化工进展 ›› 2022, Vol. 41 ›› Issue (11): 5946-5960.DOI: 10.16085/j.issn.1000-6613.2022-0052
丁兴江(), 章学来(), 朱嘉豪, 毛发, 房满庭, 冯天平
收稿日期:
2022-01-07
修回日期:
2022-02-20
出版日期:
2022-11-25
发布日期:
2022-11-28
通讯作者:
章学来
作者简介:
丁兴江(1972—),男,博士研究生,高级工程师,研究方向为相变储能材料的研究和应用。E-mail: dingxingjiang@163.com。
基金资助:
DING Xingjiang(), ZHANG Xuelai(), ZHU Jiahao, MAO Fa, FANG Manting, FENG Tianping
Received:
2022-01-07
Revised:
2022-02-20
Online:
2022-11-25
Published:
2022-11-28
Contact:
ZHANG Xuelai
摘要:
以三水合乙酸钠(SAT)为基材,添加具有微孔结构的硅藻土(DE)及十二水磷酸氢二钠(DHPD)等添加剂制备复合相变材料。取过冷度作为目标函数,进行双因素重复测量实验并分析成核剂对相变材料的过冷改性有无显著作用及成核剂之间的交互作用。将不同添加剂、不同浓度组合成数学意义上的超矩体分割成四个局部超矩体,通过正交实验分析局部超矩体域内不同添加剂浓度对相变材料过冷特性的影响。合并局部正交实验数据并进行方差分析研究不同添加剂对相变材料整体过冷特性的影响;对整体实验数据进行多元回归分析,建立过冷特性数学模型,求出符合实际应用情况的最优方案,其过冷度小于0.5℃;确定经济性条件下的优化方案,配制相应复合相变材料验证其过冷特性,进行潜热、导热的性能测试。
中图分类号:
丁兴江, 章学来, 朱嘉豪, 毛发, 房满庭, 冯天平. 三水合乙酸钠复合相变材料过冷特性实验统计分析[J]. 化工进展, 2022, 41(11): 5946-5960.
DING Xingjiang, ZHANG Xuelai, ZHU Jiahao, MAO Fa, FANG Manting, FENG Tianping. Statistical analysis for supercooling characteristics experiments of sodium acetate trihydrate composite phase change materials[J]. Chemical Industry and Engineering Progress, 2022, 41(11): 5946-5960.
因素 | DE浓度1.0% | DE浓度3.0% | DE浓度5.0% |
---|---|---|---|
DHPD浓度1.0% | 0.369 0.508 0.337 0.779 1.034 1.464 0.53 0.739 0.825 | 0.445 0.656 1.513 0.318 1.077 1.236 0.103 0.581 1.029 | 0.572 0.624 0.474 0.382 0.262 0.136 0.645 0.403 0.352 |
DHPD浓度1.5% | 0.118 0.846 0.82 0.161 0.172 0.149 0.333 0.851 0.39 | 0.265 0.706 0.615 0.355 0.862 0.439 0.461 0.388 0.409 | 0.123 0.206 0.683 1.059 0.202 0.600 0.957 0.966 0.883 |
DHPD浓度2.0% | 0.300 0.084 0.379 0.275 0.309 0.382 0.11 0.103 0.229 | 0.306 0.264 0.356 0.583 0.397 0.467 0.496 0.316 0.369 | 0.421 0.334 0.144 0.318 0.403 0.415 0.381 0.524 0.319 |
表1 DHPD 与DE双因素重复测量数据表
因素 | DE浓度1.0% | DE浓度3.0% | DE浓度5.0% |
---|---|---|---|
DHPD浓度1.0% | 0.369 0.508 0.337 0.779 1.034 1.464 0.53 0.739 0.825 | 0.445 0.656 1.513 0.318 1.077 1.236 0.103 0.581 1.029 | 0.572 0.624 0.474 0.382 0.262 0.136 0.645 0.403 0.352 |
DHPD浓度1.5% | 0.118 0.846 0.82 0.161 0.172 0.149 0.333 0.851 0.39 | 0.265 0.706 0.615 0.355 0.862 0.439 0.461 0.388 0.409 | 0.123 0.206 0.683 1.059 0.202 0.600 0.957 0.966 0.883 |
DHPD浓度2.0% | 0.300 0.084 0.379 0.275 0.309 0.382 0.11 0.103 0.229 | 0.306 0.264 0.356 0.583 0.397 0.467 0.496 0.316 0.369 | 0.421 0.334 0.144 0.318 0.403 0.415 0.381 0.524 0.319 |
DE浓度/% | DHPD 浓度/% | 均值 | 标准偏差 | 数量 | DE浓度/% | DHPD 浓度/% | 均值 | 标准偏差 | 数量 | DE浓度/% | DHPD 浓度/% | 均值 | 标准偏差 | 数量 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.0 | 1.0 1.5 2.0 | 0.73167 0.42667 0.24122 | 0.356495 0.321818 0.116824 | 9 9 9 | 3.0 | 1.0 1.5 2.0 | 0.77311 0.50000 0.39489 | 0.465562 0.190073 0.102624 | 9 9 9 | 5.0 | 1.0 1.5 2.0 | 0.42778 0.63100 0.36211 | 0.169445 0.369389 0.104085 | 9 9 9 |
总计 | 0.46652 | 0.342967 | 27 | 总计 | 0.55600 | 0.327774 | 27 | 总计 | 0.47363 | 0.260302 | 27 |
表2 DHPD 与DE双因素重复实验描述性统计量
DE浓度/% | DHPD 浓度/% | 均值 | 标准偏差 | 数量 | DE浓度/% | DHPD 浓度/% | 均值 | 标准偏差 | 数量 | DE浓度/% | DHPD 浓度/% | 均值 | 标准偏差 | 数量 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.0 | 1.0 1.5 2.0 | 0.73167 0.42667 0.24122 | 0.356495 0.321818 0.116824 | 9 9 9 | 3.0 | 1.0 1.5 2.0 | 0.77311 0.50000 0.39489 | 0.465562 0.190073 0.102624 | 9 9 9 | 5.0 | 1.0 1.5 2.0 | 0.42778 0.63100 0.36211 | 0.169445 0.369389 0.104085 | 9 9 9 |
