNN. The output of network is obtained through aggregating outputs of different wavelet SVMs. The method takes advantage of the excellent capacities of SVM to handle highdimensional problems and of the attractive properties of wavelet to represent complex functions. Four examples are given to demonstrate the application and effectiveness of the proposed method.
Approximation methods such as response surface method and artificial neural network (ANN) method are widely used to alleviate the computation costs in structural reliability analysis. However most of the ANN methods proposed in the literature suffer various drawbacks such as poor choice of parameter setting, poor generalization and local minimum. In this study, a support vector machine-based radial basis function (RBF) network method is proposed, in which the improved RBF model is used to approximate the limit state function and then is connected to a reliability method to estimate failure probability. Since the learning algorithm of RBF network is replaced by the support vector algorithm, the advantage of the latter, such as good generalization ability and global optimization are propagated to the former, thus the inherent drawback of RBF network can be defeated. Numerical examples are given to demonstrate the applicability of the improved RBF network method in structural reliability analysis, as well as to illustrate the validity and effectiveness of the proposed method.
Inspired by crystalline lenses in human eyes, liquid lenses have a simple yet elegant working principle, and result in compact optical systems. Recent numerical studies showed that membranes with variable thicknesses could affect the lens profile. However, fabrication and assembly of a liquid lens with an inhomogeneous membrane is difficult. There is also a lack of experimental studies about the changes of a lens profile during deformation. In this paper, we provided a new experimental approach for characterizing the performance of a liquid lens with an inhomogeneous membrane. A 2D axisymmetric lens model was built in finite element analysis software to theoretically study the non-linear deformation behavior of the inhomogeneous membrane. Then we provided a new approach to fabricate inhomogeneous membranes using a pre-machined aluminum mold. An optical coherence tomography (OCT) system was used to dynamically measure the changes of a lens profile without contact. Both simulation and the experiments indicated that the variation of the thickness of the membrane could affect the lens profile in a predictable manner. A negative conic constant was achieved when a plano-concave membrane was adopted in a liquid lens. Larger increments of the thickness of the membrane in the radial direction resulted in a larger contribution of a conic constant to the lens profile. The presented study offers guidance for image-quality analysis and optimization of a liquid-lens-based optical system.
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