Pipe failure rate prediction in water distribution networks using multivariate adaptive regression splines and random forest techniques

ABSTRACT

This paper presents the results of a comparison between multivariate adaptive regression splines (MARS) and random forest (RF) techniques in pipe failure prediction in two water distribution networks. In this regard, pipe diameter, pipe length, pipe installation depth, pipe age and average hydraulic pressure are considered as input variables. Results show that the RF outperforms the MARS which is found as an accurate pipe failure rate predictor. The proposed models are further evaluated through dividing the data into three parts of lower, medium and higher pipe failure rate values. According to the equations produced by MARS technique, three variables of pipe diameter, pipe age and average hydraulic pressure are distinguished as the most effective variables in predicting pipe failure rate in the first case study. Four variables of pipe diameter, pipe length, pipe age and average hydraulic pressure are determined as the most effective variables in the second case study.     

基于样条修匀公式的图像边缘检测

本文给出了一类基于Ｂ样条修匀公式的图像边缘检测算子,其过程是先利用等距Ｂ样条函数对图像｛ｆ（ｉ,ｊ）｝Ｎ－１ｉ,ｊ＝０做一个全息光滑曲面公式,进一步利用Ｂ样条函数的局部支撑性质导出,该曲面公式可以严格地局限于每点的某变邻域内计算,即Ｓ（ｘ,ｙ）＝∑（ｉ,ｊ）∈Ｎｋ,ｌ（ｘ,ｙ）ｆ（ｉ,ｊ）Ωｋ（ｘ－ｉ）Ωｌ（ｙ－ｊ）该曲面既有足够的光滑性,又有良好的保凸性;然后,基于这个光滑曲面Ｓ（ｘ,ｙ）,再通过求｜Ｓ｜的局部极大值点或求２Ｓ的零交叉来检测边缘．数值实验表明,这是一类十分成功的边缘检测算法,它简捷、可靠,便于实时处理,如可用于计算机视觉系统中的特征提取、图像分割、纹理分析等．     

曲面光顺的分片能量法

能量法是一种目前被广泛采用的光顺方法,但当数据点较多时,能量法的存储量和计算量都很大。本文研究Ｂ样条曲面光顺的分片能量法。应用该法可以在保持光顺效果的能量法基本一致的前提下,大大地减少了存储量和计算量。实例表明,这是一种行之有效的曲面光顺方法。     

贝叶斯多元线性样条在电力负荷中期预测中的应用

贝叶斯多元线性样条BMLS是基于贝叶斯框架下的分段线性回归技术,实现了回归面边界光滑性.本文分析了BMLS方法的原理,结合EUNITE网络2001年举办的电力负荷预测比赛提供的数据进行了相关数据分析,建立了相应的电力负荷中期预测模型.我们使用BMLS方法对两种训练样本集进行了训练,并计算出预测期的预测值,取得了理想的预测结果,并结合其它方法对试验结果进行了分析.文章最后总结了BMLS方法用于预测的特点,并与其它方法,如相关向量机等进行了比较.使用BMLS的模拟近似平均技术进行预测可以实现较好的精度.     

渐开线花键公法线长度测量值及其公差的计算

介绍了常用的中国GB T3478.1、美国ANSB92 .1和德国DIN5 480三种渐开线花键公法线长度的理论值、跨齿数(或跨齿槽数)及其上下偏差的计算方法,并对有关标准中相关数据查找的具体使用方法作了简明扼要的介绍。     

Global sensitivity analysis of the blade geometry variables on the wind turbine performance