总计 | 0.46652 | 0.342967 | 27 | 总计 | 0.55600 | 0.327774 | 27 | 总计 | 0.47363 | 0.260302 | 27 |
差异源 | SS | df | MS | F | P | F crit |
---|---|---|---|---|---|---|
DHPD | 1.326499 | 2 | 0.663249 | 8.730743 | 0.000403 | 3.123907 |
DE | 0.133581 | 2 | 0.066791 | 0.879206 | 0.419521 | 3.123907 |
DHPD*DE | 0.817161 | 4 | 0.20429 | 2.689193 | 0.037787 | 2.498919 |
内部 | 5.469632 | 72 | 0.075967 | |||
总计 | 7.746872 | 80 |
表3 DHPD 与DE双因素重复实验方差分析表
差异源 | SS | df | MS | F | P | F crit |
---|---|---|---|---|---|---|
DHPD | 1.326499 | 2 | 0.663249 | 8.730743 | 0.000403 | 3.123907 |
DE | 0.133581 | 2 | 0.066791 | 0.879206 | 0.419521 | 3.123907 |
DHPD*DE | 0.817161 | 4 | 0.20429 | 2.689193 | 0.037787 | 2.498919 |
内部 | 5.469632 | 72 | 0.075967 | |||
总计 | 7.746872 | 80 |
DE浓度/% | DHPD浓度(I)/% | DHPD浓度(J)/% | 均值差值(I-J) | 标准误差 | Sig.a | 差分的95%置信区间 | |
---|---|---|---|---|---|---|---|
下限 | 上限 | ||||||
1.0 | 1.0 | 1.5 | 0.305 | 0.135 | 0.033 | 0.027 | 0.583 |
2.0 | 0.490 | 0.135 | 0.001 | 0.213 | 0.768 | ||
1.5 | 1.0 | -0.305 | 0.135 | 0.033 | -0.583 | -0.027 | |
2.0 | 0.185 | 0.135 | 0.181 | -0.092 | 0.463 | ||
2.0 | 1.0 | -0.490 | 0.135 | 0.001 | -0.768 | -0.213 | |
1.5 | -0.185 | 0.135 | 0.181 | -0.463 | 0.092 | ||
3.0 | 1.0 | 1.5 | 0.273 | 0.14 | 0.062 | -0.015 | 0.561 |
2.0 | 0.378 | 0.14 | 0.012 | 0.09 | 0.667 | ||
1.5 | 1.0 | -0.273 | 0.14 | 0.062 | -0.561 | 0.015 | |
2.0 | 0.105 | 0.14 | 0.459 | -0.183 | 0.393 | ||
2.0 | 1.0 | -0.378 | 0.14 | 0.012 | -0.667 | -0.09 | |
1.5 | -0.105 | 0.14 | 0.459 | -0.393 | 0.183 | ||
5.0 | 1.0 | 1.5 | -0.203 | 0.114 | 0.088 | -0.439 | 0.032 |
2.0 | 0.066 | 0.114 | 0.571 | -0.17 | 0.301 | ||
1.5 | 1.0 | 0.203 | 0.114 | 0.088 | -0.032 | 0.439 | |
2.0 | 0.269 | 0.114 | 0.027 | 0.033 | 0.505 | ||
2.0 | 1.0 | -0.066 | 0.114 | 0.571 | -0.301 | 0.17 | |
1.5 | -0.269 | 0.114 | 0.027 | -0.505 | -0.033 |
表4 DHPD 与DE交互作用简单效应分析表
DE浓度/% | DHPD浓度(I)/% | DHPD浓度(J)/% | 均值差值(I-J) | 标准误差 | Sig.a | 差分的95%置信区间 | |
---|---|---|---|---|---|---|---|
下限 | 上限 | ||||||
1.0 | 1.0 | 1.5 | 0.305 | 0.135 | 0.033 | 0.027 | 0.583 |
2.0 | 0.490 | 0.135 | 0.001 | 0.213 | 0.768 | ||
1.5 | 1.0 | -0.305 | 0.135 | 0.033 | -0.583 | -0.027 | |
2.0 | 0.185 | 0.135 | 0.181 | -0.092 | 0.463 | ||
2.0 | 1.0 | -0.490 | 0.135 | 0.001 | -0.768 | -0.213 | |
1.5 | -0.185 | 0.135 | 0.181 | -0.463 | 0.092 | ||
3.0 | 1.0 | 1.5 | 0.273 | 0.14 | 0.062 | -0.015 | 0.561 |
2.0 | 0.378 | 0.14 | 0.012 | 0.09 | 0.667 | ||
1.5 | 1.0 | -0.273 | 0.14 | 0.062 | -0.561 | 0.015 | |
2.0 | 0.105 | 0.14 | 0.459 | -0.183 | 0.393 | ||
2.0 | 1.0 | -0.378 | 0.14 | 0.012 | -0.667 | -0.09 | |
1.5 | -0.105 | 0.14 | 0.459 | -0.393 | 0.183 | ||
5.0 | 1.0 | 1.5 | -0.203 | 0.114 | 0.088 | -0.439 | 0.032 |
2.0 | 0.066 | 0.114 | 0.571 | -0.17 | 0.301 | ||
1.5 | 1.0 | 0.203 | 0.114 | 0.088 | -0.032 | 0.439 | |
2.0 | 0.269 | 0.114 | 0.027 | 0.033 | 0.505 | ||
2.0 | 1.0 | -0.066 | 0.114 | 0.571 | -0.301 | 0.17 | |
1.5 | -0.269 | 0.114 | 0.027 | -0.505 | -0.033 |
实验序号 | DHPD | DE | XG | AON | 过冷度 |
---|---|---|---|---|---|
1 | 1.5% | 3% | 1.5% | 1.5% | 0.629 |
2 | 1.5% | 3% | 2.5% | 3% | 0.414 |
3 | 1.5% | 7% | 1.5% | 3% | 0.648 |
4 | 1.5% | 7% | 2.5% | 1.5% | 0.579 |
