A non-linear model for the dynamics of open cross-section thin-walled beams—Part I: formulation

A non-linear one-dimensional model of inextensional, shear undeformable, thin-walled beam with an open cross-section is developed. Non-linear in-plane and out-of-plane warping and torsional elongation effects are included in the model. By using the Vlasov kinematical hypotheses, together with the assumption that the cross-section is undeformable in its own plane, the non-linear warping is described in terms of the flexural and torsional curvatures. Due to the internal constraints, the displacement field depends on three components only, two transversal translations of the shear center and the torsional rotation. Three non-linear differential equations of motion up to the third order are derived using the Hamilton principle. Taking into account the order of magnitude of the various terms, the equations are simplified and the importance of each contribution is discussed. The effect of symmetry properties is also outlined. Finally, a discrete form of the equations is given, which is used in Part II to study dynamic coupling phenomena in conditions of internal resonance.     

icoshift: An effective tool for the alignment of chromatographic data

The Interval Correlation Optimised Shifting algorithm (icoshift) has recently been introduced for the alignment of nuclear magnetic resonance spectra. The method is based on an insertion/deletion model to shift intervals of spectra/chromatograms and relies on an efficient Fast Fourier Transform based computation core that allows the alignment of large data sets in a few seconds on a standard personal computer. The potential of this programme for the alignment of chromatographic data is outlined with focus on the model used for the correction function. The efficacy of the algorithm is demonstrated on a chromatographic data set with 45 chromatograms of 64,000 data points. Computation time is significantly reduced compared to the Correlation Optimised Warping (COW) algorithm, which is widely used for the alignment of chromatographic signals. Moreover, icoshift proved to perform better than COW in terms of quality of the alignment (viz. of simplicity and peak factor), but without the need for computationally expensive optimisations of the warping meta-parameters required by COW. Principal component analysis (PCA) is used to show how a significant reduction on data complexity was achieved, improving the ability to highlight chemical differences amongst the samples.     

Comparative study of the alignment method on experimental and simulated chromatographic data

One of the major problems in the signal comparison of chromatographic data is the variability of response caused by instrumental drifts and others instabilities. Measures of quality control and evaluation of conformity are inherently sensitive to shift. It is essential to be able to compare test samples to reference samples in an evolutionary analytical environment by offsetting the inevitable drift. Therefore, prior to any multivariate analysis, the alignment of analytical signals is a compulsory preprocessing step. During recent years, many researchers have taken a greater interest in the study of the alignment. The present paper is an updated review on the alignment algorithms, methods, and improvements used in chromatography. The study is dedicated to one‐dimensional signals. Several of the exposed methods have common theoretical bases and can differ through their optimization methods. The main issue for the operator is to choose the appropriate method according to the type of signals to be processed.     

基于主元分析与动态时间弯曲的故障诊断方法及应用研究

轴承是工程实际中常用而又极易损坏的部件,特别是对其早期微弱响应的辨识,具有重要的社会价值和意义。为提高运转轴承的安全可靠性和可维护性,提出了基于主元分析与动态时间弯曲距离的故障诊断方法,它可以准确对早期微弱动态响应辨识、诊断。该方法首先将典型故障样本信号与待测信号小波去噪并EMD分解,并对若干固有模态分量主元分析求取主元,然后对主元分量进行分析,获得相关特征值组成特征向量,计算待测信号与已知故障样本信号特征向量的弯曲距离,弯曲距离越小表明两信号越相似,从而辨识故障。此外,还可将其应用于转子、碰磨、齿轮故障诊断中,工程应用实例表明该方法可以准确故障分类,高效故障诊断。     

频散、声场干涉结构、波导不变量与消频散变换

针对浅海环境中利用单深度接收信号自相关函数的Warping变换方法测距时易出现的多值性问题, 提出一种双深度Warping变换融合测距方法。该方法将双深度测量场的Warping变换提取结果与具有深度差异的拷贝场本征函数信息融合, 判别简正波干涉项模态, 提高测距的准确度。此外, 针对实际海洋环境中测量场Warping变换特征峰位置难以准确提取的问题, 将Warping变换的频率不变性与图像形态学方法结合以增强特征频率结构, 提高后续测距的稳健性。海试数据处理结果显示, 测距结果与实际距离符合较好, 表明所提方法具有实际可行性。

     

Alignment and clustering strategies for GC×GC–MS features using a cylindrical mapping

Comprehensive two-dimensional gas chromatography coupled to mass spectrometry is a powerful tool to analyze complex samples. For application of the technique in studies like biomarker discovery in which large sets of complex samples have to be analyzed, extensive preprocessing is needed to align the data obtained in several injections (analyses). We developed new alignment and clustering algorithms for this type of data. New in the current procedures is the consistent way in which the phenomenon referred to as wrap-around is treated. The data analysis problems associated with this phenomenon are solved by treating the 2D display as the surface of a three-dimensional cylinder. Based on this transformation we developed a new similarity metric for features as a function of both the cylindrical distance (reflecting similarity in chromatographic behavior) and of the mass spectral correlation (reflecting similarity in chemical structure). The concepts are used in warping and clustering, and include a protection against greedy warping.     

