MARS:A TUTORIAL

This tutorial paper presents a simplified view of one of the more recently published multivariatecalibration methods particularly suited to dealing with non-linear data sets.The method is referred toas MARS and stands for multivariate adaptive regression splines.Simple examples are provided toexplain the workings of the method.     

西藏高原南部雅鲁藏布江缝合带地区地壳电性结构研究

为了探测西藏高原南部雅鲁藏布江缝合带地区地壳浅部和深部构造沿东西和南北方向的变化特征,在雅鲁藏布江缝合带地区布设了三条南北向剖面(错那—墨竹工卡、亚东—雪古拉、吉隆—措勤),采用超宽频带大地电磁测深方法进行了地壳、上地幔电性结构探测研究,发现该区主要电性结构特征为：1. 雅鲁藏布江缝合带附近表层发育大规模的高阻体,岩体延伸最深达30km以上,是冈底斯花岗岩体的反映. 2. 雅鲁藏布江缝合带的南部有小规模的良导体,在其下方和北侧发育有大规模良导体. 3. 沿剖面从南往北壳内普遍发育良导体,各良导体主体间是不连续的,规模逐渐增大,总体北倾,在缝合带附近产状较陡. 4. 在雅鲁藏布江缝合带附近良导体由西往东规模逐渐增大,导电性逐渐变好,相对雅鲁藏布江在剖面上的位置逐渐南移. 这些重要的电性特征可能是印度板块向北俯冲所形成的,深部大规模的良导体特征沿东西向的差异可能是板块碰撞引起物质沿东西向运移作用的结果.     

A TEST OF THREE FITTING CRITERIA FOR MULTIRESPONSE NON-LINEAR MODELING

This work evaluates objective functions for multiresponse non-linear modeling using computersimulations.Tests are performed under a variety of signal-to-noise ratios and noise variance-covariancestructures.The standard error of prediction for the model parameters,computed from 50 trials,is usedfor performance comparisons.The full rank and rank-deficient problems are considered.For the fullrank problem one model was investigated,a first-order two-step consecutive reaction model,and twoobjective functions were considered,the total sum of squares and the determinant criterion.Nodistinction could be made between the two objective functions for this model.For the rank-deficient case two models were investigated,a first-order two-step consecutive reactionas in the full rank case,and a pH titration model described by the Henderson-Hasselbalch equation.Three objective functions were investigated for the rank-deficient case,the total sum of squares,aweighted total sum of squares and the determinant criterion.The total sum of squares was found toperform poorly under all conditions tested compared to the weighted total sum of squares and thedeterminant criterion.The determinant criterion was found to perform much better than the other twocriteria when the data have a combination of a low signal-to-noise ratio and high variance-covariancenoise structure.     

RECENT DEVELOPMENTS IN MULTIVARIATE CALIBRATION

With the goal of understanding global chemical processes,environmental chemists have some of the mostcomplex sample analysis problems.Multivariate calibration is a tool that can be applied successfully inmany situations where traditional univariate analyses cannot.The purpose of this paper is to reviewmultivariate calibration,with an emphasis being placed on the developments in recent years.The inverseand classical models are discussed briefly,with the main emphasis on the biased calibration methods.Principal component regression(PCR)and partial least squares(PLS)are discussed,along with methodsfor quantitative and qualitative validation of the calibration models.Non-linear PCR,non-linear PLSand locally weighted regression are presented as calibration methods for non-linear data.Finally,calibration techniques using a matrix of data per sample(second-order calibration)are discussed briefly.     

THE EFFECT OF MEAN CENTERING ON PREDICTION IN MULTIVARIATE CALIBRATION

Traditionally,one form of preprocessing in multivariate calibration methods such as principal componentregression and partial least squares is mean centering the independent variables(responses)and thedependent variables(concentrations).However,upon examination of the statistical issue of errorpropagation in multivariate calibration,it was found that mean centering is not advised for some datastructures.In this paper it is shown that for response data which(i)vary linearly with concentration,(ii)have no baseline(when there is a component with a non-zero response that does not change inconcentration)and(iii)have no closure in the concentrations(for each sample the concentrations of allcomponents add to a constant,e.g.100%)it is better not to mean center the calibration data.That is,the prediction errors as evaluated by a root mean square error statistic will be smaller for a model madewith the raw data than a model made with mean-centered data.With simulated data relativeimprovements ranging from 1% to 13% were observed depending on the amount of error in thecalibration concentrations and responses.     

Evaluation of a gravel transport sensor for bed load measurements in natural flows

A recent acoustic instrument （Gravel Transport Sensor, GTS） was tested for predicting sediment transport rate （bed load rate） in gravel bed streams. The GTS operation is based on the particle collision theory of submerged obstacles in fluids. When particles collide with the GTS cylinder their momentum is recorded in the form of ping rates. The GTS is attractive for further consideration here because of its potential to provide continuous unattended local bed load measurements, especially in areas found in streams that access may be difficult under extreme conditions. Laboratory experiments coupled with numerical simulations for the same flow conditions were performed in order to determine the conditions under which particles of different size will hit the GTS cylinder and be able to register a ping rate. The GTS was able to detect the number of particles with diameter in the range of 15.9 to 25.4 mm, with reasonable accuracy, if the applied Shields effective stress τ＊e = τ＊ - τ＊cr was in the range of 0.006 to 0.015. A drawback of the tested prototype GTS, however, was that it exerted increased resistance on the incoming particles. The added drag effects increased the overall resistance that was exerted by the flow on particles and thus increased the likelihood that particles will rest in the ambient region of the cylinder instead of hitting it. Numerical simulation of the flow around the GTS cylinder revealed that changing the prototype geometry from cylindrical to ellipsoid or rhomboid will increase the likelihood of the particles hitting the instrument under the same flow conditions failed by the original tested GTS cylinder.