5 | 2.5% | 3% | 1.5% | 3% | 0.720 |
6 | 2.5% | 3% | 2.5% | 1.5% | 0.358 |
7 | 2.5% | 7% | 1.5% | 1.5% | 0.379 |
8 | 2.5% | 7% | 2.5% | 3% | 0.738 |
表5 高浓度添加剂的材料过冷正交实验设计及数据表
实验序号 | DHPD | DE | XG | AON | 过冷度 |
---|---|---|---|---|---|
1 | 1.5% | 3% | 1.5% | 1.5% | 0.629 |
2 | 1.5% | 3% | 2.5% | 3% | 0.414 |
3 | 1.5% | 7% | 1.5% | 3% | 0.648 |
4 | 1.5% | 7% | 2.5% | 1.5% | 0.579 |
5 | 2.5% | 3% | 1.5% | 3% | 0.720 |
6 | 2.5% | 3% | 2.5% | 1.5% | 0.358 |
7 | 2.5% | 7% | 1.5% | 1.5% | 0.379 |
8 | 2.5% | 7% | 2.5% | 3% | 0.738 |
序号 | DHPD | DE | DHPD*DE | XG | BLANK | DHPD*AON | AON | 过冷度 |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.629 |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 0.414 |
3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 0.648 |
4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 0.579 |
5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 0.720 |
6 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | 0.358 |
7 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 0.379 |
8 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 0.738 |
K1 | 2.270 | 2.121 | 2.160 | 2.376 | 2.373 | 2.666 | 1.945 | |
K2 | 2.195 | 2.344 | 2.305 | 2.089 | 2.092 | 1.799 | 2.520 | |
k1 | 0.568 | 0.530 | 0.540 | 0.594 | 0.593 | 0.667 | 0.486 | |
k2 | 0.549 | 0.586 | 0.576 | 0.522 | 0.523 | 0.450 | 0.630 | |
极差 | 0.019 | 0.056 | 0.036 | 0.072 | 0.070 | 0.217 | 0.144 | |
因素主→次 | DHPD*AON→AON→XG→DE→DHPD*DE→DHPD | |||||||
优方案 | AON1 XG2 DE1 DHPD2 (与表中最低值的方案一致:AON1 XG2 DE1 DHPD2 ) |
表6 高浓度添加剂的材料过冷正交实验极差分析表
序号 | DHPD | DE | DHPD*DE | XG | BLANK | DHPD*AON | AON | 过冷度 |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.629 |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 0.414 |
3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 0.648 |
4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 0.579 |
5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 0.720 |
6 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | 0.358 |
7 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 0.379 |
8 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 0.738 |
K1 | 2.270 | 2.121 | 2.160 | 2.376 | 2.373 | 2.666 | 1.945 | |
K2 | 2.195 | 2.344 | 2.305 | 2.089 | 2.092 | 1.799 | 2.520 | |
k1 | 0.568 | 0.530 | 0.540 | 0.594 | 0.593 | 0.667 | 0.486 | |
k2 | 0.549 | 0.586 | 0.576 | 0.522 | 0.523 | 0.450 | 0.630 | |
极差 | 0.019 | 0.056 | 0.036 | 0.072 | 0.070 | 0.217 | 0.144 | |
因素主→次 | DHPD*AON→AON→XG→DE→DHPD*DE→DHPD | |||||||
优方案 | AON1 XG2 DE1 DHPD2 (与表中最低值的方案一致:AON1 XG2 DE1 DHPD2 ) |
差异源 | SS | df | MS | F | P值 |
---|---|---|---|---|---|
DHPD | 0.001 | 1 | 0.001 | 0.093 | 0.781 |
DE | 0.006 | 1 | 0.006 | 0.818 | 0.432 |
AON | 0.041 | 1 | 0.041 | 5.439 | 0.102 |
DHPD*AON | 0.094 | 1 | 0.094 | 12.366 | 0.039 |
误差 | 0.023 | 3 | 0.008 | ||
总计 | 2.657 | 8 |
表7 高浓度添加剂的材料过冷正交实验方差分析表
差异源 | SS | df | MS | F | P值 |
---|---|---|---|---|---|
DHPD | 0.001 | 1 | 0.001 | 0.093 | 0.781 |
DE | 0.006 | 1 | 0.006 | 0.818 | 0.432 |
AON | 0.041 | 1 | 0.041 | 5.439 | 0.102 |
DHPD*AON | 0.094 | 1 | 0.094 | 12.366 | 0.039 |
误差 | 0.023 | 3 | 0.008 | ||
总计 | 2.657 | 8 |
实验序号 | DHPD | DE | XG | AON | 过冷度 |
---|---|---|---|---|---|
1 | 0.35% | 4% | 0.8% | 0.3% | 1.066 |
2 | 0.35% | 4% | 1.8% | 1.0% | 0.884 |
