Radar Detection-Based Modeling in a Blast Furnace: A Prediction Model of Burden Surface Descent Speed
Abstract
:1. Introduction
2. Measurement Results
2.1. Instrument Settings
2.2. Detection Results
- The BSRDs are nonuniform.
- There are similarities between the shapes of the time-adjacent BSRD samples.
3. Model Description
3.1. Kinematic Modeling Mechanism
3.2. Prediction Model
3.2.1. Approximation of Burden Vertical Descent Speed Field
3.2.2. Prediction of BSRD
- Use and to predict the future discrete BSRP, denoted as .
- Use and to calculate the future discrete BSRD, .
4. Solution of Model Parameters
4.1. Identification of EBDF Parameters
4.2. Selection of Complexity Parameter
5. Model Performance
5.1. Prediction Accuracy
5.2. Prediction Performance Decay
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Nomenclature
B | Kinematic constant |
C | Unit-impulse function |
D | Two-dimensional rectangular region |
Solution domain of EBDF | |
d | Diameter parameter of C, m |
f | Function of burden height, m |
BSRP before burden descent referring to , m | |
BSRP after burden descent referring to , m | |
BSRP before burden descent referring to , m | |
H | Depth of D, m |
Vertical distance between and the MSR, m | |
h | Variable of height, m |
Vertical distance between and , m | |
Vertical distance between and before burden descent, m | |
Vertical distance between and after burden descent, m | |
m | Number of equivalent consumption sources |
n | Number of radial detection positions |
Q | Volumetric flow rate, |
Parameter of strength of consumption of | |
R | Burden radius, width of D, m |
r | Variable of radial position, m |
Radial position parameter of , m | |
Coordinates of detection positions | |
Initial time of prediction, min | |
Prediction time, min | |
u | Burden descent speed, m/min |
Detected BSRD, m/min | |
Predicted BSRD, m/min | |
Two calculated BSRDs from a data segment, m/min | |
V | Burden velocity vector, m/min |
v | Horizontal speed of burden movement, m/min |
Gaussian function | |
Function of equivalent consumption sources | |
Shape parameter of | |
Shape parameter of | |
Two weight of coefficients in optimization |
Abbreviations
BF | Blast furnace |
MSR | Mechanical swing radar |
BSRP | Burden surface radial profile |
BSRD | Descent speed distribution along the burden surface radius |
EBDF | Equivalent radial burden descent speed field |
RMSE | Root-mean-square error |
MAE | Maximum absolute error |
PFM | Potential flow model |
KM | Kinematic model |
VFM | Viscous flow model |
KGM | Kinematic Gaussian model |
PM | Plain data-driven descriptive model |
Appendix A. A Proof of Proposition 1
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Case Source No. | 1 | 2 | ||||||
---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | |
0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | |
0.1433 | 1.6208 | 3.0873 | 3.0889 | 1.6149 | 1.1880 | 1.1928 | 3.5890 | |
0.1563 | 0.1328 | 0.0757 | 0.0764 | 0.1081 | 0.0186 | 0.0613 | 0.1270 | |
B | 0.0403 | 0.0413 |
Case | Model | BSRP | BSRD | ||
---|---|---|---|---|---|
MAE | RMSE | MAE | RMSE | ||
1 | KGM | 0.2537 | 0.1081 | 0.0561 | 0.0353 |
PM | 0.5959 | 0.2970 | 0.1429 | 0.0732 | |
2 | KGM | 0.5801 | 0.2913 | 0.1633 | 0.0987 |
PM | 0.8601 | 0.5823 | 0.2280 | 0.1325 |
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Tian, J.; Tanaka, A.; Hou, Q.; Chen, X. Radar Detection-Based Modeling in a Blast Furnace: A Prediction Model of Burden Surface Descent Speed. Metals 2019, 9, 609. https://doi.org/10.3390/met9050609
Tian J, Tanaka A, Hou Q, Chen X. Radar Detection-Based Modeling in a Blast Furnace: A Prediction Model of Burden Surface Descent Speed. Metals. 2019; 9(5):609. https://doi.org/10.3390/met9050609
Chicago/Turabian StyleTian, Jiuzhou, Akira Tanaka, Qingwen Hou, and Xianzhong Chen. 2019. "Radar Detection-Based Modeling in a Blast Furnace: A Prediction Model of Burden Surface Descent Speed" Metals 9, no. 5: 609. https://doi.org/10.3390/met9050609