USE OF THE KALMAN FILTER FOR MULTIVARIATE CALIBRATION IN A REAL SYSTEM AND ITS COMPARISON WITH CLS AND PURE COMPONENT CALIBRATION METHODS

The usefulness of the Kalman filter as an algorithm for calibration in a real system is shown. Results arecompared with classical least squares and pure component calibration. The prediction of four prioritypollutant chlorophenols in binary, ternary and quaternary mixtures was also carried out by Kalmanfiltering. The condition number, standard deviation and prediction error have been employed to choosethe most suitable wavelength range. Comparison of the standard error of prediction in the validation setshows significant differences between the evaluated chlorophenols, the best results being obtained withKalman multivariate calibration.     

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.     

THREE-WAY METHODS FOR THE CALIBRATION OF CHROMATOGRAPHIC SYSTEMS:COMPARING PARAFAC AND THREE-WAY PLS

For the calibration of chromatographic systems,different methods can be used.One class of methodsutilizes three-way approaches.The calibration problem is stated in such a way that the decompositionof a three-way array can serve for the prediction of retention on new stationary phases.Two three-way approaches are presented:the Unfold-PCA and PARAFAC models.The theory ofboth methods is presented and the differences are highlighted,the main difference being that PARAFACis a trilinear decomposition whereas Unfold-PCA is not.Both three-way methods are evaluated on asmall data set consisting of retention measurements of eight solutes at six mobile phase compositions onsix stationary phases.The differences in performance of the two models are minor,For calibration purposes,two variants of the methods are discussed:three-way PLS and an extensionof PARAFAC.Again the theory and differences between the two methods are explained.The predictiveperformance of the two methods is compared using the same data set as earlier.The differences inpredictive performance,however,are minor.Both methods are capable of predicting 98% of thevariation in the test sets.Yet,there are other considerations when comparing methods than predictiveperformance,e.g.the quality of the predictions.     

香港降水的短期气候预测

利用正规化周期回归分析方法和门限自回归理论对香港1853-1995年月降水资料进行了建模和拟合，并对1996年进行了预报试验，正规化周期回归拟合效果较好，对香港7个时距的试报准确率为71%，建立了7个时距的10年滑动平均序列的门限自回归模型，模型对序列拟合效果较理想，预报误差较小，试报准确率主国100%。     

CALIBRATION:REGRESSION MODELS FOR CONCENTRATION PROBLEMS

A brief review of the literature on point estimators in linear calibration problems is undertaken,Supportive evidence for the relative merits of the classical and inverse regression models,drawn in generalfrom the classical inferential and Bayesian approaches,is considered and the criteria for comparison ofthe estimators are discussed with respect to their suitability for certain classes of problems.Theperformance of the estimators is assessed with respect to determining the current value of ‘x’,thepercentage concentration of administered drug levels in blood in this example.No single‘best’methodof estimation appears to hold for all values of the unknown concentration when performance is assessedby criteria based on the mean square error (MSE).However,the inverse estimator would appear to besuperior to the classical for those values of unknown X close to x.     

THE CONSTRUCTION OF SIMULTANEOUS OPTIMAL EXPERIMENTAL DESIGNS FOR SEVERAL POLYNOMIALS IN THE CALIBRATION OF ANALYTICAL METHODS

In this paper a criterion is described for the construction of experimental designs for the evaluation ofcalibration models in analytical chemistry.The proposed criterion seeks a compromise between theD-optimal designs for estimating the parameters of different polynomial models.A computer algorithmis presented for a sequential construction of experimental designs using the optimality criterion.Theperformance of the optimality criterion and the computer algorithm is elaborated for the problem ofdiscrimination between a first-to a third-degree polynomial for the calibration of analytical methods.Anexperimental design consisting of replicate measurements at five distinct levels equally spaced over thecalibration range proved a good solution.     

基于纹理特征的香格里拉县冷杉林郁闭度遥感估测研究

以香格里拉县2006年TM影像、2006年森林资源二类调查小班数据为信息源,结合研究区冷杉林地面实测标准地（30m×30m）数据,提取香格里拉县冷杉林TM影像分布信息及标准地纹理特征因子（共48个）,对各因子进行相关分析;利用主成分法对纹理特征因子进行因子分析,最终选出13个纹理特征因子利用偏最小二乘法进行回归建模并进行模型精度检验。根据回归估测模型以及提取出的冷杉林各波段纹理特征因子,进行研究区冷杉林郁闭度反演。结果表明,基于遥感影像纹理特征建立的郁闭度遥感估测模型,其RE=13.8%,RMSE=10.39,精度为83.3%。研究区冷杉林郁闭度反演可知冷杉林郁闭度多分布在0.6~0.7范围内,多为中度郁闭林地。     

