A Method to Determine Transition Time for Experiments in Dynamic Processes

ABSTRACT

Process dynamics is an important consideration during the planning phase of designed experiments in dynamic processes. After changes of experimental factors, dynamic processes undergo a transition time before reaching a new steady state. To minimize experimental time and reduce costs and for experimental design and analysis, knowledge about this transition time is important. In this article, we propose a method to analyze process dynamics and estimate the transition time by combining principal component analysis and transfer function–noise modeling or intervention analysis. We illustrate the method by estimating transition times for a planned experiment in an experimental blast furnace.

KEYWORDS:

• blast furnace
• design of experiments
• intervention analysis
• principal component analysis
• time series analysis
• transfer function–noise model
• transition time

ACKNOWLEDGMENT

The authors gratefully acknowledge the financial support from the Swedish mining company LKAB, as well as the County Administrative Board under grant 303-02863-2008, and the Regional Development Fund of the European Union, grant 43206, which made this research possible. The authors thank all members of the LKAB EBF Methodology Development Project for their important contribution to the results presented here. Special thanks to Gunilla Hyllander at LKAB for valuable support. The authors thank the editor and the two anonymous reviewers for their valuable comments and suggestions that improved this article.

Notes

Note: Refers to the corresponding gas volume under standard conditions of 1 atmosphere pressure and 0°C.

Notes: The models were fitted using JMP 8.0 statistics software (SAS, Cary, NC). The standard errors for the fitted parameters are given above or below the parameter values. The arrows next to the model criteria indicate whether the corresponding criterion should be large (↑) or small (↓).

Δ¹ indicates that the first difference of the time series is modeled.

df = degrees of freedom; SD = standard deviation of the residuals; MAE = mean absolute prediction error; AIC = Akaike information criterion; SIC = Schwarz information criterion.

Notes: The standard errors for the fitted parameters are given above or below the parameter values. The arrows next to the model criteria indicate whether the corresponding criterion should be large (↑) or small (↓).

Δ¹ indicates that the first difference of the time series is modeled.

df = degrees of freedom; SD = standard deviation of the residuals; MAE = mean absolute prediction error; AIC = Akaike information criterion; SIC = Schwarz information criterion.