# Data-Driven Robust RVFLNs Modeling of a Blast Furnace Iron-Making Process Using Cauchy Distribution Weighted M-Estimation

## Abstract

Optimal operation of a practical blast furnace (BF) ironmaking process depends largely on a good measurement of molten iron quality (MIQ) indices. However, measuring the MIQ online is not feasible using the available techniques. In this paper, a novel data-driven robust modeling is proposed for online estimation of MIQ using improved random vector functional-link networks (RVFLNs). Since the output weights of traditional RVFLNs are obtained by the least squares approach, a robustness problem may occur when the training dataset is contaminated with outliers. This affects the modeling accuracy of RVFLNs. To solve this problem, a Cauchy distribution weighted M-estimation based robust RFVLNs is proposed. Since the weights of different outlier data are properly determined by the Cauchy distribution, their corresponding contribution on modeling can be properly distinguished. Thus robust and better modeling results can be achieved. Moreover, given that the BF is a complex nonlinear system with numerous coupling variables, the data-driven canonical correlation analysis is employed to identify the most influential components from multitudinous factors that affect the MIQ indices to reduce the model dimension. Finally, experiments using industrial data and comparative studies have demonstrated that the obtained model produces a better modeling and estimating accuracy and stronger robustnessmore »

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1378047

- Report Number(s):
- PNNL-SA-124471

Journal ID: ISSN 0278-0046

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Journal Name:
- IEEE Translations on Industrial Electronics

- Additional Journal Information:
- Journal Volume: 64; Journal Issue: 9; Journal ID: ISSN 0278-0046

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Blast furnace (BF); modelling; Cauchy distribution; Neural nets

### Citation Formats

```
Zhou, Ping, Lv, Youbin, Wang, Hong, and Chai, Tianyou.
```*Data-Driven Robust RVFLNs Modeling of a Blast Furnace Iron-Making Process Using Cauchy Distribution Weighted M-Estimation*. United States: N. p., 2017.
Web. doi:10.1109/TIE.2017.2686369.

```
Zhou, Ping, Lv, Youbin, Wang, Hong, & Chai, Tianyou.
```*Data-Driven Robust RVFLNs Modeling of a Blast Furnace Iron-Making Process Using Cauchy Distribution Weighted M-Estimation*. United States. doi:10.1109/TIE.2017.2686369.

```
Zhou, Ping, Lv, Youbin, Wang, Hong, and Chai, Tianyou. Fri .
"Data-Driven Robust RVFLNs Modeling of a Blast Furnace Iron-Making Process Using Cauchy Distribution Weighted M-Estimation". United States. doi:10.1109/TIE.2017.2686369.
```

```
@article{osti_1378047,
```

title = {Data-Driven Robust RVFLNs Modeling of a Blast Furnace Iron-Making Process Using Cauchy Distribution Weighted M-Estimation},

author = {Zhou, Ping and Lv, Youbin and Wang, Hong and Chai, Tianyou},

abstractNote = {Optimal operation of a practical blast furnace (BF) ironmaking process depends largely on a good measurement of molten iron quality (MIQ) indices. However, measuring the MIQ online is not feasible using the available techniques. In this paper, a novel data-driven robust modeling is proposed for online estimation of MIQ using improved random vector functional-link networks (RVFLNs). Since the output weights of traditional RVFLNs are obtained by the least squares approach, a robustness problem may occur when the training dataset is contaminated with outliers. This affects the modeling accuracy of RVFLNs. To solve this problem, a Cauchy distribution weighted M-estimation based robust RFVLNs is proposed. Since the weights of different outlier data are properly determined by the Cauchy distribution, their corresponding contribution on modeling can be properly distinguished. Thus robust and better modeling results can be achieved. Moreover, given that the BF is a complex nonlinear system with numerous coupling variables, the data-driven canonical correlation analysis is employed to identify the most influential components from multitudinous factors that affect the MIQ indices to reduce the model dimension. Finally, experiments using industrial data and comparative studies have demonstrated that the obtained model produces a better modeling and estimating accuracy and stronger robustness than other modeling methods.},

doi = {10.1109/TIE.2017.2686369},

journal = {IEEE Translations on Industrial Electronics},

issn = {0278-0046},

number = 9,

volume = 64,

place = {United States},

year = {2017},

month = {9}

}