3 | 0.35% | 6.0% | 0.8% | 1.0% | 0.634 |
4 | 0.35% | 6.0% | 1.8% | 0.3% | 0.986 |
5 | 0.7% | 4% | 0.8% | 1.0% | 1.546 |
6 | 0.7% | 4% | 1.8% | 0.3% | 0.547 |
7 | 0.7% | 6.0% | 0.8% | 0.3% | 0.929 |
8 | 0.7% | 6.0% | 1.8% | 1.0% | 0.735 |
表8 低浓度添加剂的材料过冷正交实验设计及数据表
实验序号 | DHPD | DE | XG | AON | 过冷度 |
---|---|---|---|---|---|
1 | 0.35% | 4% | 0.8% | 0.3% | 1.066 |
2 | 0.35% | 4% | 1.8% | 1.0% | 0.884 |
3 | 0.35% | 6.0% | 0.8% | 1.0% | 0.634 |
4 | 0.35% | 6.0% | 1.8% | 0.3% | 0.986 |
5 | 0.7% | 4% | 0.8% | 1.0% | 1.546 |
6 | 0.7% | 4% | 1.8% | 0.3% | 0.547 |
7 | 0.7% | 6.0% | 0.8% | 0.3% | 0.929 |
8 | 0.7% | 6.0% | 1.8% | 1.0% | 0.735 |
序号 | DHPD | DE | DHPD*DE | XG | BLANK | DHPD*AON | AON | 过冷度 |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1.066 |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 0.884 |
3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 0.634 |
4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 0.986 |
5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1.546 |
6 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | 0.547 |
7 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 0.929 |
8 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 0.735 |
K1 | 3.570 | 4.043 | 3.614 | 4.175 | 2.982 | 4.333 | 3.528 | |
K2 | 3.757 | 3.284 | 3.713 | 3.152 | 4.345 | 2.994 | 3.799 | |
k1 | 0.893 | 1.011 | 0.904 | 1.044 | 0.746 | 1.083 | 0.882 | |
k2 | 0.939 | 0.821 | 0.928 | 0.788 | 1.086 | 0.749 | 0.950 | |
极差 | 0.047 | 0.190 | 0.025 | 0.256 | 0.341 | 0.335 | 0.068 | |
因素主→次 | DHPD*AON→XG→DE→AON→DHPD→DHPD*DE | |||||||
优方案 | DHPD2 AON1 XG2 DE2(表中最低值的方案为 DHPD2 AON1 XG2 DE1) |
表9 低浓度添加剂的材料过冷正交实验极差分析表
序号 | DHPD | DE | DHPD*DE | XG | BLANK | DHPD*AON | AON | 过冷度 |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1.066 |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 0.884 |
3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 0.634 |
4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 0.986 |
5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1.546 |
6 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | 0.547 |
7 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 0.929 |
8 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 0.735 |
K1 | 3.570 | 4.043 | 3.614 | 4.175 | 2.982 | 4.333 | 3.528 | |
K2 | 3.757 | 3.284 | 3.713 | 3.152 | 4.345 | 2.994 | 3.799 | |
k1 | 0.893 | 1.011 | 0.904 | 1.044 | 0.746 | 1.083 | 0.882 | |
k2 | 0.939 | 0.821 | 0.928 | 0.788 | 1.086 | 0.749 | 0.950 | |
极差 | 0.047 | 0.190 | 0.025 | 0.256 | 0.341 | 0.335 | 0.068 | |
因素主→次 | DHPD*AON→XG→DE→AON→DHPD→DHPD*DE | |||||||
优方案 | DHPD2 AON1 XG2 DE2(表中最低值的方案为 DHPD2 AON1 XG2 DE1) |
差异源 | SS | df | MS | F | P |
---|---|---|---|---|---|
DHPD | 0.004 | 1 | 0.004 | 0.019 | 0.913 |
DE | 0.072 | 1 | 0.072 | 0.310 | 0.677 |
XG | 0.131 | 1 | 0.131 | 0.563 | 0.590 |
AON | 0.009 | 1 | 0.009 | 0.040 | 0.875 |
DHPD*DE | 0.001 | 1 | 0.001 | 0.005 | 0.954 |
DHPD*AON | 0.224 | 1 | 0.224 | 0.965 | 0.506 |
误差 | 0.232 | 1 | 0.232 | ||
总计 | 7.385 | 8 |
表10 低浓度添加剂的材料过冷正交实验方差分析表
差异源 | SS | df | MS | F | P |
---|---|---|---|---|---|
DHPD | 0.004 | 1 | 0.004 | 0.019 | 0.913 |
DE | 0.072 | 1 | 0.072 | 0.310 | 0.677 |
XG | 0.131 | 1 | 0.131 | 0.563 | 0.590 |
AON | 0.009 | 1 | 0.009 | 0.040 | 0.875 |