Formulación de elementos finitos para vigas de sección abierta formadas por laminados compuestos incluyendo las deformaciones tangenciales por cortante y torsión

In this paper we derive the field of displacements and strains for thin-walled open composite beams with composite laminated material including in their kinematics flexural and torsional shear deformations effects. The equilibrium equations are defined through the variational formulation and show that is possible to formulate C_o finite elements taking into account the torsional shear deformation. Stress-strain relationships for the cross-section of thin-walled composite beams are obtained by extending first-order laminate (FSDT: first-order shear deformation) theory and using a «free stress resultant condition at the boundary». Three different one-dimensional finite elements with C_o continuity are formulated for the study of thin-walled open composite beams and they are labelled as BSW (beam with shear and warping). The influence of the integration strategy in the BSW elements is evaluated via the shear-locking phenomenon and the rate of convergence for displacements and rotations. The stiffness matrix integration is compared using exact and reduced integration methods. Examples of pure torsion and flexo-torsion in a cantilever composite beam are performed. Numerical results are compared to those reported by other authors.     

A higher order model for thin-walled structures with deformable cross-sections

A higher order model for the analysis of linear, prismatic thin-walled structures that considers the cross-section warping together with the cross-section in-plane flexural deformation is presented in this paper. The use of a one-dimentional model for the analysis of thin-walled structures, which have an inherent complex three-dimensional (3D) behaviour, can only be successful and competitive when compared with shell finite element models if it fulfills a twofold objective: (i) an enrichment of the model in order to as accurately as possible reproduce its 3D elasticity equations and (ii) the definition of a consistent criterion for uncoupling the beam equations, allowing to identify structural deformation modes.The displacement field is approximated through a linear combination of products between a set of linear independent functions defined over the cross-section and the associated weights only dependent on the beam axis; this approximation is not constrained by any ab initio kinematic assumptions. Towards an efficient application of the approximation procedure, the cross-section is discretized into thin-walled elements, being the displacement field approximated for each element independently of the displacement direction. The approximation is thus hp refined enhancing the “capture” of the 3D structural mechanics of thin-walled structures. The beam model governing equations are obtained through the integration over the cross-section of the corresponding elasticity equations weighted by the cross-section global approximation functions.A criterion for uncoupling the beam governing equations is established, allowing to (i) retrieve the classic equations of the thin-walled beam theory both for open and closed sections and (ii) derive a set of uncoupled deformation modes representing higher order effects. The criterion is based on the solution of the polynomial eigenvalue problem associated with the beam differential equations, allowing to quantify the Saint-Venant principle for thin-walled structures. In fact, the solution of the non linear eigenvalue problem yields a twelve fold null eigenvalue (representing polynomial solutions) that are verified to represent beam classic solutions and sets of pairs and quadruplets of non-null eigenvalues corresponding to higher order modes of deformation.     

The correspondence problem for metabonomics datasets

In metabonomics it is difficult to tell which peak is which in datasets with many samples. This is known as the correspondence problem. Data from different samples are not synchronised, i.e., the peak from one metabolite does not appear in exactly the same place in all samples. For datasets with many samples, this problem is nontrivial, because each sample contains hundreds to thousands of peaks that shift and are identified ambiguously. Statistical analysis of the data assumes that peaks from one metabolite are found in one column of a data table. For every error in the data table, the statistical analysis loses power and the risk of missing a biomarker increases. It is therefore important to solve the correspondence problem by synchronising samples and there is no method that solves it once and for all. In this review, we analyse the correspondence problem, discuss current state-of-the-art methods for synchronising samples, and predict the properties of future methods.     

Deformation of short composite beam using refined theories

High-order flexural theories for short laminated composite beams subjected to mechanical and thermal loading are presented. The formulation allows for warping of the cross-section of the beam and eliminates the need for using arbitrary shear correction coefficients as in other theories. Based on higher-order shear deformation theories, the governing equations are obtained using the principle of virtual work (PVW). The justification for use of higher-order shear deformation theories is established for short and composite beams where cross-sectional warping is predominant.