Optimized time alignment algorithm for LC-MS data: correlation optimized warping using component detection algorithm-selected mass chromatograms

Correlation optimized warping (COW) based on the total ion current (TIC) is a widely used time alignment algorithm (COW-TIC). This approach works successfully on chromatograms containing few compounds and having a well-defined TIC. In this paper, we have combined COW with a component detection algorithm (CODA) to align LC-MS chromatograms containing thousands of biological compounds with overlapping chromatographic peaks, a situation where COW-TIC often fails. CODA is a variable selection procedure that selects mass chromatograms with low noise and low background (so-called "high-quality" mass chromatograms). High-quality mass chromatograms selected in each COW segment ensure that the same compounds (based on their mass and their retention time) are used in the two-dimensional benefit function of COW to obtain correct and optimal alignments (COW-CODA). The performance of the COW-CODA algorithm was evaluated on three types of complex data sets obtained from the LC-MS analysis of samples commonly used for biomarker discovery and compared to COW-TIC using a new global comparison method based on overlapping peak area: trypsin-digested serum obtained from cervical cancer patients, trypsin-digested serum from a single patient that was treated with varying preanalytical parameters (factorial design study), and urine from pregnant and nonpregnant women. While COW-CODA did result in minor misalignments in rare cases, it was clearly superior to the COW-TIC algorithm, especially when applied to highly variable chromatograms (factorial design, urine). The presented algorithm thus enables automatic time alignment and accurate peak matching of multiple LC-MS data sets obtained from complex body fluids that are often used for biomarker discovery.     

Improved parametric time warping for proteomics

We present an improved version of parametric time warping, which enables the method to be used in LC-MS measurements in proteomics. The new features include a new similarity measure for comparing warped chromatograms, an insurance against peaks at the extremes of the chromatograms disappearing because of the warping, and the possibility to select and use multiple traces in searching the optimal alignment. Moreover, we present an alignment strategy combining global and individual alignments for aligning LC-MS data that exhibit different shifts within the same sample, at the same retention time. Using an LC-MS data set consisting of E. coli homogenates that were measured in several batches over a period of six months, we show the benefits of the improved algorithm and the merits of the new strategy. The algorithm is publicly available as the R package ptw.     

薄壁箱梁剪力滞效应分析的初参数法

选取剪力滞效应引起的附加挠度作为广义位移,在定义新的剪力滞广义力矩及广义翘曲位移函数基础上,将薄壁箱梁的剪力滞变形状态从初等梁挠曲变形状态中分离出来作为一种独立的基本变形状态进行分析。对广义翘曲位移函数引入两个修正系数以充分考虑剪力滞翘曲应力的自平衡条件。提出了剪力滞翘曲应力的简便计算公式,它与初等梁弯曲应力公式具有相同的形式。用能量变分法建立了剪力滞控制微分方程,以广义力矩、广义剪力、附加挠度及其变化率作为四个初参数,给出了微分方程的初参数解。对两跨连续箱梁模型的应力计算表明:本文计算值与实测值及其它文献给出的计算值均吻合良好,从而验证了该文分析方法的正确性。挠度计算表明:剪力滞效应使该箱梁在集中荷载和均布荷载作用下的跨中挠度分别增大17%和16%。     

A procedure for analysing space frames with partial warping restraint

Stiffness matrices for three-dimensional beam elements that include the effect of warping restraint on elastic torsional response have been derived by various investigators. Using one of the available stiffness matrices and assuming that the warping boundary conditions can be specified on a member-by-member basis, an elastic ‘warping’ support is introduced to represent conditions of partial warping restraint at the member ends. The concept of a ‘warping indicator’ is then introduced to facilitate use of warping springs. Following this, static condensation is used to eliminate the restrained warping degrees-of-freedom. The condensed stiffness matrices for the elements can then be assembled to yield a global stiffness matrix. In the global matrix, continuous warping degrees-of-freedom, that is, those internal to a member represented by several elements, are expressed in local co-ordinates. The remainder are expressed in global co-ordinates. In the force recovery phase, it is shown that an ‘indirect’ method yields most accurate results for the bimoment and warping torsion when the twist function is represented by a cubic polynomial. Solutions to examples of linear elastic analysis are compared with well-known analytical solutions to demonstrate the application of the method.     

