PLS scoreloading correspondence and a biorthogonal factorization

 Malcolm Norton
 8 months 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
An 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationA New Device to Measure Instantaneous Swept Volume of Reciprocating Machines/Compressors
Purdue University Purdue epubs International Compressor Engineering Conference School of Mechanical Engineering 2004 A New Device to Measure Instantaneous Swept Volume of Reciprocating Machines/Compressors
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 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 informationComparing FEM Transfer Matrix Simulated Compressor Plenum Pressure Pulsations to Measured Pressure Pulsations and to CFD Results
Purdue University Purdue epubs International Compressor Engineering Conference School of Mechanical Engineering 2012 Comparing FEM Transfer Matrix Simulated Compressor Plenum Pressure Pulsations to Measured
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 informationModeling Ignition Delay in a Diesel Engine
Modeling Ignition Delay in a Diesel Engine Ivonna D. Ploma Introduction The object of this analysis is to develop a model for the ignition delay in a diesel engine as a function of four experimental variables:
More informationExample #1: OneWay Independent Groups Design. An example based on a study by Forster, Liberman and Friedman (2004) from the
Example #1: OneWay Independent Groups Design An example based on a study by Forster, Liberman and Friedman (2004) from the Journal of Personality and Social Psychology illustrates the SAS/IML program
More informationFlanging and Hemming of Auto Body Panels using the Electro Magnetic Forming technology
Flanging and Hemming of Auto Body Panels using the Electro Magnetic Forming technology P. Jimbert 1, I Eguia 1, M. A. Gutierrez 1, B. Gonzalez 1, G. S. Daehn 2, Y. Zhang 2, R. Anderson 3, H. Sundberg 4,
More informationPERFORMANCE AND ACCEPTANCE OF ELECTRIC AND HYBRID VEHICLES
July ECNC PERFORMANCE AND ACCEPTANCE OF ELECTRIC AND HYBRID VEHICLES Determination of attitude shifts and energy consumption of electric and hybrid vehicles used in the ELCIDIS project H. Jeeninga
More informationImprovements of Existing Overhead Lines for 180km/h operation of the Tilting Train
Improvements of Existing Overhead Lines for 180km/h operation of the Tilting Train K. Lee, Y.H. Cho, Y. Park, S. Kwon Korea Railroad Research Institute, UiwangCity, Korea Abstract The purpose of this
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 informationVibration Fatigue Analysis of Sheet Metal Fender Mounting Bracket & It's Subsequent Replacement With Plastic
Vibration Fatigue Analysis of Sheet Metal Fender Mounting Bracket & It's Subsequent Replacement With Plastic Vikas Palve Manager  CAE Mahindra Two Wheelers Ltd D1 Block, Plot No 18/2 (Part), Chinchwad,
More informationStudentLevel Growth Estimates for the SAT Suite of Assessments
StudentLevel Growth Estimates for the SAT Suite of Assessments YoungKoung Kim, Tim Moses and Xiuyuan Zhang November 2017 Disclaimer: This report is a prepublished version. The version that will eventually
More informationThe Coefficient of Determination
The Coefficient of Determination Lecture 46 Section 13.9 Robb T. Koether HampdenSydney College Tue, Apr 13, 2010 Robb T. Koether (HampdenSydney College) The Coefficient of Determination Tue, Apr 13,
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 informationSelective Coordination
Circuit Breaker Curves The following curve illustrates a typical thermal magnetic molded case circuit breaker curve with an overload region and an instantaneous trip region (two instantaneous trip settings
More informationANALYZING POWER LOSSES AND THEIR EFFECTS IN COMPLEX POWER SYSTEMS
ANALYZING OWR LOSSS AND THIR FFCTS IN COMLX OWR SYSTMS S. Stoll, U. Konigorski Institute of lectrical Information Technology, Clausthal University of Technology, Leibnizstr. 28, 38678 ClausthalZellerfeld,
More informationMultiple Imputation of Missing Blood Alcohol Concentration (BAC) Values in FARS
Multiple Imputation of Missing Blood Alcohol Concentration (BAC Values in FARS Introduction Rajesh Subramanian and Dennis Utter National Highway Traffic Safety Administration, 400, 7 th Street, S.W., Room
More informationStatistical Learning Examples
