PLS scoreloading correspondence and a biorthogonal factorization


 Malcolm Norton
 1 years ago
 Views:
Transcription
1 PLS scoreloading correspondence and a biorthogonal factorization Rolf Ergon elemark University College P.O.Box, N9 Porsgrunn, Norway telephone: telefax: Published in Journal of Chemometrics, : 87 Abstract It is established industrial practice to use the correspondence between partial least square (PLS) scores and loadings or loading weights as a means for process monitoring and control. Deviations from the normal operating point in a score plot is then related to the in uences from major process variables as shown in a loading or loading weight plot. hese relations are often presented in a biplot, i.e. appropriately scaled scores and loadings or loading weights are displayed in the same plot. As shown in the present article, however, the orthogonal PLS algorithm of Wold gives no direct theoretical and graphical correspondence, i.e. the biplot will show an angle deviation that causes an interpretational problem. he alternative nonorthogonal PLS algorithm of Martens gives direct correspondence, but the correlated latent variables may then cause another interpretational problem. As a solution to these problems the article presents a PLS factorization where both scores and loadings are orthogonal (BPLS), and we show how the Wold and Martens factorizations can easily be transformed to this solution. he result is independent latent variables as well as direct score and loading correspondence. It is also shown that the transformations involved do not a ect the predictor found by PLS regression. he scoreloading correspondence properties for the di erent PLS factorizations are discussed using principal component analysis (PCA) as a reference case. An example using industrial paper plant data is included. KEYWORDS: PLS, factorization, scoreloading correspondence Introduction and problem statement It is established industrial practice to use the correspondence between partial least squares (PLS) scores and loadings or loading weights as a means for process monitoring and control. Deviations from the normal operating point in a score plot is then related to the in uences from major process variables as shown in a loading or loading weight plot. his is normally done in a biplot, i.e. appropriately scaled scores and loadings or loading weights are displayed in the same plot. Such correspondence is of interest also in a number of other application areas ; he existing PLS algorithms are, however, not ideally suited for this purpose: he orthogonal algorithm of Wold uses independent latent variables, which in many cases re ects the underlying sources of variation. However, as shown in Section the theoretical and graphical correspondence between scores and the variable representations in the loading plots is obscured by the fact that the loadings are nonorthogonal. It is also shown that the alternative use of loading
2 weight plots is no solution to this problem. In both cases there will be an angle deviation and thus a certain lack of interpretability. he nonorthogonal algorithm of Martens uses correlated latent variables, which may be in con ict with a natural and simple interpretation. However, as shown in Section this algorithm results in a direct graphical correspondence between scores and loading weights. Each of the Wold and Martens factorizations thus have both good and less satisfying interpretational properties. A possible solution to this problem is to use a principal component analysis (PCA) factorization of the data matrix X instead of the PLS factorization, but this will in some cases give a less parsimonious model using more components, which in itself reduces the correspondence interpretability. A central problem of the present article is therefore to nd how the two PLS factorizations can be transformed to a uni ed biorthogonal solution (BPLS), where the scores are orthogonal and the loadings orthonormal, just as in PCA. Simple transformations for this purpose based on a singular value decomposition (SVD) are presented in Section, and it is also shown that these transformations do not a ect the nal PLS regression predictor. As indicated in Section, the BPLS factorization might also have interesting properties other than the ones used in the correspondence context. However, a general investigation of these properties is beyond the scope of the present article. Section discusses correspondence properties of the di erent factorizations, using PCA as a reference case, Section presents an industrial data example, and conclusions follow in Section. A biorthogonal PLS factorization Data matrix factorizations A rather general factorization of a data matrix X R Np appearing in regression is X = ^U ^R ^V + E = ^ ^V + E; () where ^U R NA and ^V R pa are matrices with orthonormal columns and ^R R AA is an invertible matrix. In SVD/PCA the matrix ^R is diagonal, resulting in X = ^U PCA ^R PCA ^V PCA + E PCA = ^ PCA ^P PCA + E PCA ; () where the score matrix ^ PCA = ^U PCA ^R PCA R NA has orthogonal columns, while the loading matrix ^P PCA = ^V PCA R pa has orthonormal columns. In PLS (a single response variable) ^R is right bidiagonal. he Wold factorization is X = ^U Wold ^ Wold ^P Wold ^W ^W + E PLS = ^ Wold ^P Wold ^W ^W + E PLS ; () where ^ Wold = ^ Wold ^ Wold R AA is diagonal, the score matrix ^ Wold R NA has orthogonal columns, the loading matrix ^P Wold R pa is nonorthogonal and the loading weight matrix ^W R pa has orthonormal columns. Note that ^V Wold = ^W ^W ^P Wold also is nonorthogonal. he Martens factorization is X = ^U Wold ^ Wold ^P Wold ^W ^W + E PLS = ^ Martens ^W + E PLS ; () where Martens = ^U Wold ^ Wold ^P Wold ^W R NA is nonorthogonal. Unifying transformations As pointed out in the introduction there is a need for a PLS factorization with an orthogonal score matrix and an orthonormal loading matrix, just as in PCA. Such a biorthogonal PLS factorization
3 (BPLS) may be found by use of SVD. After decomposition of ^ Martens, the Martens factorization () can be transformed according to X = ^ Martens ^W + E PLS = U SVD S SVD V SVD ^W + E PLS = U U S V SVD ^W + E PLS = (U S ) ^WV SVD + EPLS = ^ B ^V B + E PLS ; () resulting in ^ B = U S and ^V B = ^WV SVD. he Wold factorization () can rst be transformed to a Martens factorization according to X = ^ Wold ^P Wold ^W ^W + E PLS = ^ Martens ^W + E PLS ; () which may then be transformed to a bi orthogonal factorization according to (). Alternatively we may obtain ^ B and ^V B directly by an SVD of ^X = ^ Wold ^P Wold ^W ^W = ^ Martens ^W taken to the speci ed number of components. Note that after the unifying transformations above the loading weight matrix ^W is replaced by the loading (weight) matrix ^V B, i.e. there is no longer a need to distinguish between loadings and loading weights. Permutations As a result of the SVD decomposition used in () the ordering of components according to explaining power may get lost. In ^X = ^t B;^v B; + ^t B;^v B; + + ^t B;A^v B;A (7) the third component may for example explain more of the response variable y than the second component etc. his does not, however, a ect the total explaining power of all A components, where A is determined through validation using an ordinary PLS procedure. he ordering according to explaining power may be restored by augmenting () with a square and orthonormal permutation matrix, i.e. X = ^ B QQ ^V B + E PLS = ^ B Q ^V B Q + EPLS = ~ B ~V B + E PLS : (8) For the common case of a very low number A of total components the permutation to use is easily found by a systematic search (see example in Section ). Other cases are of little interest in a correspondence context. Final predictor It can be shown 7 that the PLS predictor based on observations collected in an X matrix and a y vector (assuming a scalar response) can be written as ^b = ^W ^W X X ^W ^W X y; (9) where ^W is found by either the Wold or the Martens algorithm. In the transformations above ^W is replaced by ^V B = ^WV SVD. Since V SVD R AA is invertible we thus nd ^b = ^V B V SVD V ^V SVD B X X ^V B V SVD V ^V SVD B X y = ^V B ^V B X X ^V B ^V B X y: () he predictor is thus unaltered after replacement of ^W by ^V B, and for the same reason it is also unaltered by the permutation matrix Q in (8).
