Multivariate correlation analysis of qualified liquid and vanadium pentoxide composition during vanadium precipitation
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摘要: 通过Pearson系数统计方法、概率密度分析方法和概率密度累积分布分析方法研究沉钒过程合格液中磷、铁、锰、硅、钒等元素对五氧化二钒成分的多元相关影响。结果表明，合格液中P、Mn含量与五氧化二钒中P含量的Pearson系数分别为0.6847、0.6663，线性相关程度最高；合格液中Mn与五氧化二钒中Mn的Pearson系数为0.3612，合格液中Fe与五氧化二钒中Si的Pearson系数为0.3564，具有一定的线性相关；合格液中P与五氧化二钒中Si的Pearson系数为−0.3291，合格液中V与五氧化二钒中P的Pearson系数为−0.2259，具有一定的负线性相关。合格液中其余元素含量与五氧化二钒中元素含量的Pearson系数的绝对值均小于0.16，说明相关性不强。五氧化二钒和合格液中P、Mn、Fe、Si、V含量均不服从正态分布，反映出统一样本过程不稳定，即生产过程不稳定，因此减少合格液成分异常波动，规避沉钒过程中对五氧化二钒质量产生较大影响的因素，可以提高五氧化二钒成分的稳定性。该研究为生产合格五氧化二钒提供了一定的理论技术支撑。Abstract: The effects of phosphorus, iron, manganese, silicon and vanadium in the qualified solution during vanadium precipitation on the composition of vanadium pentoxide were investigated through multivariate correlation analysis using Pearson coefficient statistics, probability density analysis and probability density cumulative distribution analysis methods. The results show that the Pearson coefficients of P, Mn content in qualified solution and P content in vanadium pentoxide are 0.6847 and 0.6663, respectively, with the highest degree of linear dependence. The Pearson coefficients of Mn, Fe in qualified liquid and Mn, Si in vanadium pentoxide are 0.3612 and 0.3564, respectively, indicating a certain degree of linear dependence. The Pearson coefficients of P, V in qualified liquid and Si, P in vanadium pentoxide are −0.3291 and −0.2258, respectively, representing a certain degree of negative linear correlation. The absolute value of Pearson coefficients for the content of other elements in the qualified solution and vanadium pentoxide are all less than 0.16, indicating a weak correlation. The contents of P, Mn, Fe, Si and V in vanadium pentoxide and qualified solution do not follow a normal distribution, reflecting the instability of the unified sample process, that is, the unstable production process. Therefore, it is necessary to reduce the abnormal fluctuation of qualified solution composition and avoid the factors that have relatively great impacts on the vanadium precipitation, which contributes to improve the stability of vanadium oxide composition. This work can provide some theoretical and technical support for the production of qualified vanadium oxide.
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图 1 合格液中P的概率累积分布
其中，data1是实际概率累计值；data3是拟合理论概率累计值；data2是其中拟合（重合）较好情况下的概率累计值。下同。
Figure 1. The probability cumulative distribution of P in qualified liquid
图 2 五氧化二钒中P的概率累积分布
Figure 2. The probability cumulative distribution of P in vanadium pentoxide
图 3 合格液中Mn的概率累积分布
Figure 3. The probability cumulative distribution of Mn in qualified liquid
图 4 五氧化二钒中Mn的概率累积分布
Figure 4. The probability cumulative distribution of Mn in vanadium pentoxide
图 5 合格液中Fe的概率累积分布
Figure 5. The probability cumulative distribution of Fe in qualified liquid
图 6 五氧化二钒中Fe的概率累积分布
Figure 6. The probability cumulative distribution of Fe in vanadium pentoxide
图 7 合格液中Si的概率累积分布