Statistical Learning Examples Genevera I. Allen Statistics 640: Statistical Learning August 26, 2013 (Stat 640) Lecture 1 August 26, 2013 1 / 19 Example: Microarrays arrays Highdimensional: Goals: Measures
More informationPREDICTION OF SPECIFIC FUEL CONSUMPTION IN TURBOCHARGED DIESEL ENGINES UNDER PARTIAL LOAD PERFORMANCE
European Association for the Development of Renewable Energies, Environment and Power Quality (EA4EPQ) International Conference on Renewable Energies and Power Quality (ICREPQ 12) Santiago de Compostela
More informationAvailable online at ScienceDirect. Procedia CIRP 33 (2015 )
Available online at www.sciencedirect.com ScienceDirect Procedia CIRP 33 (2015 ) 581 586 9th CIRP Conference on Intelligent Computation in Manufacturing Engineering  CIRP ICME '14 Magnetic fluid seal
More informationPLS 01 Scientific Programme
PLS 01 Scientific Programme Sunday, September 30 th 17:00 19:00 Registration Desk open at Capri Palace Hotel 19:00 Welcoming Cocktail Monday, October 1 st 8:00 8:30 Registration Desk open at Capri Palace
More informationElectromagnetic Induction (approx. 1.5 h) (11/9/15)
(approx. 1.5 h) (11/9/15) Introduction In 1819, during a lecture demonstration, the Danish scientist Hans Christian Oersted noticed that the needle of a compass was deflected when placed near a currentcarrying
More informationModeling of 17DOF Tractor Semi Trailer Vehicle
ISSN 23951621 Modeling of 17DOF Tractor Semi Trailer Vehicle # S. B. Walhekar, #2 D. H. Burande 1 sumitwalhekar@gmail.com 2 dhburande.scoe@sinhgad.edu #12 Mechanical Engineering Department, S.P. Pune
More informationFHWA/IN/JTRP2000/23. Final Report. Sedat Gulen John Nagle John Weaver Victor Gallivan
FHWA/IN/JTRP2000/23 Final Report DETERMINATION OF PRACTICAL ESALS PER TRUCK VALUES ON INDIANA ROADS Sedat Gulen John Nagle John Weaver Victor Gallivan December 2000 Final Report FHWA/IN/JTRP2000/23 DETERMINATION
More informationsponsoring agencies.)
DEPARTMENT OF HIGHWAYS AND TRANSPORTATION VIRGINIA TESTING EQUIPMENT CORRELATION RESULTS SKID 1974, 1975, and 1978 N. Runkle Stephen Analyst Research opinions, findings, and conclusions expressed in this
More informationSession Four Applying functional safety to machine interlock guards
Session Four Applying functional safety to machine interlock guards Craig Imrie Technology Specialist: Safety, NHP Electrical Engineering Products Abstract With the recent Australian adoption of functional
More informationStudy on V2Vbased AEB System Performance Analysis in Various Road Conditions at an Intersection
, pp. 110 http://dx.doi.org/10.14257/ijseia.2015.9.7.01 Study on V2Vbased AEB System Performance Analysis in Various Road Conditions at an Intersection Sangduck Jeon 1, Gyoungeun Kim 1 and Byeongwoo
More informationFEASIBILITY STYDY OF CHAIN DRIVE IN WATER HYDRAULIC ROTARY JOINT
FEASIBILITY STYDY OF CHAIN DRIVE IN WATER HYDRAULIC ROTARY JOINT Antti MAKELA, Jouni MATTILA, Mikko SIUKO, Matti VILENIUS Institute of Hydraulics and Automation, Tampere University of Technology P.O.Box
More informationSPEED CONTROL OF FOUR QUADRANT PMDC MOTOR DRIVE USING PI BASED ANN CONTROLLER
SPEED CONTROL OF FOUR QUADRANT PMDC MOTOR DRIVE USING PI BASED ANN CONTROLLER Visakh Murali 1, Anju G Pillai 2 and Vijai Jairaj 3 1 PG Student [Electrical Machines], Department of EEE, Sree Buddha College
More informationMonitoring of Shoring Pile Movement using the ShapeAccel Array Field
2359 Royal Windsor Drive, Unit 25 Mississauga, Ontario L5J 4S9 t: 9058220090 f: 9058227911 monir.ca Monitoring of Shoring Pile Movement using the ShapeAccel Array Field Abstract: A ShapeAccel Array
More informationHigher National Unit Specification. General information for centres. Electrical Motors and Motor Starting. Unit code: DV9M 34
Higher National Unit Specification General information for centres Unit title: Electrical Motors and Motor Starting Unit code: DV9M 34 Unit purpose: This Unit has been developed to provide candidates with
More informationAppendix C: Model Contest Judging Guidelines
Appendix C: Model Contest Judging Guidelines The Model Contest Judging Guidelines are presented here for Guidance of the Contest Committee, Model Contest judges, and Model (and Portable Layout) Contest
More informationThis copy is for personal use only  distribution prohibited.