DHPD*DE | 0.001 | 1 | 0.001 | 0.005 | 0.954 |
DHPD*AON | 0.224 | 1 | 0.224 | 0.965 | 0.506 |
误差 | 0.232 | 1 | 0.232 | ||
总计 | 7.385 | 8 |
实验序号 | DHPD | DE | XG | AON | 过冷度 |
---|---|---|---|---|---|
1 | 1.0% | 1% | 1% | 0.4% | 0.476 |
2 | 1.0% | 1% | 2.0% | 0.8% | 0.806 |
3 | 1.0% | 2.5% | 1% | 0.8% | 0.632 |
4 | 1.0% | 2.5% | 2.0% | 0.4% | 0.543 |
5 | 2.0% | 1% | 1% | 0.8% | 0.339 |
6 | 2.0% | 1% | 2.0% | 0.4% | 0.409 |
7 | 2.0% | 2.5% | 1% | 0.4% | 0.310 |
8 | 2.0% | 2.5% | 2.0% | 0.8% | 0.102 |
表11 高、低浓度添加剂组合的材料正交实验设计及数据表
实验序号 | DHPD | DE | XG | AON | 过冷度 |
---|---|---|---|---|---|
1 | 1.0% | 1% | 1% | 0.4% | 0.476 |
2 | 1.0% | 1% | 2.0% | 0.8% | 0.806 |
3 | 1.0% | 2.5% | 1% | 0.8% | 0.632 |
4 | 1.0% | 2.5% | 2.0% | 0.4% | 0.543 |
5 | 2.0% | 1% | 1% | 0.8% | 0.339 |
6 | 2.0% | 1% | 2.0% | 0.4% | 0.409 |
7 | 2.0% | 2.5% | 1% | 0.4% | 0.310 |
8 | 2.0% | 2.5% | 2.0% | 0.8% | 0.102 |
序号 | DHPD | DE | DHPD*DE | XG | BLANK | DHPD*AON | AON | 过冷度 |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.476 |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 0.806 |
3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 0.632 |
4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 0.543 |
5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 0.339 |
6 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | 0.409 |
7 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 0.310 |
8 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 0.102 |
K1 | 2.457 | 2.030 | 1.694 | 1.757 | 1.619 | 1.460 | 1.738 | |
K2 | 1.160 | 1.587 | 1.923 | 1.860 | 1.998 | 2.157 | 1.879 | |
k1 | 0.614 | 0.508 | 0.424 | 0.439 | 0.405 | 0.365 | 0.435 | |
k2 | 0.290 | 0.397 | 0.481 | 0.465 | 0.500 | 0.539 | 0.470 | |
极差 | 0.324 | 0.111 | 0.057 | 0.026 | 0.095 | 0.174 | 0.035 | |
因素主→次 | DHPD→DHPD*AON→DE→DHPD*DE→AON→XG | |||||||
优方案 | DHPD2 DE2 AON2 XG1(表中最低值的方案为DHPD2 DE2 AON2 XG2) |
表12 高、低浓度添加剂组合的材料正交实验极差分析表
序号 | DHPD | DE | DHPD*DE | XG | BLANK | DHPD*AON | AON | 过冷度 |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.476 |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 0.806 |
3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 0.632 |
4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 0.543 |
5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 0.339 |
6 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | 0.409 |
7 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 0.310 |
8 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 0.102 |
K1 | 2.457 | 2.030 | 1.694 | 1.757 | 1.619 | 1.460 | 1.738 | |
K2 | 1.160 | 1.587 | 1.923 | 1.860 | 1.998 | 2.157 | 1.879 | |
k1 | 0.614 | 0.508 | 0.424 | 0.439 | 0.405 | 0.365 | 0.435 | |
k2 | 0.290 | 0.397 | 0.481 | 0.465 | 0.500 | 0.539 | 0.470 | |
极差 | 0.324 | 0.111 | 0.057 | 0.026 | 0.095 | 0.174 | 0.035 | |
因素主→次 | DHPD→DHPD*AON→DE→DHPD*DE→AON→XG | |||||||
优方案 | DHPD2 DE2 AON2 XG1(表中最低值的方案为DHPD2 DE2 AON2 XG2) |
差异源 | SS | df | MS | F | P |
---|---|---|---|---|---|
DHPD | 0.210 | 1 | 0.210 | 24.416 | 0.016 |
DE | 0.025 | 1 | 0.025 | 2.848 | 0.190 |
AON | 0.002 | 1 | 0.002 | 0.289 | 0.628 |
DHPD*AON | 0.061 | 1 | 0.061 | 7.051 | 0.077 |
误差 | 0.026 | 3 | 0.009 | ||
总计 | 1.959 | 8 |
表13 高、低浓度添加剂组合的材料正交实验方差分析表
差异源 | SS | df | MS | F | P |
