Dynamic systems


1. Introduction. Dynamic systems.  
2. Explorative study of dynamics  
3. The H-method for dynamic data.  
4. Regression including lags.  
5. Graphic analysis.  
6. Case study  
7. Kalman Filter type of methods.  
8. Periodicity studies.  
9. Trend analysis.  
10. Importance of variables.  
11. CovProc methods.  
12. Regression coefficients.   
13. Predictions in dynamic systems.  
14. Positive solutions  
15. Analysis of residuals.  
16. Inertia in dynamic systems  
17. Confidence intervals  
18. Outlier detection  
19. Sensitivity analysis  
20. Case study  
21. Guidelines for presentation of results  

In industry there is great interest in methods that can handle dynamic systems containing many variables. The reason is the importance of getting measurements and also that measurement instruments are getting cheaper. A great challenge for industry is that many modern measurement instruments provide with numerous measurement values. For instance, a NIR (Near Infra-Red) instrument may give 1056 values for each sample. In process control environments it can be considerable savings to use NIR instruments to supervise the processes compared with traditional process control instruments.

The H-method has been applied with success to analyse dynamic systems, where many variables have been measured. The background for the success is that data often show sign of reduced rank. The H-method appropriately identifies the appropriate rank and the subset of variables that should be used in the analysis.

Kalman Filer type of methods are popular in many industrial applications. The experience in industry is that these methods function well when there are few variables, say less than 10. If there are more than around 20 they typically break down. Already with 10 to 20 variables the predictions derived from these methods deteriorates.

The H-method provides with stable solutions to Kalman Filter type of methods. See a short introduction to some of the ideas.