Journal of KONES Powertrain and Transport, Vol. 19, No. 4 2012      EXPERIMENTAL INVESTIGATION OF DEFLECTOR S ANGLE INFLUENCE ON ENERGY ABSORPTION Roman Gieleta, Wies aw Barnat, Tadeusz Niezgoda Military
More informationControl of Static Electricity during the Fuel Tanker Delivery Process
Control of Static Electricity during the Fuel Tanker Delivery Process Hanxiao Yu Victor Sreeram & Farid Boussaid School of Electrical, Electronic and Computer Engineering Stephen Thomas CEED Client: WA/NT
More informationLegal Metrology Control of a Liquefied Petroleum Gas Transfer Standard and Field Practice
Legal Metrology Control of a Liquefied Petroleum Gas Transfer Standard and Field Practice KunChih Tsai, WinTi Lin, JiunnHaur Shaw, ChengTsair Yang, ChunMin Su Center for Measurement Standards, CMS/ITRI
More informationLinking the Virginia SOL Assessments to NWEA MAP Growth Tests *
Linking the Virginia SOL Assessments to NWEA MAP Growth Tests * *As of June 2017 Measures of Academic Progress (MAP ) is known as MAP Growth. March 2016 Introduction Northwest Evaluation Association (NWEA
More informationPIPELINE REPAIR OF CORROSION AND DENTS: A COMPARISON OF COMPOSITE REPAIRS AND STEEL SLEEVES
Proceedings of the 2014 10th International Pipeline Conference IPC2014 September 29  October 3, 2014, Calgary, Alberta, Canada IPC201433410 PIPELINE REPAIR OF CORROSION AND DENTS: A COMPARISON OF COMPOSITE
More informationASTM B117 Testing Quality Control
ASTM B117 Testing Quality Control ASTM B117 Testing, also known as a Standard Practice for Operating Salt Spray (Fog), is used to analyze relative corrosion for specimens of metals and coated metals exposed
More informationNORDAC 2014 Topic and no NORDAC
NORDAC 2014 Topic and no NORDAC 2014 http://www.nordac.net 8.1 Load Control System of an EV Charging Station Group Antti Rautiainen and Pertti Järventausta Tampere University of Technology Department of
More informationMB3600CH30 Laboratory FTNIR analyzer for biodiesel applications Suitable for production optimization and product quality assessment
Measurement & Analytics Measurement made easy MB3600CH30 Laboratory FTNIR analyzer for biodiesel applications Suitable for production optimization and product quality assessment FTNIR optimizing productivity
More informationOregon DOT SlowSpeed WeighinMotion (SWIM) Project: Analysis of Initial Weight Data
Portland State University PDXScholar Center for Urban Studies Publications and Reports Center for Urban Studies 71997 Oregon DOT SlowSpeed WeighinMotion (SWIM) Project: Analysis of Initial Weight Data
More informationAvailable online at ScienceDirect. Physics Procedia 67 (2015 )
Available online at www.sciencedirect.com ScienceDirect Physics Procedia 67 (2015 ) 518 523 25th International Cryogenic Engineering Conference and the International Cryogenic Materials Conference in 2014,
More informationBASIC MECHATRONICS ENGINEERING
MBEYA UNIVERSITY OF SCIENCE AND TECHNOLOGY Lecture Summary on BASIC MECHATRONICS ENGINEERING NTA  4 Mechatronics Engineering 2016 Page 1 INTRODUCTION TO MECHATRONICS Mechatronics is the field of study
More informationLinking the New York State NYSTP Assessments to NWEA MAP Growth Tests *
Linking the New York State NYSTP Assessments to NWEA MAP Growth Tests * *As of June 2017 Measures of Academic Progress (MAP ) is known as MAP Growth. March 2016 Introduction Northwest Evaluation Association
More informationTechnical Series, Edition 16
Totally Integrated Power Technical Series, Edition 16 Transformer Selection according to Utilisation Profiles siemens.com/tipcs 1. Regulations concerning efficiency requirements of drytype transformers
More informationSPECTRO XRF Report SPECTRO XEPOS. Analysis of Raw Material prepared as Fused Bead in the Cement Industry. Summary
Nr. XRF43 SPECTRO XEPOS Summary The SPECTRO XEPOS simultaneous XRF spectrometer provides a fast, reliable and economic solution to analyze raw material fused bead for the cement industry. Analysis of