4 Discussion on BPLS properties In the same way as in PCA, the BPLS factorization results in a score matrix with orthogonal columns and a loading matrix with orthonormal columns. his makes a comparison with PCA natural. he PCA factorization () may be found from solutions of the eigenvalue problem associated with the spectral decomposition 8 X X^p i = ^p i^i ; () X X = ^p ^^p + ^p ^^p + : : : + ^p p^p^p p = ^P^^P ; () where ^ ^ : : : ^ p, ^P ^P = I and ^P^P = I, and where ^ is diagonal. Using A components this results in X X = ^p ^^p + ^p ^^p + : : : + ^p A^A^p A + E PCAE PCA = ^P PCA ^ PCA ^P PCA + E PCAE PCA = ^P PCA ^ PCA ^ PCA ^P PCA + E PCAE PCA ; () which is also found from (). he BPLS factorization (), on the other hand, uses a loading matrix ^V B that is a linear combination ^V B = ^PL B = ^Pl ^Pl ^Pl A () such that and a score matrix such that ^V B ^V B = L B ^P ^PL B = L B L B = I; () ^ B = X ^V B = X^PL B () ^ B ^ B = L B ^P X X^PL B (7) is diagonal, just as ^ PCA ^ PCA = ^ PCA. However, this does not imply that ^V B can be found as a solution of an eigenvalue problem, except for A = p, in which case L B = I and thus ^V B = ^P. Note that ^W in the ordinary PLS factorizations also is a linear combination of ^P with L Martens L Martens = I, but that ^ Martens ^ Martens is nondiagonal 9. Also ^V Wold = ^W ^W ^P Wold is a linear combination of ^P, but then with L Wold L Wold = I. Although in itself interesting, further relations between the BPLS and other factorizations are beyond the scope of the present correspondence context. Score and loading correspondence General discussion As indicated in the introduction, correspondence between PLS scores and loadings is related to correspondence in several other multivariate display techniques used in PCA, correspondence factor analysis, spectral map analysis, factor analysis in the strict statistical sense etc.. he common step in these methods is the factorization of the data matrix X, but the methods di er with respect to the processing of the data prior to the factorization, and to the factorization method used. Comparison of factorization methods We will here use PCA as a reference. From the general factorization () and the relation ^V Wold = ^W ^W ^P Wold used in () follow the least squares solutions 8> ^ = X ^V ^V ^V = <>: X^P PCA = X ^V PCA PCA X ^W ^P Wold ^W = X ^V Wold Wold PLS X ^W = X ^V Martens X ^V B Martens PLS BPLS, (8)
5 where the orthonormality of ^P PCA, ^W and ^V B is used. Using the notation X = x x x p = N and ^ = ^t ^t ^t A = ^ ^ ^ N it follows that a given observation i results in scores 8 >< ^ i = >: ^P i PCA PCA i ^W ^P ^W Wold Wold PLS i ^W Martens PLS ^V i B BPLS, (9) where ^P PCA, ^W, and ^V B are orthonormal, while ^W ^P Wold ^W is not. Introducing the notation ^P PCA = ^p ^p ^p A = ^ ^ ^ p, ^W = ^w ^w ^w A = ^! ^! ^! p, ^V B = ^v B; ^v B; ^v B;A = ^#B; ^#B; ^#B;p and ^V Wold = ^v Wold; ^v Wold; ^v Wold;A = ^#Wold; ^#Wold; ^#Wold;p, and assuming centered data, a speci c observation i = x ij results in 8 < ^ i = : x ij ^ j x ij ^! j x ij ^#B;j PCA Martens PLS BPLS, () while ^ i = x ij ^# Wold;j Wold PLS. () Assuming orthogonal coordinate systems, the vector ^ i in the score plots thus has the same direction as the vector ^ j, ^! j or ^# j in the corresponding loading or loading weight plots for PCA, Martens PLS and BPLS. For x ij = the vectors will coincide (see example in Section ). For the Wold PLS solution, on the other hand, the vector ^ i and the corresponding vector in any of the possible loading or loading weight plots ( ^V Wold, ^W or ^P Wold ) will not have the same directions. he reason for this is that the ^V Wold matrix used in the factorization is not orthogonal, and plotting projections of ^W or ^P Wold instead of ^V Wold does not remedy the situation (see example in Section ). Relation to predictive power he correspondence discussion and results above are limited to the di erent factorization methods, and are thus not related to the predictive power of the di erent regression methods. his means that the good interpretational properties of PCA and BPLS to a certain extent may be undermined by prediction errors. Industrial data example he example uses multivariate regression data from a paper production plant ;. he problem considered here is to monitor a given paper quality y i (the second column in the rst data set) from six known process variables i = i i i i i i (columns to 9 in the rst data set), and for the purpose of nding PLS factorizations all N = 9 samples of i and y i are used. he rst three process variables i, i and i were varied systematically through an experiment, taking the values, and . he next three variables were constructed as i = i, i = i and i = i. he three constructed variables i i, i i and i i are also included in the data set, but for the paper quality chosen they have little predictive power, and for clarity of presentation they are not used in the present example.