---|---|---|---|---|---|
DHPD | 0.210 | 1 | 0.210 | 24.416 | 0.016 |
DE | 0.025 | 1 | 0.025 | 2.848 | 0.190 |
AON | 0.002 | 1 | 0.002 | 0.289 | 0.628 |
DHPD*AON | 0.061 | 1 | 0.061 | 7.051 | 0.077 |
误差 | 0.026 | 3 | 0.009 | ||
总计 | 1.959 | 8 |
实验序号 | DHPD | DE | XG | AON | 过冷度 |
---|---|---|---|---|---|
1 | 0.6% | 3.5% | 1% | 0.6% | 0.671 |
2 | 0.6% | 3.5% | 2.0% | 1.2% | 0.872 |
3 | 0.6% | 6.5% | 1% | 1.2% | 0.864 |
4 | 0.6% | 6.5% | 2.0% | 0.6% | 0.995 |
5 | 1.2% | 3.5% | 1% | 1.2% | 0.606 |
6 | 1.2% | 3.5% | 2.0% | 0.6% | 0.755 |
7 | 1.2% | 6.5% | 1% | 0.6% | 0.677 |
8 | 1.2% | 6.5% | 2.0% | 1.2% | 1.051 |
表14 中等浓度添加剂组合的材料正交实验设计及数据表
实验序号 | DHPD | DE | XG | AON | 过冷度 |
---|---|---|---|---|---|
1 | 0.6% | 3.5% | 1% | 0.6% | 0.671 |
2 | 0.6% | 3.5% | 2.0% | 1.2% | 0.872 |
3 | 0.6% | 6.5% | 1% | 1.2% | 0.864 |
4 | 0.6% | 6.5% | 2.0% | 0.6% | 0.995 |
5 | 1.2% | 3.5% | 1% | 1.2% | 0.606 |
6 | 1.2% | 3.5% | 2.0% | 0.6% | 0.755 |
7 | 1.2% | 6.5% | 1% | 0.6% | 0.677 |
8 | 1.2% | 6.5% | 2.0% | 1.2% | 1.051 |
序号 | DHPD | DE | DHPD*DE | XG | BLANK | DHPD*AON | AON | 过冷度 |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.671 |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 0.872 |
3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 0.864 |
4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 0.995 |
5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 0.606 |
6 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | 0.755 |
7 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 0.677 |
8 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 1.051 |
K1 | 3.402 | 2.904 | 3.271 | 2.818 | 3.341 | 3.323 | 3.098 | |
K2 | 3.089 | 3.587 | 3.220 | 3.673 | 3.150 | 3.168 | 3.393 | |
k1 | 0.851 | 0.726 | 0.818 | 0.705 | 0.835 | 0.831 | 0.775 | |
k2 | 0.772 | 0.897 | 0.805 | 0.918 | 0.788 | 0.792 | 0.848 | |
极差 | 0.078 | 0.171 | 0.013 | 0.214 | 0.048 | 0.039 | 0.074 | |
因素主→次 | XG→DE→DHPD→AON→DHPD*AON→DHPD*DE | |||||||
优方案 | XG1 DE1 DHPD2 AON1(表中最低值的方案为XG1 DE1 DHPD2 AON2) |
表15 中等浓度添加剂组合的材料正交实验极差分析表
序号 | DHPD | DE | DHPD*DE | XG | BLANK | DHPD*AON | AON | 过冷度 |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.671 |
2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 0.872 |
3 | 1 | 2 | 2 | 1 | 1 | 2 | 2 | 0.864 |
4 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 0.995 |
5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 0.606 |
6 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | 0.755 |
7 | 2 | 2 | 1 | 1 | 2 | 2 | 1 | 0.677 |
8 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 1.051 |
K1 | 3.402 | 2.904 | 3.271 | 2.818 | 3.341 | 3.323 | 3.098 | |
K2 | 3.089 | 3.587 | 3.220 | 3.673 | 3.150 | 3.168 | 3.393 | |
k1 | 0.851 | 0.726 | 0.818 | 0.705 | 0.835 | 0.831 | 0.775 | |
k2 | 0.772 | 0.897 | 0.805 | 0.918 | 0.788 | 0.792 | 0.848 | |
极差 | 0.078 | 0.171 | 0.013 | 0.214 | 0.048 | 0.039 | 0.074 | |
因素主→次 | XG→DE→DHPD→AON→DHPD*AON→DHPD*DE | |||||||
优方案 | XG1 DE1 DHPD2 AON1(表中最低值的方案为XG1 DE1 DHPD2 AON2) |
差异源 | SS | df | MS | F | P |
---|---|---|---|---|---|
DHPD | 0.012 | 1 | 0.012 | 4.657 | 0.12 |
DE | 0.058 | 1 | 0.058 | 22.176 | 0.018 |
XG | 0.091 | 1 | 0.091 | 34.752 | 0.01 |
AON | 0.011 | 1 | 0.011 | 4.137 | 0.135 |
误差 | 0.008 | 3 | 0.003 | ||
总计 | 5.447 | 8 |