Figure 7. The probability cumulative distribution of Si in qualified liquid
图 8 五氧化二钒中Si的概率累积分布
Figure 8. The probability cumulative distribution of Si in vanadium pentoxide
图 9 五氧化二钒中V2O5的概率累积分布
Figure 9. The probability cumulative distribution of V2O5 content in vanadium pentoxide
表 1 合格液样本数据
Table 1. Data of qualified liquid samples
元素 样本数量/个 含量/(g·L−1) 方差 标准差 均值 中位数 V 820 23.3528 23.2600 5.3362 2.3100 P 820 0.0182 0.0170 7.3699×10−5 0.0086 Mn 819 13.6500 13.6500 9.1627 3.0270 Si 820 0.4639 0.4600 0.0132 0.1148 Fe 819 0.0406 0.0400 4.9814×10−4 0.0223 
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表 2 五氧化二钒样本数据
Table 2. Vanadium pentoxide samples data
成分 样本数量/个 含量/% 方差 标准差 均值 中位数 V2O5 2046 98.4312 98.4600 0.3315 0.5757 P 2051 0.0235 0.0220 1.1502×10−4 0.0107 Mn 1608 0.2843 0.2600 0.0142 0.1194 Si 2046 0.1728 0.1600 0.0056 0.0748 Fe 2046 0.2671 0.2600 0.0187 0.1366
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表 3 合格液中P与五氧化二钒中各元素的相关系数(Pearson系数)
Table 3. Correlation coefficient between P in qualified liquid and various elements in vanadium pentoxide
r(V2O5-Mn，HGY-P) r(V2O5-Fe，HGY-P) r(V2O5-Si，HGY-P) r(V2O5-V2O5，HGY-P) r(V2O5-P，HGY-P) 0.2025 −0.0922 −0.3291 0.0670 0.6847
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表 4 合格液中P与五氧化二钒中P各阶段的相关系数(Pearson系数)
Table 4. Correlation coefficients of P in qualified liquid and P in vanadium pentoxide at various stages
1段 2段 3段 4段 5段 6段 合计 0.5024 0.5580 0.8138 0.7046 0.6422 0.7162 0.6847
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表 5 合格液中Mn与五氧化二钒中各元素的相关系数（Pearson系数）
Table 5. Correlation coefficient between Mn in qualified liquid and various elements in vanadium pentoxide
r(V2O5-Mn，HGY-Mn) r(V2O5-Fe，HGY-Mn) r(V2O5-Si，HGY-Mn) r(V2O5-V2O5，HGY-Mn) r(V2O5-P，HGY-Mn) 0.3612 0.0145 −0.1088 −0.0815 0.6663
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表 6 合格液中Fe与五氧化二钒中各元素的相关系数（Pearson系数）
Table 6. Correlation coefficient between Fe in qualified liquid and various elements in vanadium pentoxide
r(V2O5-Mn，HGY-Fe) r(V2O5-Fe，HGY-Fe) r(V2O5-Si，HGY-Fe) r(V2O5-V2O5，HGY-Fe) 0.0705 0.0296 0.3564 −0.1455
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表 7 合格液中Si与五氧化二钒中各元素的相关系数（Pearson系数）
Table 7. Correlation coefficient between Si in qualified liquid and various elements in vanadium pentoxide
r(V2O5-Mn，HGY-Si) r(V2O5-Fe，HGY-Si) r(V2O5-Si，HGY-Si) r(V2O5-V2O5，HGY-Si) r(V2O5-P，HGY-Si) −0.1538 0.0258 −0.0357 0.0482 0.1302
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表 8 合格液中V与五氧化二钒中各元素的相关系数（Pearson系数）
Table 8. Correlation coefficient between V in qualified liquid and various elements in vanadium pentoxide
r(V2O5-Mn，HGY-V) r(V2O5-Fe，HGY-V) r(V2O5-Si，HGY-V) r(V2O5-V2O5，HGY-V) r(V2O5-P，HGY-V) 0.0429 −0.1599 0.0977 0.0126 −0.2259
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表 9 合格液中pH与五氧化二钒中各元素的相关系数（Pearson系数）
Table 9. Correlation coefficient between pH in qualified solution and various elements in vanadium pentoxide
r(V2O5-Mn，HGY-pH) r(V2O5-Fe，HGY-pH) r(V2O5-Si，HGY-pH) r(V2O5-V2O5，HGY-pH) r(V2O5-P，HGY-pH) 0.0403 −0.0804 −0.0380 0.0115 −0.0150
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