statistical methods for the analysis, monitoring and optimization … · 2014-04-07 ·...

Multivariate statistical methods for the analysis, monitoring and optimization of

processesJay Liu

Dept. of Chemical EngineeringPukyong National University

1유준, Copyright ©

Credits

• Prof. John MacGregor @ McMaster University– “father” of multivariate statistics & industrial applications– Course outline and topics covered are similar to his course

• Mr. Kevin Dunn @ McMaster University/ConnectMV– Most of this lecture materials come from his

• Prosensus– Providing one‐year ProMV academic license for free.– Providing materials for tutorials

유준, Copyright © 2

1. Introduction

Extracting value from data• Engineers can use large quantities of data:

1. Improve process understanding2. Troubleshooting process problems3. Improving, optimizing and controlling processes4. Predictive modeling (inferential sensors)5. Process monitoring

We will come back to these in the next class


• Throughout this course,

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Convention in Multivariate statistics

유준, Copyright ©

Data Characteristics



• Today

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Near‐Infrared spectrum

≫


Data Analysis Purpose

• Summary & trouble‐shooting• Predictive modeling (Regression)• Labeling or grading (Classification)• Process & product design• Scale‐up & product transfer• QSAR (Quantitative Structure Activity Relationships)• And many more


Examples: trouble‐shooting

• Undetected process changes @ pulp digester• Didn’t know when & why the changes occurred• Data: 301 obs., 22 vars.

• 22 time‐series plots? 231 Scatter plots?


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PCA score plot

Cluster 2

Cluster 1


• PCA gives ONE excellent summary• Two distinct clusters in a t1‐t2 score plotCluster 1: obs.1000~1030, obs.1192~1300Cluster 2: obs.1031~1191


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PCA Contribution plot

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• PCA gives candidates of root‐cause• During the period of cluster 2, v1 and v2 fluctuated while they were maintained constant level during the period of cluster 1.


Examples: predictive modeling

• Measurement of biodiesel quality• Spec. & methods given in ASTM

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Costs too much time & money!


Examples: predictive modeling

• PLS gives ONE accurate multivariate calibration model for biodiesel & impurities.

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PLS model

Components Biodiesel MEOH Freeglycerin

MonoGlyceride

Di Glyceride

Tri Glyceride

R2 value 0.999 0.994 0.995 0.996 0.994 0.994


Issues faced with engineering data



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Can be up to 30% (or more!).


Examples of large data sets

• Typical fab processes– Data size: order of terabytes in a few days

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Database merging in a data‐mining package

Databases in a typical fab process


What is a latent variable?

• Fortunately (& unfortunately at the same time), all variables are not independent.• Redundant images of few “latent” variables



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Protein profile

I am a doctor!

Metabolic profile

Gene expression

Clinical History/Q&A


Latent variable methods

(Multivariate statistical methods = latent variable methods)

• Principal component analysis (PCA)– a.k.a Karhunen‐Loève transform or Hotelling transform

• Factor analysis• Fisher’s discriminant analysis• Independent component analysis• Principal component regression• Partial least squares (or projection to latent structures)

• …..


statistical methods for the analysis, monitoring and optimization … · 2014-04-07 ·...

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