Prediction Model of Converter Oxygen Consumption Based on Recursive …
105
Model Parameter Setting and Evaluation Indicators
The experiment environment is mainly based on Windows7, python3, and sci-kitlearn(v-0.22.2). The recursive division depth is set to 2, and the minimum divided
subset capacity is 100. Multi-layer Perceptron (MLP) and Support Vector Regression (SVR) are as the subspace prediction models for experiments. SVR’s hyperparameters contain: regularization parameter C ∈ {1, 0.3, 0.1}, relaxation factor
ς ∈ {0.3, 0.1, 0.03}, RBF kernel function; MLP has three layers, with hyperparameters: the number of hidden layer neurons N ∈ {10, 30, 90}, regularization coefficient
α ∈ {0.03, 0.1, 0.3}, the initial learning rate is 0.01, the optimizer is Adam, and the
maximum number of iterations is 300. C, ς in SVR and N , α in MLP are optimized
through grid search and K-fold cross-validation on the corresponding training set.
As for converter oxygen consumption prediction, in the current research, the main
evaluation indicators mainly include the Accuracy (ACC) with prediction error in a
certain range, Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and
Mean Absolute Percentage Error (MAPE), the calculation formula is shown below.
ACC =
n
m
, M AE =
1
m
m
i=1
|y i − ˆ
y i |, R M S E =
1
m
m
i=1
(y i − ˆ
y i ) 2 , M AP E =
1
m
m
i=1
y i − ˆ
y i
y i
.
Where, m is the number of test samples; n is the number of samples whose
prediction absolute error is within 800 m
3 ; y i is the true value of oxygen consumption
of the i-th sample, and y i
is its corresponding model estimate.
Experimental Results and Analysis
Feature Space Division and Analysis
The feature space is divided after normalizing all samples. As shown in Fig. 5 with
three level charts, it is the feature space division process on the training set. In the
first level chart, the training set contains 1,073 samples with the feature space S.
y O2 is the oxygen consumption variable, and its MSE is 0.025, and its distribution is
scattered.
In the second level chart, firstly, according to the principle of feature space division, namely, the principle of minimum MSE, the divided feature variable x
(5) is
obtained, namely, the scrap steel quality, and the critical point is x
(5)
= 0.254, the
feature space S is divided into S 1 and S 2 . The S 1 contains 295 samples, y O2 ’s MSE
is 0.014, therefore y O2 ’s distribution is much more concentrated than that in S. S 2
contains 778 samples, y O2 ’s MSE is 0.02. Compared with S, its distribution is more
concentrated.
105
Model Parameter Setting and Evaluation Indicators
The experiment environment is mainly based on Windows7, python3, and sci-kitlearn(v-0.22.2). The recursive division depth is set to 2, and the minimum divided
subset capacity is 100. Multi-layer Perceptron (MLP) and Support Vector Regression (SVR) are as the subspace prediction models for experiments. SVR’s hyperparameters contain: regularization parameter C ∈ {1, 0.3, 0.1}, relaxation factor
ς ∈ {0.3, 0.1, 0.03}, RBF kernel function; MLP has three layers, with hyperparameters: the number of hidden layer neurons N ∈ {10, 30, 90}, regularization coefficient
α ∈ {0.03, 0.1, 0.3}, the initial learning rate is 0.01, the optimizer is Adam, and the
maximum number of iterations is 300. C, ς in SVR and N , α in MLP are optimized
through grid search and K-fold cross-validation on the corresponding training set.
As for converter oxygen consumption prediction, in the current research, the main
evaluation indicators mainly include the Accuracy (ACC) with prediction error in a
certain range, Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and
Mean Absolute Percentage Error (MAPE), the calculation formula is shown below.
ACC =
n
m
, M AE =
1
m
m
i=1
|y i − ˆ
y i |, R M S E =
1
m
m
i=1
(y i − ˆ
y i ) 2 , M AP E =
1
m
m
i=1
y i − ˆ
y i
y i
.
Where, m is the number of test samples; n is the number of samples whose
prediction absolute error is within 800 m
3 ; y i is the true value of oxygen consumption
of the i-th sample, and y i
is its corresponding model estimate.
Experimental Results and Analysis
Feature Space Division and Analysis
The feature space is divided after normalizing all samples. As shown in Fig. 5 with
three level charts, it is the feature space division process on the training set. In the
first level chart, the training set contains 1,073 samples with the feature space S.
y O2 is the oxygen consumption variable, and its MSE is 0.025, and its distribution is
scattered.
In the second level chart, firstly, according to the principle of feature space division, namely, the principle of minimum MSE, the divided feature variable x
(5) is
obtained, namely, the scrap steel quality, and the critical point is x
(5)
= 0.254, the
feature space S is divided into S 1 and S 2 . The S 1 contains 295 samples, y O2 ’s MSE
is 0.014, therefore y O2 ’s distribution is much more concentrated than that in S. S 2
contains 778 samples, y O2 ’s MSE is 0.02. Compared with S, its distribution is more
concentrated.