6 Prediction Although prediction as such is not the main topic in the present context, some results are included as a background for the correspondence results presented below. As a rst step samples to were used to nd PLS regression (PLSR and BPLSR) and principal component regression (PCR) predictors using di erent numbers of components, while the samples to 9 were used for validation. Centered and standardized data were used, and the validation results are given in able. he BPLSR results were obtained by use of three components and a permutation matrix Q such that after the permutation (8) the ordering was,, (the best possible ordering found by trial and error). he fact that the two rst BPLSR components explain more than the two rst PLSR components may be due to the very limited number of samples. able : RMSEP results for di erent predictors. No. of components RMSEP PLSR RMSEP BPLSR RMSEP PCR Correspondence In a second step all N = 9 samples were used to nd PLS and BPLS factorizations and the corresponding loading and loading weight matrices using A = components. In accordance with (8) the BPLS score and loading matrices after the component permutation are denoted ~ B and ~V B. New X data were subsequently introduced as X test = ; () 7 and the new scores together with the predictor loadings and loading weights for the two rst components were plotted (Fig. ). o ease the interpretation of the results ^ test Wold and ^W etc. are plotted in the same plots (biplots). For the Wold algorithm there is generally a distinction between ^V Wold = ^W ^W ^P Wold and ^P Wold, although ^V Wold = ^P Wold for the rst two components (all except the last). he results are in agreement with the theoretical discussion in Section above, i.e. only the Martens PLS and the BPLS factorizations show total correspondence between scores and loadings/loading weights.
7 PC PC (Wold) and W(PLS) (Wold) and V(Wold)=P(Wold) (Martens) and W(PLS) (BPLS) and V(BPLS)..... PC... PC Figure. Loadings/loading weights ^V Wold, ^W and ~V B (o) for the modeling data, and scores ^ test Wold, ^ test Martens and ~ test B (x) for the X test data () with the Wold PLS, Martens PLS and BPLS factorizations. Note the total correspondence for the Martens PLS and BPLS factorizations only. Since the Xvariables are correlated, the test data () are not realistic in the present case. However, a realistic test observation is test = : () he result of this is shown in Fig., where the de ciency of the ^ test Wold and ^W plot is clearly demonstrated. Use of ^ test Wold and ^V Wold = ^P Wold gives in fact a somewhat more correct picture of the in uences of variables and, although total correspondence is found only by use of ^ test Martens and ^W or ~ test B and ~V B. 7
8 PC PC (Wold) and W(PLS) (Wold) and V(Wold)=P(Wold) (Martens) and W(PLS) (BPLS) and V(BPLS)..... PC.... PC Figure. Loadings/loading weights ^V Wold, ^W and ~V B (o) for the modeling data, and scores ^ test test Wold, ^ Martens and ~ test B (x) for the test data () with the Wold PLS, Martens PLS and BPLS factorizations. he parallelograms indicate the target score vector for test assuming total scoreloading/loading weight correspondence. Note that the Martens PLS and BPLS scores only are on target. Conclusions he existing PLS factorizations causes some interpretational problems with respect to scoreloading correspondence (orthogonal PLS of Wold) or latent variables covariance (nonorthogonal PLS of Martens). As a solution a new PLS factorization (BPLS) has been developed, which just as the PCA factorization has both an orthogonal score matrix and an orthonormal loading matrix. he two wellknown PLS algorithms of Wold and Martens can easily be transformed into a BPLS algorithm, without altering the nal predictor for the chosen number of components. he scoreloading/loading weight correspondence properties have been analyzed for the PCA, PLS Wold, PLS Martens and BPLS factorizations, and it has been shown that all of these except the PLS Wold factorization show total correspondence. he PLS Martens solution, however, has the drawback of using correlated latent variables, while the new BPLS factorization uses independent latent variables. An example using industrial paper plant data illustrates the potential BPLS advantages in process monitoring applications. References [] Skagerberg B, Sundin L. Multidimensional monitoring of complex industrial processes, ABB Review 99;/9:8 8
9 [] hielemans A, Lewi PJ, Massart DL. Similarities and Di erences among Multivariate Display echniques Illustrated by Belgian Cancer Mortality Distribution Data. Chemometrics Intell. Lab. Syst. 988;:77. [] Kvalheim OM, Karstang V. Interpretation of LatentVariable Regression Models. Chemometrics and Intelligent Laboratory Systems 989;7:9. [] Martens H, Næs. Multivariate Calibration, Wiley: New York, 989;. [] Manne R. Analysis of two partialleastsquares algorithms for multivariate calibration. Chemometrics Intell. Lab. Syst. 987;: [] Esbensen KH. Multivariate Data Analysis  in practice, Camo ASA: rondheim, Norway, ; 8. [7] Helland IS. On the structure of partial least squares regression. Communications in statistics 988;7:87. [8] Johnson AJ, Wichern DW. Applied Multivariate Statistical Analysis, PrenticeHall: Englewood Cli s, NJ, 99;8. [9] Kalivas JH. Interrelationships of multivariate regression methods using eigenvector basis sets. J. Chemometrics 999; :. [] Aldrin M. Moderate projection pursuit regression for multivariate response data. Computational Statistics and Data Analysis 99; :. [] StatLibDatasets Archive Website. [ June 999]. 9
Preface... xi. A Word to the Practitioner... xi The Organization of the Book... xi Required Software... xii Accessing the Supplementary Content...
Contents Preface... xi A Word to the Practitioner... xi The Organization of the Book... xi Required Software... xii Accessing the Supplementary Content... xii Chapter 1 Introducing Partial Least Squares...
