Matematik og visualisering giver overblik over myriader af data

Transcription

1 Matematik og visualisering giver overblik over myriader af data Thomas Skov, ssociate Professor, PhD Quality & Technology, Department of Food Science, Faculty of Science, University of openhagen, Denmark / genda Where am I from? Measure, understand, control, improve Why and what is multivariate? Principal omponent nalysis Model parameters MSP 1

2 Q&T Quality & Technology Quality & Technology Department of Food Science Faculty of Science University of openhagen Quality & Technology Department of Food Science Faculty of Life Sciences University of openhagen Rolighedsvej 3 DK 1958 Frederiksberg Phone /64 Fax QULITY & TEHNOLOGY 211 Quality & Technology New sensor technology and advanced data analysis for health/food science and industry Key reas Metabolomics Molecular functionality and health effects of plant foods Spectroscopic Quality ontrol and Process nalytical Technology Key Tools hemometrics Flavour analysis by G-MS Optical spectroscopy and nuclear magnetic resonance QULITY & TEHNOLOGY 211 2

3 Q&T Permanent Scientific Staff Søren Balling Engelsen Professor SPETROSOPY Rasmus Bro Professor MULTIWY Åse Hansen ssociate professor ERELS Mikael gerlin Pedersen ssociate professor FLVOUR Frans van den Berg ssociate professor PT Flemming Hofmann Larsen ssociate professor NMR Nanna Viereck ssociate professor NMR Birthe Pontoppidan Møller Åsmund Rinnan ssociate professor ssociate professor PLNT FOODS HEMOMETRIS José Manuel migo ssociate professor HEMOMETRIS Thomas Skov ssociate professor HEMOMETRIS QULITY & TEHNOLOGY 211 Q&T Mission 212 Q&T Q&T conducts research, provides education and offers industrial collaboration in the areas of: hemometrics and applied biospectroscopy Metabolomics and process analytical technology PT Plant food research and applications to improve food quality and health Quality & Technology Department of Food Science Faculty of Life Sciences University of openhagen Rolighedsvej 3 DK 1958 Frederiksberg Phone /64 Fax QULITY & TEHNOLOGY 211 3

4 PT & hemometrics So what is hot at Q&T at the moment? Develop methods for multivariate experiments! E.g. how to extract the most (relevant) information from data E.g. how to predict the final product quality from all the process variables and the raw material pply methods so that a process can be optimized before, during or after the production step E.g. feed backward/forward control E.g. controlling the water content of pellets in a freeze drying process QULITY & TEHNOLOGY 211 Process nalytical Technology PT! 4

5 Multivariate what is that? Univariate vs. multivariate - ovariance! Upper limit Pressure Sample no. Lower limit 2 Sample no. 4 6 Temperature 8 1 Lower limit Upper limit 5

6 Sale of cars Sale of Sale of cars Sale of orrelation/causality 3 Sale of 1 2 ausal correlation: If changes then we know B changes! Indirect correlation: If changes we cant say if B changes! Prize on cars orrelation/causality 3 Sale of 1 $$$ 2 ausal correlation: If changes then we know B changes! Indirect correlation: If changes we cant say if B changes! Prize on cars 6

7 4 lassification of unknown sample process over time 3 Factory 3 Factory Unknown

8 Visual classification from process parameters Factory Factory Or by inspecting the numbers! Unknown

9 Peak Intensities of variable 5 (peak 1) 25 Factory Factory U Intensities of peak 1 vs. peak Peak 1 9

10 Principal omponent nalysis graphics! Scores -X -Y U X-expl: 77%,3,2% Principal component analysis how? X 3 X 3 (Strength) X X 1 (Fe 2 O 3 ) X 2 X 2 (l 2 O 3 ) 1

11 Direction in data of largest variation X 3 (Strength) Direction of first loading X X 1 (Fe 2 O 3 ) X 2 (l 2 O 3 ) P Loading, P X 3 (Strength) p 1 = (-.85,.51,.12): the length of a loading is 1 X 1 (Fe 2 O 3 ) X 2 (l 2 O 3 ) 11

12 P Score, T X 3 (Strength) X t 1 = X 1 (Fe 2 O 3 ) X 2 X 2 (l 2 O 3 ) The 2 nd loading spans the direction which orthogonal to P1 loading captures the second largest variation X 3 (Strength) Direction of second loading In an n-dimensional system, the full collection of {P1,,Pn} is a rotation of the original co-ordinate system, hence it spans the same space. X 1 (Fe 2 O 3 ) X 2 (l 2 O 3 ) 12

13 Ok let us put the pieces together Scores Variable Loadings Fe 2 O l 2 O 3.51 Strength.12 We know now that Fe 2 O 3 is important for the variation in our data. Strength seems not to be important l 2 O 3 is negatively correlated to Fe 2 O 3 one goes up the other one goes down!! But what is this variation? Does it have a meaning? olored according to yield! olored according to quality! Observations Fe 2 O 3 is important for the yield! Strength not! ausality? Quality does not seem to depend on the three selected parameters but what if we add more parameters? 13

14 Multivariate Statistical Process ontrol MSP P MSP ontrol harts (P based) T: mount of model Q: Distance to the model D: Distance to the model center Projection of a new batch on P model Q-statistic (Squared Residual Error) D-statistic (Hotelling s T 2 ) 14

15 EXMPLE: Batch Process Data Time Batch NO Normal Operating onditions (NO) Variable Simulated data set 1 NO batches 8 process variables 9 time intervals P-based MSP Time Batch NO 1 st time interval Variable P 1 T X 1 Variable E 1 Batch 1 P T

16 MSP using P Time Batch NO NO Up to 2 nd time interval Variable P 2 T X 2 Variable Time E 2 Batch 1 2 P T MSP using P Time NO NO NO NO Batch NO NO Up to K th time interval Variable X K Variable Time Batch K P P K T E K T K K 16

17 contribution contribution MSP results for a new batch What happens here? 1 8 Q time interval 2 15 Seems ok here! D time interval onfidence limit ontribution plots at time interval t 1 No problems! t variable variable 17

18 contribution contribution ontribution plots at time interval 4 4 D 2 Q variable variable Troubleshooting! - What does this mean? - an I use the product still? - Is variable #5 important? - How can I adjust the process so that variable #5 comes back into acceptable ranges = how to reduce the Q for variable #5? - The answer lies in knowledge of the process 18

19 P#2 an P go into an HMI then? Yes indeed! Requires some process knowledge to ensure that all interactions are known (P), which parameters are relevant and irrelevant (P) MSP Batch process monitoring weapon of choice P MSP State Space P#1 19

20 Thanks to Frans van den Berg Jonas Thygesen Hamid Babamoradi and YOU! 2