薄壁箱梁纵向剪滞翘曲函数精度选择的研究

根据箱形结构纵向翘曲位移函数设置的基本原理,选择一系列符合箱梁基本翘曲模式的翘曲位移函数,然后以最小势能原理为基础,综合考虑剪力滞后效应、剪切变形和转动惯量的影响,推导出相应翘曲位移函数箱形截面梁的振动控制微分方程和边界条件,据此得出箱形结构的固有频率方程。依据固有频率方程求出特定边界条件下相应翘曲位移函数箱形结构的自振频率,然后借助自振频率的大小对所设置翘曲位移函数的精确度做出评判。静力分析算例结果证明了翘曲位移函数精度选择的必要性,该文将解析解与数值解结果进行了比较,证明了方法的有效性。     

Compensation of torsional vibrations in rods by piezoelectric actuation

In this paper, the piezoelectric compensation of torsional vibrations in rods caused by external excitations is studied. As an illustrative example, a laminated rod containing piezoelectric shear actuators is assumed to be fixed at the one end, and the other end is subjected to a torsional couple; additionally, a distributed torsional couple per unit length is acting. In such a system, cross-sectional warping is known to be present. The consideration of piezoelectric eigenstrains requires an extension of Saint Venant’s theory of torsion, which is achieved by introducing an additional warping function. Using D’Alembert’s principle, the boundary value problems for Saint Venant’s warping function, the additional warping function and the torsional angle are obtained. From the latter boundary value problems, the distribution of piezoelectric actuation is derived in order to completely compensate the external excitations, i.e. an analytical solution of the corresponding shape control problem is obtained. Finally, the results are verified by means of three-dimensional finite element computations.     

Prediction of turn down warping during hot plate rolling based on a Gaussian function

Turn down warping is a shape defect observed at the front end of a plate during hot rolling. To produce a flat plate without warping, a precise prediction of turn down warping is essential to achieve optimal control. Therefore, we propose a model based on a Gaussian function to predict turn down warping. The model uses the results from numerical analyses of hot plate rolling. The finite element code MARC was used for the numerical analysis. Hot plate rolling processing parameters, such as roll diameter, plate dimension, rolling speed, and pass line were all considered in the model. To verify the accuracy of the prediction model, the numerical results obtained by FEM were confirmed with data measured during industrial hot plate rolling. For the actual measurements of turn down warping, image processed high speed camera data from the exit side of the rolling were used. The results show that the proposed Gaussian function model can successfully predict turn down warping of a plate’s front end under various hot plate rolling conditions.     

考虑剪切变形时薄壁箱梁的挠曲分析

为分析剪切效应对薄壁箱梁受力特性的影响,利用微板的面内剪切及平衡微分方程,分别推导出不考虑和考虑薄壁箱梁各板面内剪切效应的弯曲位移函数。选取剪切效应引起的附加挠度作为广义位移,通过定义的剪切广义力矩及剪切翘曲位移函数,将剪切变形状态从全梁挠曲变形状态中分离出来,作为独立的变形状态进行分析。为满足全截面翘曲应力的自平衡条件,引入两个截面特性参数对广义剪切翘曲位移函数进行了修正。数值算例表明,按该文推导的薄壁箱梁剪切弯曲位移函数计算的两跨连续梁跨中截面应力与实测值及有限元值吻合良好。挠度计算表明:剪切效应使得该箱梁在集中和均布荷载作用下跨中挠度分别增大27%和24%。     

Analogies between Kirchhoff plates and Saint-Venant beams under torsion

Torsion of linearly elastic homogeneous and orthotropic Saint-Venant beams is based on the solution of a Neumann-like boundary value problem for the cross-sectional warping. Equivalence of differential conditions of elastic equilibrium for the beam twist stresses in terms of warping function and for the bending-twisting moments in a Kirchhoff plate is assessed. The analogy provides new exact solutions in the theory of thin plates. Examples are developed for composite plates with no kinematic boundary constraints. Elliptic and equilateral triangle shapes provide useful benchmarks for computational mechanics.     

徐变对水泥路面板湿度翘曲及应力影响研究

水泥混凝土路面板的温湿度翘曲和交通荷载的耦合作用是其发生疲劳破坏的主要原因之一。湿度梯度及湿度翘曲在路面板中的存在时间较为持续长久,不可避免地会受到混凝土徐变的影响。该文进行了干燥和密闭状态下水泥混凝土梁的弯曲徐变试验,提出弯曲徐变度和徐变系数的计算方法,并将上述徐变参数植入有限元程序中模拟分析徐变对结合式和分离式混凝土路面板翘曲变形和应力发展影响。结果表明:干燥状态下的弯曲徐变是密闭状态下徐变的1.67倍;徐变能够降低翘曲变形、翘曲应力及与荷载耦合情况下的总应力;徐变对结合式路面板的翘曲变形和应力发展影响较大,徐变降低了36%的湿度翘曲变形和45%的翘曲应力;在板角交通荷载的耦合作用下,徐变可使结合式路面板的总应力降低34%。因此徐变是合理分析混凝土路面板的翘曲变形和应力发展不可忽略的因素。     