More informationAn Introduction to Partial Least Squares Regression
An Introduction to Partial Least Squares Regression Randall D. Tobias, SAS Institute Inc., Cary, NC Abstract Partial least squares is a popular method for soft modelling in industrial applications. This
More informationInvestigation in to the Application of PLS in MPC Schemes
Ian David Lockhart Bogle and Michael Fairweather (Editors), Proceedings of the 22nd European Symposium on Computer Aided Process Engineering, 1720 June 2012, London. 2012 Elsevier B.V. All rights reserved
More informationProfessor Dr. Gholamreza Nakhaeizadeh. Professor Dr. Gholamreza Nakhaeizadeh
Statistic Methods in in Data Mining Business Understanding Data Understanding Data Preparation Deployment Modelling Evaluation Data Mining Process (Part 2) 2) Professor Dr. Gholamreza Nakhaeizadeh Professor
More informationPARTIAL LEAST SQUARES: APPLICATION IN CLASSIFICATION AND MULTIVARIABLE PROCESS DYNAMICS IDENTIFICATION
PARIAL LEAS SQUARES: APPLICAION IN CLASSIFICAION AND MULIVARIABLE PROCESS DYNAMICS IDENIFICAION Seshu K. Damarla Department of Chemical Engineering National Institute of echnology, Rourkela, India Email:
More informationOptimization of Seat Displacement and Settling Time of Quarter Car Model Vehicle Dynamic System Subjected to Speed Bump
Research Article International Journal of Current Engineering and Technology EISSN 2277 4106, PISSN 23475161 2014 INPRESSCO, All Rights Reserved Available at http://inpressco.com/category/ijcet Optimization
More informationEstimation of Unmeasured DOF s on a Scaled Model of a Blade Structure
Estimation of Unmeasured DOF s on a Scaled Model of a Blade Structure Anders Skafte 1, Rune Brincker 2 ABSTRACT This paper presents a new expansion technique which enables to predict mode shape coordinates
More informationBurn Characteristics of Visco Fuse
Originally appeared in Pyrotechnics Guild International Bulletin, No. 75 (1991). Burn Characteristics of Visco Fuse by K.L. and B.J. Kosanke From time to time there is speculation regarding the performance
More information9.2 User s Guide SAS/STAT. The PLS Procedure. (Book Excerpt) SAS Documentation
SAS/STAT 9.2 User s Guide The PLS Procedure (Book Excerpt) SAS Documentation This document is an individual chapter from SAS/STAT 9.2 User s Guide. The correct bibliographic citation for the complete manual
More informationAPPLICATION OF A PCA MODEL APPROACH FOR MISFIRE MONITORING. Paul J. King 1 and Keith J. Burnham 2
APPLICATION OF A PCA MODEL APPROACH FOR MISFIRE MONITORING Paul J. King 1 and Keith J. Burnham 2 1 Powertrain Control Systems and Calibration, Jaguar Cars Limited, Coventry, CV3 4BJ, U.K. 2 Control Theory
More informationOptimization of Chromatogram Alignment Using A Class Separability Criterion
Optimization of Chromatogram Alignment Using A Class Separability Criterion Gopal Yalla Department of Mathematics and Computer Science Department of Chemistry College of the Holy Cross April 28, 2015 Gopal
More informationSAS/STAT 13.1 User s Guide. The PLS Procedure
SAS/STAT 13.1 User s Guide The PLS Procedure This document is an individual chapter from SAS/STAT 13.1 User s Guide. The correct bibliographic citation for the complete manual is as follows: SAS Institute
More informationImproving Analog Product knowledge using Principal Components Variable Clustering in JMP on test data.
Improving Analog Product knowledge using Principal Components Variable Clustering in JMP on test data. Yves Chandon, Master BlackBelt at Freescale Semiconductor F e b 2 7. 2015 TM External Use We Touch
More informationIMA Preprint Series # 2035
PARTITIONS FOR SPECTRAL (FINITE) VOLUME RECONSTRUCTION IN THE TETRAHEDRON By QianYong Chen IMA Preprint Series # 2035 ( April 2005 ) INSTITUTE FOR MATHEMATICS AND ITS APPLICATIONS UNIVERSITY OF MINNESOTA
More informationLecture 2. Review of Linear Regression I Statistics Statistical Methods II. Presented January 9, 2018
Review of Linear Regression I Statistics 211  Statistical Methods II Presented January 9, 2018 Estimation of The OLS under normality the OLS Dan Gillen Department of Statistics University of California,
More informationSvante Wold, Research Group for Chemometrics, Institute of Chemistry, Umeå University, S Umeå, Sweden
Submitted version, June 2004 The PLS method  partial least squares projections to latent structures  and its applications in industrial RDP (research, development, and production). Svante Wold, Research
More informationPARTIAL LEAST SQUARES: WHEN ORDINARY LEAST SQUARES REGRESSION JUST WON T WORK
PARTIAL LEAST SQUARES: WHEN ORDINARY LEAST SQUARES REGRESSION JUST WON T WORK Peter Bartell JMP Systems Engineer peter.bartell@jmp.com WHEN OLS JUST WON T WORK? OLS (Ordinary Least Squares) in JMP/JMP
More informationThe Degrees of Freedom of Partial Least Squares Regression
The Degrees of Freedom of Partial Least Squares Regression Dr. Nicole Krämer TU München 5th ESSECSUPELEC Research Workshop May 20, 2011 My talk is about...... the statistical analysis of Partial Least
More informationTesting for seasonal unit roots in heterogeneous panels using monthly data in the presence of cross sectional dependence
Testing for seasonal unit roots in heterogeneous panels using monthly data in the presence of cross sectional dependence Jesús Otero Facultad de Economía Universidad del Rosario Colombia Jeremy Smith y
More informationUsing MATLAB/ Simulink in the designing of Undergraduate Electric Machinery Courses
Using MATLAB/ Simulink in the designing of Undergraduate Electric Machinery Courses Mostafa.A. M. Fellani, Daw.E. Abaid * Control Engineering department Faculty of Electronics Technology, BeniWalid, Libya
More informationSimulation of Voltage Stability Analysis in Induction Machine
International Journal of Electronic and Electrical Engineering. ISSN 09742174 Volume 6, Number 1 (2013), pp. 112 International Research Publication House http://www.irphouse.com Simulation of Voltage
