青岛大学2013数学建模试题

1、A题试题：机电设备故障诊断模式识别问题机电设备通常由于结构复杂，引起设备故障的原因众多，影响了设备的正常运行及生产安全。如何快速准确地识别故障的类型是广泛使用各类机电设备的工业生产、交通运输等行业和领域面临的迫切问题。假设某机电设备的多发故障有故障I、故障II和故障III共三种，三种故障可由能够直接测量的特征1、特征2和特征3的数值来间接判断。为便于分析，这里对特征1、特征2和特征3均进行了归一化处理，60组故障特征样本及对应故障类型见表一。表一故障特征（已归一化处理）特征1特征2特征3特征1特征2特征3特征1特征2特征30.8310.2830.2140.1340.7110.2930.2460

2、.4280.6610.8570.1750.3190.3440.8710.4200.1240.3180.8310.7520.3650.1790.2820.8090.3180.2820.4310.8750.7720.2550.3730.1160.9150.4240.2330.4470.6860.8720.290.1360.2580.7920.2230.3410.3560.6750.9590.1710.1320.3090.7870.1130.1820.3890.6190.7670.2500.3040.3330.7420.2670.4030.4270.6880.7340.2910.3150.2620.

3、8110.1250.0520.3770.6540.9190.2930.2180.1990.8160.1090.2130.4310.6860.7870.3360.3450.2780.7360.2140.3770.2060.6830.8500.3270.2010.2130.6690.2330.3810.4460.620.7400.3220.3390.2610.8930.3930.1510.4360.7440.8080.1720.2890.3820.7620.0920.3290.4440.8080.8880.2500.3060.3360.8230.2750.1330.2830.7410.9200.3

4、460.4380.2950.7540.4070.2670.3130.7120.8700.3300.2710.2620.8970.4280.1020.4020.6620.7660.4570.3170.1580.8120.4390.2870.4960.6820.6890.3490.2970.2910.6980.2400.0250.3020.6270.9770.3710.4220.1350.8610.1260.2010.1670.8170.7520.4210.4250.2340.6830.3940.3510.3930.743故障I故障II故障III问题： 1）根据表一数据建立三种故障特征与三种不同类

5、型故障间的数学模型。2）应用第1问数学模型，计算并判断以下故障特征样本分别属于哪种故障类型： A (0.816,0.107,0.320), B (0.504,0.527,0.453), C (0.137,0.386,0.818), D (0.205,0.832,0.337)。 3）分析所建数学模型的优缺点及改进措施。说明：编程语言不限，需说明软件运行环境并提交程序以验证算法的有效性B题在某地区开掘水渠。已测定水渠经过的若干个位置(表1)。开掘的水渠的垂直横断面如图1. 为了简化问题，忽略高度差异。x76507950825085508850915094509750y465048905100519

6、05220519051304890x1005010350106501095011250115501185012150y46504470432042004080393038403720x1245012750130501335013650139501425014550y36603630357035403600369037803900表1：河道经过的若干个点的位置（单位：m）182 图1：水渠横截面A 图2：水渠俯视图问题1：估计水渠施工的总土石方量。问题2：如果将水渠的分成6截，每截土石方工作量相同，分段点应该取在什么位置？问题3：设平行于水渠修一条路。河道中挖出的土石方要运往A(9500,4000)处(可以看作土石方堆积处入口)。为了