从 Levinson 高阶梁理论的一致变分到高次翘曲梁理论

将矩形截面梁的截面翘曲位移设定为3次Legendre多项式的形式,利用弹性力学平面应力问题分项的不完全的广义变分原理,导出高次翘曲梁理论,得到形式简单易求解的方程。由于引入轴向拉伸的情况,使梁的平面内变形问题得以统一;计及了梁表面剪切荷载的作用,并严格满足表面剪应力边界条件;通过引入轴向位移约束参考点间距离的概念对梁端翘曲约束作更精致地描述,且使得该理论包含了变分一致或者不一致的高阶剪切梁理论。该理论的推导还表明,Levinson梁理论的变分不一致仅仅局限于有转角约束的梁端。通过算例,将高次翘曲梁理论与弹性力学平面应力问题以及Timoshenko梁理论、Levinson梁理论进行比较,初步显示出该理论的优越性。     

一种考虑剪滞效应的斜支承连续箱梁挠曲扭转分析方法

通过在支承坐标系下考虑约束条件,提出一种适用于斜支承连续箱梁挠曲扭转分析的薄壁箱梁单元。该单元具有10 个自由度,可方便地考虑斜支承连续箱梁的剪滞效应和扭翘变形。选取挠曲剪滞微分方程和约束扭转微分方程的齐次解作为单元位移函数,推导出单元刚度矩阵各元素的具体表达式。从剪滞翘曲应力的轴向平衡条件出发,建立双室箱形断面的剪滞翘曲位移函数,并给出了剪滞翘曲几何特性的一般计算公式。用所编制的电算程序SSCBA 对一个3 跨斜支承双室连续箱梁模型进行计算,计算值与实测值和ANSYS 壳单元结果均吻合较好,证实该箱梁单元是可靠的。计算表明:在跨中偏心荷载作用下,斜支承连续箱梁的剪滞翘曲变形和约束扭转翘曲变形对应力分布具有显著影响。     

基于拓扑优化的直升机旋翼桨叶剖面设计

提出了一种基于拓扑优化的直升机旋翼桨叶剖面设计方法。采用了有限元方法计算直升机旋翼桨叶剖面刚度特性, 截面考虑了剪切和翘曲变形, 并消除了翘曲位移和刚体位移之间的耦合作用。基于SIMP拓扑优化算法, 以旋翼桨叶平均柔度或者剖面刚度为设计目标, 桨叶重量为约束函数, 建立了旋翼桨叶拓扑优化模型。提出的敏度求解算法具有较高的计算精度, 采用序列线性规划算法对旋翼桨叶剖面进行优化设计。结果表明在展长较小并且承受均布升力载荷情况下, Ⅱ型截面梁的柔度最小, 而当展长增大时, 工字梁截面具有最小的柔度。此外, 旋翼桨叶外载荷等对优化结果也有较大的影响。提出的拓扑优化方法适合于概念设计阶段的直升机旋翼桨叶剖面设计。     

基于协调翘曲场的开闭口混合薄壁截面杆件约束扭转一维有限元分析

开口及闭口薄壁杆件约束扭转问题已由经典Timoshenko和Benscoter理论解决。然而,开闭口混合薄壁截面杆件约束扭转分析必须考虑开、闭口部分翘曲能力的差异,翘曲剪流形成机理有待进一步研究。该文假定开、闭口截面翘曲分别满足Vlasov和Umanskii假定,考虑开、闭口截面公共节点翘曲连续性要求,建立含有待定翘曲参数的协调翘曲模型。由截面受力平衡,确定翘曲参数显式列式,提出开闭口混合薄壁截面杆件约束扭转分析的一维有限元模型。算例及参数分析结果表明,基于Umanskii第二理论的Ⅰ类方法在悬臂板及闭口周边引入附加剪流,影响翘曲剪应力精度。基于Umanskii第二理论的Ⅱ类方法只能计算截面板件平均剪应力,无法反映真实翘曲剪流分布。基于Vlasov约束扭转假定的Beam-189单元忽略闭口周边约束效应产生的附加翘曲及剪流,影响翘曲正应力和剪应力精度。该文方法与Shell-63单元能得到基本吻合的变形与应力结果,说明一维梁元能正确反映开闭口混合薄壁截面杆件约束扭转及翘曲刚度。     

The collapse of open sections under bending and compression

The nonlinear behaviour of beams of thin-walled open section under bending and compression is investigated experimentally and theoretically. Two collapse modes of a channel section are identified, which are shown to be dependent on the position of the applied forces in relation to the null points of the warping function. A simplified finite element formulation is shown to predict the behaviour in the plastic regime.     