More informationSum of ranking differences (SRD) to ensemble multivariate calibration model merits for tuning parameter selection and comparing calibration methods
"This accepted author manuscript is copyrighted and published by Elsevier. It is posted here by agreement between Elsevier and MTA. The definitive version of the text was subsequently published in [ANALYTICA
More informationAssignment 3 solutions
Assignment 3 solutions Question 1: SVM on the OJ data (a) [2 points] Create a training set containing a random sample of 800 observations, and a test set containing the remaining observations. library(islr)
More informationGearbox Fault Detection
Gearbox Fault Detection At the University of Iowa, detecting wind turbine gearbox faults based on vibration acceleration data provided by NREL is augmented by data mining techniques. By Andrew Kusiak and
More informationACSEP  Applications and Control of Power Electronic Systems
Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2018 205  ESEIAAT  Terrassa School of Industrial, Aerospace and Audiovisual Engineering 710  EEL  Department of Electronic Engineering
More informationArticle: Sulfur Testing VPS Quality Approach By Dr Sunil Kumar Laboratory Manager Fujairah, UAE
Article: Sulfur Testing VPS Quality Approach By Dr Sunil Kumar Laboratory Manager Fujairah, UAE 26th September 2017 For over a decade, both regional ECA and global sulphur limits within marine fuels have
More informationCEMENT AND CONCRETE REFERENCE LABORATORY PROFICIENCY SAMPLE PROGRAM
CEMENT AND CONCRETE REFERENCE LABORATORY PROFICIENCY SAMPLE PROGRAM Final Report ASR ASTM C1260 Proficiency Samples Number 5 and Number 6 August 2018 www.ccrl.us www.ccrl.us August 24, 2018 TO: Participants
More informationLaboratory Tests, Modeling and the Study of a Small DoublyFed Induction Generator (DFIG) in Autonomous and GridConnected Scenarios
Trivent Publishing The Authors, 2016 Available online at http://triventpublishing.eu/ Engineering and Industry Series Volume Power Systems, Energy Markets and Renewable Energy Sources in SouthEastern
More informationThe reverse order law (ab) # = b (a abb ) a in rings with involution
The reverse order law (ab) # = b (a abb ) a in rings with involution Dijana Mosić and Dragan S. Djordjević Abstract Several equivalent conditions for the reverse order law (ab) # = b (a abb ) a in rings
More informationImproved PV Module Performance Under Partial Shading Conditions
Available online at www.sciencedirect.com Energy Procedia 33 (2013 ) 248 255 PV Asia Pacific Conference 2012 Improved PV Module Performance Under Partial Shading Conditions Fei Lu a,*, Siyu Guo a, Timothy
More informationTimeDependent Behavior of Structural Bolt Assemblies with TurnaSure Direct Tension Indicators and Assemblies with Only Washers
TimeDependent Behavior of Structural Bolt Assemblies with TurnaSure Direct Tension Indicators and Assemblies with Only Washers A Report Prepared for TurnaSure, LLC Douglas B. Cleary, Ph.D., P.E. William
More informationA REPORT ON THE STATISTICAL CHARACTERISTICS of the Highlands Ability Battery CD
A REPORT ON THE STATISTICAL CHARACTERISTICS of the Highlands Ability Battery CD Prepared by F. Jay Breyer Jonathan Katz Michael Duran November 21, 2002 TABLE OF CONTENTS Introduction... 1 Data Determination
More informationPREDICTION OF FUEL CONSUMPTION
PREDICTION OF FUEL CONSUMPTION OF AGRICULTURAL TRACTORS S. C. Kim, K. U. Kim, D. C. Kim ABSTRACT. A mathematical model was developed to predict fuel consumption of agricultural tractors using their official
More informationGetting Started with Correlated Component Regression (CCR) in XLSTATCCR
Tutorial 1 Getting Started with Correlated Component Regression (CCR) in XLSTATCCR Dataset for running Correlated Component Regression This tutorial 1 is based on data provided by Michel Tenenhaus and
More informationShock tube based dynamic calibration of pressure sensors
Shock tube based dynamic calibration of pressure sensors C. E. Matthews, S. Downes, T.J. Esward, A. Wilson (NPL) S. Eichstädt, C. Elster (PTB) 23/06/2011 1 Outline Shock tube as a basis for calibration
More informationEnergy Management for Regenerative Brakes on a DC Feeding System
Energy Management for Regenerative Brakes on a DC Feeding System Yuruki Okada* 1, Takafumi Koseki* 2, Satoru Sone* 3 * 1 The University of Tokyo, okada@koseki.t.utokyo.ac.jp * 2 The University of Tokyo,
More informationPHYS 2212L  Principles of Physics Laboratory II
PHYS 2212L  Principles of Physics Laboratory II Laboratory Advanced Sheet Faraday's Law 1. Objectives. The objectives of this laboratory are a. to verify the dependence of the induced emf in a coil on
More informationAtmospheric Chemistry and Physics. Interactive Comment. K. Kourtidis et al.
Atmos. Chem. Phys. Discuss., www.atmoschemphysdiscuss.net/15/c4860/2015/ Author(s) 2015. This work is distributed under the Creative Commons Attribute 3.0 License. Atmospheric Chemistry and Physics
More informationME scope Application Note 29 FEA Model Updating of an Aluminum Plate
ME scope Application Note 29 FEA Model Updating of an Aluminum Plate NOTE: You must have a package with the VES4500 MultiReference Modal Analysis and VES8000 FEA Model Updating options enabled to reproduce
More informationTopic 5 Lecture 3 Estimating Policy Effects via the Simple Linear. Regression Model (SLRM) and the Ordinary Least Squares (OLS) Method
Econometrics for Health Policy, Health Economics, and Outcomes Research Topic 5 Lecture 3 Estimating Policy Effects via the Simple Linear Regression Model (SLRM) and the Ordinary Least Squares (OLS) Method
More informationDomaininvariant Partial Least Squares (dipls) Regression: A novel method for unsupervised and semisupervised calibration model adaptation
Domaininvariant Partial Least Squares (dipls) Regression: A novel method for unsupervised and semisupervised calibration model adaptation R. NikzadLangerodi W. Zellinger E. Lughofer T. Reischer 2 S.