More informationESTIMATING THE LIVES SAVED BY SAFETY BELTS AND AIR BAGS
ESTIMATING THE LIVES SAVED BY SAFETY BELTS AND AIR BAGS Donna Glassbrenner National Center for Statistics and Analysis National Highway Traffic Safety Administration Washington DC 20590 Paper No. 500 ABSTRACT
More informationEmission factor modeling in Istituto Motori  KEM. Maria Vittoria Prati, Livia Della Ragione, Giovanni Meccariello, Maria Antonietta Costagliola
Emission factor modeling in Istituto Motori  KEM Maria Vittoria Prati, Livia Della Ragione, Giovanni Meccariello, Maria Antonietta Costagliola This presentation is dedicated to the memory of Mario Rapone
More informationStandard Drives A & D SD Application Note
SENSORLESS VECTOR CONTROL (SVC) Version A, 30.07.99 More detail of Vector Control principles are explained in DA64 Section 2. Some examples of SVC are given in Sections 4.2, 4.3 and 4.4. The MICROMASTER
More informationTest rig for rod seals contact pressure measurement
Tribology and Design 107 Test rig for rod seals contact pressure measurement G. Belforte 1, M. Conte 2, L. Mazza 1, T. Raparelli 1 & C. Visconte 1 1 Department of Mechanics, Politecnico di Torino, Italy
More informationWLTP. The Impact on Tax and Car Design
WLTP The Impact on Tax and Car Design Worldwide Harmonized Light Vehicle Testing Procedure (WLTP) The impact on tax and car design The Worldwide Harmonized Light Vehicle Testing Procedure (WLTP) is set
More informationVoltage Sag Mitigation in IEEE 6 Bus System by using STATCOM and UPFC
IJSTE  International Journal of Science Technology & Engineering Volume 2 Issue 01 July 2015 ISSN (online): 2349784X Voltage Sag Mitigation in IEEE 6 Bus System by using STATCOM and UPFC Ravindra Mohana
More informationInverter control of low speed Linear Induction Motors
Inverter control of low speed Linear Induction Motors Stephen Colyer, Jeff Proverbs, Alan Foster Force Engineering Ltd, Old Station Close, Shepshed, UK Tel: +44(0)1509 506 025 Fax: +44(0)1509 505 433 email:
More informationIMGCCNR Activities to Improve the Force Chain in Italy. C. Ferrero and C. Marinari Istituto di Metrologia G. Colonnetti (IMGCCNR) Torino  ITALY
IMGCCNR Activities to Improve the Force Chain in Italy C. Ferrero and C. Marinari Istituto di Metrologia G. Colonnetti (IMGCCNR) Torino  ITALY Abstract The IMGCCNR recently acquired two new deadweight
More informationIndustrial Maintenance Technology Student Learning Outcomes
Industrial Maintenance Technology Student Learning Outcomes February, 2017 ~ f ) FDTC Curriculum Map Program: Industrial Maintenance Technology Course# Course Title Credits Hours Lecture Lab Program Outcomes
More informationOperational Experience with Startup Optimization for Steam Boilers. E.ON s Staudinger, Heyden, Ingolstadt und Zolling Power Plants
Operational Experience with Startup Optimization for E.ON s Staudinger, Heyden, Ingolstadt und Zolling Power Plants Starting up economically BoilerMax is a predictive boiler loadmargin computer implementing
More informationMarc ZELLAT, Driss ABOURI and Stefano DURANTI CDadapco
17 th International Multidimensional Engine User s Meeting at the SAE Congress 2007,April,15,2007 Detroit, MI RECENT ADVANCES IN DIESEL COMBUSTION MODELING: THE ECFM CLEH COMBUSTION MODEL: A NEW CAPABILITY
More informationFacts, Fun and Fallacies about Finless Model Rocket Design
Facts, Fun and Fallacies about Finless Model Rocket Design Introduction Finless model rocket design has long been a subject of debate among rocketeers wishing to build and fly true scale models of space
More informationThe New ISO/CD Standard
The New ISO/CD 16355 Standard and the Effect of Ratio Scale in QFD Thomas M. Fehlmann, Zürich Eberhard Kranich, Duisburg Euro Office AG E: info@epo.com H: www.epo.com Budapest, Hotel Kempinsky October
More informationAEC PHOTOVOLTAIC TEST FACILITY FIRST YEAR TEST DATA
AEC PHOTOVOLTAIC TEST FACILITY FIRST YEAR TEST DATA James Krumsick Alternative Energy Consortium 100 West 13 th Eugene, OR 97405 email: jpkrumsick@aol.com Frank Vignola Rich Kessler University of Oregon