表16 中等浓度添加剂组合的材料正交实验方差分析
差异源 | SS | df | MS | F | P |
---|---|---|---|---|---|
DHPD | 0.012 | 1 | 0.012 | 4.657 | 0.12 |
DE | 0.058 | 1 | 0.058 | 22.176 | 0.018 |
XG | 0.091 | 1 | 0.091 | 34.752 | 0.01 |
AON | 0.011 | 1 | 0.011 | 4.137 | 0.135 |
误差 | 0.008 | 3 | 0.003 | ||
总计 | 5.447 | 8 |
序号 | DHPD(X1) | DE(X2) | XG(X3) | AON(X4) | DE*XG (X5=X2*X3) | 过冷度 |
---|---|---|---|---|---|---|
1 | 1.5% | 3% | 1.5% | 1.5% | 0.00045 | 0.629 |
2 | 1.5% | 3% | 2.5% | 3% | 0.00075 | 0.414 |
3 | 1.5% | 7% | 1.5% | 3% | 0.00105 | 0.648 |
4 | 1.5% | 7% | 2.5% | 1.5% | 0.00175 | 0.579 |
5 | 2.5% | 3% | 1.5% | 3% | 0.00045 | 0.720 |
6 | 2.5% | 3% | 2.5% | 1.5% | 0.00075 | 0.358 |
7 | 2.5% | 7% | 1.5% | 1.5% | 0.00105 | 0.379 |
8 | 2.5% | 7% | 2.5% | 3% | 0.00175 | 0.738 |
9 | 0.35% | 4% | 0.8% | 0.3% | 0.00032 | 1.066 |
10 | 0.35% | 4% | 1.8% | 1.0% | 0.00072 | 0.884 |
11 | 0.35% | 6.0% | 0.8% | 1.0% | 0.00048 | 0.634 |
12 | 0.35% | 6.0% | 1.8% | 0.3% | 0.00108 | 0.986 |
13 | 0.7% | 4% | 0.8% | 1.0% | 0.00032 | 1.546 |
14 | 0.7% | 4% | 1.8% | 0.3% | 0.00072 | 0.547 |
15 | 0.7% | 6.0% | 0.8% | 0.3% | 0.00048 | 0.929 |
16 | 0.7% | 6.0% | 1.8% | 1.0% | 0.00108 | 0.735 |
17 | 1.0% | 1% | 1% | 0.4% | 0.00010 | 0.476 |
18 | 1.0% | 1% | 2.0% | 0.8% | 0.00020 | 0.806 |
19 | 1.0% | 2.5% | 1% | 0.8% | 0.00025 | 0.632 |
20 | 1.0% | 2.5% | 2.0% | 0.4% | 0.00050 | 0.543 |
21 | 2.0% | 1% | 1% | 0.8% | 0.00010 | 0.339 |
22 | 2.0% | 1% | 2.0% | 0.4% | 0.00020 | 0.409 |
23 | 2.0% | 2.5% | 1% | 0.4% | 0.00025 | 0.31 |
24 | 2.0% | 2.5% | 2.0% | 0.8% | 0.00050 | 0.102 |
25 | 0.6% | 3.5% | 1% | 0.6% | 0.00035 | 0.671 |
26 | 0.6% | 3.5% | 2.0% | 1.2% | 0.00070 | 0.872 |
27 | 0.6% | 6.5% | 1% | 1.2% | 0.00065 | 0.864 |
28 | 0.6% | 6.5% | 2.0% | 0.6% | 0.00130 | 0.995 |
29 | 1.2% | 3.5% | 1% | 1.2% | 0.00035 | 0.606 |
30 | 1.2% | 3.5% | 2.0% | 0.6% | 0.00070 | 0.755 |
31 | 1.2% | 6.5% | 1% | 0.6% | 0.00065 | 0.677 |
32 | 1.2% | 6.5% | 2.0% | 1.2% | 0.00130 | 1.051 |
表17 汇总的整体正交实验数据
序号 | DHPD(X1) | DE(X2) | XG(X3) | AON(X4) | DE*XG (X5=X2*X3) | 过冷度 |
---|---|---|---|---|---|---|
1 | 1.5% | 3% | 1.5% | 1.5% | 0.00045 | 0.629 |
2 | 1.5% | 3% | 2.5% | 3% | 0.00075 | 0.414 |
3 | 1.5% | 7% | 1.5% | 3% | 0.00105 | 0.648 |
4 | 1.5% | 7% | 2.5% | 1.5% | 0.00175 | 0.579 |
5 | 2.5% | 3% | 1.5% | 3% | 0.00045 | 0.720 |
6 | 2.5% | 3% | 2.5% | 1.5% | 0.00075 | 0.358 |
7 | 2.5% | 7% | 1.5% | 1.5% | 0.00105 | 0.379 |
8 | 2.5% | 7% | 2.5% | 3% | 0.00175 | 0.738 |
9 | 0.35% | 4% | 0.8% | 0.3% | 0.00032 | 1.066 |
10 | 0.35% | 4% | 1.8% | 1.0% | 0.00072 | 0.884 |
11 | 0.35% | 6.0% | 0.8% | 1.0% | 0.00048 | 0.634 |
12 | 0.35% | 6.0% | 1.8% | 0.3% | 0.00108 | 0.986 |
13 | 0.7% | 4% | 0.8% | 1.0% | 0.00032 | 1.546 |
14 | 0.7% | 4% | 1.8% | 0.3% | 0.00072 | 0.547 |
15 | 0.7% | 6.0% | 0.8% | 0.3% | 0.00048 | 0.929 |
16 | 0.7% | 6.0% | 1.8% | 1.0% | 0.00108 | 0.735 |
17 | 1.0% | 1% | 1% | 0.4% | 0.00010 | 0.476 |
18 | 1.0% | 1% | 2.0% | 0.8% | 0.00020 | 0.806 |
19 | 1.0% | 2.5% | 1% | 0.8% | 0.00025 | 0.632 |
20 | 1.0% | 2.5% | 2.0% | 0.4% | 0.00050 | 0.543 |
21 | 2.0% | 1% | 1% | 0.8% | 0.00010 | 0.339 |
22 | 2.0% | 1% | 2.0% | 0.4% | 0.00020 | 0.409 |
23 | 2.0% | 2.5% | 1% | 0.4% | 0.00025 | 0.31 |
24 | 2.0% | 2.5% | 2.0% | 0.8% | 0.00050 | 0.102 |