More informationWaveletPLS Regression: Application to Oil Production Data
WaveletPLS Regression: Application to Oil Production Data Benammou Saloua 1, Kacem Zied 1, Kortas Hedi 1, and Dhifaoui Zouhaier 1 1 Computational Mathematical Laboratory, saloua.benammou@yahoo.fr 2 ZiedKacem2004@yahoo.fr
More informationFractional Factorial Designs with Admissible Sets of Clear TwoFactor Interactions
Statistics Preprints Statistics 112008 Fractional Factorial Designs with Admissible Sets of Clear TwoFactor Interactions Huaiqing Wu Iowa State University, isuhwu@iastate.edu Robert Mee University of
More informationFeatured Articles Utilization of AI in the Railway Sector Case Study of Energy Efficiency in Railway Operations
128 Hitachi Review Vol. 65 (2016), No. 6 Featured Articles Utilization of AI in the Railway Sector Case Study of Energy Efficiency in Railway Operations Ryo Furutani Fumiya Kudo Norihiko Moriwaki, Ph.D.
More informationChapter 5 ESTIMATION OF MAINTENANCE COST PER HOUR USING AGE REPLACEMENT COST MODEL
Chapter 5 ESTIMATION OF MAINTENANCE COST PER HOUR USING AGE REPLACEMENT COST MODEL 87 ESTIMATION OF MAINTENANCE COST PER HOUR USING AGE REPLACEMENT COST MODEL 5.1 INTRODUCTION Maintenance is usually carried
More informationA Viewpoint on the Decoding of the Quadratic Residue Code of Length 89
International Journal of Networks and Communications 2012, 2(1): 1116 DOI: 10.5923/j.ijnc.20120201.02 A Viewpoint on the Decoding of the Quadratic Residue Code of Length 89 HungPeng Lee Department of
More informationSupervised Learning to Predict Human Driver Merging Behavior
Supervised Learning to Predict Human Driver Merging Behavior Derek Phillips, Alexander Lin {djp42, alin719}@stanford.edu June 7, 2016 Abstract This paper uses the supervised learning techniques of linear
More informationINTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY
[Sarvi, 1(9): Nov., 2012] ISSN: 22779655 IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY A Sliding Mode Controller for DC/DC Converters. Mohammad Sarvi 2, Iman Soltani *1, NafisehNamazypour
More informationAppendices for: Statistical Power in Analyzing Interaction Effects: Questioning the Advantage of PLS with Product Indicators
Appendices for: Statistical Power in Analyzing Interaction Effects: Questioning the Advantage of PLS with Product Indicators Dale Goodhue Terry College of Business MIS Department University of Georgia
More informationOil Palm Ripeness Detector (OPRID) and NonDestructive Thermal Method of Palm Oil Quality Estimation
Oil Palm Ripeness Detector (OPRID) and NonDestructive Thermal Method of Palm Oil Quality Estimation Abdul Rashid Mohamed Shariff, Shahrzad Zolfagharnassab, Alhadi Aiad H. Ben Dayaf, Goh Jia Quan, Adel
More informationPOWER QUALITY IMPROVEMENT BASED UPQC FOR WIND POWER GENERATION
International Journal of Latest Research in Science and Technology Volume 3, Issue 1: Page No.6874,JanuaryFebruary 2014 http://www.mnkjournals.com/ijlrst.htm ISSN (Online):22785299 POWER QUALITY IMPROVEMENT
More informationLocomotive Allocation for Toll NZ
Locomotive Allocation for Toll NZ Sanjay Patel Department of Engineering Science University of Auckland, New Zealand spat075@ec.auckland.ac.nz Abstract A Locomotive is defined as a selfpropelled vehicle
More informationAnalysis on natural characteristics of fourstage main transmission system in threeengine helicopter
Article ID: 18558; Draft date: 20170612 23:31 Analysis on natural characteristics of fourstage main transmission system in threeengine helicopter Yuan Chen 1, Rupeng Zhu 2, Yeping Xiong 3, Guanghu
More informationME scope Application Note 25 Choosing Response DOFs for a Modal Test
ME scope Application Note 25 Choosing Response DOFs for a Modal Test The steps in this Application Note can be duplicated using any ME'scope Package that includes the VES3600 Advanced Signal Processing
More informationThe use of PARAFAC in the analysis of CDOM fluorescence
The use of PARAFAC in the analysis of CDOM fluorescence Kate Murphy 1,2 1. Smithsonian Environmental Research Center, Edgewater USA 2. The University of New South Wales, Dept. of Civil and Environmental
More informationIndustrial Controls Training System. Motor Drives. Courseware Sample F0
Industrial Controls Training System Motor Drives Courseware Sample 87669F0 A First Edition Published October 2013 2011 by LabVolt Ltd. Printed in Canada All rights reserved ISBN 9782896404698 (Printed
More informationInfluence of Parameter Variations on System Identification of Full Car Model
Influence of Parameter Variations on System Identification of Full Car Model Fengchun Sun, an Cui Abstract The car model is used extensively in the system identification of a vehicle suspension system
More informationA Unified Regularized Group PLS Algorithm Scalable to Big Data
A Unified Regularized Group PLS Algorithm Scalable to Big Data Pierre Lafaye de Micheaux 1, Benoit Liquet 2, Matthew Sutton 3 21 October, 2016 1 CREST, ENSAI. 2 Université de Pau et des Pays de l Adour,
More informationTechnical Papers supporting SAP 2009
Technical Papers supporting SAP 29 A metaanalysis of boiler test efficiencies to compare independent and manufacturers results Reference no. STP9/B5 Date last amended 25 March 29 Date originated 6 October