复合材料薄壁梁力学特性分析

综述了人们在建立研究复合材料薄壁梁力学特性的非线性梁理论及分析结构剖面特性,确立结构算子参数等方面所做的工作以及这些研究工作的特点。同时,结合作者的工作,介绍了近年来各国学者在复合材料薄壁梁力学特性研究上的进展。      

Advanced 3D beam element of arbitrary composite cross section including generalized warping effects

In this paper, an advanced 20 × 20 stiffness matrix and the corresponding nodal load vector of a member of arbitrary composite cross section is developed taking into account shear lag effects due to both flexure and torsion (the case of the three‐dimensional beam element of arbitrary homogeneous cross section is treated as a special one). The composite member consists of materials in contact each of which can surround a finite number of inclusions. Nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions. Ten boundary value problems with respect to the kinematical components are formulated and solved employing the analog equation method, a BEM‐based technique. The aforementioned boundary value problems are formulated employing either an improved stress field arising from the correction of shear stress components or the stress field arising directly from displacement considerations. The warping functions and the geometric constants including the additional ones due to warping are evaluated employing a pure BEM approach, that is, only boundary discretization of the cross section is used. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The deviations arising from the use of the advanced 20 × 20 stiffness matrix and the classical 12 × 12 or 14 × 14 ones employed in commercial software packages are illustrated through examples of great practical interest. Moreover, the influence of nonuniform warping effects necessitating the use of the aforementioned ‘advanced’ stiffness matrix is also demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.     

3-D beam element of variable composite cross section including warping effect

Summary. In this paper, a boundary element method is developed for the construction of a 14 × 14 stiffness matrix and a nodal load vector that take into account the additional warping degrees of freedom in a member of arbitrary variable composite cross section. The member is subjected to an arbitrarily concentrated or distributed twisting moment and consists of materials in contact each of which can surround a finite number of inclusions. The developed method takes into account the variable torsional and warping rigidities along the member length. Two boundary value problems with respect to the variable along the beam angle of twist and to the primary warping function are formulated and solved employing a pure BEM approach, that is only boundary discretization is used. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The discrepancy in the elements of the resulting stiffness matrix using the developed procedure and a fine mesh of elements having average values for the cross section parameters necessitates the consideration of the derivatives of the variable torsional and warping rigidities along the member length. Moreover, the influence of the warping effect, especially in composite members of open form cross section of variable thickness, is analyzed in examples demonstrating the importance of the inclusion of the warping degrees of freedom in the analysis of a space frame.     

Resolving and quantifying overlapped chromatographic bands by transmutation

A new chemometric technique called "transmutation" is developed for the purpose of sharpening overlapped chromatographic bands in order to quantify the components. The "transmutation function" is created from the chromatogram of the pure component of interest, obtained from the same instrument, operating under the same experimental conditions used to record the unresolved chromatogram of the sample mixture. The method is used to quantify mixtures containing toluene, ethylbenzene, m-xylene, naphthalene, and biphenyl from unresolved chromatograms previously reported. The results are compared to those obtained using window factor analysis, rank annihilation factor analysis, and matrix regression analysis. Unlike the latter methods, the transmutation method is not restricted to two-dimensional arrays of data, such as those obtained from HPLC/DAD, but is also applicable to chromatograms obtained from single detector experiments. Limitations of the method are discussed.     

A C1 finite element including transverse shear and torsion warping for rectangular sandwich beams

A new three‐noded C¹ beam finite element is derived for the analysis of sandwich beams. The formulation includes transverse shear and warping due to torsion. It also accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper and lower surfaces of the beam. The transverse shear deformation is represented by a cosine function of a higher order. This allows us to avoid using shear correction factors. A warping function obtained from a three‐dimensional elasticity solution is used in the present model. Since the field consistency approach is accounted for interpolating the transverse strain and torsional strain, an exact integration scheme is employed in evaluating the strain energy terms. Performance of the element is tested by comparing the present results with exact three‐dimensional solu‐tions available for laminates under bending, and the elasticity three‐dimensional solution deduced from the de Saint‐Venant solution including both torsion with warping and bending. In addition, three‐dimensional solid finite elements using 27 noded‐brick elements have been used to bring out a reference solution not available for sandwich structures having high shear modular ratio between skins and core. A detailed parametric study is carried out to show the effects of various parameters such as length‐to‐thickness ratio, shear modular ratio, boundary conditions, free (de Saint‐Venant) and constrained torsion. Copyright © 1999 John Wiley & Sons, Ltd.