SIMPLE VALIDATORY TOOLS FOR JUDGING THE PREDICTIVE PERFORMANCE OF PARAFAC AND THREE-WAY PLS

The methods PARAFAC and three-way PLS are compared with respect to their ability to predictreversed-phase retention values.Special attention is paid to simple validatory tools,the meaning and useof which are explained.The simple validatory tools consist of percentages of explained variation in the training set and thosethat can be calculated with the use of markers.These markers are special(reference)solutes,the retentionvalues of which are used to gain information about a new object for which predictions are wanted.Different validatory tools can be calculated with the use of these marker retention values:percentagesof used variation and mean sum of squared residuals after applying the model to these marker retentionvalues.The validatory tools are evaluated on their power to estimate their test set counterparts:thepercentages of explained variation in the test set and mean sum of squared prediction errors in the test set.Two different data sets from reversed-phase chromatography are used to evaluate the validatory tools.The first data set has a high signal-to-noise ratio and is measured under the same measurementconditions.The second data set has a low signal-to-noise ratio and is measured under differentmeasurement conditions.Some of the simple validatory tools seem to have relevance to their test setcounterparts,even in the case of the second data set.     

COMPARISON OF MEASUREMENT METHODS BASED ON A MODEL FOR THE ERROR STRUCTURE

Comparison of methods is a technique often used for investigation of systematic errors of measurementmethods.As concerns the design and analysis of such comparisons,much variety of opinion and practiceexists.In one approach a few specimens are measured several times by different operators in differentlaboratories(reproducibility conditions)and in another approach several specimens are measured on oneor a few occasions by one operator in the same laboratory(repeatability conditions).In this paper amodel for the error structure of measurements is formulated and it is emphasized that one has todistinguish between two types of systematic errors:the first type depends only on the level of themeasured quantity and the second type is specific for the separate specimens.On the basis of this modelthe information which can be obtained from the different designs of method comparisons is discussed.A new approach for the analysis of method comparisons with many specimens is also proposed.     

灰色预测理论在沙漠化监测中的应用

本文在农牧交错带沙漠化信息系统的基础上，根据数据库中的部分内容，以榆林县为例，用灰色系统的理论及ＧＭ（１，１）预测模型，分别对该县的人口及沙漠化土地进行预测研究，研究结果为；到２０００年，榆林县人口为４４．０３万人，比１９７５年净增人口１８．０５万人，占１９７５年总人口的６９．４９％，人口密度达６２．３９人／ｋｍ￣２，比１９７７年联合国沙漠化会议提出的２０人／ｋｍ￣２，为干旱地带的人口对土地压力的临界值高４２．３９人／ｋｍ￣２；榆林县重度、中度、轻度沙漠化土地面积分别为２０．６９６５万ｈａ，１５．０１２６ｈａ和１０．７１０５万ｈａ。严重沙漠化土地面积比１９７５年减少约１９万ｈａ，中度沙漠化土面积比１９７５年增加约４．８万ｈａ，轻度沙漠化土地面积比１９７５年增加５．６万ｈａ，总的趋势是沙漠化土地面积减少。     

青藏高原东北部最近两次冰期降温幅度的初步估算

基于冰楔假型和原生沙楔证据，青藏高原东北部倒数第二次冰期的气温比现在低１２℃以上，末次冰期最盛期低１１℃以上。高原上冰期的降温幅度明显大于同纬度的其他地区，因此青藏高原对气候变化的放大作用在其本身也有表现。青藏高原冰期降温幅度增大的原因可能主要在于冰期中冰川与荒漠面积增加导致的地面反射率增高。     

THE KERNEL ALGORITHM FOR PLS

A fast and memory-saving PLS regression algorithm for matrices with large numbers of objects ispresented.It is called the kernel algorithm for PLS.Long(meaning having many objects,N)matricesX (N×K)and Y(N×M)are condensed into a small(K×K)square‘kernel’matrix X~TYY~TX of sizeequal to the number of X-variables.Using this kernel matrix X~TYY~TX together with the small covariancematrices X~TX(K×K),X~TY(K×M)and Y~TY(M×M),it is possible to estimate all necessaryparameters for a complete PLS regression solution with some statistical diagnostics.The newdevelopments are presented in equation form.A comparison of consumed floating point operations isgiven for the kernel and the classical PLS algorithm.As appendices,a condensed matrix algebra versionof the kernel algorithm is given together with the MATLAB code.     

LIKELIHOOD TECHNIQUES FOR INTERLABORATORY CALIBRATION IN THE NATIONAL STREAM SURVEY

Techniques for testing for and estimating relative bias between two laboratories are developed andapplied to a survey of the chemistry of streams in the United States.The design of the quality assuranceprogram allows estimation of linear corrections for bias as well as testing of the hypothesis of linearity,Designs of this type are useful,but improvements are suggested.     