More informationInternational Journal of Advance Research in Engineering, Science & Technology
Impact Factor (SJIF): 4.542 International Journal of Advance Research in Engineering, Science & Technology eissn: 23939877, pissn: 23942444 Volume 4, Issue 4, April2017 Simulation and Analysis for
More informationForecasting China s Inflation in a DataRich. Environment
Forecasting China s Inflation in a DataRich Environment ChingYi Lin Department of Economics, National Tsing Hua University Chun Wang Department of Economics, Brooklyn College, CUNY Abstract Inflation
More informationPVP Field Calibration and Accuracy of Torque Wrenches. Proceedings of ASME PVP ASME Pressure Vessel and Piping Conference PVP2011
Proceedings of ASME PVP2011 2011 ASME Pressure Vessel and Piping Conference Proceedings of the ASME 2011 Pressure Vessels July 1721, & Piping 2011, Division Baltimore, Conference Maryland PVP2011 July
More informationCDI15 6. Haar wavelets (1D) 1027, 1104, , 416, 428 SXD
CDI15 6. Haar wavelets (1D) 1027, 1104, 1110 414, 416, 428 SXD Notations 6.1. The Haar transforms 6.2. Haar wavelets 6.3. Multiresolution analysis 6.4. Compression/decompression James S. Walker A primer
More informationREMOTE SENSING MEASUREMENTS OF ONROAD HEAVYDUTY DIESEL NO X AND PM EMISSIONS E56
REMOTE SENSING MEASUREMENTS OF ONROAD HEAVYDUTY DIESEL NO X AND PM EMISSIONS E56 January 2003 Prepared for Coordinating Research Council, Inc. 3650 Mansell Road, Suite 140 Alpharetta, GA 30022 by Robert
More informationDynamic Coefficients in Hydrodynamic Bearing Analysis Steven Pasternak C.O. Engineering Sleeve and Sleevoil Bearings 8/10/18 WP0281
Dynamic Coefficients in Hydrodynamic Bearing Analysis Steven Pasternak C.O. Engineering Sleeve and Sleevoil Bearings 8/10/18 WP0281 Hydrodynamic Bearing Basics Hydrodynamic journal bearings operate by
More informationUnderstanding the benefits of using a digital valve controller. Mark Buzzell Business Manager, Metso Flow Control
Understanding the benefits of using a digital valve controller Mark Buzzell Business Manager, Metso Flow Control Evolution of Valve Positioners Digital (Next Generation) Digital (First Generation) Analog
More informationHeat Transfer Enhancement for Double Pipe Heat Exchanger Using Twisted Wire Brush Inserts
Heat Transfer Enhancement for Double Pipe Heat Exchanger Using Twisted Wire Brush Inserts Deepali Gaikwad 1, Kundlik Mali 2 Assistant Professor, Department of Mechanical Engineering, Sinhgad College of
More informationINVITED REVIEW PAPER. Faisal Ahmed*, LaeHyun Kim**, and YeongKoo Yeo*,
Korean J. Chem. Eng., 30(1), 1119 (2013) DOI: 10.1007/s118140120107z INVITED REVIEW PAPER Statistical data modeling based on partial least squares: Application to melt index predictions in high density
More informationA UNIFYING VIEW ON MULTISTEP FORECASTING USING AN AUTOREGRESSION
doi: 10.1111/j.14676419.2009.00581.x A UNIFYING VIEW ON MULTISTEP FORECASTING USING AN AUTOREGRESSION Philip Hans Franses and Rianne Legerstee Econometric Institute and Tinbergen Institute, Erasmus University
More informationA.I. Ropodi, D.E. Pavlidis, D. Loukas, P. Tsakanikas, E.Z. Panagou and G.J.E. NYCHAS.
A.I. Ropodi, D.E. Pavlidis, D. Loukas, P. Tsakanikas, E.Z. Panagou and G.J.E. NYCHAS Email: gjn@aua.gr ..an alternative approach is needed within the PAT concept This work aims to investigate the potential
More informationINTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 5, No 2, 2014
INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 5, No 2, 2014 Copyright by the authors  Licensee IPA Under Creative Commons license 3.0 Research article ISSN 0976 4399 The impacts of
More informationMODELING SUSPENSION DAMPER MODULES USING LSDYNA
MODELING SUSPENSION DAMPER MODULES USING LSDYNA Jason J. Tao Delphi Automotive Systems Energy & Chassis Systems Division 435 Cincinnati Street Dayton, OH 4548 Telephone: (937) 4556298 Email: Jason.J.Tao@Delphiauto.com
More informationPredicting Tractor Fuel Consumption
University of Nebraska  Lincoln DigitalCommons@University of Nebraska  Lincoln Biological Systems Engineering: Papers and Publications Biological Systems Engineering 24 Predicting Tractor Fuel Consumption
More informationComplex Power Flow and Loss Calculation for Transmission System Nilam H. Patel 1 A.G.Patel 2 Jay Thakar 3
IJSRD International Journal for Scientific Research & Development Vol. 2, Issue 04, 2014 ISSN (online): 23210613 Nilam H. Patel 1 A.G.Patel 2 Jay Thakar 3 1 M.E. student 2,3 Assistant Professor 1,3 Merchant
More informationSimulation of Performance Parameters of Spark Ignition Engine for Various Ignition Timings
Research Article International Journal of Current Engineering and Technology ISSN 22774106 2013 INPRESSCO. All Rights Reserved. Available at http://inpressco.com/category/ijcet Simulation of Performance
More informationDETERMINATION OF OPERATING CHARACTERISTICS OF NAVAL GAS TURBINES LM2500
Journal of KONES Powertrain and Transport, Vol. 18, No. 3 2011 DETERMINATION OF OPERATING CHARACTERISTICS OF NAVAL GAS TURBINES LM2500 Bogdan Pojawa, Ma gorzata Ho dowska Polish Naval Academy Department
More informationTEST REPORT. Test Report for Mating Cycle Validation of Mini Circuits QBL Series QuickLock Test Cables.