The need for implementing efficient blade designs gains relevance as wind turbine developments require longer blades. The design of blade geometry, traditionally divided in 2D airfoils and spanwise distributions, is usually addressed as an optimization problem. A correct identification of the design variables is crucial to avoid unnecessary computational cost or insufficient exploration of the design space. This paper deals with the identification of the design variables that affect the wind turbine performance. First, the number of design variables for an accurate airfoil representation is resolved. A methodology, based on statistical hypothesis testing applied to the airfoil approximation errors, is presented to assess the accuracy of types of B‐splines. Second, the study is extended to chord and twist distributions besides airfoil geometry with the purpose of assessing the sensitive blade variables in the wind turbine performance. Global sensitivity analysis as multi‐variable linear regressions and variance‐based methods are used. Latin hypercube sampling is applied to generate efficient inputs. MATLAB‐based code is developed to obtain outputs: annual energy production, maximum blade tip deflection, overall sound power level and blade mass. As result of the study, a list of non‐affecting variables is deduced. These variables can be avoided in the optimization without loss of gain in the performance. The method is a powerful tool to analyse in a preliminary phase a design problem involving a high amount of variables and complex physical relations by means of combining different multi‐disciplinar calculation codes and performing statistical treatments. Copyright © 2017 John Wiley & Sons, Ltd.     

High‐quality rendering of smooth isosurfaces

Animation and visualization of rectilinear data require interpolation schemes for smooth image generation. Piecewise trilinear interpolation, the de facto standard for interpolating rectilinear data, usually leads to significant visual artifacts in the resulting imagery. These artifacts reduce the confidence in the resulting visualization and may even lead to false interpretations of the data. This paper is concerned with the generation of smooth isosurface image sequences, obtained by casting rays through the image plane and computing their intersections with an isosurface. We describe a novel solution to this problem: we replace trilinear interpolation by tricubic interpolation, smoothing out the artifacts in the images; and we simplify the ray–isosurface intersection calculations by rotating and resampling the original rectilinear data in a second rectilinear grid—a grid with one family of grid planes parallel to the image plane. Our solution significantly reduces artifacts in individual images and leads to smooth animations. Copyright © 1999 John Wiley & Sons, Ltd.     

Finite strip buckling and free vibration analysis of stepped rectangular composite laminated plates

A general spline finite strip method is presented which allows the spline knots to be located arbitrarily along the plate strip and also facilitates the use of analytical integration in evaluating strip properties. The development takes place in the contexts of first‐order shear deformation plate theory and of classical plate theory, and encompasses composite laminated material. The prediction of natural frequencies and buckling stresses of stepped rectangular plates is considered using the new approach in which refinement of knot spacings is used local to a step change. The superstrip concept is used as part of an efficient solution procedure. A number of applications demonstrate the validity and practicability of the developed method. Copyright © John Wiley & Sons, Ltd.     

A numerical solution of nonlinear parabolic-type Volterra partial integro-differential equations using radial basis functions

In this paper, an effective numerical method for solving nonlinear Volterra partial integro-differential equations is proposed. These equations include the partial differentiations of an unknown function and the integral term containing the unknown function which is the “memory” of problem. This method is based on radial basis functions (RBFs) and finite difference method (FDM) which provide the approximate solution. These techniques play the important role to reduce a nonlinear partial integro-differential equation to a linear system of equations. Some illustrative examples are shown to describe the method. Numerical examples confirm the validity and efficiency of the presented method.     

Imposing Dirichlet boundary conditions with Nitsche's method and spline‐based finite elements

A key challenge while employing non‐interpolatory basis functions in finite‐element methods is the robust imposition of Dirichlet boundary conditions. The current work studies the weak enforcement of such conditions for B‐spline basis functions, with application to both second‐ and fourth‐order problems. This is achieved using concepts borrowed from Nitsche's method, which is a stabilized method for imposing constraints on surfaces. Conditions for the stability of the system of equations are derived for each class of problem. Stability parameters in the Nitsche weak form are then evaluated by solving a local generalized eigenvalue problem at the Dirichlet boundary. The approach is designed to work equally well when the grid used to build the splines conforms to the physical boundary of interest as well as to the more general case when it does not. Through several numerical examples, the approach is shown to yield optimal rates of convergence. Copyright © 2010 John Wiley & Sons, Ltd.