SAMSE 2018 IOP Conf. Series: Materials Science and Engineering 490 (2019) 062027
IOP Publishing doi:10.1088/1757-899X/490/6/062027
model parameters V and J were determined by PSO optimization; and finally, the OCS would be initiated to iteratively update the model in case the prediction deviation of the new sample individual was beyond the set error limit. 3.Results and Discussion 3.1. Model Performance Evaluation Indicator To objectively and independently evaluate the performance of the OCS-PCA-PSO-LSSVM soft-sensor model, the initial sample data set was divided into a training sample set, a validation set, and a test set in time order, of which the training sample set contained 100 sample individuals, used for parameter estimation of the model; the validation sample set contained 50 sample individuals, used for parameter optimization of the model; and the test sample set contained the remaining 25 sample individuals, used for performance evaluation of the model. The performance evaluation indicators include: maximum deviation (MAXE)/mg•L -1 , maximum relative deviation (MAXRE)/%, mean absolute deviation (MAE)/mg•L -1 , mean relative deviation (MRE)/% ,root mean square error (RMSE) / mg • L -1 , standard deviation (STD) / mg • L -1 , etc., and their respective definition formula are as follows:
ˆ y y
(11)
MAXE max {
}
i
i
{1,2, , } n
i
ˆ y y y i
i
(12)
MAXRE max {
} 100% u
{1,2, , } n
i
i
1 n
n
i ¦
ˆ y y
MAE
(13)
i
1
i
ˆ
|
|
1 n
y y
i y
n
¦
(14)
MRE
100%
u
i
i
1
i
1 n
n
( ¦ i
2
ˆ y y
RMSE
)
(15)
i
1
i
1
n
1 1 ¦ i
2
STD
(
)
e e
(16)
i
n
1 n ¦ 1 n
Where, i y ˆ denote the experimental value and predicted value of the model regarding COD of the i th sample individual, respectively. Among the above statistical performance indicators, MAXE, MRE, RMSE and STD are absolute accuracy indicators, of which, MAXE measures the limit boundary conditions of the model according to the maximum predicted deviation of the sample individuals, and MRE and RMSE measure the accuracy of the model according to the average prediction accuracy of the sample individuals. while STD measures the stability of the model according to the degree of dispersion of the prediction deviation of the sample individuals. Considering the objective difference between the magnitudes of different physical quantities, MAXRE and MRE are relative accuracy indicators. The former measures the deviation of the prediction results based on a single sample individual, and the latter does the same based on the average of sample individuals. The smaller the values of these statistics are, the better the performance of the model will be indicated. 3.2. Experimental Results and Analysis ˆ i i e y y , i i i e e , while i y and As described in Section 2.2.1 above, in order to satisfy that the pivot element under the OCS-PCA-PSO-LSSVM method contain enough initial variable information, and the cumulative information contribution rate of the d th extracted pivot element is now required to be above 85%. Based on the information of the eight latent roots of the correlation matrix for the training sample set
6
Made with FlippingBook Digital Publishing Software