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数学建模模拟题——编程
题目重述
矿石加工质量控制问题
矿石加工是一个复杂的过程,在加工过程中,电压、水压、温度作为影响矿石加工的重要因素,直接影响着矿石产品的质量
假设矿石加工过程需要经过系统I和系统II两个环节,两个环节不分先后,其他条件(电压、水压等)保持不变。生产技术人员可以通过传入调温指令,调节温度来改变产品质量。其中系统I和II的温度数据见附件1和附件2。矿石加工过程为2小时整(即:在调节温度2个小时后,可检测得到该调节温度所对应的矿石产品质量的评价指标(A,B,C,D)),假设每次温度调节之后的2个小时内不会传入新的调温指令,附件1和附件2中的温度数据记录了系统的实时温度,调温指令下达后系统温度基本与调温指令设定的温度相同,但是有轻微波动。
问题一
2022-01-13至2022-01-22 10天的生产数据
在给定的2022-01-23原矿参数和系统设定温度下,给出产品质量预测结果。
时间系统I设定温度系统II设定温度指标A指标B指标C指标D
2022-01-231404.89859.77
2022-01-231151.75859.77
问题二
假设原矿参数和产品目标质量已知(系统温度未知),请建立数学模型,估计产品目标质量所对应的系统温度。
在给定的2022-01-24原矿参数和目标产品质量下,给出系统设定温度(假设调温指令设定的温度与系统温度相同)。
时间指标A指标B指标C指标D系统I设定温度系统II设定温度
2022-01-2479.1722.7210.5117.05
2022-01-2480.1023.3411.0313.29
问题三
给出指定系统设定温度,预测矿石产品合格率的方法。在给定的2022-04-08和2022-04-09原矿参数、过程数据和系统设定温度下,给出合格率预测结果,并建立数学模型对给出的合格率的准确性进行评价。
时间系统I设定温度系统II设定温度合格率
2022-04-08341.40665.04
2022-04-091010.32874.47
时间系统I设定温度系统II设定温度合格率
2022-04-08341.40665.04
2022-04-091010.32874.47
问题四
建立数学模型分析在指定合格率的条件下,如何设定系统温度的方法,并完成以下任务:
(1)适当的敏感性分析;
(2)对结果准确性的分析;
(3)判断能否达到表中给出的2022-04-10和2022-04-11产品的合格率要求,如果可以达到,给出系统设定温度(假设系统温度与调温指令设定的温度相同),并将结果填入表。
时间合格率能否达到系统I设定温度系统II设定温度
2022-04-1080%
2022-04-1199%