More informationo f Tip Relief on Transmission
E v a l u a t i o n o f M e t h o d s f o r C a l c u l a t i n g E f f e c t s o f Tip Relief on Transmission E r r o r, N o i s e a n d S t r e s s i n L o a d e d S p u r G e a r s Dr. David Palmer
More informationAssemblies for Parallel Kinematics. Frank Dürschmied. INA reprint from Werkstatt und Betrieb Vol. No. 5, May 1999 Carl Hanser Verlag, München
Assemblies for Parallel Kinematics Frank Dürschmied INA reprint from Werkstatt und Betrieb Vol. No. 5, May 1999 Carl Hanser Verlag, München Assemblies for Parallel Kinematics Frank Dürschmied Joints and
More informationFriction Characteristics of Steel Pistons for Diesel Engines
Friction Characteristics of Steel Pistons for Diesel Engines The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation As Published
More informationCars and vans CO2 regulations: even ambitious EU standards deliver less than half transport emission reductions needed to meet 2030 climate targets
Cars and vans CO2 regulations: even ambitious EU standards deliver less than half transport emission reductions needed to meet 2030 climate targets October 2017 Summary Road transport is one of the few
More informationMouse Trap Racer Scientific Investigations (Exemplar)
Mouse Trap Racer Scientific Investigations (Exemplar) Online Resources at www.steminabox.com.au/projects This Mouse Trap Racer Classroom STEM educational kit is appropriate for Upper Primary and Secondary
More informationEXPLANATORY NOTE. AMC & GM to Part21
European Aviation Safety Agency Rulemaking Directorate EXPLANATORY NOTE AMC & GM to Part21 1. GENERAL Executive Director Decision 2011/006/R amends Decision 2003/01/RM of 17 October 2003 (AMC & GM to
More information4th European PVHybrid and MiniGrid Conference, Glyfada, Greece, May 2008
Stability in MiniGrids with Large PV Penetration under Weather Disturbances Implementation to the power system of Kythnos Evangelos Rikos 1, Stathis Tselepis 1, Aristomenis Neris 2 1. Centre for Renewable
More informationDetection of Sulfur Compounds in Natural Gas According to ASTM D5504 with an Agilent Dual Plasma Sulfur Chemiluminescence Detector
Detection of Sulfur Compounds in Natural Gas According to ASTM D554 with an Agilent Dual Plasma Sulfur Chemiluminescence Detector Application Note Author Rebecca Veeneman Abstract Sulfur compounds in natural
More informationDRIVER SPEED COMPLIANCE WITHIN SCHOOL ZONES AND EFFECTS OF 40 PAINTED SPEED LIMIT ON DRIVER SPEED BEHAVIOURS Tony Radalj Main Roads Western Australia
DRIVER SPEED COMPLIANCE WITHIN SCHOOL ZONES AND EFFECTS OF 4 PAINTED SPEED LIMIT ON DRIVER SPEED BEHAVIOURS Tony Radalj Main Roads Western Australia ABSTRACT Two speed surveys were conducted on nineteen
More informationTHE EFFECT OF INNER CATALYST APPLICATION ON DIESEL ENGINE PERFORMANCE
THE EFFECT OF INNER CATALYST APPLICATION ON DIESEL ENGINE PERFORMANCE Anna Janicka, Zbigniew J. Sroka, Wojciech Walkowiak Wrocław University of Technology wyb. Wyspiańskiego 27 50370 Wroclaw tel./fax.
More informationAtomic Absorption Spectroscopy
Atomic Absorption Spectroscopy Atomic absorption spectroscopy (AAS) is a widely used technique for determining a large number of metals. In the most common implementation of AAS, a liquid sample containing
More informationMeasurement made easy. Predictive Emission Monitoring Systems The new approach for monitoring emissions from industry
Measurement made easy Predictive Emission Monitoring Systems The new approach for monitoring emissions from industry ABB s Predictive Emission Monitoring Systems (PEMS) Experts in emission monitoring ABB
More informationThermal balance of a single cylinder diesel engine operating on alternative fuels
Energy Conversion & Management 41 (2000) 1533±1541 www.elsevier.com/locate/enconman Thermal balance of a single cylinder diesel engine operating on alternative fuels E.A. Ajav a, *, Bachchan Singh b, T.K.