东北地区粮食生产潜力的分析与预测

在东北地区粮食生产发展过程及原因系统分析的基础上,根据统计资料,资源环境遥感调查和实地考察,定位试验的最新数据,分别阐述与粮食增产有关的种植业与大农业结构调整,水资源开发,中低产田改造,物质投入,科技与政策投入潜力。采用土地生物生产能力模型和趋势外推法预测该区２０１０年,２０３０年粮食产以及可提供的区际商品粮数量。     

THE EFFECT OF MISLABELED SAMPLES ON THE PERFORMANCE OF THE LINEAR LEARNING MACHINE

Over the past 15 years the linear learning machine has been applied to a large number of chemicalproblems.The learning machine approach is conceptually simple and does not require knowledge aboutthe statistical distribution of the data.However,there are problems associated with this approach.Oneproblem which has not been investigated is the influence of mislabeled samples on the positioning of thehyerplane in feature space.If a few samples in a data set are incorrectly tagged prior to training(i.e.thesamples are labeled as members of class 2 even though they are actually members of class 1),it is stilIpossible using the linear learning machine to achieve a classification success rate of 100% for the trainingset.However,unfavorable results will be obtained for the prediction set.The magnitude of this effect andits potential implications regarding the proper use of the linear learning machine are discussed.     

SHORT COMMUNICATION A PROGRAM FOR THE SIMULTANEOUS POTENTIOMETRIC DETERMINATION OF PROTONATION CONSTANTS AND ELECTRODE CALIBRATION PARAMETERS

A program for the potentiometric determination of the protonation constants of mononuclear polyproticsubstances is described.A maximum of twelve parameters can be determined simultaneously,includingup to six protonation constants,four electrode calibration parameters,the protolysis constant of thesolvent and the titrant concentration.Optimization is carried out by using the non-simplifiedNewton-Raphson method,which is potentiated by the Marquardt algorithm and a distance speeding-upcoefficient.A direct search method is also used to improve the initial set of values.Variances arecalculated very accurately,since the real Hessian function is used.Statistical weights and ionic strengthcorrections are also considered,The program has been tested by using simulated titration curves ofpolyprotic acids with close constants.     

PARAMETER ESTIMATION OF MULTI-CONSTITUENT WATER QUALITY MODEL FOR THE LIANGXI RIVER BY MARQUARDT METHOD

l.Illtr0ducti0l1TheLiangyiRiver,l0catedinthesouthwest0fWuxiCity,JiangsuProvinceofChina,isthemainsewagedrainagesystemofWuxi.WuxiwaterworksisnearthelnouthoftheLiangxiRivertotheTaihuLake.Tl1ewaterquality0ftl1eri\lerl1aseffectontheTaihuLakeaswellasthepublicl1ealth.Withtheincreasil1gIycomplexc0nstituentsoftheseWagandwastewterfromthecity,waterqualityvariab1es(111ulti-constituents)oftl1erivern1ustbef[111vcol1sidered.Hereco111est110LiangxiXivermulti-constituentwaterqtalitym0del.Ifthestatevaria…     

MODELLING OF LOCAL CLIMATE FOR PREDICTION OF ROAD SLIPPERINESS

Recent research for the Swedish Road Weather Information System (WIS) is discussed along with a method for determining temperature variations attributable to topography during different weather situations. Topographical areas are classified according to factors determining temperature differences. The investigation concentrates on areas where great temperature differences occur during different weather situations, producing a risk of local road slipperiness. Geographical factors analyzed and discussed include valleys, height differences, shadow areas, bridges, and regional climate. Cold air pool intensities are shown to be influenced by weather but a variation between different valleys also occurs owing to valley width, area of cold air production, wind shelter, and ratio between height and width of valley slopes. During neutral or unstable lapse rate conditions, the lowest road surface temperature is closely related to the air temperature and decreases with increasing altitude above sea level. Screened areas have a lower surface temperature than areas exposed to sun. Factors such as bridge size and type also affect road surface temperature on bridges. These different factors are integrated into a local climatological model. [Key words: topoclimatology, local climatology, modelling, road slipperiness, road surface temperature.]     

DENSIFICATION PROCESS WITHIN THE NEAR-SURFACE LAYER OF THE ANTARCTIC ICE SHEET

The densification process within the near-surface layer of Antarctic Ice Sheet is dominated by the environment and exhibits geographic zonality, In this article, the processes are found to be of three types: warm, cold and alternate, on the basis of the studies on a lot of shallow snow/firm cores from Wilkes Land, Antarctica, and the available data. Warm type densification takes place mainly on the periphery of the Antarctic Ice Sheet, where the mean annual temperature is about --10----15℃. High temperature in summer and consequent melting and infiltration are the main factors influencing the densification process. Cold type densification occurs in the huge central region of the Antarctica, where the mean annual temperature is below --25℃, with the maximum below 0℃ in summer. In this region, ice sintering is a main cause for the densification. The alternate type densification occurs in the transition zone between the above two regions, where the mean annual temperature is --15----25℃ and the highest     

甘肃省人口规模及地区分布变化

人口发展的区域差异是甘肃省社会经济发展不平衡的重要表现之一，也是其不平衡的重要原因之一。对甘肃省1990年第四次人口普查和2000年第五次人口普查数据进行实证分析和统计分布检验的结果表明，从第四次人口普查到2000年第五次人口普查，甘肃省人口在规模扩大的同时，人口的地区分布差异反而有所减小，主要原因之一是各市人口增长差异有所缩小。实现甘肃社会经济的可持续发展，必须在有效控制人口总量增长的同时，高度重视对人口发展区域差异的合理调控。