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<>一、预测类
指通过分析已有的数据或者现象,找出其内在发展规律,然后对未来情形做出预测的过程。
根据已知条件和求解目的,往往将预测类问题分为:小样本内部预测,大样本内部预测。
<>解决预测类赛题的一般步骤:
1、确定预测目标;
2、收集、分析资料;
3、选择合适的预测方法进行预测;
4、分析评价预测方法及其结果
5、修正预测结果
6、给出预测结果
<>常见的预测方法
差值与拟合的方法:适合小样本内部预测
回归分析法:适合中、大样本内部预测
灰色预测方法:适合小样本的未来预测(有固定趋势)
时间序列方法:适合中、大样本的随机因素或周期特征的未来趋势未来预测
神经网络方法:适合大(特大)样本未来预测
<>预测类赛题案例
<>二、评价类
指按照一定的标准对事物的发展或者现状进行划分的过程在数学建模中题点可提现在对生态环境,社会建设,方案策略等进行评价。评价类赛题往往没有明确的指标体系和评价标准,往往需要查阅各种资料进行构建的,因此没有明确答案
赛题分析:解决评价类赛题的关键是指标体系的构建,构建完指标体系后在选择合适的评价方法即可,体系建立应秉承全面、准确、独立三要素
<>解决评价类赛题的一般步骤
1、明确评价目的;
2、确定被评价对象
3、建立评价指标体系
4、确立各指标对应的权重系数
5、选择或构造综合评价模型
6、计算各系统的综合评价值
7、给出综合评价结果
<>三、机理分析类赛题
机理分析是根据对现实对象特性的认识,分析其因果关系,找出反应内部机理的规律。在求解机理分析类问题时首先需要探寻与问题相关的物理,化学,经济等相关的知识,然后通过对已知数据或现象
的分析对事物的内在规律做出必要的假设,最后通过构建合适的方程或关系式对其内在规律进行数值表达
赛题分析:机理分析立足于建立事物内部的规律,相对于其他类型的赛题均有章可循,机理分析赛题往往需要结合众多关联知识才可以进行求解,如空气动力学,流体力学,热力学等
<>四、优化类赛题