TITLE: Test Report for Mating Cycle Validation of Mini Circuits QBL Series QuickLock Test Cables. 1. Background & Introduction MiniCircuits has introduced a QBL Series of test cables is based upon an
More informationINFLUENCE OF CROSS FORCES AND BENDING MOMENTS ON REFERENCE TORQUE SENSORS FOR TORQUE WRENCH CALIBRATION
XIX IMEKO World Congress Fundamental and Applied Metrology September 6 11, 2009, Lisbon, Portugal INFLUENCE OF CROSS FORCES AND BENDING MOMENTS ON REFERENCE TORQUE SENSORS FOR TORQUE WRENCH CALIBRATION
More informationTheoretical and Experimental Investigation of Compression Loads in Twin Screw Compressor
Purdue University Purdue epubs International Compressor Engineering Conference School of Mechanical Engineering 2004 Theoretical and Experimental Investigation of Compression Loads in Twin Screw Compressor
More informationAnalysis and Correlation for Body Attachment Stiffness in BIW
Analysis and Correlation for Body Attachment Stiffness in BIW Jiwoo Yoo, J.K.Suh, S.H.Lim, J.U.Lee, M.K.Seo Hyundai Motor Company, S. Korea ABSTRACT It is known that automotive body structure must have
More informationHydraulic Drive Head Performance Curves For Prediction of Helical Pile Capacity
Hydraulic Drive Head Performance Curves For Prediction of Helical Pile Capacity Don Deardorff, P.E. Senior Application Engineer Abstract Helical piles often rely on the final installation torque for ultimate
More informationOnline Appendix for Subways, Strikes, and Slowdowns: The Impacts of Public Transit on Traffic Congestion
Online Appendix for Subways, Strikes, and Slowdowns: The Impacts of Public Transit on Traffic Congestion ByMICHAELL.ANDERSON AI. Mathematical Appendix Distance to nearest bus line: Suppose that bus lines
More informationPredicting Solutions to the Optimal Power Flow Problem
Thomas Navidi Suvrat Bhooshan Aditya Garg Abstract Predicting Solutions to the Optimal Power Flow Problem This paper discusses an implementation of gradient boosting regression to predict the output of
More informationDamping Ratio Estimation of an Existing 8story Building Considering SoilStructure Interaction Using Strong Motion Observation Data.
Damping Ratio Estimation of an Existing story Building Considering SoilStructure Interaction Using Strong Motion Observation Data by Koichi Morita ABSTRACT In this study, damping ratio of an exiting
More informationToleranceBased TimeCurrent Coordination
S&C IntelliRupter PulseCloser Fault Interrupter Outdoor Distribution (15.5 kv, 27 kv, and 38 kv) ToleranceBased TimeCurrent Coordination Table of Contents Section Page Section Page Overview Background....
More informationPASSING ABILITY OF SCC IMPROVED METHOD BASED ON THE PRING
PASSING ABILITY OF SCC IMPROVED METHOD BASED ON THE PRING K D Chan*, Leppo Concrete Sdn Bhd, Malaysia K C G Ong, National University of Singapore, Singapore C T Tam, National University of Singapore,
More informationA Cost Benefit Analysis of Faster Transmission System Protection Schemes and Ground Grid Design
A Cost Benefit Analysis of Faster Transmission System Protection Schemes and Ground Grid Design Presented at the 2018 Transmission and Substation Design and Operation Symposium Revision presented at the
More informationCOMPUTER CONTROL OF AN ACCUMULATOR BASED FLUID POWER SYSTEM: LEARNING HYDRAULIC SYSTEMS
The 2 nd International Workshop Ostrava  Malenovice, 5.7. September 21 COMUTER CONTROL OF AN ACCUMULATOR BASED FLUID OWER SYSTEM: LEARNING HYDRAULIC SYSTEMS Dr. W. OST Eindhoven University of Technology
More informationCONSTRUCT VALIDITY IN PARTIAL LEAST SQUARES PATH MODELING
Association for Information Systems AIS Electronic Library (AISeL) ICIS 2010 Proceedings International Conference on Information Systems (ICIS) 112010 CONSTRUCT VALIDITY IN PARTIAL LEAST SQUARES PATH
More informationComputer Aided Transient Stability Analysis
Journal of Computer Science 3 (3): 149153, 2007 ISSN 15493636 2007 Science Publications Corresponding Author: Computer Aided Transient Stability Analysis Nihad M. AlRawi, Afaneen Anwar and Ahmed Muhsin
More informationCostEfficiency by Arash Method in DEA
Applied Mathematical Sciences, Vol. 6, 2012, no. 104, 51795184 CostEfficiency by Arash Method in DEA Dariush Khezrimotlagh*, Zahra Mohsenpour and Shaharuddin Salleh Department of Mathematics, Faculty
More informationEvaluation of Renton Ramp Meters on I405
Evaluation of Renton Ramp Meters on I405 From the SE 8 th St. Interchange in Bellevue to the SR 167 Interchange in Renton January 2000 By Hien Trinh Edited by Jason Gibbens Northwest Region Traffic Systems
More informationinter.noise 2000 The 29th International Congress and Exhibition on Noise Control Engineering August 2000, Nice, FRANCE
Copyright SFA  InterNoise 2000 1 inter.noise 2000 The 29th International Congress and Exhibition on Noise Control Engineering 2730 August 2000, Nice, FRANCE IINCE Classification: 0.0 EFFECTS OF TRANSVERSE
More informationBAC and Fatal Crash Risk
BAC and Fatal Crash Risk David F. Preusser PRG, Inc. 7100 Main Street Trumbull, Connecticut Keywords Alcohol, risk, crash Abstract Induced exposure, a technique whereby notatfault driver crash involvements
More informationINTRODUCTION. I.1  Historical review.
INTRODUCTION. I.1  Historical review. The history of electrical motors goes back as far as 1820, when Hans Christian Oersted discovered the magnetic effect of an electric current. One year later, Michael
More informationReliability and Validity of Seat Interface Pressure to Quantify Seating Comfort in Motorcycles
Reliability and Validity of Seat Interface Pressure to Quantify Seating Comfort in Motorcycles Sai Praveen Velagapudi a,b, Ray G. G b a Research & Development, TVS Motor Company, INDIA; b Industrial Design
More informationEnhancing Wheelchair Mobility Through Dynamics Mimicking
Proceedings of the 3 rd International Conference Mechanical engineering and Mechatronics Prague, Czech Republic, August 1415, 2014 Paper No. 65 Enhancing Wheelchair Mobility Through Dynamics Mimicking
More informationAN RPM to TACH Counts Conversion. 1 Preface. 2 Audience. 3 Overview. 4 References
AN 17.4 RPM to TACH Counts Conversion 1 Preface 2 Audience 3 Overview 4 References This application note provides look up tables for the calculation of RPM to TACH Counts for use with the EMC2103, EMC2104,
More information