1 ( W s + W i ) C 0 W s W i δ i

Table 1. Single factor analysis of variance

3. 边际影响模型

$\frac{\partial Y}{\partial {W}_{s}}=\frac{\left({C}_{1}-{C}_{0}\right)}{\sum {W}_{i}{\delta }_{i}}$

$\frac{\partial Y}{\partial {W}_{i}}=\frac{{C}_{1}\sum {W}_{i}{\delta }_{i}-\left(\left({C}_{1}-{C}_{0}\right){W}_{s}+{C}_{1}\sum {W}_{i}\right){\delta }_{i}}{{\sum {W}_{i}{\delta }_{i}}^{\text{​}}}$

Figure 1. Marginal influence diagram of indicators on carbon (left) and manganese (right) element yields

Table 2. Ranking table of marginal impact of factors affecting carbon and manganese

4. 灰色关联度模型

${Q}_{o}=\left\{{Q}_{o}\left(k\right)|k=1,2,\cdots ,n\right\}=\left({Q}_{o}\left(1\right),{Q}_{o}\left(2\right),\cdots ,{Q}_{o}\left(n\right)\right)$

${Q}_{j}=\left\{{Q}_{j}\left(k\right)|k=1,2,\cdots ,n\right\}=\left({Q}_{j}\left(1\right),{Q}_{j}\left(2\right),\cdots ,{Q}_{j}\left(n\right)\right),j=1,2,\cdots ,23$

${r}_{i}\left(k\right)=\frac{\underset{s}{\mathrm{min}}\underset{t}{\mathrm{min}}|{Q}_{0}\left(t\right)-{Q}_{s}\left(t\right)|+\rho \underset{s}{\mathrm{max}}\underset{t}{\mathrm{max}}|{Q}_{0}\left(t\right)-{Q}_{s}\left(t\right)|}{|{Q}_{0}\left(t\right)-{Q}_{i}\left(t\right)|+\rho \underset{s}{\mathrm{max}}\underset{t}{\mathrm{max}}|{Q}_{0}\left(t\right)-{Q}_{s}\left(t\right)|}$

$Co{r}_{i}=\frac{1}{n}\underset{k=1}{\overset{n}{\sum }}{r}_{i}\left(k\right)$

Figure 2. Relevance analysis of carbon (left) and manganese (right) elements

Table 3. Ranking of correlation degree of influencing factors of carbon and manganese recovery

5. 灰色关联度模型的灵敏度检验

6. 结语

Figure 3. Sensitivity analysis diagram based on correlation coefficient

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