More informationNextgeneration SCADA and Control Technologies for Largescale Use of Photovoltaic Generation on Electric Power Grid
Hitachi Review Vol. 60 (2011), No. 3 143 Nextgeneration SCADA and Control Technologies for Largescale Use of Photovoltaic Generation on Electric Power Grid Masahiro Watanabe Tsukasa Onishi Takahiro Omori
More informationReverse order law for the MoorePenrose inverse in C*algebras
Electronic Journal of Linear Algebra Volume 22 Volume 22 (2011) Article 5 2011 Reverse order law for the MoorePenrose inverse in C*algebras Dijana Mosic Dragan S. Djordjevic Follow this and additional
More informationTHERMAL MANAGEMENT OF AIRCRAFT BRAKING SYSTEM
ABSTRACT THERMAL MANAGEMENT OF AIRCRAFT BRAKING SYSTEM Shivakumar B B 1, Ganga Reddy C 2 and Jayasimha P 3 1,2,3 HCL Technologies Limited, Bangalore, Karnataka, 560106, (India) This paper presents the
More informationEngineering Diploma Resource Guide ST280 ETP Hydraulics (Engineering)
Engineering Diploma Resource Guide ST80 ETP Hydraulics (Engineering) Introduction Hydraulic systems are a fundamental aspect of engineering. Utilised across a variety of sectors including aviation, construction,
More informationDieselDriven Compressor Torque Pulse Measurement in a Transport Refrigeration Unit
Purdue University Purdue epubs International Compressor Engineering Conference School of Mechanical Engineering 214 DieselDriven Compressor Torque Pulse Measurement in a Transport Refrigeration Unit
More informationRepeated recycling of corrugated containers and its effect on strength properties
FOREST PRODUCTS LABORATORY (Madison, Wis, 53705) FOREST SERVICE, U.S. DEPARTMENT OF AGRICULTURE Approved Technical Article Keywords Recycling Corrugating medium Physical properties Mechanical properties
More informationTITLE: EVALUATING SHEAR FORCES ALONG HIGHWAY BRIDGES DUE TO TRUCKS, USING INFLUENCE LINES
EGS 2310 Engineering Analysis Statics Mock Term Project Report TITLE: EVALUATING SHEAR FORCES ALONG HIGHWAY RIDGES DUE TO TRUCKS, USING INFLUENCE LINES y Kwabena Ofosu Introduction The impact of trucks
More informationProviding Energy Management of a Fuel CellBattery Hybrid Electric Vehicle Fatma Keskin Arabul, Ibrahim Senol, Ahmet Yigit Arabul, Ali Rifat Boynuegri
Vol:9, No:8, Providing Energy Management of a Fuel CellBattery Hybrid Electric Vehicle Fatma Keskin Arabul, Ibrahim Senol, Ahmet Yigit Arabul, Ali Rifat Boynuegri International Science Index, Energy and
More informationTheoretical and Experimental Study on Energy Efficiency of Twin Screw Blowers Compared to Rotary Lobe Blowers
Theoretical and Experimental Study on Energy Efficiency of Twin Screw Blowers Compared to Rotary Lobe Blowers Mr. Gert Van Leuven Team leader Product Development Atlas Copco Airpower n.v., Wilrijk, Belgium
More informationCOAL FIRE QUANTIFICATION AND DETECTION USING THE DLR EXPERIMENTAL BISPECTRAL INFRARED DETECTION (BIRD) SMALL SATELLITE
COAL FIRE QUANTIFICATION AND DETECTION USING THE DLR EXPERIMENTAL BISPECTRAL INFRARED DETECTION (BIRD) SMALL SATELLITE Anke Tetzlaff a,b, Andreas Hirner a, Boris Zhukov a*, Claudia Kuenzer a and Stefan
More informationData Bulletin. Wire Temperature Ratings and Terminations INTRODUCTION WHY ARE TEMPERATURE RATINGS IMPORTANT?
Data Bulletin March 2002 Lexington, KY, USA Wire Temperature Ratings and Terminations INTRODUCTION WHY ARE TEMPERATURE RATINGS IMPORTANT? Table 1: Insulation Type Figure 1: Figure 2: Ampacity of a 1/0
More information