Moving least squares differential quadrature method and its application to the analysis of shear deformable plates

A moving least squares differential quadrature (MLSDQ) method is developed and employed for the analysis of moderately thick plates based on the first‐order shear deformation theory (FSDT). To carry out the analysis, the governing equations in terms of the generalized displacements (transverse deflection and two rotations) of the plate are formulated by employing the moving least squares approximation. The weighting coefficients used in the MLSDQ approximation are computed through a fast computation of shape functions and their derivatives. Numerical examples illustrating the accuracy, stability and convergence of the MLSDQ method are presented. Effects of support size, order of completeness and node irregularity on the numerical accuracy are investigated. Copyright © 2003 John Wiley & Sons, Ltd.     

Squeeze-and-breathe evolutionary Monte Carlo optimization with local search acceleration and its application to parameter fitting

Estimating parameters from data is a key stage of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy datasets. Over the years, a variety of heuristics have been proposed to solve this complex optimization problem, with good results in some cases yet with limitations in the biological setting. In this work, we develop an algorithm for model parameter fitting that combines ideas from evolutionary algorithms, sequential Monte Carlo and direct search optimization. Our method performs well even when the order of magnitude and/or the range of the parameters is unknown. The method refines iteratively a sequence of parameter distributions through local optimization combined with partial resampling from a historical prior defined over the support of all previous iterations. We exemplify our method with biological models using both simulated and real experimental data and estimate the parameters efficiently even in the absence of a priori knowledge about the parameters.     

FEM for evaluation of weight functions for SIF, COD and higher-order coefficients with application to a typical wedge splitting specimen

In the evaluation of accurate weight functions for the coefficients of first few terms of the linear elastic crack tip fields and the crack opening displacement (COD) using the finite element method (FEM), singularities at the crack tip and the loading point need to be properly considered. The crack tip singularity can be well captured by a hybrid crack element (HCE), which directly predicts accurate coefficients of first few terms of the linear elastic crack tip fields. A penalty function technique is introduced to handle the point load. With the use of these methods numerical results of a typical wedge splitting (WS) specimen subjected to wedge forces at arbitrary locations on the crack faces are obtained. With the help of appropriate interpolation techniques, these results can be used as weight functions. The range of validity of the so-called Paris equation, which is widely used in the evaluation of the COD from the stress intensity factors (SIFs), is established.     

The inverse transformation of angular spectrum propagation algorithm and its application to phase retrieval

An angular spectrum propagation (ASP) algorithm with a scaling parameter to simulate optical diffraction propagation through optical systems is studied. The alterable observation size is obtained by adding the scaling parameter to the Collins formula. A directly mathematical inverse transformation of the ASP algorithm (IASP) is proposed to calculate the source optical field from the known observation optical field, and the results are proved more precise. The IASP algorithm is applied to execute the phase retrieval to derive the aberrations of optical systems from intensity profiles measured in the observation plane. The derived aberrations are fitted by Zernike polynomials under the constraint that the wavefront aberrations are smooth. Numerical simulations are performed to test the accuracy of this method.     

A new hybrid real-coded genetic algorithm and its application to parameters identification of soils

Inverse analysis using an optimization method based on a genetic algorithm (GA) is a useful tool for obtaining soil parameters in geotechnical fields. However, the performance of the optimization in identifying soil parameters mainly depends on the search ability of the GA used. This study aims to develop a new efficient hybrid real-coded genetic algorithm (RCGA) being applied to identify parameters of soils. In this new RCGA, a new hybrid strategy is proposed by adopting two crossovers with outstanding ability, namely the Simulated Binary Crossover and the simplex crossover. In order to increase the convergence speed, a chaotic local search technique is used conditionally. The performance of the proposed RCGA is first validated by optimizing mathematical benchmark functions. The results demonstrate that the RCGA has an outstanding search ability and faster convergence speed compared to other hybrid RCGAs. The proposed new hybrid RCGA is then further evaluated by identifying soil parameters based on both laboratory tests and field tests, for different soil models. All the comparisons demonstrate that the proposed RCGA has an excellent performance of inverse analysis in identifying soil parameters, and is thus recommended for use based on all the evaluations carried out in this paper.     

小波双三次高倍插值搜索算法的遥感图像重建

由于光学遥感成像的距离较远和CCD物理尺寸的限制,获得的图像分辨率都比较低。为了在保持原始图像信息的情况下,提高图像的空间分辨率,改善图像的峰值信噪比,在深入分析前期研究中提出的小波双三次插值搜索算法的基础上,建立了小波双三次高倍插值搜索算法。该算法可以根据需要重建出原始遥感图像的高倍高分辨率遥感图像。实验结果表明,新算法重建出原始图像的2×2倍高分辨率图像的细节信息和视觉效果最好,3×3倍和4×4倍次之,5×5倍较差,更高倍数的高分辨率重建图像不宜在实际应用中采用。     

Power spectrum estimation of complex signals and its application to Wigner-Ville distribution: A group delay approach

In this paper, a method of estimating the power spectrum of a complex signal based on the Group Delay function (GD) is proposed and also applied to the Wigner-Ville Distribution (WVD) to reduce the ripple effect due to the truncation of the autocorrelation sequence. The proposed method is realised by the GD for a complex signal and the modified GD concept. This extends the performance advantages of the modified GD applicable to a real signal, to a complex one. Further, its application to WVD, reduces the truncation/ripple effect without sacrificing any frequency resolution, as nocommon window function is used. Significant improvement in performance, in terms of reduction in variance without any compromise on resolution and higher noise immunity, has been found over those of the periodogram and windowed WVD.     

High‐accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain

Based on the differential quadrature (DQ) rule, the Gauss Lobatto quadrature rule and the variational principle, a DQ finite element method (DQFEM) is proposed for the free vibration analysis of thin plates. The DQFEM is a highly accurate and rapidly converging approach, and is distinct from the differential quadrature element method (DQEM) and the quadrature element method (QEM) by employing the function values themselves in the trial function for the title problem. The DQFEM, without using shape functions, essentially combines the high accuracy of the differential quadrature method (DQM) with the generality of the standard finite element formulation, and has superior accuracy to the standard FEM and FDM, and superior efficiency to the p‐version FEM and QEM in calculating the stiffness and mass matrices. By incorporating the reformulated DQ rules for general curvilinear quadrilaterals domains into the DQFEM, a curvilinear quadrilateral DQ finite plate element is also proposed. The inter‐element compatibility conditions as well as multiple boundary conditions can be implemented, simply and conveniently as in FEM, through modifying the nodal parameters when required at boundary grid points using the DQ rules. Thus, the DQFEM is capable of constructing curvilinear quadrilateral elements with any degree of freedom and any order of inter‐element compatibilities. A series of frequency comparisons of thin isotropic plates with irregular and regular planforms validate the performance of the DQFEM. Copyright © 2009 John Wiley & Sons, Ltd.