25 | 0.6% | 3.5% | 1% | 0.6% | 0.00035 | 0.671 |
26 | 0.6% | 3.5% | 2.0% | 1.2% | 0.00070 | 0.872 |
27 | 0.6% | 6.5% | 1% | 1.2% | 0.00065 | 0.864 |
28 | 0.6% | 6.5% | 2.0% | 0.6% | 0.00130 | 0.995 |
29 | 1.2% | 3.5% | 1% | 1.2% | 0.00035 | 0.606 |
30 | 1.2% | 3.5% | 2.0% | 0.6% | 0.00070 | 0.755 |
31 | 1.2% | 6.5% | 1% | 0.6% | 0.00065 | 0.677 |
32 | 1.2% | 6.5% | 2.0% | 1.2% | 0.00130 | 1.051 |
差异源 | SS | df | MS | F | P |
---|---|---|---|---|---|
DHPD | 1.367 | 4 | 0.342 | 2.309 | 0.06 |
DE | 0.956 | 4 | 0.239 | 1.614 | 0.173 |
XG | 1.2 | 3 | 0.4 | 2.701 | 0.047 |
AON | 0.385 | 4 | 0.096 | 0.651 | 0.627 |
DE*XG | 2.506 | 5 | 0.501 | 3.385 | 0.006 |
误差 | 24.871 | 168 | 0.148 | ||
总计 | 128.046 | 192 |
表18 汇总的整体正交实验方差分析表
差异源 | SS | df | MS | F | P |
---|---|---|---|---|---|
DHPD | 1.367 | 4 | 0.342 | 2.309 | 0.06 |
DE | 0.956 | 4 | 0.239 | 1.614 | 0.173 |
XG | 1.2 | 3 | 0.4 | 2.701 | 0.047 |
AON | 0.385 | 4 | 0.096 | 0.651 | 0.627 |
DE*XG | 2.506 | 5 | 0.501 | 3.385 | 0.006 |
误差 | 24.871 | 168 | 0.148 | ||
总计 | 128.046 | 192 |
项目 | 过冷度 | DHPD | XG | DE*XG |
---|---|---|---|---|
过冷度 | 1 | -0.637 | -0.09 | 0.289 |
DHPD | -0.637 | 1 | 0.318 | 0.093 |
XG | -0.09 | 0.318 | 1 | 0.599 |
DE*XG | 0.289 | 0.093 | 0.599 | 1 |
表19 变量之间相关系数表(Pearson 相关性)
项目 | 过冷度 | DHPD | XG | DE*XG |
---|---|---|---|---|
过冷度 | 1 | -0.637 | -0.09 | 0.289 |
DHPD | -0.637 | 1 | 0.318 | 0.093 |
XG | -0.09 | 0.318 | 1 | 0.599 |
DE*XG | 0.289 | 0.093 | 0.599 | 1 |
模型 | R | R2 | 调整R2 | 标准估计的误差 | Durbin-Watson |
---|---|---|---|---|---|
1 | 0.736 | 0.542 | 0.491 | 0.169504 | 2.596 |
表20 模型概览表
模型 | R | R2 | 调整R2 | 标准估计的误差 | Durbin-Watson |
---|---|---|---|---|---|
1 | 0.736 | 0.542 | 0.491 | 0.169504 | 2.596 |
模型 | 平方和 | df | 均方 | F | Sig. | |
---|---|---|---|---|---|---|
1 | 回归 | 0.918 | 3 | 0.306 | 10.653 | 0.000 |
残差 | 0.776 | 27 | 0.029 | |||
总计 | 1.694 | 30 |
表21 模型方差分析表
模型 | 平方和 | df | 均方 | F | Sig. | |
---|---|---|---|---|---|---|
1 | 回归 | 0.918 | 3 | 0.306 | 10.653 | 0.000 |
残差 | 0.776 | 27 | 0.029 | |||
总计 | 1.694 | 30 |
模型 | 非标准化系数 | 标准系数 | t | Sig. | ||
---|---|---|---|---|---|---|
B | 标准误差 | Beta | ||||
1 | (常量) | 0.864 | 0.097 | 8.881 | 0 | |
DHPD | -21.26 | 4.678 | -0.629 | -4.545 | 0 | |
XG | -6.468 | 7.261 | -0.153 | -0.891 | 0.381 | |
DE *XG | 238.347 | 88.822 | 0.44 | 2.683 | 0.012 |
表22 模型系数估计表
模型 | 非标准化系数 | 标准系数 | t | Sig. | ||
---|---|---|---|---|---|---|
B | 标准误差 | Beta | ||||
1 | (常量) | 0.864 | 0.097 | 8.881 | 0 | |
DHPD | -21.26 | 4.678 | -0.629 | -4.545 | 0 | |
XG | -6.468 | 7.261 | -0.153 | -0.891 | 0.381 | |
DE *XG | 238.347 | 88.822 | 0.44 | 2.683 | 0.012 |
模型 | 维数 | 特征值 | 病态指数 | 方差比例 | |||
---|---|---|---|---|---|---|---|
(常量) | DHPD | XG | DE*XG | ||||
1 | 1 | 3.604 | 1 | 0.01 | 0.01 | 0 | 0.01 |
2 | 0.243 | 3.854 | 0.01 | 0.39 | 0 | 0.39 | |
3 | 0.11 | 5.719 | 0.43 | 0.56 | 0.03 | 0.29 | |
4 | 0.043 | 9.173 | 0.56 | 0.03 | 0.97 | 0.31 |
表23 模型共线性诊断表
模型 | 维数 | 特征值 | 病态指数 | 方差比例 | |||
---|---|---|---|---|---|---|---|
(常量) | DHPD | XG | DE*XG | ||||
1 | 1 | 3.604 | 1 | 0.01 | 0.01 | 0 | 0.01 |
2 | 0.243 | 3.854 | 0.01 | 0.39 | 0 | 0.39 | |
3 | 0.11 | 5.719 | 0.43 | 0.56 | 0.03 | 0.29 | |
4 | 0.043 | 9.173 | 0.56 | 0.03 | 0.97 | 0.31 |
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